Australian Curriculum Mathematics - Measurement and Geometry: Year 4 - Ages 9-10

RIC-6097 6.3/949

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 4) Published by R.I.C. Publications® 2013 Copyright© Linda Marshall 2013 ISBN 978-1-921750-94-6 RIC– 6097

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For all Australian Curriculum material except elaborations: This is an extract from the Australian Curriculum.

Elaborations: This may be a modified extract from the Australian Curriculum and may include the work of other authors.

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Foundation) Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 1) Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 2) Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 3) Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 4) Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 5) Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 6)

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AUSTRALIAN CURRICULUM MATHEMATICS RESOURCE BOOK: MEASUREMENT AND GEOMETRY (YEAR 4) Foreword Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 4) is one in a series of seven teacher resource books that support teaching and learning activities in Australian Curriculum Mathematics. The books focus on the measurement and geometry content strands of the national maths curriculum. The resource books include theoretical background information, resource sheets, hands-on activities and assessment activities, along with links to other curriculum areas.

r o e t s Bo r e p ok u S Contents

Format of this book .................................................. iv – v

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Using units of measurement...................................... 2–57 • UUM – 1

• Shape – 2

Compare and describe two dimensional shapes that result from combining and splitting common shapes, with and without the use of digital technologies(ACMMG088)

– – – – – –

– – – – – –

Teacher information ............................................................................... 2–4 Hands-on activities ..................................................................................5–7 Links to other curriculum areas .................................................................... 8 Resource sheets .................................................................................... 9–14 Assessment ........................................................................................ 15–16 Checklist .................................................................................................... 17

• UUM – 2

Convert between units of time (ACMMG085)

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Teacher information .................................................................................. 30 Hands-on activities .................................................................................... 31 Links to other curriculum areas .................................................................. 32 Resource sheets .................................................................................. 33–35 Assessment ............................................................................................... 36 Checklist .................................................................................................... 37

• UUM – 4

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Teacher information ........................................................................... 38–39 Hands-on activities .................................................................................... 40 Links to other curriculum areas .................................................................. 41 Resource sheets .................................................................................. 42–51 Assessment ........................................................................................ 52–53 Checklist .................................................................................................... 54

Answers ............................................................................ 55–57

Shape .................................................................... 58–79 • Shape – 1 Compare the area of regular and irregular shapes by informal means (ACMMG087) – – – – – –

Location and transformation ................................ 80–113 • L&T – 1 Use simple scales, legends and directions to interpret information contained in basic maps (ACMMG090) – – – – – –

Teacher information ........................................................................... 80–81 Hands-on activities ............................................................................. 82–83 Links to other curriculum areas .................................................................. 84 Resource sheets .................................................................................. 85–90 Assessment ........................................................................................ 91–92 Checklist .................................................................................................... 93

• L&T – 2

Create symmetrical patterns, pictures and shapes with and without digital technologies (ACMMG091) – – – – – –

Teacher information .................................................................................. 94 Hands-on activities ............................................................................. 95–96 Links to other curriculum areas .................................................................. 97 Resource sheets ................................................................................ 98–108 Assessment .................................................................................... 109–111 Checklist .................................................................................................. 112

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Use am and pm notation and solve simple time problems (ACMMG086) – – – – – –

Answers ............................................................................ 78–79

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Teacher information ........................................................................... 18–19 Hands-on activities ............................................................................. 20–21 Links to other curriculum areas .................................................................. 22 Resource sheets .................................................................................. 23–26 Assessment ........................................................................................ 27–28 Checklist .................................................................................................... 29

• UUM– 3 – – – – – –

Teacher information ........................................................................... 66–67 Hands-on activities ............................................................................. 68–69 Links to other curriculum areas .................................................................. 70 Resource sheets .................................................................................. 71–75 Assessment ............................................................................................... 76 Checklist .................................................................................................... 77

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Compare objects using familiar metric units of area and volume (ACMMG290) – – – – – –

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Use scaled instruments to measure and compare lengths, masses, capacities and temperature (ACMMG084)

Teacher information ........................................................................... 58–59 Hands-on activities .................................................................................... 60 Links to other curriculum areas .................................................................. 61 Resource sheets .................................................................................. 62–63 Assessment ............................................................................................... 64 Checklist .................................................................................................... 65

Answers ................................................................................ 113

Geometric reasoning............................................ 114–121 • GR – 1 Compare angles and classify them as equal to, greater than or less than a right angle (ACMMG089) – – – – – –

Teacher information ....................................................................... 114–115 Hands-on activities .................................................................................. 116 Links to other curriculum areas ................................................................ 117 Resource sheets .............................................................................. 118–119 Assessment ............................................................................................. 120 Checklist .................................................................................................. 121

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 4)

R.I.C. Publications® www.ricpublications.com.au

iii

FORMAT OF THIS BOOK This teacher resource book includes supporting materials for teaching and learning in all sections of the Measurement and Geometry content strand of Australian Curriculum Mathematics. It includes activities relating to all sub-strands: Using units of measurement, Shape, Location and transformation, and Geometric reasoning. All content descriptions have been included, as well as teaching points based on the Curriculum’s elaborations. Links to the proficiency strands have also been included.

Each section supports a specific content description and follows a consistent format, containing the following information over several pages: • teacher information with related terms, student vocabulary, what the content description means, teaching points and problems to watch for • hands-on activities • links to other curriculum areas

• resource sheets • assessment sheets.

• a checklist

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Answers relating to the resource and assessment pages are included on the final page of the section for each sub-strand (Using units of measurement, Shape, Location and transformation, and Geometric reasoning).

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The length of each content description section varies.

Teacher information includes background information relating to the content description, as well as related terms, desirable student vocabulary and other useful details which may assist the teacher.

Related terms includes vocabulary associated with the content description. Many of these relate to the glossary in the back of the official Australian Curriculum Mathematics document; additional related terms may also have been added.

What this means provides a general explanation of the content description.

the teacher would use—and expect the students to learn, understand and use—during mathematics lessons.

description.

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The proficiency strand(s) (Understanding, Fluency, Problem solving Solving or Reasoning) reasoning) relevant to each content description are shown listed. in bold.

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C.Publ i cat i ons Teaching points provides a listn of the main teaching •f owhich rr evi ew pur poseso l y • Student vocabulary includes words points relating to the content

What to look watchforforsuggests suggestsany any difficulties and misconceptions the students might encounter or develop.

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Hands-on activities includes descriptions or instructions for games or activities relating to the content descriptions or elaborations. Some of the hands-on activities are supported by resource sheets. Where applicable, these will be stated for easy reference.

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 4)

R.I.C. Publications® www.ricpublications.com.au

FORMAT OF THIS BOOK Links to other curriculum areas includes activities in other curriculum areas which support the content description. These are English (literacy), Information and Communication Technology (ICT), Health and Physical Education (ethical behaviour, personal and social competence) and Intercultural Understanding (History, Geography, the Arts, and Languages).

This section may list many links or only a few. It may also provide links to relevant interactive websites appropriate for the age group.

r o e t s Bo r e p ok u S Resource sheets are provided to support teaching and learning activities for each content description. The resource sheets could be cards for games, charts, additional worksheets for class use or other materials which the teacher might find useful to use or display in the classroom. For each resource sheet, the content description to which it relates is given.

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Cross-curricular links reinforce the knowledge that mathematics can be found within, and relate to, many other aspects of student learning and everyday life.

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C.Publ i cat i ons Assessment pages are included. These support provided in the hands-on •f orr evi e wactivities pu r p o sesonl y• activities or resource sheets.

o c . che e r o t r s super Each section has a checklist which teachers may find useful as a place to keep a record of the results of assessment activities, or their observations of hands-on activities.

Answers for resource pages (where appropriate) and assessment pages are provided on the final page of each sub-strand section.

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 4)

R.I.C. Publications® www.ricpublications.com.au

v

Sub-strand: Using units of measurement—UUM – 1

Use scaled instruments to measure and compare lengths, masses, capacities and temperature (ACMMG084)

RELATED TERMS

TEACHER INFORMATION What this means

Scaled instruments

• Students need to use instruments that have clearly marked gradations; e.g. rulers for length, weighing scales (e.g. kitchen scales, bathroom scales) for mass, graduated jugs and containers for capacity and thermometers for temperature.

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Perimeter

• A measure of the distance around the boundary of a two-dimensional shape.

• Weighing scales need to have gradations shown on them, not a digital display.

• Thermometers also should have the mercury (or similar) band that sits alongside a scale and moves as the temperature changes. Similarly, if reading a food thermometer, the display needs to be graduated not digital. The use of a digital thermometer requires no skill in terms of reading the instrument.

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• Measuring tools that have markings (or gradations) to indicate regular units. For example, a 30 cm ruler has marks (scales) for every centimetre and smaller ones for every millimetre; weighing scales may have marks to show every 10 grams, 50 grams or 100 grams; measuring jugs may have every 10 millilitres shown on the scale; and a thermometer may have every 10 degrees marked heavily and every single degree marked with a lighter line.

• Temperature is measured in degrees Celsius (°C). This is based on the freezing point of water being 0 °C; and the boiling point of water being 100 °C. (When measuring temperature, degrees Celsius are the same as degrees centigrade; but in Australia we use Celsius.)

• The degrees used for measuring angles are different from the degrees used for measuring temperature.

Teaching points © R. I .

C.Publ i cat i ons •f orr evi ew pur posesonl y• • The amount of matter an object Mass

contains, commonly measured in grams, kilograms and tonnes.

• The metric units for mass are grams (g), kilograms (kg) and tonnes (t).

For Year 4 students, tonnes would not be used.

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• The force of gravity acting on an object, used to measure mass (actually measured in Newtons).

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• Note 1: It is correct to use the verb ‘to weigh’.

• Note 2: At this year level, students may use the terms ‘weight’ and ‘mass’ interchangeably, although it is best if the teacher uses the correct terminology.

Capacity

• The amount a container can hold.

This is different from volume, which is how much space it takes up.

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• The metric units for capacity are millilitres (mL), litres (L) and kilolitres (kL), with kilolitres not required in Year 4.

Weight

2

General • The metric units for length are millimetres (mm), centimetres (cm), metres (m) and kilometres (km).

• The unit for measuring temperature is degrees Celsius (°C). It is considered metric as the difference between the temperature of water at freezing point (0 °C) and boiling point (100 °C) is divided into 100 equal gradations.

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• Note the use of the upper case ‘L’ for the abbreviation of litres; it is also used for mL and kL. This is to distinguish it from the number 1.

• A gap is always left between the number of units and the abbreviation of the unit; e.g. 5 cm, 8 kg, 375 mL, etc. and no full stop is used at the end of the abbreviation (unless it is at the end of a sentence).

• Abbreviations of metric units never use the ‘s’ at the end, e.g. ‘5 cm’ not ‘5 cms’; ‘8 kg’ not ‘8 kgs’; ‘375 mL’ not ‘375 mLs’ and ‘30 °C’ not ‘30 °Cs’. Of course, if the unit is written in full, the ‘s’ is needed; e.g. ‘5 centimetres’, ‘8 kilograms’, ‘375 millilitres’ and ‘30 degrees Celsius’.

• Students need to consider what to do when measuring, if the units don’t come out even. Judgments about whether to use ‘half units’; ‘a bit more than …’ or ‘a bit less than …’ can be discussed.

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 4)

R.I.C. Publications® www.ricpublications.com.au

Sub-strand: Using units of measurement—UUM – 1

Use scaled instruments to measure and compare lengths, masses, capacities and temperature (ACMMG084) Conversions Length 10 mm = 1 cm 100 cm = 1 m 1000 mm = 1 m

1000 g = 1 kg Capacity

1000 mL = 1 L

• Students need to have had experience measuring with non-metric (non-standard) units in order to appreciate the need for common metric units. This would involve the communication of measures to another person; for example, ‘the pencil is 17 pebbles long’; ‘the pencil case weighs the same as 12 marbles’ or ‘the cup holds 5 scoops of water’ make little sense, unless you have access to the pebbles, marbles or cups used. This is not appropriate when measuring temperature, as there is no non-standard units that could be used.

• Students need to develop ‘referents’ for length, mass and capacity. For example, students being aware that their little finger is approximately one centimetre in width and that a big stride is about a metre long. For mass, when holding an item to be estimated, most people mentally compare the item to something they know such as a tub of margarine or a bag of sugar. Capacity is often problematic because of marketing, where a 2-litre soft drink bottle looks as if it holds more than a 2-litre tub of ice-cream. Temperature is also problematic, but students could be aware of what is considered a hot day (maybe 40 °C) and a cold day (maybe 15 °C). This will vary depending on the local climate.

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• Students need to be fluent with conversions of common metric units of measure for length, mass and capacity (see left). Discussion could centre on needing to know about multiplying and dividing by ten, or powers of ten. Discuss the meanings of the prefixes; e.g. milli, centi, kilo.

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1000 m = I km Mass

TEACHER INFORMATION (CONTINUED)

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• Students need to know the units that are appropriate for measuring different items. For example, we would not usually measure the length of a room in millimetres; the mass of a balloon in kilograms; or the capacity of a bucket in millilitres.

• Ideally students should be the ones to choose the tools and units when measuring. However, at first they will need a lot of guidance in this.

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• National tests usually have questions where students are required to interpret scaled instruments. They need to have had many experiences actually doing this, not just watching.

Length • There are two types of rulers: dead-end (where the ‘zero’ is level with the end of the ruler) and waste-end (where the ‘zero’ is situated a little way in from the end of the ruler).

o c . che e r o t r s super • Dead end

1 cm

2

3

4

Waste end

0 1 cm

2

3

4

• Students may need specific teaching on how to use a ruler. For example, they should have their non-writing hand spanned out so that the ruler is more stable and won’t move easily; they line up the item to be measured with the ‘zero’ on the ruler and read along to the end of item.

• Ensure that all students’ rulers are in centimetres and millimetres, not inches.

• Drawing a line of a particular length is a different skill from measuring a line of a particular length.

• Students need to be able to express distances in terms of metres and centimetres, or just in centimetres. When students are conversant with numbers to two decimal places, they can record distances using decimals—e.g. 1.3 metres—and know that this is the same as 1 metre and 30 centimetres.

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 4)

R.I.C. Publications® www.ricpublications.com.au

3

Sub-strand: Using units of measurement—UUM – 1

Use scaled instruments to measure and compare lengths, masses, capacities and temperature (ACMMG084)

TEACHER INFORMATION (CONTINUED) Student vocabulary centimetres metres grams kilograms millilitres litres

Celsius

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perimeter long

longer

longest short

shorter

• When using metric units for mass, students may use a pan balance and weights, kitchen scales or bathroom scales. Kitchen and bathroom scales may have a dial or a digital readout. It is a useful skill to be able read a dial, although students may need some assistance with this at first, particularly when not all graduations are marked; e.g. masses marked only in 5 or 10 gram intervals. There is little skill involved in reading a digit display.

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degrees

Mass • When estimating and measuring mass, the teacher needs to ensure that the masses of the items to be measured are not always obvious (i.e. that students cannot determine comparisons simply by looking).

To do this, you need items that have similar masses but different volumes; e.g. a golf ball and a table tennis ball; and items that are the same size but have different masses; e.g. lidded tins filled with different materials.

Capacity • Students may need help with strategies for measuring capacity, particularly when not all gradations are marked on a measuring container. Many measuring containers mark only every 5 or 10 millilitres.

Temperature • Many thermometers have their graduated scales marked at every degree, but only labelled at intervals of 5° or 10°. Students may need help when reading temperatures between those intervals.

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heavy

heavier

heaviest light lighter lightest

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holds the most holds the least hot hotter cold colder

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• Most thermometers have both Celsius and Fahrenheit markings.

Ideally it would be good to have only Celsius, but this may not be possible. In this case, mention needs to be made of the two scales and why Australia switched to Celsius many years ago (in the early 1970s) because of the metric nature of the scale, and the fact that it was the most commonly used measure of temperature globally. The USA still uses the Fahrenheit scale and the UK tends to give temperatures using both scales.

What to look for

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• Students unsure of what attribute to measure; i.e. length, mass or capacity.

• Students using inappropriate units of measurement.

• Students using inappropriate tools to measure; e.g. using a ruler to measure the length of a basketball court, bathroom scales to weigh a pencil case, or a medicine measure to calculate the capacity of a bucket.

• Students having useful referents for length, mass, capacity and temperature.

Proficiency strand(s): Understanding Fluency Problem solving Reasoning

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 4)

R.I.C. Publications® www.ricpublications.com.au

Sub-strand: Using units of measurement—UUM – 1

HANDS–ON ACTIVITIES Estimate before measuring in all these activities

Length • Students each cut a piece of paper tape (or ribbon) of various lengths or the teacher cuts them and hands them out, one per student. In groups of 5 or 6, students estimate how long each of the tapes is and orders the pieces from shortest to longest. Students decide how they will record this data. The student with the piece estimated to be the shortest measures the first paper tape; all the students then have the opportunity to revise their other estimates based on this new knowledge. Then each student measures his or her own piece of tape and the group places them in order from shortest to longest. How did the lengths of each piece and the final order compare to their estimates? Finally, the group decides how to display its results.

r o e t s Bo r e p ok u S Bella

45 cm

We estimated 35 cm

Josh

41 cm

39 cm

Emma

38 cm

36 cm

Ben

30 cm

30 cm

Natalie

24 cm

22 cm

Jean

22 cm

20 cm

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Our paper tapes

We put all the tapes in the right order, but our estimates were just a bit low.

• Students can estimate and measure lengths using the resource sheets on pages 9, 10 and 14.

• Students need to be able to round to the nearest gradation. When measuring very small lengths, students may measure to the nearest millimetre or centimetre. For longer lengths, they may round to the nearest metre or round to the nearest centimetre using decimal notation (e.g. the length of this room is 6.3 metres).

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• Measuring the length of curved items. Students use pieces of string to determine the lengths of objects that cannot be measured directly using a ruler and then straighten the string out against a ruler to obtain a measurement in millimetres or centimetres. (See activity on page 10.)

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Perimeter • Introduce the concept of perimeter by students measuring the edges of objects and shapes and adding the lengths together to find the distance around them; for example, finding the perimeter of their desks and comparing that to the perimeter of the teacher’s desk. Students may use 30-cm rulers, metre tapes or metre rulers to undertake the measuring. At this stage, students are not expected to look for or use a formula for calculating the perimeters of squares or rectangles; merely know that perimeter is the measurement of length around the border of a shape. Because of this, students can calculate the perimeter of irregular quadrilaterals and other shapes. For example, What is the perimeter of your foot? Your hand? Which has the greater perimeter?

