Maths Rescue Series: Book 2 by Teacher Superstore

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rescue maths

Book 2 Measurement, Chance and data

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© Ready-Ed Publications - 2003. Published by Ready-Ed Publications (2003) P.O. Box 276 Greenwood W.A. 6024 Email: info@readyed.com.au Website: www.readyed.com.au COPYRIGHT NOTICE Permission is granted for the purchaser to photocopy sufficient copies for non-commercial educational purposes. However, this permission is not transferable and applies only to the purchasing individual or institution. ISBN 1 86397 565 9

Information on the Series About The Books

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This series has been created for classroom teachers and parents to use for home or class work - with students of a range of abilities taken into consideration. The focus will be on reinforcement of “the basics” in maths, as well as activities aimed at developing understanding of classroom activities in mathematics. Students with Specific Learning Difficulties experience a range of problems with their academic learning. These aspects include:• Difficulties with word recognition and comprehension • Coping with pages that are too cluttered and with too many differing requirements • Being able to sequence, recall and apply strategies in abstract situations • Striving to process formation - while working to meet deadlines • Having trouble with personal organization with their schoolwork. The books in this series are designed with these problems in mind, and whilst pages are designed for the student with learning difficulties, they can also be used as a simple and straightforward introduction to concepts or a reinforcement of mathematical strategies for the whole class. The books will follow a basic format, with a variety of homework topics usually containing a choice of two worksheets.

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Content of the Books

The Three Books in the Series Book One: Number - Written Calculations Book Two: Measurement, Chance and Data Book Three: Number - Applications Curriculum Links and Learning Outcomes The aim of the activities is to focus on one concept per page, therefore, only one outcome in a strand from the relevant Mathematics outcomes will usually be addressed. Strands and outcomes focused on in this book are shown on pages 4 to 6. Learning Outcomes for each page are specified at the top of the page. Information in Specific Learning Difficulties This section will contain information from a variety of referenced sources including online literature and recommendations from trained and experienced consultants. Information will include descriptions of the various learning difficulties and ideas for strategies in the classroom and at home. A list of website addresses containing information and ideas is provided for teachers and parents. Student Lifesavers Many students with Specific Learning Difficulties become overwhelmed when expected to recall basic facts when carrying out more complex calculations. Students may grasp a concept, but be unable to apply the strategy because they are struggling to remember tables and combinations. To focus on the teaching point and alleviate stress for students, these tables and charts can be kept within easy access for the students. Charts include multiplication tables, addition and subtraction charts, number lines, rules and formulas and measurement conversions. “Parent Power” Pages The information provided on Specific Learning Difficulties at the beginning of this book can also be photocopied and given to parents who are requesting additional information. However, it should be made clear that this is a guide only, and contact with local recognised Specific Learning Difficulty associations or Child Development Centres should be made if there are any particular concerns. Parent Power pages can be photocopied and sent home at the commencement of each unit and include: • terminology; • mathematical strategies and examples; • learning and practice ideas in the home and community. It is also suggested that teachers photocopy answers to each section and include these when sending home the Parent Power Page. This enables parents to feel confident in checking their child’s work and giving them valuable, immediate feedback. Progress Charts It is widely appreciated that success is built on success, and the more students are able to track their own progress, the more likely they are to be motivated to attempt the next stage in their learning. Students can keep these progress charts as an ongoing record of their homework. Skill Drills Some students work best with structured, timed drills. Drill practice can be very helpful in developing skills in automatic recall. The drill charts in this book are designed so that the length of time and the starting position for the drill can be changed according to the student’s abilities. A record of the score can be kept so that the student can track their progress.

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Contents

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Information on the Series ....................................................................................................................... 2 State and National Curriculum Links ................................................................................................. 4 - 6 Specific Learning Difficulties .................................................................................................................. 7 How are Individuals With Specific Learning Difficulties Affected? ........................................................... 9 General Strategies for the Home ........................................................................................................... 11 Internet References .............................................................................................................................. 12 Parent Power Maths Words ............................................................................................................................. 13 Measurement ............................................................................................................................. 14 Time ........................................................................................................................................... 16 Progress Chart What Can I Do? ......................................................................................................................... 19 Activity Sheets Measuring Perimeter 1 ............................................................................................................... 21 Measuring Perimeter 2 ............................................................................................................... 22 Area 1 ........................................................................................................................................ 23 Area Calculation 1 ..................................................................................................................... 24 Area Calculation 2 ..................................................................................................................... 25 Area of a Triangle 1 .................................................................................................................... 26 Area of a Triangle 2 .................................................................................................................... 27 Circumference 1 ......................................................................................................................... 28 Circumference 2 ......................................................................................................................... 29 Litres and Millilitres 1 ................................................................................................................. 30 Litres and Millilitres 2 ................................................................................................................. 31 Kilograms and Grams 1 ............................................................................................................. 32 Kilograms and Grams 2 ............................................................................................................. 33 Volume 1 .................................................................................................................................... 34 Volume 2 .................................................................................................................................... 35 What’s the Time? Help Sheet .................................................................................................... 36 What’s the Time? 1 ................................................................................................................... 37 What’s the Time? 2 ................................................................................................................... 38 What’s the Time? 3 ................................................................................................................... 39 What’s the Time? 4 ................................................................................................................... 40 What’s the Time? Estimates ..................................................................................................... 41 Looking at Calendars 1 .............................................................................................................. 42 Looking at Calendars 2 .............................................................................................................. 43 Looking at Timetables 1 ............................................................................................................. 44 Looking at Timetables 2 ............................................................................................................. 45 Looking at Timetables 3 ............................................................................................................. 46 Range, Mode, Median and Mean 1 ............................................................................................ 47 Range, Mode, Median and Mean 2 ............................................................................................ 48 Bar Graphs and Line Graphs 1 .................................................................................................. 49 Bar Graphs and Line Graphs 2 .................................................................................................. 50 Venn Diagrams 1 ....................................................................................................................... 51 Venn Diagrams 2 ....................................................................................................................... 52 ANSWERS .......................................................................................................................................... 53

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Curriculum Links - State Curriculum Documents Activities in this book mainly address the following outcomes in the Measurement Strands of the relevant documents, with some content from Chance and Data.

Activity

New South Wales

Queensland

Measuring Perimeter 1

Length M 3.2

Length, Mass, Area & Volume M 3.1

Measuring Perimeter 2

Length M 3.2

Length, Mass, Area & Volume M 3.1

Area 1

Area M 3.3

Length, Mass, Area & Volume M 3.1

Area M 3.3

Length, Mass, Area & Volume M 3.1

Area M 3.3

Length, Mass, Area & Volume M 3.1

Area M 3.3

Length, Mass, Area & Volume M 3.1

Area M 3.3

Length, Mass, Area & Volume M 3.1

Area M 3.3, WM 3.3

Length, Mass, Area & Volume M 3.1

Circumference 2

Area M 3.3, WM 3.3

Length, Mass, Area & Volume M 3.1

Litres and Millilitres 1

Capacity and Volume M 3.4(a)

Length, Mass, Area & Volume M 3.1

Litres and Millilitres 2

Capacity and Volume M 3.4(a)

Length, Mass, Area & Volume M 3.1

Kilograms and Grams 1

Mass M 3.5