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• Students could use string to measure the distance around larger objects to find the perimeter. For example, How can we find the distance around this hoop?

• An activity which helps develop the concept of perimeter can be found on page 11. Students will require pattern blocks to complete this activity.

We used string to work out the perimeter of the garden bed. We laid it along a metre ruler. It is 12.7 metres.

Estimate before measuring in all these activities

Mass • Bathroom scales can be available so that the mass of students can be recorded at regular intervals. Be aware that some students may be sensitive to having their mass disclosed. For this reason, it may preferable to weigh other items such as a class pet. However, this is unlikely to offer the opportunity to measure in kilograms on bathroom scales, so other items will need to be found for weighing heavier objects; e.g. a bucket of sand, a box of Base Ten Blocks, a box of books.

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 4)

R.I.C. Publications® www.ricpublications.com.au

5

Sub-strand: Using units of measurement—UUM – 1

HANDS–ON ACTIVITIES (CONTINUED) Estimate before measuring in all these activities

Mass • Compare the masses of objects in the same containers; e.g. a bucket of sand, water, gravel, beanbag beans. This will reinforce the reality that we cannot estimate the mass of an object just by looking at it; we need to actually pick it up or handle it in some way.

• Set up a class shop with various items that need to be purchased by weight such as nuts in shells, or students can make fruit and other items from plasticine or clay for sale by the gram or kilogram. These products may include items such as 100 gram ‘bars of chocolate’. These can be used in discussions about how many of them you would need to have one kilogram of ‘chocolate’. When making up items that weigh 100 grams, students would need to read the scales very carefully to try to be as close to the correct weight as possible.

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• To practise measuring items that are light, such as paperclips, macaroni, rice or nails, students may look at how many they would need to have a mass of 10 grams.

They could then arrange these individual objects in order from lightest to heaviest, and record their data in a way of their choosing.

Weighing

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• Students estimate then weigh various items on kitchen scales and then place them in order from lightest to heaviest.

Use some items that are light but large and some that are small but heavy; e.g. place in order from lightest to heaviest a cricket ball, balloon, golf ball, table tennis ball and basketball. Remember to give students the opportunity to revise their estimates after they have weighed the first item. Students choose how they will record their findings. (See also page 12.)

We measured 10 grams of rice, macaroni, nails and paperclips. We had: Rice

Macaroni

Nails

112

16

6

Paperclips 15

This means that one piece of rice is the lightest, then one piece of macaroni, a paperclip and a nail, which is the heaviest.

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Capacity

Estimate before measuring in all these activities

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Measuring capacity

bottle

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70 mL

jug

Item

My estimate

Actual capacity

100 mL

350 mL

Holds the least

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• Have four or five objects of quite different capacities for students to compare. Students estimate which of the containers will hold the most sand/water/beans etc. and which will hold the least. They then measure the first container by filling it and pouring the contents into a graduated container or jug. Based on this knowledge, students revise their other estimates then measure the other containers. Finally, the containers are put in order from the one that holds the least to the one that holds the most. (See also page 13.)

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200 mL

200 mL

300 mL

250 mL

small bucket

500 mL

600 mL

750 mL

kettle

400 mL

500 mL

400 mL Holds the most

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 4)

R.I.C. Publications® www.ricpublications.com.au

Sub-strand: Using units of measurement—UUM – 1

HANDS–ON ACTIVITIES (CONTINUED) Our containers in order of capacity 750 700 650 600 550 500 450 400 350 300 250 200 150 100 50

small bucket

kettle

bottle

jug

mug

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• Students compare three or four differently-shaped containers by trying to decide which one will hold the nearest to 500 millilitres (500 mL). They then measure each container to see if their estimation was correct. This activity could be extended to the students making judgements about which will hold nearest to 375 millilitres (375 mL), which is the size of most soft drink cans; 600 millilitres (600 mL), the size of many cartons of flavoured milk drinks; and 1 litre (1 L), which is the size of many milk and juice cartons, etc.

Capacity in millilitres

• Students could use data such as that from the table on page 6 and make a bar graph using 1-cm grid paper. They may need help deciding on the scale to be used on the y-axis.

Containers

Temperature

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• Students may need to be shown how to read the scale on a thermometer. Discussion could relate to the markings on the scale: do they go up by 5°, 10° or some other amount? Students may also need to be aware that the ‘degrees’ used for measuring temperature are different from the ‘degrees’ used in measuring angles.

• Discuss what constitutes ‘hot’ and ‘cold’ and the fact that they are relative terms; e.g. hot compared to what? Depending on the geographical location, we may consider a hot day to be 38° or 25°. Similarly, a cold night could be 15° or -1°.

Students need to be aware that the Celsius scale uses 0° as the freezing point of water and 100° as the boiling point.

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Temperature in the same week in May at 2.00 pm

Degrees Celsius

Degrees Celsius

Temperature in a week in May at 10.00 am

27 26 25 24 23 22 21 20 19 18 17

Mon.

Tue.

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• As part of a daily (morning) routine, students could take turns in reporting on the current temperature. This could be recorded for a week (Monday to Friday) and students could then graph the results. They could compare this to the temperature at 2:00 pm on each of the days and discuss the differences. For further comparison, the graphs of a week’s temperatures could be kept for February, April, July and September (or whatever months). This would offer opportunities to look at differences in seasonal temperatures.

Wed. Day

Thur.

Fri.

27 26 25 24 23 22 21 20 19 18 17

Mon.

Tue.

Wed. Day

Thur.

Fri.

• Use a thermometer to measure the temperature of a cup of room-temperature water, a cup of boiling water (very carefully) and a cup of very cold water (maybe with ice blocks). Discuss the results.

• Have a medical thermometer that can be used under the armpit. Record the results from the students. Discuss what is considered a ‘normal’ temperature (‘normal’ is considered anywhere between 36.4 °C and 37.2 °C (although a wide range of body temperatures has been found in healthy people) and what is considered a fever (a mild fever is considered to be up to 39 °C).

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 4)

R.I.C. Publications® www.ricpublications.com.au

7

Sub-strand: Using units of measurement—UUM – 1

LINKS TO OTHER CURRICULUM AREAS English • Read Knee high Nigel by L Anolt. This is the story of five giants, one of whom, though still a giant, is considerably smaller than the others. They argue over the building of castles and go their separate ways with unsuccessful results.

• Read Actual size by S Jenkins. This book has fantastic drawings of animals, actual size (large and small). Make sure to get the English edition in centimetres.

• Look at Jim and the beanstalk by Raymond Briggs. This offers the opportunity to look at length and an intuitive sense of scale.

• The idea of mass is highlighted in Elephee’s walk by H Nakano. The smallest creature is the one to finally cause a downfall.

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• Read Drip, drop by Sarah Weeks. This book follows a mouse who has a leak in his roof as he tries to decide which kitchen container to use to catch the water.

Information and Communication Technology

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• A website where students work out the length of a ruler to the nearest half a centimetre can be found <http://www. bgfl.org/bgfl/custom/resources_ftp/client_ftp/ks2/maths/measures/index.htm> Students need to write the answer in digits, and use the full word ‘centimetre’ for the unit of measure.

• The same website cited above has a kitchen scale with parcels, and students need to read the scale and write in how much each one weighs. They can use either grams or kilograms as the unit of measure—e.g. 1.2 kilograms or 1200 grams—and again they need to write the full word, not an abbreviation.

• The same website also has the option of students reading a graduated scale on a measuring jug. The answer is to be written in digits for the amount of water, and the full word ‘millilitre’ (not mL) for the unit of measure; however the jug shows the abbreviation as ‘ml’, which is incorrect. This could be a discussion point with the students.

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Health and Physical Education

• Link studies of health to the measurement of the students’ body temperatures using an under-the-arm thermometer.

Science

• Opportunities for measuring mass with kitchen scales will arise during cooking activities.

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• Students organise to collect water from a dripping tap (or set a tap to drip slowly). Catch the water in a graduated container for one minute or five minutes if a slow drip. Students may transfer the water from a normal container to a graduated container after collection if easier. Students predict how much water would be wasted by the leaking tap after ten minutes, an hour or other time periods. Discuss this in relation to studies of the environment.

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 4)

R.I.C. Publications® www.ricpublications.com.au

Sub-strand: Using units of measurement—UUM – 1

RESOURCE SHEET Body parts In pairs, measure the length: • of your arm from your shoulder to your elbow • of your hand from your wrist to the end of your longest finger • of your leg from your knee to your ankle • around your head at your forehead.

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Show the results on the graph below.

Me

My partner

Me

My partner

Me

My partner

60 cm

50 cm

My partner

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Me

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70 cm

30 cm

20 cm

10 cm

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Arms

Hands

Legs

Heads

Mark with a circle the person who has the longer length for each of the four measures. Compare your results to those of other groups.

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 4)

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9

Sub-strand: Using units of measurement—UUM – 1

RESOURCE SHEET How long are they?

Measure each of the different lines below. You may need more than a ruler to work out some of them.

Line 1 Line 2

Line 5

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Write the numbers of the lines in order from the longest to the shortest.

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 4)

R.I.C. Publications® www.ricpublications.com.au

CONTENT DESCRIPTION: Use scaled instruments to measure and compare lengths, masses, capacities and temperature

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Line 3

Sub-strand: Using units of measurement—UUM – 1

RESOURCE SHEET Pattern block perimeter graph Measure the perimeter of each of the six different pattern blocks. Place the measures on the graph below by colouring the boxes to the correct height.

18 cm 17 cm 16 cm

14 cm

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15 cm

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13 cm

11 cm

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10 cm

7 cm

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4 cm 3 cm

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CONTENT DESCRIPTION: Use scaled instruments to measure and compare lengths, masses, capacities and temperature

12 cm

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2 cm 1 cm

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 4)

R.I.C. Publications® www.ricpublications.com.au

11

Sub-strand: Using units of measurement—UUM – 1

RESOURCE SHEET How much do they weigh?

1. Estimate the masses of five objects chosen by your teacher. Write your estimates in the ‘My estimate’ column. Then weigh the first object. Write that in the ‘Real mass’ column and work out the difference between it and your estimate. If you think it’s a good idea, you can change the rest of your estimates by crossing out what you had before and writing your new estimate next to it.

r o e t s Bo r e p Yes No ok Did your estimates get better? u S Object My estimate Real mass Difference

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2. List the objects you used in the table above, in order, from lightest to heaviest, on the lines below.

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3. Look at the pictures below and write a number from 1 to 6 to show the lightest (1) to the heaviest (6).

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 4)

R.I.C. Publications® www.ricpublications.com.au

CONTENT DESCRIPTION: Use scaled instruments to measure and compare lengths, masses, capacities and temperature

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Now weigh the rest of your objects. Write each of the masses in the ‘Real mass’ column and work out the differences and write them in the ‘Difference’ column.

Sub-strand: Using units of measurement—UUM – 1

RESOURCE SHEET How much do they hold?

1. Estimate the capacities of five different containers. Write these in the ‘My estimate’ column. Then fill the first object with water, sand or rice and pour into a measuring jug. Write the amount in the ‘Real capacity’ column and work out the difference between it and your estimate. If you think it’s a good idea, you can change the rest of your estimates by crossing out what you had before and writing your new estimate next to it.

r o e t s Bo r e p ok u S No Did your estimates get better? Yes My estimate

Real capacity

Difference

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CONTENT DESCRIPTION: Use scaled instruments to measure and compare lengths, masses, capacities and temperature

Object

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Now work out the capacity of the rest of your containers. Write each of the capacities in the ‘Real capacity’ column, and work out the differences and write them in the ‘Difference’ column.

2. List the objects you used in the table above, in order, from holds the least to holds the most, on the lines below.

. te o c 3. Colour all the objects below that you can use to measure capacity. . che e r o t r s super

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 4)

R.I.C. Publications® www.ricpublications.com.au

13

Sub-strand: Using units of measurement—UUM – 1

RESOURCE SHEET Measure hunt Find items that belong in each of the boxes below.

Between 0.5 metre and 1½ metres

Between 5 grams and 10 grams

Between 50 grams and 60 grams

Between 1 kilogram and 1½ kilograms

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Between 50 mL and Between 1 litre and e Between 5 mL and 10 mLc her80 mL st r super o 1½ litres

14

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 4)

R.I.C. Publications® www.ricpublications.com.au

CONTENT DESCRIPTION: Use scaled instruments to measure and compare lengths, masses, capacities and temperature

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Between 1 mm and 5 mm Between 1 cm and 10 cm

Assessment 1

Sub-strand: Using units of measurement—UUM – 1

NAME:

DATE: Measurement tasks

1. Find three (3) things in the classroom that are about 10.5 cm long.

2. Measure the longest side of your calculator and the width of your desk in millimetres.

r o e t s Bo r e width of desk = p ok u 3. Measure the length of three (3) different hands (wrist to middle fingertip) in the S classroom in cm and write them in order from shortest to longest.

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longest side of calculator =

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5. Find four (4) items of different masses. Weigh them to the nearest gram and list them in order from lightest to heaviest.

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Lightest

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CONTENT DESCRIPTION: Use scaled instruments to measure and compare lengths, masses, capacities and temperature

4. Find three (3) things in the classroom that weigh about 450 grams.

6. Find three (3) containers in the classroom that have a capacity of about half a litre.

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7. Find four (4) items of different capacities. Measure them to the nearest millilitre and list in order from holding the least to holding the most.

Least

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 4)

Most

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15

Assessment 2

Sub-strand: Using units of measurement—UUM – 1

NAME:

DATE: Reading scales

1. Work out the mass on each of the scales below.

KG

120 140 140 140 140 100 140 80 60 240 260 40 20 0 280

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2. Work out the capacity shown on each of the containers below.

250 mL

200

60

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50

100 mL

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100 150

80 60

40

100

30

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40

10

20

mL

50

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100

100

100

100

100

100

100

100

90

90

90

90

90

90

90

90

80

80

80

80

80

80

80

80

70 60

70 60

70 60

70 60

70 60

70 60

70 60

70 60

50

50

50

50

50

50

50

50

40

40

40

40

40

40

40

40

30

30

30

30

30

30

30

30

20

20

20

20

20

20

20

20

10 0

10 0

10 0

10 0

10 0

10 0

10 0

10 0

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 4)

R.I.C. Publications® www.ricpublications.com.au

CONTENT DESCRIPTION: Use scaled instruments to measure and compare lengths, masses, capacities and temperature

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S

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1 kg

Checklist

Sub-strand: Using units of measurement—UUM – 1

Use scaled instruments to measure and compare lengths, masses, capacities and temperature (ACMMG084) Use scaled instruments to measure and compare … masses

capacities

temperatures

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STUDENT NAME

lengths

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 4)

R.I.C. Publications® www.ricpublications.com.au

17

Sub-strand: Using units of measurement—UUM – 2

Compare objects using familiar metric units of area and volume (ACMMG290)

RELATED TERMS

TEACHER INFORMATION What this means

Comparison

• Relates to making judgements about only two shapes or objects.

The vocabulary of comparison for area and volume is ‘bigger’ or ‘smaller’.

• To compare objects according to area, use square centimetres (cm2) and square metres (m2).

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• To compare objects according to volume, students would most commonly use cubic centimetres (cm3), although students could investigate how big a cubic metre (m3) is.

Teaching points

Ordering

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Area

• The amount of surface on an object.

Volume

• The amount of space an object takes up.

• Estimation should be encouraged in all measurement activities.

Area • Students need to be aware that squares are the most commonly used units for measuring area. This knowledge comes after experiences of filling areas using other shapes such as circles, and discussion of the need for no gaps or overlaps. Although there are many other shapes that tessellate (fit together perfectly), the square is the easiest to use as a measure of area. In the metric system, we use the units of square centimetres (cm2), square metres (m2), square kilometres (km2) and hectares (ha). At Year 4, square kilometres and hectares would not be introduced.

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• Relates to making judgements about three or more shapes or objects. It is also known as seriation.

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C.Publ i cat i ons •canf orr evi ew pur posesonl y• • The amount a container hold.

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• An example of this difference is if you consider an esky™. The amount of room it takes up in a cupboard is its volume. The amount it can hold is its capacity.

Displacement volume

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• The volume of liquid displaced by an object immersed in that liquid.

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Capacity

• Comparisons of area may be made by tracing each of the shapes onto 1 cm grid paper and counting how many squares (1 cm2) are covered in each, and then considering the difference. There are three methods of dealing with the pieces that are not full squares. The first is to count any squares that are more than half covered as one square and not count any that have less than half of the square covered. The second method is to add pieces that are parts of squares together to equal whole squares. The third is to count all the squares that have any part covered, and divide this amount by two. The resulting calculations of areas using any of these methods would be very similar.

• Experiences in area should be designed so that students recognise that area is an attribute that is independent of position and shape.

So, for example, a seven-piece tangram in the shape of a square has the same area as when the seven pieces have been rearranged into a rectangle, triangle or any other shape or picture. This understanding of conservation of area is important, and students need many experiences, with clear explanations, to consolidate it.

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• Formulas for calculating the area of regular shapes such as squares and rectangles should not be introduced at this year level.

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 4)

R.I.C. Publications® www.ricpublications.com.au

Sub-strand: Using units of measurement—UUM – 2

Compare objects using familiar metric units of area and volume(ACMMG290)

TEACHER INFORMATION (CONTINUED) Volume • Comparisons of volume may be made by building objects with 1 cm3 cubes and counting how many cubes were used for each object.

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1. Partly fill a container, mark the water level (an elastic band is good for this), place the object into the water and measure the distance the water level has risen.

2. Place the object in an empty container, fill or partly fill the container to cover the object, mark the water level, remove the object, mark the new water level and measure the difference in height.

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• To calculate the volume of both regular and irregular objects, displacement may be measured; i.e. students can measure the difference in height of water in the container or the amount of water displaced using a measuring jug or similar (see UUM – 1). There are three ways to measure displacement:

3. Fill a container to the top with water, place in the object and catch and measure amount of water in the overflow.

• Note: The mass of the objects to be displaced has no bearing on the displacement (volume). So, for example, a golf ball and a ping-pong ball will displace the same amount of water as they are of similar volumes, even though the golf ball is much heavier.

What to look for © R. I .

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• Students understanding of conservation of area; that the area doesn’t change if they cut and reform a shape, as long as there are no overlaps.

• Students using systematic ways to calculate (count) the number of squares that form the area of a shape.

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• Students unable to decide how to work out the volume of buildings using 1 cm3 cubes.

• Students confused about the concept of displacement for measuring volume (it is quite a sophisticated concept).

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covers more (as in area) covers less covers most covers least volume displacement overflow

Proficiency strand(s): Understanding Fluency Problem solving Reasoning

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 4)

R.I.C. Publications® www.ricpublications.com.au

19

Sub-strand: Using units of measurement—UUM – 2

HANDS-ON ACTIVITIES Estimate before measuring in all these activities

Area

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There are 4 full squares in the shape and 6 that are more than half a square, but not a full square. So the area is about 10 squares or 10 cm2.

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• Students draw a simple shape onto 1 cm2 grid paper. Discuss how they might find the area of their shapes. It may be best to start with shapes that consist of straight lines on the lines of the grid paper. To work out the area, they count the squares enclosed by their shape. It would be good if they figure out a systematic way to do this, for example counting in straight lines and putting a stroke in each square as they count it. Later, they may make shapes that have part-squares or curves, where working out the area is a little more complicated. However, counting squares is still the easiest way to calculate the area. Students can discuss what to do when there are bits of squares left over. There are three options: The first is to count any squares that are more than half covered as one square and not count any that have less than half of the square covered. The second method is to add pieces that are parts of squares together to equal whole squares. The third is to count all the squares that have any part covered, and divide this amount by two. The resulting calculations of areas using any of these methods would be very similar.

• Use a geoboard to make figures using unit squares. Students make shapes (with right angles only) on the board pegs using elastic bands, and count the number of squares enclosed to find the area. Students could then be asked to make a shape that encloses a particular number of squares (for example six squares) and find as many different shapes as they can. Discuss whether two shapes that are the same other than their orientation (i.e. shapes that have been rotated or reflected) can be considered as different examples.

• The two below would be considered the same figure.

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• Students experiment with squares enclosed on the geoboard on the diagonal. Discuss how they might calculate the area of the square.

• Students investigate puzzles with tangrams (See the resource sheet on page 23). What happens to the area when we rearrange the pieces? Discuss what happens to the area of the rearranged shapes. By this stage, students should understand the concept of conservation of area; that the area of each new shape made with the seven pieces has not changed because nothing has been added or taken away and there are no overlaps.

• There are four levels of difficulty when working with tangrams. The easiest of them is to have a full-sized outline of each individual piece, so the students place each piece directly over its outline. The second level is to have the overall outline shown at full size, but not the boundaries of the individual pieces. The third level is to have all the pieces shown on the diagram, but on a smaller scale. Finally, the most difficult level is to have only the overall outline shown and on a smaller scale so that the pieces cannot be placed directly over them. At this stage, it would not be expected that all students would be able to handle the third and fourth levels.

20

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 4)

R.I.C. Publications® www.ricpublications.com.au

Sub-strand: Using units of measurement—UUM – 2

HANDS-ON ACTIVITIES (CONTINUED) • Students could make pictures of their choice using all seven pieces. They can be given general instructions such as make an animal using all of your pieces, or the activities could be very directed by having the students make a particular shape such as a rectangle or being given a particular picture of a shape they are to construct.

• Students could investigate whether there is a link between area and perimeter, using 1 cm2 grid paper. This would only be a simple exploration that would be followed up in later year levels, so the figures used would be quite simple. For example, draw some shapes using six squares (similar to the geoboard activity). This means that each of the shapes has an area of 6 cm2. Then look at the perimeter of each of the shapes, and discuss whether the perimeters are all the same and, if not, why not.

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Shape 1

Shape

Area

Perimeter

1

6 squares

10 units

2

6 squares

12 units

3

6 squares

14 units

4

6 squares

12 units

• Students consolidate these skills with the resource sheets on pages 24 and 25.

Volume

Shape 4

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Shape 2

• Use 1 cm3 cubes (Base Ten small cubes or Centicubes) to construct buildings from a given number of cubes; e.g. Make as many buildings using 6 cubes as you can. Each cube must connect to another along a complete face. Discuss whether any of the buildings are the same, or if some are reflections of others. Is a building 6 blocks high the same as a building 6 blocks long? What is the same about all of the buildings; what is different? What is the volume of each of them? Students record their results in a way of their choice.

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• Chocolate box problem: A company that makes chocolates that are exactly 1 cm3 in size is looking at how best to package them. They want to have 12 chocolates in each box. What might the boxes look like? What about if they can have two layers of chocolates in each box? Or three or more layers? What about if there are to be 15 chocolates in the box? Or 24 chocolates? Students use centicubes or the small Base Ten cubes to investigate the options. Discussion should involve the volume of each of the boxes being considered.

• Give students ’plans’ of models that they then construct. At this stage, only have models that are one cube high (one storey high). Discuss how many cubes are used in each model, and the fact that this is the volume of the model.

Students could then make their own models according to certain criteria such as the number of cubes to be used, and draw plans for them. Or they could design their own plans for their partner to construct. These activities could lead to the students compiling a class book of model plans. In each plan, attention should be drawn to their volumes.

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My plan has 6 + 4 + 2 cubes, which means it has a volume of 12 cubes.

• Students use cubes to build a 2 x 3 array. Count and record the number of cubes used. Now add another layer of 2 x 3 cubes and count and record the number of cubes. Continue in the same way with another layer. Discuss the results. This introduces the idea that volume can be worked out by counting equal layers of cubes. Links could be made to multiplication, but at this stage, students do not need to take this any further by the introduction of formulas for the volume of solids.

• Students can practise their volume and measurement skills with the resource sheet on page 25.

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 4)

R.I.C. Publications® www.ricpublications.com.au

21

Sub-strand: Using units of measurement—UUM – 2

LINKS TO OTHER CURRICULUM AREAS English • Read Alexander’s outing by Pamela Allen. This is a story about a duck that falls into a hole. It offers possibilities for discussion about volume.

• Read Marilyn Burns’ book Spaghetti and meatballs for all! A mathematical story. This book would be a good introduction to discussions about area and perimeter.

Information and Communication Technology • There is an area explorer that can be found at <http://www.shodor.org/interactivate/activities/AreaExplorer/> This produces shapes on a grid, and the students are required to count the squares and key in its area. The perimeter of the shape is given.

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• Work with tangrams offers the opportunity to see that the area of a shape does not change when the pieces are rearranged, as long as there are no overlaps and no pieces missing. Type “tangrams” into a search engine (such as Google™) to find some wonderful images of tangrams.

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The Arts

• Students could look at the models they have made as part of the work on volume and try to draw them on isometric dot paper, thus producing a drawing of three-dimensional shapes from a corner perspective. A site where you can download free isometric dot paper is <http://highered.mcgraw-hill.com/sites/dl/free/0072532947/78543/ IsometricDotPap.pdf> It would be best to start by drawing just one cube, and then continue on to draw more complex models such as those produced in the model activities.

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 4)

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Sub-strand: Using units of measurement—UUM – 2

RESOURCE SHEET Seven piece tangram Cut out your tangram pieces. Re-form, using all seven pieces, to make a large triangle. Then make a large rectangle, parallelogram and trapezium. Consider the area of each of your new shapes. Has it changed at all?

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What other shapes can you make using all your tangram pieces?

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CONTENT DESCRIPTION: Compare objects using familiar metric units of area and volume

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 4)

R.I.C. Publications® www.ricpublications.com.au

23

Sub-strand: Using units of measurement—UUM – 2

RESOURCE SHEET What is the area? – 1 1. Count the squares to find the area of each shape. (a)

(b) A=

(c)

cm2

cm2

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cm2

cm2

cm2

A=

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A=

A=

2. Draw each shape on the empty grid and write each shape’s area. (a) Square with 4 cm sides

cm2

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(b) Rectangle with 6 cm and 2 cm sides.

2

(c)

2

cm2

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 4)

R.I.C. Publications® www.ricpublications.com.au

CONTENT DESCRIPTION: Compare objects using familiar metric units of area and volume

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Sub-strand: Using units of measurement—UUM – 2

RESOURCE SHEET What is the area? – 2 Work out the area of each of the shapes below in square centimetres.

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1. The duck

2. The house

cm2

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cm2

Chips

CONTENT DESCRIPTION: Compare objects using familiar metric units of area and volume

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cm2 Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 4)

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Sub-strand: Using units of measurement—UUM – 2

RESOURCE SHEET Rolling rectangles You will need:

1 piece of A4 paper scissors sticky tape pasta or beans

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cardboard to stand cylinders on

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Cut the paper in half, and make two different cylinders from the pieces. Try not to overlap the edges when you make the joins.

Estimate first, and then check your estimate.

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2. Place each cylinder upright on a piece of cardboard, and fill with pasta or beans, being careful not to spill any. Do the cylinders hold the same amount?

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3. What can you say about the area of each piece of paper?

4. What can you say about the volume of the pasta or beans?

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 4)

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CONTENT DESCRIPTION: Compare objects using familiar metric units of area and volume

© R. I .

C.Publ i cat i ons •f orr evi ew pur posesonl y• 1. Does each tube hold the same amount?

Assessment 1

Sub-strand: Using units of measurement—UUM – 2

NAME:

DATE: Areas

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1. On the square paper below, draw as many shapes as you can that are 12 cm2 in area.

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CONTENT DESCRIPTION: Compare objects using familiar metric units of area and volume

2. Work out the area of the footprints below and decide which has the greater area.

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 4)

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Assessment 2

Sub-strand: Using units of measurement—UUM – 2

NAME:

DATE: Finding volume

Build the models below using 1 cm3 cubes. Then work out the volume of each model.

1.

2.

cm3

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3.

cm3

cm3

cm3

Can you find a way to work out the volume of the models below without building them?

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cm3

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cm3

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cm3

Write the numbers of the models in order from least volume to most volume.

Least

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 4)

Most

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CONTENT DESCRIPTION: Compare objects using familiar metric units of area and volume

© R. I .

C.Pu bl i cat i ons 6.

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5.

Checklist

Sub-strand: Using units of measurement—UUM – 2

Finds shortcuts to calculating volumes of layered constructions

Finds volumes of objects by counting 1 cm3 cubes

Finds shortcuts to calculating areas of shapes

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STUDENT NAME

Finds areas of regular and irregular shapes by counting 1 cm2 squares

Compare objects using familiar metric units of area and volume (ACMMG290)

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29

Sub-strand: Using units of measurement—UUM – 3

Convert between units of time (ACMMG085)

RELATED TERMS

TEACHER INFORMATION What this means

Conversions of time:

• Students need to be aware of whether multiplication or division is the correct operation for each particular conversion.

60 seconds = 1 minute 60 minutes = 1 hour 24 hours = I day 7 days = 1 week 2 weeks = 1 fortnight

365 days = 1 year

366 days = 1 leap year 12 months = 1 year

10 years = 1 decade

100 years = 1 century

1000 years = 1 millennium

• Although most measures of time are not decimal, timing of some sporting events can go into tenths or hundredths of a second. For example, in Olympic running or swimming events, the difference between the first and second places may be as little as 0.03 of a second. These times are also recorded in decimal format; e.g. Australian Robert Hurley won the men’s 400 metres freestyle race at the World Shortcourse Championships in August 2010 in a time of 3:41.58, that is three minutes and forty-one point five eight seconds. This is a strange mix of Base 60 and decimal.

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52 weeks = 1 year

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• Calculating time conversions involves the use of many different bases.

Students need to know the conversion rates in order to solve many time problems: 60 (seconds in a minute; minutes in an hour), 24 (hours in a day), 7 (days in a week), 4 (weeks in a month), 52 (weeks in a year), 12 (months in a year), 365 (days in a year), 366 (days in a leap year). The only base ten units are 10 years in a decade, 10 decades in a century and 10 centuries in a millennium.

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• Standard abbreviations for units for time are seconds (s), minutes (min) and hours (h); the other units do no have standard abbreviations. Note: ‘sec’ and ‘hr’ are commonly used abbreviations for second and hour, but they are not the correct ones.

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Student vocabulary second minute hour day

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• When converting measures of time, students need to be able to multiply and divide, sometimes using quite large numbers; the use of calculators would be encouraged.

• To help decide whether to multiply or divide, encourage students to consider whether there would be more or fewer of the new units than the original; i.e. does their answer make sense in the context?

o c . che e r o t r s super What to look for

• When converting between units of time, students knowing whether to multiply or divide in a particular situation.

week fortnight month year leap year decade century millennium (plural, millennia)

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Proficiency strand(s): Understanding Fluency Problem solving Reasoning

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 4)

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Sub-strand: Using units of measurement—UUM – 3

HANDS-ON ACTIVITIES • Lengths of time: Write the following lengths of time on card and ask the students to order them from the shortest to longest time period: second, minute, hour, day, week, fortnight, month, year, leap year, decade, century, millennium.

(See page 33.) Once the students have agreed on the order, ask them to suggest some other words that might fit at either end or between the words. For example, ‘millisecond’ could be placed before second, ‘season’ between month and year.

• Time problems and puzzles: Pose questions that require conversions of time. The teacher or students can write the problems. A class set could be compiled by copying the best questions onto cards. (See also pages 34 and 35.)

• Investigate how many days are in each of the seasons. This could lead to students researching when each season begins and ends and whether this varies according to their geographical location. For example, in the tropical regions there are only two recognised seasons: the wet season and the dry season. Students could compare all the different results obtained.

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• Students could look at how many days are in each month and thus how many days in each of the different terms, seasons or semesters.

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• This unit links with multiplication and division units. Because this unit on conversions between units of time means that there may well be remainders when multiplying or dividing, the use of calculators to assist with the computation is encouraged. In any calculations where remainders are produced, discussion could centre on what the remainders may mean. This may simply involve knowing that the remainder represents a little bit more than the resulting whole number in the solution. The focus in this unit is on which is the appropriate operation to use in any given situation: multiplication or division. The related multiplication and division content descriptions are: – Develop efficient mental and written strategies and use appropriate digital technologies for multiplication and division where there is no remainder (ACMNA076) – Solve word problems by using number sentences involving multiplication and division where there is no remainder (ACMNA082)

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Sub-strand: Using units of measurement—UUM – 3

LINKS TO OTHER CURRICULUM AREAS English • Use the book Tick tock by James Dunbar as a stimulus book for discussion about different time periods.

• Read Just a minute! by T Slater.

Information and Communication Technology • A game that requires students to convert different units of time can be found at <http://www.sheppardsoftware.com/ mathgames/time/TimeConversions.htm> • A website that enables you to convert between different units of time can be found at <http://www.unit-conversion. info/time.html>

History and Geography

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• Discussion of the alternation of day and night could lead to an introduction to the concept of the earth’s rotation. The teacher could use a light source such as a torch and a globe to show how the rotation of the earth results in periods of daylight and periods of darkness.

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• A website that lists the expected maximum life spans in years for a large range of animals can be found at <http://sonic. net/~petdoc/lifespan.htm>

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• A website that lists the Top 10 short life spans of animals/insects/plants can be found at <http://victoryv.hubpages. com/hub/top-10-Short-life-Small-lifespan-animalsinsectsplants>

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• The above two websites could provide a useful opportunity to investigate different life spans and then convert these into other units of time measurement.

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 4)

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Sub-strand: Using units of measurement—UUM – 3

RESOURCE SHEET Lengths of time

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minute

week

century

month

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Cut out these cards and place the times in order from the shortest duration to the longest. Make a record of your list.

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decade

CONTENT DESCRIPTION: Convert between units of time

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Sub-strand: Using units of measurement—UUM – 3

RESOURCE SHEET Time problems Work out the answers to the following time problems.

A dragonfly usually lives for about 2688 hours.

How old are you: in months?

How many days is that?

Howr many weeks? o e t s B r in days? e How many months? oo p u k The world record for the marathon is S Have you lived for more 2:03:38. What does this mean? than a million seconds? Yes

No

Yes

No

Yes

No

A million minutes?

A million hours?

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in weeks?

How many minutes is that?

How many seconds?

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C.PThe ub l i cat i o ns is 9 years.

•f orr evi ew p ur posesonl y• How many months is that?

The oldest documented female, Jeanne Calment of France, lived to be 122 years and 164 days.

How many days old was she?

The Jurassic Period lasted for about 54 million years.

o c . che How many decades? e r o t r s super How many millennia is that?

How many centuries?

Make your own time problems for a friend to solve.

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 4)

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CONTENT DESCRIPTION: Convert between units of time

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The oldest known koi fish was 82 490 days old.

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How many weeks?

How many hours is that?

Sub-strand: Using units of measurement—UUM – 3

RESOURCE SHEET Time puzzles 1. Write three activities that might take each period of time below to complete.

About an hour

A few hours

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A few minutes

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C.Publ i cat i ons •f orr evi ew pur posesonl y• 2. It takes you 10 000 hours to learn to be a racing car driver.

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(b) How many days is that? (c) How many weeks is that?

. t e 12 000 minutes

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3. Put these time periods in order from shortest to longest.

CONTENT DESCRIPTION: Convert between units of time

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(a) How many minutes is that?

4. 1 decade =

14 days

510 seconds

days

5. 2555 days =

years

6. 650 hours =

minutes

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Assessment 1

Sub-strand: Using units of measurement—UUM – 3

NAME:

DATE: Time conversions quiz

Write the answers to the questions in this quiz. Show how you worked out the answer in the space.

2. How many hours are there in two weeks?

3. 1 hour = 3600

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4. How many minutes are there in 2¼ hours?

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1. How many days are in three weeks?

5. A turtle in a zoo lived for 140 years. How many decades is that?

6. Which is longer, 4½ days or 9000 minutes?

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o c . che e r o t 10. Put the following time periods inr order from the shortest time s to the longest time: super 13 days

48 hours

259 200 seconds

36 hours

144 hours

1 fortnight

Shortest

Longest

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 4)

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CONTENT DESCRIPTION: Convert between units of time

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8. Which has more days, the first half of the year (January – June) or the second half (July – December)? Or are they the same?

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7. How many seconds are there in 8¼ hours?

Checklist

Sub-strand: Using units of measurement—UUM – 3

Convert between units of time (ACMMG085) Can convert units of time between … hours and days

weeks and months

years and beyond

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STUDENT NAME

seconds and minutes

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Sub-strand: Using units of measurement—UUM – 4

Use am and pm notation and solve simple time problems (ACMMG086)

RELATED TERMS

TEACHER INFORMATION

am (ante meridiem)

What this means

• From the Latin words meaning before noon

• It is expected that students can tell the time to the nearest minute but, until now, have not distinguished between morning and afternoon using the am or pm notation.

pm (post meridiem)

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• Calculations of time difference can be quite difficult because of the non-decimal nature of time. For example, if using a timetable and calculating how long before the next bus, a calculator may actually hamper the process. If the bus arrives at 4:25 and it is currently 3:47, you cannot simply key 4.25 into a calculator and subtract 3.27; the result would be 0.78, which a child could incorrectly interpret as 78 minutes. In this case, the number of minutes until 4:00 would be calculated first (13 minutes), and the extra 25 minutes until the desired time (4:25) added to give a total waiting time of 38 minutes.

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• From the Latin words meaning after noon

• It may be useful to explain the origins of am and pm. They are from the Latin ‘ante meridiem’ and ‘post meridiem’, meaning ‘before midday’ and ‘after midday’.

Teaching points

• Students need to realise that duration requires a starting and finishing time. Ideas relating to duration could begin with discussions about the duration of familiar routine events; e.g. How long do we spend each week in the computer room?

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• Due to its display of numerals, a digital clock represents the ‘now’ and cannot be used to demonstrate or measure time past or time in the future by counting. The analogue clock lends itself to this type of counting.

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• Writing of time should use a colon between the hours and minutes; for example, twelve o’clock should be 12:00 not 12.00. This helps emphasise the fact that time is not decimal.

• Reiterating the difficulties faced with the use of decimals for timing, the time of 3:41.58 would need another 0.42 of a second to become 3:42, not 0.02 of a second (i.e. hundredths of a second, not Base 60).

This is another very good reason to use the colon to separate the hours and minutes and help avoid confusion.

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• Later is longer: Some students find it confusing, when asked to compare the times of events, if one event begins before the other.

They will often choose the ‘longer’ duration according to the finish time rather than the total time. For example, if one train trip goes from 2:15 to 3:00 and another goes from 2:30 to 3:05, some students may believe that the second trip is longer because it finishes five minutes later than the first, whereas in fact, the first trip is longer as it takes 45 minutes while the second trip takes only 35 minutes.

• Classrooms should have both an analogue clock and a digital clock, preferably side-by-side. Regularly seeing the two different displays for the same time of day helps students realise that there are two equally valid ways to read the time. There are some large clocks available commercially that clearly show the time in both formats.

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 4)

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Sub-strand: Using units of measurement—UUM – 4

Use am and pm notation and solve simple time problems (ACMMG086)

TEACHER INFORMATION (CONTINUED) Student vocabulary o’clock half past quarter past quarter to

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xx:25 (e.g. 3:25) xx:52 (e.g. 3:52)

am (ante meridiem) pm (post meridiem)

• The spoken time reflects the written digital time; e.g. 11:28 would be said as eleven twenty-eight, and not twenty-eight minutes after/past eleven. The time 7:31 would be said as seven thirty-one, not twenty-nine minutes to 8, or thirty-one minutes after/past seven. With times such as 3:05, whether we say oh instead of zero or whether we verbalise the initial zero at all, depends on community practice. However, the zero must be used in the written form. When am and pm are used, they are simply spoken as the letters am or pm.

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clockwise

• It is generally recommended that ‘quarter to an hour’ is the only instance that students deal with times to the next hour. For example, we would use 5:52 rather than 8 minutes to 6. These times ‘to’ an hour may be dealt with informally as the need arises.

• National tests usually have several questions on time, including calculating time differences.

What to look for

• Students missing an internal zero when writing the time; e.g. writing 11:5 am rather than 11:05 am • Students using the wrong base (e.g. Base 10) for time calculations.

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• Students using a calculator inappropriately when subtracting one time from another to find the duration of an event.

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• Students unable to decide which operation is appropriate when calculating time problems.

o c . che e r o t r s super Proficiency strand(s): Understanding Fluency Problem solving Reasoning

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Sub-strand: Using units of measurement—UUM – 4

HAND-ON ACTIVITIES • An activity in which students need to add on a specific amount of time would help promote the idea that working out time durations can be done using complementary addition. Refer to the adding time game on pages 42 to 44. Note: The first twelve time cards have times finishing in 5 or 0 (e.g. 3:30), while the second twelve have them finishing in other digits (e.g. 7:42). The three spinners also have different levels of difficulty. The first spinner has time durations of 5 minutes, 10, 20, 30, 40 and 50 minutes. The second spinner has durations of 5 minutes, 15, 25, 35, 45 and 55 minutes.

The third spinner has 2 minutes, 14, 27, 36, 49 and 51 minutes.

• For calculating relatively short durations of time, the easiest method is to calculate the amount of time until the next hour; the number of full hours to the finish time and then add on any remaining minutes. Students may need guided practice at this. For example, if an event starts at 3:47 pm and finishes at 6:28 am, students might say:

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3:47 pm until 4:00 pm is 33 minutes 4:00 pm until 6:00 am is 14 hours

6:00 am until 6:28 am is 28 minutes

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In order to calculate the total duration; students would add 33 minutes and 14 hours and 28 minutes. This gives a total time of 14 hours and 61 minutes. When the minutes in the final calculation come to more than 60, as in this example, this would need to be converted to hours and minutes and then added to the total number of hours. So in this example, it would be 1 hour and 1 minute (61 minutes) add 14 hours, giving an overall total of 15 hours and 1 minute.

• Estimation activities could offer a reason to work out durations of time (see page 51). Students estimate how long different events during the day may take, then, as they occur, they record the start time and later the finish time. They use these to work out the duration of each activity. Students could then order the events from the one taking the least amount of time to the one taking the most.

Activity

Estimate

Time started

Jogging around the oval

Time finished

Duration

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Rehearsal for a class play

Packing away the art material

• Students look at a television guide and make a list of their favourite programs. Students then record how long each program runs by looking at the start and finish times in the guide and calculating the differences. Order the list of favourite programs by their durations.

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• Students design a television timetable of their own for a ‘Favourite Saturday’. Students must incorporate all of the class members’ favourite shows into their timetable and allow suitable time allocations for each of the programs. For example, if their timetable starts at 7:00 am and their first show runs for 75 minutes, they need to program for the second show to start at 8:15.

• Collect timetables for buses, trains, aircraft, etc. Use these to pose problems related to the length of journeys. If the timetables are shown in 24-hour time, you may need to adjust them to show 12-hour time using ‘am’ and ‘pm’. Note: actual flying time may not be the same as the difference between take off and arrival times if there are different time zones between the arrival and destination points. It may be better to find timetables where this doesn’t occur, or create your own. (See also page 45.) Students may be interested in looking at events of interest where this is a factor, for example, if any of them are about to travel. In this case, students could look at the start and finish times and calculate the difference, then look at the published travel time and discuss why there is some discrepancy. For example, if flying from Adelaide to Melbourne, a flight leaves Adelaide at 7:20 am and arrives in Melbourne at 9:10 am. This is a duration of 1 hour and 50 minutes, but the airline timetable states that the duration of the flight is 1 hour and 20 minutes. This would lead to discussion about the time difference between Adelaide and Melbourne (or between South Australia and Victoria).

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• Car rally game: A game for 2 – 4 students, with a further student acting as the judge. The teacher nominates how many laps of the rally track they need to do. Students take turns to roll a six-sided dice and move on the racetrack that number of spaces. They pick up a time problem card from the pack and answer the question. All the cards are numbered. The judge checks the answer for the particular card number against the judge’s answer board. If their answer is correct they stay where they are; if it is incorrect they move back three places. The first player to complete the required number of laps of the rally track is the winner. Note: There are 18 time problem cards, with space for another six cards if the teacher or students wish to add more. (See pages 46–50.) The car rally game board (page 47) can be enlarged before photocopying onto card and laminating.

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 4)

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Sub-strand: Using units of measurement—UUM – 4

LINKS TO OTHER CURRICULUM AREAS English • Students write a travel story involving time (of day) differences or write a diary of imaginary travels.

Information and Communication Technology • Use websites from commercial travel companies to access timetables; e.g. from train and bus companies, airlines, ferries. In most of these sites, you can put in start and destination cities, along with any dates of your choice. You will get start and finish times, and, in many cases, how long the actual travel takes. If going across time zones, this may be useful.

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History and Geography

• Students could look at flight schedules to different countries and how long the flights take to get there. They could also investigate the different times zones, both within Australia and internationally, and how these affect flight times.

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The Arts

Languages

• Learn how to say the time in a different language.

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• If looking at other countries, students could illustrate a travel diary, looking for interesting features of the different physical environments.

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Sub-strand: Using units of measurement—UUM – 4

RESOURCE SHEET Adding time game You will need:

A set of time cards (See page 44) Time spinner (1, 2 or 3) Paper to record the scores

Players take it in turns to turn over a time card and spin the spinner. (As shown in the diagram, use either a pencil or a split pin and arrow to spin the spinner.) Add the required number of minutes to the time shown on the time card. The other player has their turn and does the same thing. The player with the later time wins that round and scores one point. The player with the highest score after 10 rounds (or until the teacher stops the game) is the winner.

Teac he 20 mi nu r te

Spinner 1

5 minutes

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 4)

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CONTENT DESCRIPTION: Use am and pm notation and solve simple time problems

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10 m i nu t e s

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Sub-strand: Using units of measurement—UUM – 4

RESOURCE SHEET Spinner 2

s 55 m e t inu nu i m tes 45

tes nu mi 25

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5m i nu t e s

35 minutes

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tes nu mi 14

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36 minutes

CONTENT DESCRIPTION: Use am and pm notation and solve simple time problems

Spinner 3

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Sub-strand: Using units of measurement—UUM – 4

RESOURCE SHEET Adding time game (cards)

3:30

7:45

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10:55

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11:11

3:19

5:39

Note: You may wish to enlarge these before photocopying onto card and laminating.

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 4)

R.I.C. Publications® www.ricpublications.com.au

CONTENT DESCRIPTION: Use am and pm notation and solve simple time problems

7:42

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Sub-strand: Using units of measurement—UUM – 4

RESOURCE SHEET Get there on time Below are the schedules for an airline that flies out of Perth to other cities and towns in Western Australia.

1. Work out how long each flight takes.

Destination

Departure

Arrival

Duration of flight

Perth to Kalgoorlie

11:55 am

1:00 pm

Perth to Karratha

10:50 am

12:50 pm

Perth to Newman

11:25 am

1:10 pm

9:55 am 12:20 pm r o e t s B r e oo p Perth to Exmouth 9:30 am 11:50 am u k S Perth to Geraldton 4:35 pm 5:40 pm

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Perth to Broome

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2. List the flights in order from the one that takes the least amount of time to the one that takes the most.

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CONTENT DESCRIPTION: Use am and pm notation and solve simple time problems

Perth to Paraburdoo

Shortest to longest flights: 1.

2.

3.

4.

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3. (a) Are there any that are the same?

5.

6.

Yes

No

(b) If so, which flights?

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 4)

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Sub-strand: Using units of measurement—UUM – 4

RESOURCE SHEET Car rally game A game for 2 – 4 players, plus a judge You will need: Set of time problem cards One counter per player

r o e t s Bo r e pboard ok judge’s answer u S

Game board

Rules:

1. Put all the players’ counters on ‘Start’.

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1 x six-sided dice

2. The teacher nominates how many laps students need to complete during the game.

3. Player 1 rolls the dice and moves forward that number of places. He or she then picks up a time problem card and answers the question. Each card is numbered. The judge finds the answer to the question card on their answer board. If the player has answered the question correctly, his or her counter stays where it is. If the answer is incorrect, they move the counter back 3 places.

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4. Players take turns to roll the dice and complete their move by answering the question, then either staying where they are if correct or moving back 3 places if incorrect. (Remind students to use ‘am’ or ‘pm’ in their answers.)

5. The winner is the first player to complete the nominated number of laps of the circuit.

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 4)

R.I.C. Publications® www.ricpublications.com.au

CONTENT DESCRIPTION: Use am and pm notation and solve simple time problems

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Sub-strand: Using units of measurement—UUM – 4

RESOURCE SHEET

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START

SH FINI

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Sub-strand: Using units of measurement—UUM – 4

RESOURCE SHEET Car rally game time problem cards – 1 2

Billy wants to catch the bus to town. It leaves at 2:35 pm. It takes him 15 minutes to walk to the bus stop. What time should he leave home?

Jan’s mum is picking her up after the movies.

The movie starts at 10:30 am and goes for 55 minutes. When should her mum get there to pick her up?

3 Ian’s flight leaves at 3:20 am and arrives at his destination at 6:10 am. How long is the flight?

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1

4

5

6

Mary’s favourite TV show starts at 3:45 pm and runs for 45 minutes. What time does it finish?

Chris ran the crosscountry race in a time of 1 hour and 24 minutes. He finished the race at 3:00 pm. What time did he start?

At 11:55 pm, Emma’s baby sister woke up and cried for 20 minutes. What time did the baby stop crying?

7

8

9

Joshua catches a bus to school at 7:42 am.

Yesterday, his bus was running 12 minutes late. What time did the bus arrive at his stop?

Isabella’s computer has a battery that lasts for 35 minutes. If she logs on at 6:50 pm, when will her battery run out?

The flight to Hobart was scheduled for 9:12 am, but was brought forward to 8:55 am. How much earlier is it now?

Ben completed a fun run in 1½ hours. He finished at 3:00 pm.

What time did he start?

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10 The train to the city was due to leave at 9:52 am. It was delayed for 15 minutes. What time did it leave?

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 4)

R.I.C. Publications® www.ricpublications.com.au

CONTENT DESCRIPTION: Use am and pm notation and solve simple time problems

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Natalie is going to her friend’s house at 4:15 pm. It takes her 20 minutes to walk there. What time should she leave home?

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Sub-strand: Using units of measurement—UUM – 4

RESOURCE SHEET Car rally game time problem cards – 2 14

The school bus broke down at 8:35 am. It took 45 minutes to get it going again. What time was it able to leave?

Karen missed her 3:16 am flight. The next flight left at 4:12 am.

How much later was that flight?

15 Bonnie couldn’t remember what time she put the oven on, but had set the timer for 1 hour and 20 minutes.

It rang at 8:40 pm. At what time must she have set it?

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16

17

What is the difference between these two times?

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13

18

1.10 am

The bedroom clock was running 27 minutes fast. When the clock showed the time as 6:55 am, what was the real time?

James had a dental appointment at 4:25 pm, but got there half an hour early. At what time did he arrive?

19

20

21

5.12 pm

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CONTENT DESCRIPTION: Use am and pm notation and solve simple time problems

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49

Sub-strand: Using units of measurement—UUM – 4

RESOURCE SHEET Judge’s answer board Solution

1

Billy wants to catch the bus to town. It leaves at 2:35 pm. It takes him 15 minutes to walk to the bus stop. What time should he leave home?

2:20 pm

2

Jan’s mum is picking her up after the movies. The movie starts at 10:30 am and goes for 55 minutes. When should her mum get there to pick her up?

11:25 am

3

Ian’s flight leaves at 3:20 am and arrives at his destination at 6:10 am.

How long is the flight?

2 hours and 50 minutes

4

Mary’s favourite TV show starts at 3:45 pm and runs for 45 minutes.

What time does it finish?

4:30 pm

5

Chris ran the cross-country race in a time of 1 hour and 24 minutes. He finished the race 1:36 pm at 3:00 pm. What time did he start?

6

At 11:55 pm, Emma’s baby sister woke up and cried for 20 minutes. What time did the baby stop crying?

7

Natalie is going to her friend’s house at 4:15 pm. It takes her 20 minutes to walk there.

What time should she leave home?

8

Joshua catches a bus to school at 7:42 am. Yesterday his bus was running 12 minutes late. What time did the bus arrive at his stop?

9

Isabella’s computer has a battery that lasts for 35 minutes. If she logs on at 6:50 pm, when will her battery run out?

10

The train to the city was due to leave at 9:52 am. It was delayed for 15 minutes.

What time did it leave?

11

The flight to Hobart was scheduled for 9:12 am, but was brought forward to 8:55 am.

How much earlier is it now?

12

Ben completed a fun run in 1½ hours. He finished at 3:00 pm.

What time did he start?

1:30 pm

13

The school bus broke down at 8:35 am. It took 45 minutes to get it going again.

What time was it able to leave?

9:20 am

14

Karen missed her 3:16 am flight. The next flight left at 4:12 am.

How much later was that flight?

56 minutes

15

Bonnie couldn’t remember what time she put the oven on, but had set the timer for 1 hour and 20 minutes. It rang at 8:40 pm. At what time must she have set it?

16

What is the difference between these two times?

17

The bedroom clock was running 27 minutes fast. When the clock showed the time as 6:55 am, what was the real time?

18

James had a dental appointment at 4:25 pm, but got there half an hour early.

At what time did he arrive?

r o e t s Bo r e p ok u S

12:15 am

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7:25 pm

10:07 am

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1:10 am

7:20 pm

7 hours and 58 minutes

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3:55 pm

20 21 22 23 24

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 4)

R.I.C. Publications® www.ricpublications.com.au

CONTENT DESCRIPTION: Use am and pm notation and solve simple time problems

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17 minutes

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Problem

Sub-strand: Using units of measurement—UUM – 4

RESOURCE SHEET A one-day time line Below is a time line for one day (your teacher will tell you what day of the week to use). Fill in the rest of the times for this day, write a description of the events throughout the day and work out how long each activity goes for. Remember to use ‘am’ and ‘pm’ on your time line.

Time

Activity

10:00 am

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9:00 am

Duration

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6:00 pm

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 4)

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51

Assessment 1

Sub-strand: Using units of measurement—UUM – 4

NAME:

DATE: Bob’s beaut bus business

Bob has set up a business for short and long distance buses. His buses are based in Canberra and operate to and from all state and territory capital cities other than Hobart. They run twice a day. Below is his timetable for Sundays.

From Canberra to …

Destination

Bus #

Adelaide

12

Brisbane

14

Brisbane

36

Darwin

21

Darwin

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7

Destination

Bus #

Adelaide 70 9:15 am r o e t s AdelaideBo120 11:55 am r 2:45 am e p ok11:25 am 11:25 am Brisbane 140 u Brisbane 360 8:35 am S4:20 pm 9:15 am

7:00 am

Darwin

210

06

10:30 pm

Darwin

060

Melbourne

28

1:00 pm

Melbourne

280

Melbourne

19

5:15 pm

Melbourne

190

Perth

35

7:30 am

Perth

350

Perth

Sydney Sydney

Departs at

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Adelaide

Departs at

Return to Canberra from …

7:30 am

7:00 pm

1:00 pm 7:45 pm 7:30 am

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C.Pu bl i cat i o ns6:15 am 42 Sydney 420 31o 2:50 pm Sydney 310 2:15 pm •f rr ev i ew pu r poses onl y• 6

2:30 pm

Perth

160

11:10 am

3. What is the difference in leaving time between the earliest and latest buses heading out of Canberra?

. tis the second trip from o 4. How much latere c .

Melbourne than the fic rst one? e her the first st r o 5. What is the time difference between s r u e p and second bus from Brisbane to Canberra?

6. The trip from Sydney to Canberra takes 1½ hours in the bus. What time will each of the two buses arrive in Canberra?

7. What is the time difference between the first and second bus to Perth?

8. How much later is the second trip from Darwin to Canberra than the first one?

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 4)

R.I.C. Publications® www.ricpublications.com.au

CONTENT DESCRIPTION: Use am and pm notation and solve simple time problems

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2. Where is the latest bus leaving from Canberra going?

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1. What is the destination of the earliest bus to leave Canberra on Sundays?

Assessment 2

Sub-strand: Using units of measurement—UUM – 4

NAME:

DATE: Jake and Phoebe’s journey

Jake and Phoebe recently had a holiday in New Zealand.

Can you help them fill in some times for their travel diary?

1. Jake and Phoebe needed to catch a train from Newcastle to Sydney to board their plane. The train left Newcastle on Monday at 3:23 pm and arrived at Sydney Central Station at 6:10 pm. How long was their journey?

Teac he r trains?

3. The trip to the airport only takes 13 minutes. What time did they arrive there?

4. When Jake and Phoebe arrived in Christchurch on Tuesday, they hired a car and drove for 3 hours and 30 minutes, then decided to stop for lunch. They picked up the car at 9:30 am. What time did they stop for lunch?

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r o e t s Bo r e p ok u 2. The train from Sydney Central to the airport left at S 6:55 pm. How long did they have to wait between

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6. After two days, Jake and Phoebe caught a ferry to get to the North Island. It left Picton at 2:40 pm and arrived in Wellington at 6:00 pm. How long was the ferry ride?

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5. After a one-hour lunch stop, Jake and Phoebe decide to do some more sightseeing. They drove around the Christchurch area and then stopped to book a hotel at 5:20 pm. How long did they drive for after their lunch?

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CONTENT DESCRIPTION: Use am and pm notation and solve simple time problems

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o c . che e r o t r s r u pe 7. The next day, they caught as bus from Wellington to Rotorua. The bus left Wellington at 7:50 pm and arrived in Rotorua at 3:30 am. How long was the bus trip?

8. After three days in Rotorua, Jake and Phoebe went to Auckland. They caught a bus that arrived in Auckland at 6:00 pm. The journey took 4 hours and 15 minutes.

What time did they leave Rotorua?

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 4)

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Checklist

Sub-strand: Using units of measurement—UUM – 4

Can calculate start or finish times when given a time duration

Can calculate durations of time

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STUDENT NAME

Understands the difference between am and pm

Use am and pm notation and solve simple time problems (ACMMG086)

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 4)

R.I.C. Publications® www.ricpublications.com.au

Answers

Sub-strand: Using units of measurement

UUM – 1 Page 10

UUM – 2 Resource sheet – How long are they?

Line 1: 48 cm Line 2: 17.5 cm Line 3: 16 cm Line 4: 6.5 cm Line 5: 19.5 cm Line 6: 21 cm In order from longest to shortest: Line 1, Line 6, Line 5, Line 2, Line 3, Line 4

Page 24 1. (a) (b) (c) (d) (e) 2. (a) (c)

Resource sheet – What is the area? – 1 7 cm2 10 cm2 13 cm2 23 cm2 24 cm2 A = 16 cm2 A = 30 cm2

Resource sheet – Pattern block perimeter graph (Approximate answers)

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Assessment 1 – Areas

1.

12 cm2

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12 cm2

12 cm2

12 cm2

Resource sheet – How much do they weigh?

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12 cm2

2. Footstep A: 17–18 cm2 Footstep B: 27–28 cm2 Footstep B has the greater area.

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Resource sheet – How much do they hold?

1. Teacher check 2. Teacher check 3. The bowl, spoon, measuring jug and bucket should be shaded.

Page 15

Resource sheet – Rolling rectangles

The volume of the two cylinders will be different, even though the area of the paper is the same.

1. Teacher check 2. Teacher check 3. In order from lightest to heaviest: paperclip, mouse, jug, books, bike, elephant Page 13

1. The duck: 15 cm2 2. The house: 17 cm2 3. The chip packet: about 19 cm2

Page 26

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Resource sheet – What is the area? – 2

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18 cm 17 cm 16 cm 15 cm 14 cm 13 cm 12 cm 11 cm 10 cm 9 cm 8 cm 7 cm 6 cm 5 cm 4 cm 3 cm 2 cm 1 cm

A = 12 cm2 A = 9 cm2

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Page 11

(b) (d)

Assessment 1 – Measurement tasks

Page 28

Assessment 2 – Finding volume

1. 6 cm3 2. 5 cm3 3 3. 9 cm 4. 14 cm3 5. 24 cm3 6. 16 cm3 7. 15 cm3 8. 24 cm3 In order from least to most volume, the models are: 2. (5 cm3), 1. (6 cm3), 3. (9 cm3), 4. (14 cm3), 7. (15 cm3), 6. (16 cm3), 5. and 8. (both 24 cm3)

Teacher check Page 16

Assessment 2 – Reading scales

1. 5 kg, 80 kg, 1 kg, 2.5 kg 2. 3 L, 30 mL, 70 mL, 150 mL 3. 20 °C, 70 °C, 45 °C, 100 °C

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Answers

Sub-strand: Using units of measurement

UUM – 3 Page 33

Resource sheet – Lengths of time

second, minute, hour, day, week, fortnight, month, year, leap year, decade, century, millennium Page 34

Resource sheet – Time problems

Answers will vary

112 days 16 weeks 4 months

Yes Yes No

2 hours, 3 minutes and 38 seconds just over 123½ minutes 7418 seconds

226 years

54 000 millennia 540 000 centuries 5 400 000 decades

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108 months 468 weeks

Page 35

Resource sheet – Time puzzles

1. Teacher check 2. (a) 600 000 minutes (b) 416 days (approx.) (c) 59 weeks (approx.)

3. In order from shortest to longest: 510 seconds, 21 hours, 12 000 minutes, 14 days 4. 3650 days 5. 7 years 6. 39 000 minutes

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44 724½ days (if using 365¼ days in a year) which is 1 073 388 hours OR 44 694 days (if using 365 days in a year) which is 1 072 656 hours

Page 36

Assessment 1 – Time conversions quiz

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

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21 days 336 hours seconds 135 minutes 14 decades 9000 minutes (150 hours); 4½ days (108 hours) 29 700 seconds More in 2nd half; 184 days from July – December; January – June has 181 days or 182 in a leap year. leap year In order from shortest to longest: 36 hours (1½ days) 48 hours (2 days) 259 200 seconds (3 days) 144 hours (6 days) 13 days fortnight (14 days)

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 4)

R.I.C. Publications® www.ricpublications.com.au

Answers

Sub-strand: Using units of measurement

UUM – 4 Resource sheet – Get there on time

Destination

Departure

Perth to Broome

9:55 am

12:20 pm 2 hours and 25 minutes

Perth to Exmouth

9:30 am

11:50 am 2 hours and 20 minutes

Perth to Geraldton

4:35 pm

5:40 pm 1 hour and 5 minutes

Perth to Kalgoorlie

11:55 am

1:00 pm 1 hour and 5 minutes

Perth to Karratha

10:50 am

Perth to Newman

11:25 am

1:10 pm 1 hour and 45 minutes

2:30 pm

4:15 pm 1 hour and 45 minutes

8:05 am

10:10 am 2 hours and 5 minutes

Perth to Paraburdoo Perth to Port Hedland

Arrival

Duration of flight

12:50 pm 2 hours

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Shortest to longest flights: 1. Geraldton These two are the same duration 2. Kalgoorlie 3. Newman These two are the same duration 4. Paraburdoo 5. Karratha 6. Port Hedland 7. Exmouth 8. Broome Page 52

Page 53 1.

2.

3.

4.

5.

6.

7.

8.

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2:45 am to Adelaide Darwin at 10.30 pm 19 hours and 45 minutes 6 hours and 45 minutes 2 hours and 50 minutes 7:45 am and 3:45 pm 7 hours 11½ hours

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2.

3.

4.

5.

6.

7.

8.

Assessment 1 – Bob’s beaut bus business

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Assessment 2 – Jake and Phoebe’s journey

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2 hours and 47 minutes 45 minutes 7:08 pm 1:00 pm 3 hours and 20 minutes 3 hours and 20 minutes 7 hours and 40 minutes 1:45 pm

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Sub-strand: Shape—Shape – 1

Compare the area of regular and irregular shapes by informal means (ACMMG087)

RELATED TERMS

TEACHER INFORMATION

Comparison

What this means

• Relates to making judgements about only two shapes. The vocabulary of comparison for area is ‘bigger’ or ‘smaller’.

• This unit is similar to UUM – 2: Compare objects using familiar metric units of area and volume.

Area

• Either counting centimetre squares or overlaying one shape on the other and counting the difference in the number of squares would be the most appropriate methods of comparing the areas of two shapes.

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Regular shapes

• Any shapes with all sides congruent (equal length) and all angles congruent (equal number of degrees). For example, the shape below is a regular pentagon, as all five sides are the same length and all the angles are the same size (120°).

Teaching points

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• The amount of surface on an object.

• ‘Informal means’ implies that formulas for calculating area of regular shapes are not required (nor are they suggested for UUM – 2).

• Estimation should be encouraged in all measurement activities.

Area

• Students need to be aware that squares are the most commonly used units for measuring area. This knowledge comes after experiences of filling areas using other shapes such as circles and discussion of the need for no gaps or overlaps. Although there are many other shapes that tessellate (fit together perfectly), the square is the easiest to use as a measure of area.

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• Any shapes where not all the sides are congruent and not all the angles are congruent, as in the pentagon below.

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Irregular shapes

• Comparisons of area may be made by tracing each of the shapes onto 1 cm grid paper and counting how many squares (1 cm2) are covered in each, and then considering the difference. There are three methods of dealing with the pieces that are not full squares. The first is to count any squares that are more than half covered as one square and not count any that have less than half of the square covered. The second method is to add pieces that are parts of squares together to equal whole squares. (Note: Using different-coloured pencils to match same parts of squares is a useful method to keep track of the number of squares to count.) The third method is to count all the squares that have any part covered, and divide this amount by two. The resulting calculations of areas using any of these methods would be very similar.

• Formulas for calculating the area of regular shapes such as squares and rectangles should not be introduced at this year level.

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• Experiences in area should be designed so that students recognise area is an attribute that is independent of position and shape. So, for example, if students tape pages of newspaper into a square that is 1 metre by 1 metre, it has same area (1 m2) as if that square is cut in half diagonally and stuck back together as a large triangle, or any other re-arrangement of cutting and sticking, as long as there are no overlaps or pieces left out. This understanding of conservation of area is important and students may need many experiences, with clear explanations, to consolidate it.

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 4)

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Sub-strand: Shape—Shape – 1

Compare the area of regular and irregular shapes by informal means (ACMMG087)

TEACHER INFORMATION (CONTINUED) Student vocabulary area

What to look for

regular shapes

• Students understanding of conservation of area; that the area doesn’t change if we cut and reform a shape, as long as there are no overlaps.

irregular shapes

• Students unable to find a way to compare the areas of two shapes.

diagonal

• Students using systematic ways to calculate (count) the number of squares that form the area of a shape.

square triangle

circle

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rectangle

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Sub-strand: Shape—Shape – 1

HANDS-ON ACTIVITIES • To remind students of the need for a standard unit of area (cm2 or m2), they may need to revisit activities where they cover the surface of shapes using non-standard units. This may include activities such as looking at how many of each student’s handprints are needed to cover the top of his or her desk. Discussion could arise as to why there is a variety of answers to this question (different hand sizes, gaps and/or overlaps). Other units to measure area could be tried, such as counters, triangles or footprints and lead to the realisation that the square is the best unit as squares tessellate (fit together with no gaps or overlaps) and can be standardised (square centimetres, square metres etc.).

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• Students use squares of paper and find different ways to cut them in half with one straight cut and reform them into other shapes. Discussion should centre on the area of the shapes being the same, as long as all the pieces are used and there are no overlaps.

• Students could use other regular shapes and investigate cutting them in half with one straight cut and reforming them into other shapes.

• Students draw regular and/or irregular shapes onto paper, cut them out and trace around the edges onto 1 cm2 grid paper. They could also draw them directly onto the grid paper. The gives them to opportunity to compare the areas of different shapes by counting, after estimating which one would have the larger area (see page 63).

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This shape has an area of about 16 cm2. It is the smaller shape. I thought it would be the larger one.

This shape has an area of about 18 cm2.

It is the bigger shape.

• The teacher could print 1 cm2 grid paper onto overhead transparencies (see page 62), and students could then use these to overlay any shapes and work out the areas by counting the squares. It may help to put the transparencies into a plastic sleeve and also place the shape into the sleeve. This would hold the shape steady so that students can count the squares more easily.

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Sub-strand: Shape—Shape – 1

LINKS TO OTHER CURRICULUM AREAS English • Read Marilyn Burns’ book Spaghetti and meatballs for all! A mathematical story. This book would be a good introduction to discussions about area and perimeter.

Information and Communication Technology • There is an area explorer that can be found at <http://www.shodor.org/interactivate/activities/AreaExplorer/> This produces shapes on a grid and students are required to count the squares and key in their areas. The perimeter of the shape is given.

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• Work with tangrams offers the opportunity to see that the area of a shape does not change when the pieces are rearranged, as long as there are no overlaps and no pieces missing. Type “tangrams” into a search engine (such as Google™) to find some wonderful images of tangrams.

The Arts

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• Students could look at ways to make shape puzzles for other students to solve. They start with a basic regular or irregular polygon and look at how one or two straight cuts could be made, so that the pieces can be re-formed into a different shape. Discussion would arise about any changes to the area of the shapes when they are re-formed (the area would be the same if there are no gaps, omissions or overlaps).

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Sub-strand: Shape—Shape – 1

RESOURCE SHEET

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1 cm2 grid paper

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CONTENT DESCRIPTION: Compare the area of regular and irregular shapes by informal means

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Sub-strand: Shape—Shape – 1

RESOURCE SHEET Estimating areas

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Estimate the area of each shape, then check your answers by working out the area.

Write your estimates below.

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Assessment 1

Sub-strand: Shape—Shape – 1

NAME:

DATE: Problem areas

1. Estimate first, then work out which of the two shapes below has the greater area. (a) Which shape do you think has the greater area?

B

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CONTENT DESCRIPTION: Compare the area of regular and irregular shapes by informal means

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Checklist

Sub-strand: Shape—Shape – 1

Finds shortcuts to calculating areas of shapes

Finds areas of irregular shapes by counting 1 cm2 squares

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STUDENT NAME

Finds areas of regular shapes by counting 1 cm2 squares

Compare the area of regular and irregular shapes by informal means (ACMMG087)

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Sub-strand: Shape—Shape – 2

Compare and describe two dimensional shapes that result from combining and splitting common shapes, with and without the use of digital technologies (ACMMG088)

TEACHER INFORMATION

RELATED TERMS

What this means

Comparison

• Relates to making judgements about only two shapes. The vocabulary of comparison for area is ‘bigger’ or ‘smaller’.

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• Whenever the curriculum mentions ‘shapes’ it is referring to two dimensions; when it mentions ‘objects’ it is referring to three dimensions • Note: All two-dimensional shapes we use with students have a third dimension of depth, but we generally accept that paper shapes and manipulatives such as pattern blocks and Attribute Blocks can be used to represent two-dimensional shapes.

• Looking at properties of shapes is a useful way to classify them.

Students can look for similarities and differences when investigating common shapes and the relationships between them.

• The halving shapes activities in the previous unit of work (Shape – 1) is also appropriate for this unit of work.

Teaching points

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Two-dimensional shapes; Three-dimensional objects:

• Common shapes include triangles (equilateral, isosceles and scalene; right angled and acute angled), quadrilaterals (squares, rectangles, trapeziums, rhombuses, kites, parallelograms) circles, pentagons, hexagons and octagons. For definitions of these shapes, see pages 71–73. A useful reference is Maths terms and tables by Bana, Marshall and Swan (R.I.C. Publications – RIC-1069).

• Students need to know the names of the common shapes and be able to describe them.

• Students need to aware that some shapes can be classified in different ways—for example, a square also fits into the categories of rectangle, parallelogram and rhombus—but a rectangle, parallelogram and rhombus may not necessarily be a square. To help clarify this, we may refer to a square as a ‘special rectangle’ etc. and discuss why this is the case.

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• A rhombus is a shape that has four equal sides and two pairs of opposite equal angles. In geometry, there is no shape called a ‘diamond’. The shapes below are rhombuses, although the second shape is a special rhombus; i.e. a square.

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• Students need to see irregular two-dimensional shapes as well as regular ones. They should also appear in different orientations, as in the examples of hexagons below. National testing questions often use irregular shapes and unusual orientations.

• National tests usually contain a question that requires students to identify lines of symmetry. Students will need to have had many experiences folding and cutting shapes and exploring the resulting shapes.

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Sub-strand: Shape—Shape – 2

Compare and describe two dimensional shapes that result from combining and splitting common shapes, with and without the use of digital technologies(ACMMG088)

TEACHER INFORMATION (CONTINUED) Student vocabulary polygon

What to look for • Students unable to recognise, name or describe common shapes.

equilateral triangle isosceles triangle

• Students not recognising shapes when they appear in different orientations.

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scalene triangle

right angled triangle

acute angled triangle

• Students unable to classify shapes in different ways (i.e. that a square also fits the criteria of being a rectangle, parallelogram and rhombus).

• Students incorrectly using the term ‘diamond’ for a rhombus.

square

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quadrilateral

rectangle

trapezium rhombus kite

parallelogram pentagon

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circle

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Sub-strand: Shape—Shape – 2

HANDS-ON ACTIVITIES • Have definitions charts available to help students recognise, name and know the features of common shapes (see pages 71–73). These can be photocopied for individual use or for students to take home, or enlarged as wall charts.

Groups of students could also make their own definition charts. A useful reference is Maths terms and tables by Bana, Marshall and Swan (R.I.C. Publications – RIC-1069).

• Discuss the properties of shapes, including the diagonals. For example, a parallelogram has 4 sides, 2 pairs of opposite equal parallel sides, 2 pairs of opposite equal (congruent) angles, 2 diagonals that bisect each other (cut each other in half) and the triangles formed by each diagonal are congruent (exactly the same size and shape as each other). (See page 74.)

• Using any two pattern block pieces, students investigate creating different shapes. The two pieces may be the same shape or two different shapes. They must join along a full side. Ask: How many different shapes can you make? Can you name all the shapes you have made? How many are regular polygons? How many are irregular polygons?

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• Look at ways to demonstrate and record classifications. For example, classify the six different pattern block shapes with a Venn Diagram using overlapping sorting hoops or circles drawn on paper. (Sorting hoops may be bought commercially or made quite cheaply using thin reticulation pipe and a joiner.) The overlapping section of the Venn Diagram must contain shapes that fit into both categories; in this case they are quadrilaterals that all have equal sides.

Equal sides

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Note: This information may also be shown using a Carroll Diagram.

Quadrilateral

Not a quadrilateral

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• Carroll Diagrams usually have one attribute and a negative of that attribute for each of the categories. There may not always be an item in every box such as the one above where there are no shapes that are not a quadrilateral and have no equal sides.

• Trace around a variety of polygons, both regular and irregular. Divide each into component triangles by ruling in all the diagonals from one point. Investigate the number of triangles in each shape. Students try to find the rule (there are always two fewer triangles than the number of sides in the shape).

The square has four sides and two triangles. The pentagon has five sides and three triangles. The octagon has eight sides and six triangles.

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Sub-strand: Shape—Shape – 2

HANDS-ON ACTIVITIES (CONTINUED) • Cut a paper rectangle across the two diagonals. Investigate some of the shapes that can be made using the four pieces.

This links to the unit on area (UUM – 2) and the previous unit on shape (Shape – 1) in that the area of the original shape is the same as the area of the re-formed shape, as long as there are no gaps, omissions or overlaps. (See page 75.)

• Investigate the different shapes that can be formed by cutting regular and irregular polygons along one or more diagonal.

• Use paper strips, rolled up newspaper of different lengths or straws cut to different lengths to investigate triangles. Ask students: Can we make a triangle using three equal length pieces? What sort of triangle would it be? Can we make a triangle if the pieces are 12 cm, 6 cm and 5 cm long? Why/Why not? If I have one piece that is 15 cm long and another that is 7 cm long, what size must a third piece be in order to make an isosceles triangle? Is there more than one answer to the previous question?

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• Outdoors, use ropes about 6–8 metres long, tied into a loop. In groups of 4 to 6, students investigate polygons according to given directions. Make an equilateral triangle; a right-angled triangle; a scalene triangle; a square; a kite; a shape with two opposite parallel and equal sides; a five-sided shape etc. Discuss the results.

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• Use of technology would make more sense to students if they have plenty of practice actually cutting and re-forming paper shapes.

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Sub-strand: Shape—Shape – 2

LINKS TO OTHER CURRICULUM AREAS English • Read The greedy triangle by Marilyn Burns. This book looks at the attributes of different shapes such as pentagons and hexagons. It is a nice shape story that describes some real life uses of a variety of two-dimensional shapes.

Information and Communication Technology • Illuminations have a wonderful website that enables students to draw a polygon of their choice, then draw in some or all of the diagonals and cut the shape along those diagonals. Each of the parts of the shape can then be moved around the board and rejoined into different shapes. This site can be found at <http://illuminations.nctm.org/ActivityDetail. aspx?id=72>

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• A website that offers a quiz on two-dimensional shapes can be found at <http://www.mathsisfun.com/shape.html> • A website where you sort triangles into Venn Diagrams can be found at <http://www.crickweb.co.uk/ks2numeracyshape-and-weight.html#triangles>

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• A website that shows various shapes and their lines of symmetry can be found at <http://www.innovationslearning. co.uk/subjects/maths/information/shape_facts/shape_facts.htm> (Unfortunately, they use the term ‘trapezoid’ rather than ‘trapezium’.)

• A sorting shapes activity can be found at <http://www.bbc.co.uk/bitesize/ks2/maths/shape_space/shapes/play/popup. shtml> • A two-dimensional shape quiz can be found at <http://teams.lacoe.edu/documentation/classrooms/amy/ geometry/6-8/activities/quad_quest/quad_quest.html> • A shape matching concentration game can be found at <http://www.math-play.com/shapes-game.html>

• A dynamic website that allows students to manipulate any of the four points on a quadrilateral to make different shapes can be found at <http://www.amblesideprimary.com/ambleweb/sketchpad/quadrilateral.htm>

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• Students cut and re-form shapes, rearranging them into designs and pictures that they can then decorate.

• Students make a ‘shape mobile’ using a variety of two-dimensional shapes. Shapes are to be correctly labelled as part of this activity.

• Investigate the names of common shapes in another language.

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Sub-strand: Shape—Shape – 2

RESOURCE SHEET Shapes chart Definition

Diagram

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Quadrilateral: any four-sided shape

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Triangle: any three-sided polygon

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Hexagon: a six-sided polygon

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Pentagon: a five-sided polygon

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CONTENT DESCRIPTION: Compare and describe two dimensional shapes that result from combining and splitting common shapes, with and without the use of digital technologies

Polygon: any two-dimensional shape having three (3) or more straight sides

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Sub-strand: Shape—Shape – 2

RESOURCE SHEET Triangles chart Definition

Diagram

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Isosceles triangle: a triangle with two sides equal and two equal angles

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Equilateral triangle: a triangle with all sides equal and all angles equal

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Right-angled triangle: a triangle with one angle a right angle

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Scalene triangle: a triangle with no sides or angles equal

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CONTENT DESCRIPTION: Compare and describe two dimensional shapes that result from combining and splitting common shapes, with and without the use of digital technologies

Triangle: any polygon that has three sides

Sub-strand: Shape—Shape – 2

RESOURCE SHEET Quadrilaterals chart Definition

Diagram

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Rectangle: a four-sided shape with all angles right angles

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Square: a four-sided shape that has all sides the same length and all angles 90°

Rhombus: a four-sided shape with all four sides the same length

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Trapezium: a four-sided shape with only one pair of parallel sides

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CONTENT DESCRIPTION: Compare and describe two dimensional shapes that result from combining and splitting common shapes, with and without the use of digital technologies

Quadrilateral: any polygon that has four sides

o c . c e Kite: a four-sided symmetrical hershape st r o su with two shorter equal sides and two r e p longer equal sides Parallelogram: a four-sided shape with both pairs of opposite sides parallel

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Sub-strand: Shape—Shape – 2

RESOURCE SHEET Draw my shape

(a) I have four sides, with none of them equal.

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(b) I have three sides and one of my angles is 90°.

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(h) I have four sides, but only one pair of parallel sides.

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I am any eight-sided shape.

(j)

I am a triangle with two equal sides and two equal angles.

2. Now write some of your own shape puzzles for a partner to solve.

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CONTENT DESCRIPTION: Compare and describe two dimensional shapes that result from combining and splitting common shapes, with and without the use of digital technologies

1. In each box below, draw the correct shapes to match each of the descriptions, and write in their shape names.

Sub-strand: Shape—Shape – 2

RESOURCE SHEET Make my shapes

1. Use all four triangles to make:

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• one parallelogram

• one large equilateral triangle • one large isosceles triangle.

2. Record your different shapes in the box.

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3. (a) Are there any other shapes you can find using all four triangles? Yes

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On paper, draw a rectangle that is approximately 14 cm by 8 cm, or cut out the rectangle at the bottom of the page. Use a ruler to draw the two diagonals, then cut along all the lines. You will end up with four triangles.

No

(b) If Yes, record your shape(s) on the back of this sheet.

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Assessment 1

Sub-strand: Shape—Shape – 2

NAME:

DATE: What I know about shapes

Fill in the boxes in the table below. (Note: Two boxes will be left blank.)

Drawing

Square

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Diagonals

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Equilateral triangle

Description

Kite

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Pentagon

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Parallelogram

Hexagon

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CONTENT DESCRIPTION: Compare and describe two dimensional shapes that result from combining and splitting common shapes, with and without the use of digital technologies

Shape

Checklist

Sub-strand: Shape—Shape – 2

Uses ICT to draw common 2-D shapes

Combines and splits common 2-D shapes

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STUDENT NAME

Compares and describes common 2-D shapes

Compare and describe two dimensional shapes that result from combining and splitting common shapes, with and without the use of digital technologies (ACMMG088)

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Answers

Sub-strand: Shape

Shape 1 Page 63

Resource sheet – Estimating areas A = 34.5 cm2 B = approx. 40 cm2 C = 28 cm2 D = 43.5 cm2

Teacher check estimations. Actual areas are:

Page 64

Assessment 1 – Problem areas

1. (a) Teacher check

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(c) Shape B is about 38 cm2 (accept 36 to 40)

(b) Shape A is about 44 cm

Shape 2 Page 74 1.

Resource sheet – Draw my shape

(a) I have four sides, with none of them equal.

(b) I have three sides and one of my angles is 90°.

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(the picture could be of any 4-sided shape) I am a quadrilateral.

(d) I am a shape with five equal sides.

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I am a regular pentagon.

I am a square.

(e) My opposite sides are equal and parallel; not all angles are equal.

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I am a parallelogram.

(g) I have three equal sides and three equal angles.

I am a rhombus (not a diamond).

(h) I have four sides but only one pair of parallel sides.

I am an equilateral triangle. (i)

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I am a right-angled triangle.

I am any eight-sided shape.

I am a trapezium. (j)

I am a triangle with two equal sides and two equal angles.

(or any other 8-sided shape) I am an octagon.

I am an isosceles triangle.

2. Teacher check

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Answers

Sub-strand: Shape

Page 75

Resource sheet – Make my shapes

1. Two rhombuses of the same size and area

Two right-angled triangles of the same size and area

One large isosceles triangle

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One kite

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One large equilateral triangle

2.–3.

One parallelogram

Teacher check

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Square

Assessment 1 – What I know about shapes

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Description

Diagonals

Has 4 equal sides and 4 equal angles Has 2 diagonals that bisect each (90°) other at right angles

Kite

Has 2 short sides and 2 long sides and 2 equal angles

Has 2 diagonals that cross each other at right angles

Has 2 pairs of equal opposite sides and 4 equal angles (90°)

Has 2 diagonals that bisect each other

Rectangle

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Parallelogram

Hexagon

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Equilateral triangle

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Has 5 diagonals

Has 2 pairs of opposite equal sides and 2 pairs of opposite equal angles

Has 2 diagonals that bisect each other, forming 2 congruent triangles

Has 6 sides and 6 angles

Has 9 diagonals

Note: The pentagon and hexagon shown above are regular. As long as the drawings have five sides and six sides, they will still be correct.

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Sub-strand: Location and transformation— L&T – 1

Use simple scales, legends and directions to interpret information contained in basic maps (ACMMG090)

RELATED TERMS

TEACHER INFORMATION What this means

• In the context of location, a scale is the ratio of measurements of a diagram to corresponding measurements of an enlarged or reduced version; e.g. if the scale on a map is 1:10 000, then 1 cm on a map represents 10 000 centimetres (or 100 metres) at the actual location.

• Being able to understand simple scales so that an instruction such as 1 cm = 3 km makes sense and students can work out that a 4 centimetre length on a map means the distance is 12 kilometres.

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Legend (Key)

• Being able to interpret legends and understand that certain symbols on a street map indicates a are used to indicate particular items; e.g. public phone.

• Being able to use simple coordinates for determining the position of an item on a map.

• Students being able to give and receive directions to determine location.

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Scale

• A guide to symbols used in a map.

Teaching points

Coordinates (Cartesian coordinates)

• There is a link between working out distances on a map by using a scale and multiplication (ratios). The scale factors should be such that the multiplication is within the students’ experience. Where they are beyond their experience, the use of calculators is encouraged.

• A pair of numbers or symbols that represent a position on a grid.

Understanding of this concept of naming coordinates is essential in later years when using a grid with negative coordinates and two or four quadrants, or later still, when graphing functions in algebra and trigonometry.

• Teacher models the use of appropriate language of location; e.g. north, south, east, west, north-west, left, right, clockwise, anticlockwise, between.

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1 Note: In the Year 5 national tests, there is usually a question that involves 1 2 3 4 5 coordinates. One of the distracters is always the reverse order to the correct answer. So in the example above, if the correct answer was (2, 4), (4, 2) would appear as one of the choices.

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• When using coordinates for grid references, name the across horizontal (x-axis) first followed by the up/down vertical (y-axis). For example, in the diagram to the right, the is at (2,4), not (4,2). The is at (4,2).

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• Before using maps and coordinates, students need to understand: – the need for a horizontal and vertical axis – the way the two axes are labelled

– when reading points on a map, the horizontal axis is always read before the vertical axis – any specific location on a map can be found using both the horizontal and vertical coordinates on the grid.

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 4)

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Sub-strand: Location and transformation— L&T – 1

Use simple scales, legends and directions to interpret information contained in basic maps (ACMMG090)

TEACHER INFORMATION (CONTINUED) Student vocabulary

• Students who are not able to give and/or follow simple directions when using a simple map.

scale legend key coordinate across axis up axis

vertical

• Students who confuse the terms left and right, clockwise and anticlockwise and the four compass points.

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one axis; two axes

• Students who are unable to interpret a simple scale or work out corresponding distances.

• Students who are unable to use a legend to locate particular features on a map.

• Students who, when using coordinates for map references, use the up-down (horizontal; y-axis) first followed by the across (vertical; x-axis) instead of the other way around.

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horizontal

What to look for

compass north

south east

west

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north-west south-east

south-west clockwise

anticlockwise

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left right

centimetres

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metres

kilometres

o c . che e r o t r s super Proficiency strand(s): Understanding Fluency Problem solving Reasoning

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 4)

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Sub-strand: Location and transformation— L&T – 1

HANDS-ON ACTIVITIES • To help students learn the system of coordinates (horizontal axis being named before the vertical one), games and activities can be used. These could include using grids for codes and games. ‘Dingo’s Lair’ is one such game; see pages 85 and 86. Also see the ‘Secret agent code’ activity on page 87 and the ‘Spy codes’ assessment on page 90. Students could also be encouraged to write their own grid codes. Note: All 26 letters of the alphabet do not need to be used in a code. They may contain only as many letters as are needed for the message, with maybe a few extras as ‘red herrings’.

The example below could be used to encode the names of several students: 5

R

N

4

A

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O

2

P

Y

S

1

E

A

J

B

H

C

D

Penny: (C,3) (A,1) (E,5) (E,5) (E,3)

Sarah: (B,2) (D,4) (B,5) (D,4) (E,1)

E

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Jason: (C,1) (D,4) (B,2) (A,3) (E,5)

• Write coordinates for positions on simple drawings. For example, in the drawing below, describe the positions of the clown’s eyes, nose etc. Students could also be given the outline of a clown face (or any other item) and then asked to put certain features at particular coordinates.

5

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2

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• Students consolidate their understanding of coordinates using the ‘Mapping the neighbourhood’ activity on page 88 and the ‘Wizard’s Land map’ activity on pages 89 and 90.

• Compare plans or maps of old and new suburbs and discuss similarities and differences. Look at the layout of the streets, parks, shops etc. Discuss why they might be different now.

• If going on a class excursion, maps of areas can often be downloaded in advance and then used to initiate discussion on the symbols, legends and scale used in the map. For example, if going to a zoo, the different symbols used to show various animal enclosures could be discussed. Students could look at the scale of the map for the distances between displays and, using metre sticks or trundle wheels and lengths of rope, lay out on the school oval how long particular pathways are.

• Students could be asked to draw plans of regions such as the classroom using a simple scale; the teacher might need to give the students the scale factor to be used, particularly in the students’ early attempts. For example, the students might be asked to make the scale 1 centimetre = 50 centimetres. Discussion could then revolve around the dimension of the room itself and how big desks, chairs, boards etc. would need to be on their maps. If looking at a larger area, students could also be asked to provide a legend; for example, a map of the school grounds may have a legend that shows the path to the school, the oval boundaries, the drink fountain etc.

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 4)

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Sub-strand: Location and transformation— L&T – 1

HANDS-ON ACTIVITIES (CONTINUED) • Show a road map of the local area around the school so students can describe the position of local features. Ask questions such as: How far is it from the school to the shops? What is used on the map to show a shopping centre? How big is the park nearest to the shops? What is the shortest way to get from the library to the police station? How many sets of traffic lights would you go through if you were cycling from the school to the nearest letterbox? What is the biggest building on the map?

• Obtain a plan of a large shopping centre. Discuss how to get from one section to another and what distances are involved.

Look at the symbols used to designate different types of shops. For example, students plan the shortest route to: – do the grocery shopping – buy some jewellery – have a meal – get a haircut – see a movie

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– go to the bank

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– go to the movies after going to the bank and having lunch.

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 4)

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Sub-strand: Location and transformation— L&T – 1

LINKS TO OTHER CURRICULUM AREAS English • Read The once upon a time map book by B Hennessy and P Joyce. This book takes a trip to six different well-known story lands with maps, coordinates, routes, hidden objects and points of interest. Each map has a grid overlay so that coordinates can be used to locate certain features. They each have a key (legend) indicating features such as rock paths, giant’s stairs, camel road etc.

Information and Communication Technology • A map of the Perth Zoo can be found at <http://www.perthzoo.wa.gov.au/visit/zoo-map/>

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• Various maps of Kings Park in Perth can be found at <http://www.bgpa.wa.gov.au/kings-park/maps> • An interactive map of Taronga Park Zoo can be found at <http://www.taronga.org.au/taronga-zoo/map-visit-planner> • An interactive map of the Melbourne Zoo can be found at <http://www.zoo.org.au/Melbourne/Zoo_Map>

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• A map of the Alma Park Zoo in Brisbane can be found at <http://www.almaparkzoo.com.au/images/stories/pdfs/alma_ park_zoo_guide_map.pdf> • The Adelaide Zoo map can be found at <http://www.zoossa.com.au/adelaide-zoo/zoo-information/zoo-map>

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History and Geography

• Integrate use of maps in studies of other countries. Look at key features and what they tell you about the environment.

• On large sheet of plastic or paper, students design a layout for a model to be made of the school or some other structure; paying attention to the scale of the model. This could link to studies in history where they look at the journeys of early explorers and map their travels by constructing a large map. The teacher could lead discussion about an appropriate scale for the map.

The Arts

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• Students could draw their own maps, using intuitive or more formal ideas of scale. Ideally, features that are similar in size in real life should appear on the maps that the students construct as similar in size.

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 4)

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Sub-strand: Location and transformation— L&T – 1

RESOURCE SHEET Dingo’s Lair game board

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CONTENT DESCRIPTION: Use simple scales, legends and directions to interpret information contained in basic maps

You will need the Dingo’s Lair game board (below), a counter for each player and the two dice (see page 86). Each player throws the dice in turn. The first dice (1, 2 or 3) determines where the counter moves across and the second dice (one, two or three) where it moves upwards. If players land on a ‘volcano’ they return to ‘Start’. The winner is the first to reach either Sandy Beach or Rocky Beach.

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 4)

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Sub-strand: Location and transformation— L&T – 1

RESOURCE SHEET

s r e p u S

3

one

two

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two

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one

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 4)

R.I.C. Publications® www.ricpublications.com.au

CONTENT DESCRIPTION: Use simple scales, legends and directions to interpret information contained in basic maps

3

Bo ok

1 2

Teac he r

1 or e t

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2

Dingo’s Lair dice

Sub-strand: Location and transformation— L&T– 1

RESOURCE SHEET Secret agent code Look at the code grid below and the messages at the bottom of this page. Note that in this code the bold numbers are always written first. To discover the message, run your finger along the lower line first to find the bold number, then straight up from there to the Italic number level.

Check: To find (5, 7) run your finger along the lower numbered line of the code grid to 5, then straight up to the level of 7 and you will find the letter S.

r o e t s Bo r e p ok u W S

Do this for each pair of numbers (coordinates) and decode the messages.

8 7

J

Y

C

G

S

6V

L

O

5

B

K

H

X

U

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1 0

I 0

1

F 2

3

4

5

Q M

6

7

8

9

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2

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CONTENT DESCRIPTION: Use simple scales, legends and directions to interpret information contained in basic maps

T

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9

10 11

. te o (3, 2) – (5, 7) (7, 3) (1, 7) (5, 3) (7, 3) (8, 8) – (3, 2) (10, 8) (7, 3) (1, 3) (8, 8) – (3, 2) (3, 6) c . c (4, 9) (3, 2) (6, 8) (5, 7) –h (8, 2) (5, 7) (7, 3) (5, 7) – (1, 7) (7,r 6)e (4, 4) (7, 3) er o st super Message 1

Message 2 (8, 5) (1, 1) (5, 7) – (3, 6) (1, 1) (5, 1) (7, 3) – (9, 1) (3, 2) (6, 8) – (4, 4) (7, 3) (10, 4) (7, 3) (1, 3) (4, 4) – (7, 6) (1, 3) – (1, 1) (8, 8)

Now make your own messages for a friend.

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 4)

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Sub-strand: Location and transformation— L&T – 1

RESOURCE SHEET Mapping the neighbourhood 1. Study the map and answer the questions below.

1

3

5

7

9

11

13

15

17

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4

8

10

12

14

Tyrell Street

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(a) What street is the school in? (b)

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(d) What will you find opposite the school in Gordon Street?

(e)

(f)

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(c) What will you find on the corner of Gordon and Tyrell Streets?

o c . che e There is a vacant block of land between r o t r s super and How many houses are in Victoria Court?

2. Draw … (a) a car outside house number 7 Porter Street. (b) a school crossing sign in front of the school. (c) a slide to the south of the swing at the park. (d) a bus at a bus stop in Tyrell Street near the Williams Street corner.

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 4)

R.I.C. Publications® www.ricpublications.com.au

CONTENT DESCRIPTION: Use simple scales, legends and directions to interpret information contained in basic maps

Victoria Court

6

Williams Street

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Gordon Street

Porter Street

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 4)

1

2

3

R.I.C. Publications® www.ricpublications.com.au

8 km 1 cm = 2 km

scale:

A

B

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legend:

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Gravel path

D

Wizard’s Land

Goldmine

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Monster marsh Marsh

Wizard’s Castle

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5

Dragon’s mountain Mountain

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Grassy path

Enchanted Forest

E

Sandy beach

Rapids

Rocky beach

F

Shipwreck Bay

Bridge

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CONTENT DESCRIPTION: Use simple scales, legends and directions to interpret information contained in basic maps

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Sub-strand: Location and transformation— L&T– 1

RESOURCE SHEET Wizard’s Land

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Sub-strand: Location and transformation— L&T – 1

RESOURCE SHEET Wizard’s Land questions Pirates land their ship just south of Shipwreck Bay, at (E,1). Help them get about the island by answering the questions below.

1. They want to get to Gorgon’s Goldmine first, so that they have some riches.

Describe what type of paths and the route they would take to get there.

4. While in the Skull Cave, the pirates make a canoe to help them access some areas.

(b)

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(c) In what directions will they be heading?

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C.Publ i cat i ons •f orr evi ew pur posesonl y• What three things do they pass on the way?

(a) What is the best way for them to use it to get to their ship in (E,1)?

5. The Wizard has the power to see all that happens in his land. He decides that he will hide in the Enchanted Forest to catch the pirates. Use directions such as north, south-west etc. and distances to describe his route there from his castle.

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6. The monsters that live on the island live in huts. What are the coordinates of the huts?

7. How far is it from the bridge to the Wizard’s castle?

8. Think about a place on the island where the Wizard could hide his treasure. Write directions on the back of this sheet to show how to get there from the pirate ship.

Swap your directions with a partner and work out where the treasures were hidden.

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 4)

R.I.C. Publications® www.ricpublications.com.au

CONTENT DESCRIPTION: Use simple scales, legends and directions to interpret information contained in basic maps

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3. They want to steer well clear of the Monster Marsh on their travels. What are the coordinates of the marsh?

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r o e t s Bo r e 2. The pirates know aboutp the Skull Cave, and want to set upo a camp there. Use u directions such as north, south-west etc. and distances (usingk the scale at the S bottom of the map) to explain how to get from the Goldmine to the cave.

Assessment 1

Sub-strand: Location and transformation— L&T– 1

NAME:

DATE: Spy codes

Look at the code grid below and the messages at the bottom of this page. Note that in this code the bold numbers are always written first. To discover the message, run your finger along the lower line first to find the bold number, then straight up from there to the ‘unbold’ number to find the corresponding letter.

Check: To find (5, 3) run your finger along the lower numbered line of the code grid to 5, then straight up to the level of 3 and you will find the letter L.

r o e t s Bo r e p ok u W J S

Do this for each pair of numbers (coordinates) and decode the messages.

8

K

O B

7

Z E

6

U

T

Q

D

I

G

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A

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V 4

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6

7

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9

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CONTENT DESCRIPTION: Use simple scales, legends and directions to interpret information contained in basic maps

5

C

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10 11

o c (9, 5) – (8, 6) (2, 3) (9,c 5) (10, 3) (1, 8) – (4, 9) (4, 6) – (2, 3) (6,e 2).

(4, 0) (4, 6) – (8, 3) (6, 8) h r (5, 3) (4, 0) (4, 6) (6, 5) – (8,e 6) (2, 3) (4, 6) – (9, 8) (6, t (6, 5) (4, 6) r s8)o s uper Message 1

Now put the message below into code and write your name in code at the end.

The password for the file is maths.

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Assessment 2

Sub-strand: Location and transformation— L&T – 1

NAME:

DATE: Lakeview Resort

Below is part of a map of Lakeview, a town that borders a lake. Use the map to answer the following questions: Legend

Central Park

7

public phone

MAIN ST St Andrews Church

post box

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library park

church

1 cm = 500 m

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CR ES

VIEW ST

P

DR NT CE CR

D BLV ORE H KES LA

Prince Park

IEW KV AR

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BISHOP ST

1

West Park

G O RD ON ST

SHORT ST

3 2

BAY RD

FISHERMANS BLVD

4

LAKEVIEW AVE

A DR JACARAND

5

MONTGOMERY BLVD

BARRY RD

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1 2 3 4 5 6 7 1. Jenny and Kim met at the corner of Short Street and Jacaranda Dive. What would they find there?

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2. They walk from there to the library. Describe the shortest way for them to get there.

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o c . che e r o 3. A new building is going up on ar corner at (3, 4).

What roads t s intersect there? super 4. What is the name of the park at (5, 7)?

6. What is the shortest way to get from the post box to the lake?

7. About how far is it from the church to the park on Parkview Crescent?

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 4)

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CONTENT DESCRIPTION: Use simple scales, legends and directions to interpret information contained in basic maps

6

Checklist

Sub-strand: Location and transformation— L&T– 1

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Identifies relative positions on a map

Uses simple coordinates

Interprets simple legends

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CONTENT DESCRIPTION: Use simple scales, legends and directions to interpret information contained in basic maps

STUDENT NAME

Interprets simple scales

Use simple scales, legends and directions to interpret information contained in basic maps (ACMMG090)

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 4)

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93

Sub-strand: Location and transformation— L&T – 2

Create symmetrical patterns, pictures and shapes with and without digital technologies (ACMMG091)

RELATED TERMS

TEACHER INFORMATION

Symmetry (reflectional or

What this means

bilateral symmetry)

• We say that a shape that has no lines of symmetry is asymmetrical.

• The correspondence, in size, form and arrangement, of parts on opposite sides of a line, point or plane; e.g. the butterfly below is symmetrical about the vertical line.

• Symmetry seems to be a concept that pleases the eye and is achieved naturally by most students (and adults) when using equipment such as pattern blocks or construction material in free play.

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• In this unit, students are creating symmetrical patterns, pictures and shapes, not simply identifying whether they are symmetrical or not.

mirror line

• With two-dimensional shapes, folding and cutting are common ways to determine reflectional symmetry about a line.

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Teaching points

Transparent mirror

• Transparent mirrors are useful tools for this purpose.

• A clear plastic tool used with symmetry; it has the reflective quality of a mirror, but can also be seen through so that it reflects the front side of the shape onto the other side (also known as a mira or georeflector).

• Transparent mirrors may also be used to determine whether threedimensional objects are symmetrical about a plane.

• Students may need to be shown the correct way to handle a transparent mirror. Directions for this can be found on page 99.

• Symmetry often occurs in the natural environment; e.g. pine cones, reflections of the landscape in a lake, many leaves and plants.

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• Use appropriate pieces of art and craft work from different cultures as examples of the use of symmetry in design.

• National tests usually include questions about symmetry; students need many experiences folding and cutting shapes to be able to visualise the results of these actions.

Plane symmetry

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What to look for

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• This applies to three-dimensional objects where half of the object corresponds in size, form and arrangement to the other half on the opposite side of a plane. For example, the cube below, has nine planes of symmetry, one of which is shown.

• Students are able to identify lines of symmetry in given situations; are able to identify more than one line of symmetry, where appropriate; and are able to identify shapes and objects with no lines of symmetry (i.e. they are asymmetrical).

o c . che e r o t r s super • Students holding the transparent mirror correctly.

symmetry symmetrical line of symmetry plane of symmetry asymmetrical reflection transparent mirror

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Proficiency strand(s): Understanding Fluency Problem solving Reasoning

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 4)

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Sub-strand: Location and transformation— L&T– 2

HANDS-ON ACTIVITIES

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4 lines of symmetry

1 line of symmetry

No lines of symmetry

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• Cutting shapes 1. Use templates of common two-dimensional shapes (see page 98). The shapes could be enlarged and copied onto card. Students trace and cut them out, then fold each one in half, looking for lines of symmetry where one side folds over the other exactly. Some of the shapes may have more than one line of symmetry, in which case students open out the shape and fold in a different way and repeat this until they have found all the lines of symmetry.

In the case of a circle, there are an infinite number of lines of symmetry. If students simply state that there are ‘lots’ of them, that would be a good outcome. Include some shapes that are asymmetrical (have no lines of symmetry) such as a parallelogram. Intuitively, many students look at this shape and attempt to draw a ‘line of symmetry’ between the parallel lines. However, if they fold it looking for two equal halves, they will find there are no lines of symmetry. A similar activity can be found on page 99.

5 lines of symmetry

• Cutting shapes 2. Fold a sheet of paper in half, draw and cut out a simple pattern keeping part of the fold intact and open out. Try a different design after folding into quarters. Discuss the fact that the first type of single fold produces only one line of symmetry, whereas folding the paper into quarters produces two lines of symmetry. A variation of this activity can be found on page 106.

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• Students classify two-dimensional shapes according to whether they have one line of symmetry, two or more lines of symmetry or no lines of symmetry.

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One line of symmetry

o c . che e r o t r s super Two or more lines of symmetry

No lines of symmetry

• The activity above can be done with students investigating any lines of symmetry in letters of the alphabet (choose a font for upper case letters that best suits this activity; e.g. Arial).

One line of symmetry

Two or more lines of symmetry

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 4)

No lines of symmetry

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Sub-strand: Location and transformation— L&T – 2

HANDS-ON ACTIVITIES (CONTINUED)

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• Making old-fashioned paper doilies is a useful way to investigate symmetry. Students use a square piece of paper and fold in half, in half again, and in half a further time, making sure there is a common vertex or corner about which to cut. They then cut shapes and designs around the folds, again making sure there are still connections left on each of the folds. When opened out, a symmetrical doily effect can be seen. The more pieces taken out, the more intricate the pattern. Each of the fold lines is a line of symmetry in the shape. Students could investigate what happens if they are able to make a further fold, although it may get a little difficult to cut through the layers.

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• Students experiment with what happens when they fold a piece of paper in half and cut out a shape. What shapes do they get when their paper is opened up? Students investigate how they could achieve certain shapes before they cut, such as a heart shape. Students need to think about how their planned shape looks when folded in half in order to complete this activity; rather than cutting and not finding out what they have made until after they have opened it out.

This can later be extended to investigating what happens when the paper is folded in half and half again and then cut in particular ways.

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• Students use pattern blocks to make symmetrical patterns, designs and pictures. Students could also make half of a pattern or design and have a partner complete the other half to produce a symmetrical effect. (See also pages 102–104.)

• Students use other manipulatives such as square tiles, Cuisenaire™ (coloured) rods, blocks etc. to make symmetrical patterns or to make half of a pattern for their partner to complete. (See also page 105.)

• Students look in magazines for pictures that are symmetrical and make a ‘Symmetry book’, which may also include their own pictures and designs. They could include a page labelled ‘asymmetrical’ and find or draw appropriate pictures.

• Students use their transparent mirror to complete the house activity on page 106 and the scenery picture on page 107.

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 4)

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Sub-strand: Location and transformation— L&T– 2

LINKS TO OTHER CURRICULUM AREAS Information and Communication Technology • Numerous pages of images of Indigenous rock art can be found through a basic internet search. Many of these pieces are not symmetrical, but showing some of this work to students can lead to discussions about which ones are and are not symmetrical.

• There is a simple symmetry ‘game’ that can be found at <http://www.innovationslearning.co.uk/subjects/maths/ activities/year3/symmetry/shape_game.asp> What is good about this game is when you (deliberately) get a question wrong, the explanation as to why the answer is incorrect is very good, showing the shape folding on itself.

• A series of symmetry activities with three levels of difficulty can be found at <http://www.haelmedia.com/ OnlineActivities_txh/mc_txh4_001.html>

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• A large number of different activities about symmetry can be found at <http://greatmathsgames.com/Symmetry/index. htm> • Some beautiful images of symmetry in both nature and human-made drawings and structures can be found through an internet search for ‘symmetry’.

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• A simple activity where a series of dots are joined to make half a pattern and students fill in the other half can be found at <http://www.softschools.com/math/geometry/symmetry_game/> Note: Each line section has to be made by clicking on two dots and cannot be done continuously by just assuming that it will join to the dot just used.

• Stained glass windows. Students make stained glass windows by using a square of black paper to make a structure, as described on page 96 for paper doilies, and gluing coloured cellophane paper on one side to cover the holes. If students make 2 exact copies of the outline structure, the second one can then be glued onto the back so that they can be attached onto a window where the light would show through the different colours.

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Layer shapes and cellophane, then glue together.

Stained glass window shape

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Coloured cellophane shapes (cut slightly larger than spaces)

Second stained glass window shape

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Glue together and attach to a real window.

• Students create patterns, designs and pictures that have one, two or more lines of symmetry by painting, using crayons, by folding and cutting.

• Students use clay or plasticine to create objects that have reflectional symmetry. These may be animals and insects such as lizards and butterflies, or items such as tiles, pots and baskets that are symmetrical.

• Students make beads from flour and water following the steps from the website below. Once they are painted and baked, students thread them onto string in a symmetrical arrangement. <http://www.wikihow.com/Make-Beads-from-Flour-and-Water>

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Sub-strand: Location and transformation— L&T – 2

RESOURCE SHEET 2-D shapes: Looking for symmetry

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CONTENT DESCRIPTION: Create symmetrical patterns, pictures and shapes with and without digital technologies

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Enlarge shapes and photocopy for students to cut and fold to look for lines of symmetry.

Sub-strand: Location and transformation— L&T– 2

RESOURCE SHEET Symmetry A shape is symmetrical if it is exactly the same on each side of a line: the line of symmetry.

Part 1:

Line of symmetry

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Fold a piece of coloured paper in half.

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Cut out any interesting shape.

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Glue it onto a large piece of paper.

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One line of symmetry

folded edge

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Fold a piece of coloured paper in half and in half again.

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Cut out a shape that begins at one fold and ends at the two folds.

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1 fold

. tof coloured paper in half then in half again. o Fold a piece e c . c Now make one moreh fold through the folded corner r ine the centre. e o r st s Cut out a shape making sure theu folded corner is in the centre of your shape. r pe fold

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Two lines of symmetry 2 folds

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CONTENT DESCRIPTION: Create symmetrical patterns, pictures and shapes with and without digital technologies

Part 2:

fold

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Open it out.

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How many lines of symmetry can you see?

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Glue your shape onto the paper, mark in the lines of symmetry and label them.

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Sub-strand: Location and transformation— L&T – 2

RESOURCE SHEET Using a transparent mirror

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page rather than the mirror; move it until one half of the figure reflects onto the other half. Draw along the ridge with your pencil to mark in the line of symmetry. The first butterfly has been done for you.

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Line of symmetry

3. Now use the mirror to check for lines of symmetry in any other shapes you can find. Some shapes and objects will have one line of symmetry; some will have more than one line of symmetry; and some may have no lines of symmetry at all (which means they are asymmetrical).

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CONTENT DESCRIPTION: Create symmetrical patterns, pictures and shapes with and without digital technologies

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1. Hold the mirror on your desk, as shown in the picture. There is a ‘right’ and ‘wrong’ side for looking through the mirror. The ‘right’ side has a slanted edge which is placed face down on the paper. In this position, the mirror’s slanted edge will be touching the desk and you can move it to the line of symmetry to show you a reflection.

Sub-strand: Location and transformation— L&T– 2

RESOURCE SHEET Half pictures

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CONTENT DESCRIPTION: Create symmetrical patterns, pictures and shapes with and without digital technologies

Use a transparent mirror and place it on the dotted line for each picture. Look through the mirror and draw the other half of the picture by tracing over the reflections. Remember to rotate the page rather than the mirror.

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Sub-strand: Location and transformation— L&T – 2

RESOURCE SHEET Finish the pattern – 1 1. Place pattern blocks over the picture below. Now build the rest of the picture on the other side of the dotted line. The dotted line is the line of symmetry.

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2. Trace around the pattern blocks you used so you can see the full symmetrical pattern. You may want to add some extra blocks to each side to make the pattern bigger, but remember to keep it symmetrical.

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CONTENT DESCRIPTION: Create symmetrical patterns, pictures and shapes with and without digital technologies

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Line of symmetry

Sub-strand: Location and transformation— L&T– 2

RESOURCE SHEET Finish the pattern – 2 1. Place pattern blocks over the picture below. Now build the rest of the picture on each side of the dotted lines. The dotted lines are the two lines of symmetry.

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CONTENT DESCRIPTION: Create symmetrical patterns, pictures and shapes with and without digital technologies

Line of symmetry

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2. Trace around the pattern blocks you used so you can see the full symmetrical pattern. You may want to add some extra blocks to each section to make the pattern bigger, but remember to keep it symmetrical.

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Sub-strand: Location and transformation— L&T – 2

RESOURCE SHEET Finish the pattern – 3 1. Use pattern blocks to make a design in one of the quarters below. Now complete the design by adding blocks on each side of the dotted lines. The dotted lines are the two lines of symmetry.

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symmetry

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2. Trace around the pattern blocks you used so you can see the full symmetrical pattern.

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CONTENT DESCRIPTION: Create symmetrical patterns, pictures and shapes with and without digital technologies

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Line of symmetry

Sub-strand: Location and transformation— L&T– 2

RESOURCE SHEET Tile pattern

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CONTENT DESCRIPTION: Create symmetrical patterns, pictures and shapes with and without digital technologies

1. Use coloured tiles to cover the squares below. Now build the rest of the picture on the other side of the dotted line. The dotted line is the line of symmetry.

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G = green

Y = yellow

R = red

B = blue

2. Trace around the tiles you used and colour them so you can see the full symmetrical pattern. You may want to add some extra tiles to each side to make the pattern bigger, but remember to keep the pattern symmetrical.

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Sub-strand: Location and transformation— L&T – 2

RESOURCE SHEET Finish the house Below is half of a picture of a house. Use a transparent mirror to complete the other half of the picture.

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 4)

R.I.C. Publications® www.ricpublications.com.au

CONTENT DESCRIPTION: Create symmetrical patterns, pictures and shapes with and without digital technologies

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Line of symmetry

Sub-strand: Location and transformation— L&T– 2

RESOURCE SHEET Reflections in the lake

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CONTENT DESCRIPTION: Create symmetrical patterns, pictures and shapes with and without digital technologies

Below is a picture of a landscape next to a lake. Use a transparent mirror to draw a reflection of it in the lake.

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Sub-strand: Location and transformation— L&T – 2

RESOURCE SHEET Paper people You will need: • • •

a strip of coloured paper about 20 cm x 10 cm a template, below scissors

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1. Fold your strip of coloured paper in half and half again.

5 cm

10 cm

2. On the front of your paper, draw around the template.

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3. Cut out the person though all the layers of paper, being careful to keep the ‘hands’ intact.

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5. Which people are walking the same way? Which are reflections of each other? ch e r er Write about them. o st super 4. Unfold your paper people. Give them names and draw in eyes and smiles.

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CONTENT DESCRIPTION: Create symmetrical patterns, pictures and shapes with and without digital technologies

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20 cm

Assessment 1

Sub-strand: Location and transformation— L&T– 2

NAME:

DATE: Finish the flower

1. Place pattern blocks over the picture below. Now build the rest of the picture on the other side of the dotted line. The dotted line is the line of symmetry. Do you think it looks like a flower?

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CONTENT DESCRIPTION: Create symmetrical patterns, pictures and shapes with and without digital technologies

Line of symmetry

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2. Trace around the pattern blocks you used so you can see the full symmetrical pattern.

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Assessment 2

Sub-strand: Location and transformation— L&T – 2

NAME:

DATE: Mirror magic

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2. Now use it to draw in any lines of symmetry in the shapes below. There may be more than one line of symmetry or none at all.

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 4)

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CONTENT DESCRIPTION: Create symmetrical patterns, pictures and shapes with and without digital technologies

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1. Use a transparent mirror to complete the pictures below.

Assessment 3

Sub-strand: Location and transformation— L&T– 2

NAME:

DATE: Finish the snowflake

Below is quarter of a picture. Use a transparent mirror to complete the other three pieces of the picture.

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CONTENT DESCRIPTION: Create symmetrical patterns, pictures and shapes with and without digital technologies

Line of symmetry

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What can you say about your snowflake?

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Checklist

Sub-strand: Location and transformation— L&T – 2

Creates symmetrical designs

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STUDENT NAME

Uses a transparent mirror correctly

Create symmetrical patterns, pictures and shapes with and without digital technologies (ACMMG091)

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Answers

Sub-strand: Location and transformation

L&T – 1 Page 87

Page 102

Resource sheet – Finish the pattern – 1

Page 103

Resource sheet – Finish the pattern – 2

Resource sheet – Secret agent code

Message 1: a secret agent always uses code Message 2: his life may depend on it.

Page 88

Resource sheet – Mapping the neighbourhood

1. (a) Victoria Court (b) Tyrell, Williams and Porter streets (c) Tennis court (d) Milk bar (e) Porter Street and Victoria Court (f ) 7 2. Teacher check Page 90

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Students’ own designs, with 2 lines of symmetry Page 105

Resource sheet –Wizard’s Land questions

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Resource sheet – Tile pattern

B R R B

G Y G Y G Y G Y G Y G Y R B B R

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Note: It does not make a checkerboard pattern, i.e. NOT. R B Y G Y G Y G R B

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1. Head north on a gravel path, then west on a gravel path, then north on a grassy path to the goldmine.

2. Travel north-east for about 12 kilometres. Then head east for about 6 kilometres.

3. (A,1) and (B,1) 4. (a) Along the river. (b) Bridge, rapids, rocky beach. (c) South-east, then south, and finally south-west.

5. Head south along the gravel path for about 4 km; then east on a grassy path for about 7 km; turn north-east along grassy path for about 8 km; turn right (east) along a gravel path and over the bridge (about 18 km), then head north along a grassy path for about 4 km to the Enchanted Forest.

6. (D,3) 7. About 28 kilometres.

8. Teacher check

Resource sheet – Finish the pattern – 3

B R G Y G Y G Y B R

Resource sheet – Finish the house

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Assessment 1 – Finish the flower

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Assessment 2 – Mirror magic

Assessment 1 – Spy codes

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Message 1: I think we have solved the code Message 2: (8, 6) (2, 3) (4, 6) – (4, 4) (6, 2) (8, 3) (8, 3) (4, 9) (6, 8) (9, 1) (6, 5) – (7, 4) (6, 8) (9, 1) – (8, 6) (2, 3) (4, 6) (7, 4) (9, 5) (5, 3) (4, 6) – (9, 5) (8, 3) – (1, 1) (6, 2) (8, 6) (2, 3) (8, 3) And the student’s name in code at the end.

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Resource sheet – Reflections in the lake

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Assessment 2 – Lakeview Resort

1. A public phone 2. Go east along Short St, turn right (south) on Lakeview Ave to the end; left (east) along Lakeshore Blvd to the end; left (north) on Fishermans Blvd; right (east) on Crescent Dve to the end. The library is at the end of the street.

3. Bay Road and Lakeview Avenue 4. Central Park 5. Head north-west to Fishermans Boulevard then south to the lake.

6. About 2.5 to 3 kilometres (2500–3000 metres).

1. Teacher check 2.

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Assessment 3 – Finish the snowflake

It has two lines of symmetry.

L&T – 2 Page 101

Resource sheet – Half pictures

Teacher check Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 4)

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Sub-strand: Geometric reasoning—GR–1

Compare angles and classify them as equal to, greater than or less than a right angle (ACMMG089)

RELATED TERMS

TEACHER INFORMATION What this means

Angle

• Two lines with a common end point called a vertex, or the extent of rotation about a point.

• Common angles (those of approximately 90°, and half of that, 45°) are ones students should recognise.

r o e t s Bo r e p ok u S • Students compare other angles to a right angle.

• Students know and understand the terms acute, obtuse and reflex angles.

Right angle 90°

Acute angle

• Less than 90°.

Obtuse angle

• The use of a protractor is not encouraged at this year level.

Teaching points

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• Knowledge that a full turn is the same as 360° (four right angles) and that half a turn is 180° (two right angles).

• Angles are classified by their size in their relationship to the right angle (90°). (Refer to the related terms, left.)

• Right angles are used extensively in most buildings; for example, where walls meet the floor and the ceiling, the corners of rooms and most of the angles in the construction of cupboards. Also books and paper mostly have 90° angles.

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• Many doors open to 180°, though if near a corner, they may only open to about 90°.

Straight angle

• Show right angles in different orientations. This is to help avoid a common misconception that we can have right angles and ‘left angles’.

• Exactly 180°.

Reflex angle

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One rotation

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• Students can get an intuitive idea of the size of angles when making comparisons; for example, that some of the angles on the trapezium piece of pattern blocks are greater than a right angle (they are obtuse angles) and also much bigger than the size of the angles on the triangular block, which are less than a right angle (they are acute angles). At this stage, they do not need to measure the angles on the blocks.

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• Greater than 90°, but less than 180°.

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• It is important to make angles with different arm lengths so students realise that the length of the arms does not affect the size of an angle.

• National tests often include a question on angles, where students identify the largest or smallest angles from a set of angles that have different lengths on the arms.

• A full turn to end up at the start; 360°.

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Sub-strand: Geometric reasoning—GR–1

Compare angles and classify them as equal to, greater than or less than a right angle (ACMMG089)

TEACHER INFORMATION (CONTINUED)

RELATED TERMS (CONTINUED)

What to look for

Degree

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• Students are aware that acute angles are angles that are less than 90°, obtuse angles are between than 90° and 180° and reflex angles are between 180° and 360°.

• Students are aware that a straight angle is 180° (which is two right angles) and a full rotation or full turn is 360° (which is four right angles).

• Students confused by the length of the arms of an angle; thinking that an angle with short arms is less than an angle of lesser degrees but with longer arms. Students with this misconception would judge that the first angle below is larger than the second, because of the length of the arms. In fact, the second angle is larger.

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• A unit of measure of an angle, based on there being 360° in a circle.

Students need to be aware that degrees are also used to measure temperature, but this is not the same as the measure for angle.

• Students know the properties of a right angle (90°) and can represent them without the use of a protractor. (Note: Protractors are not encouraged at this year level.)

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acute angle forty-five degree angle obtuse angle reflex angle straight angle full rotation degrees arms (of an angle)

Proficiency strand(s): Understanding Fluency Problem solving Reasoning

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Sub-strand: Geometric reasoning—GR–1

HANDS-ON ACTIVITIES • In this unit, students will mostly compare angles to the right angle (90°). This will involve recognising that a straight angle is two right angles (180°) and a full turn is four right angles (360°). Discuss the idea that right angles occur all around us, including the corners of pieces of paper, books, corners in rooms etc.

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• Students make an angle demonstrator (see page 118). They use these to show various angles such as 90°, half of a right angle (45°), any other acute angle (without the need to give a size in degrees), an obtuse angle (between 90° and 180°), a straight angle, a reflex angle (between 180° and 360°) and a full turn. Students find ways to record their results.

Discuss what an angle that is half the size of a right angle (i.e. 45°) would look like. Play games where the teacher (or a student) calls out an angle size and the students make that angle with their angle demonstrator and hold it up for the teacher to check. Choices would include: right angle, acute angle, 45° angle, obtuse angle, straight angle, reflex angle and full turn.

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• Discuss whether an angle demonstrator such as the one above would be different if the two circles used to make it were larger. It may be useful if the teacher made one with a larger diameter (maybe 30 cm instead of 10 cm). Students could compare a right angle using both angle demonstrators and see that it is still 90°. This would link to the concept that the size of the angle is independent of the length of the angle’s arms.

• Students make an angle unit measure; which is a way to compare angles without a protractor. This involves using a circle of light card. Students fold the circle in half, in half again, a 3rd time and finally a 4th time. When this is opened out, there are 16 equal (or very nearly equal) segments that become the units of the angle unit measure. Students can use these to measure the size of angles in terms of the number of segments needed on their angle unit measure. Help students make the link to the fact that four of these angle unit segments make a right angle (90°), eight make a straight angle and sixteen make a full turn (i.e. all of the segments).

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• Students could use the angle unit measure above and work out how many degrees are in two segments (half of 90°; i.e.

45°). They could then use the angle unit measure to find and measure angles of 45°.

• Naming angles memory game: Use the cards on page 119, enlarged and laminated. Students place the cards face down on the desk and take turns turning over two cards. If they match, the player keeps the cards. If they don’t, they turn the cards back over. The player with the most cards at the end is the winner.

• Angle Snap game: Again, use the cards on page 119, enlarged and laminated, but this time use two sets for each single student. Students shuffle the cards and deal them out face down. Each student then turns over their top card onto a single discard pile. If their card matches the one already on the top of the discard pile, then the first player to call ‘Snap’ and put their hand on the card gets all the cards in the discard pile. Play ends when one person runs out of cards. Note: Matches would include any two of the following: a picture of an angle (there are two different orientations of each); the type of angle (e.g. acute angle) and the number of degrees.

• The hour and minute hands on a clock make angles as they turn. Students could discuss what angles are formed at certain times; e.g. 3 o’clock; 9:15, 12 o’clock, 9 o’clock, 12:07. They could be challenged to think of times on an analogue clock where the hands would form an acute angle, times which produce an obtuse angle, times for a right angle etc.

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Sub-strand: Geometric reasoning—GR–1

LINKS TO OTHER CURRICULUM AREAS English • Make vocabulary cards with drawings and definitions for new words associated with angles; for example, right angle, acute angle, obtuse angle, reflex angle, straight angle and full turn. Each of the cards could also make mention of degrees of turn; e.g. 90°, less than 90°, between 90° and 180°, between 180° and 360°, exactly 180° and exactly 360°.

• Read What’s your angle, Pythagoras? by J Ellis. This book is written as a story of Pythagoras’ discovery of the properties of right-angled triangles.

Information and Communication Technology

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• A short movie that uses angles to solve problems, called Pirate Kate’s treasure map contains angle ideas including 90°, 180°, 360° and 270°. It can be found at <http://www.nationalstemcentre.org.uk/elibrary/maths/resource/6048/anglespirate-s-lost-treasure>

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• A website that asks students to decide whether the angles shown are greater than a right angle, exactly a right angle or less than a right angle can be found at <http://au.ixl.com/math/year-3/angles-greater-less-or-equal-to-right-angle> The explanation when an incorrect answer is entered is very good.

The Arts

• Students make ‘angular’ art works and compare and label the different angles used.

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• A website where you can move the mouse on an arm of an angle within a circle and it will increase or decrease the angle and label it as acute, right, obtuse, or reflex can be found at <http://www.mathsisfun.com/rightangle.html> It also gives a measure of the angle so students can see, for example, an angle of 89° as acute, then move to 90° as a right angle.

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 4)

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Sub-strand: Geometric reasoning—GR–1

RESOURCE SHEET Make and use an angle demonstrator

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. te o • Place one circle inside the other as shown. Your can now turn one circle of your c . chthe angle demonstrator within other to show different angles. e r er o st super

• Use your angle demonstrator to show a right angle (90°), an acute angle (less than 90°), an obtuse angle (between 90° and 180°) a straight angle (180°), and a reflex angle (between 180° and 360°). Draw these onto a sheet of paper and label them. How can you show a full turn?

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 4)

R.I.C. Publications® www.ricpublications.com.au

CONTENT DESCRIPTION: Compare angles and classify them as equal to, greater than or less than a right angle

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Teac he r

• Make two (2) circles about the same size as the one below; one in a light colour, the other in a darker colour. Carefully cut a line to the centre as shown below.

Sub-strand: Geometric reasoning—GR–1

RESOURCE SHEET Naming angle memory game

Acute angle

45°

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180°

Full turn

360°

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Obtuse angle

Reflex angle

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CONTENT DESCRIPTION: Compare angles and classify them as equal to, greater than or less than a right angle

Straight angle

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You may wish to enlarge these before photocopying onto card and laminating.

Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 4)

R.I.C. Publications® www.ricpublications.com.au

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Assessment 1

Sub-strand: Geometric reasoning—GR–1

NAME:

DATE: What do you know about angles?

Write what you know about each of the types of angles below and draw an example of each one.

A straight angle

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An acute angle

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. teangle o An obtuse A reflex angle c . che e r o t r s super

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 4)

R.I.C. Publications® www.ricpublications.com.au

CONTENT DESCRIPTION: Compare angles and classify them as equal to, greater than or less than a right angle

A full turn

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A right angle

Checklist

Sub-strand: Geometric reasoning—GR–1

Recognises full turns

Recognises straight angles

Recognises obtuse angles

Recognises acute angles

Recognises reflex angles

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STUDENT NAME

Recognises right angles

Compare angles and classify them as equal to, greater than or less than a right angle (ACMMG089)

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Australian Curriculum Mathematics resource book: Measurement and Geometry (Year 4)

R.I.C. Publications® www.ricpublications.com.au

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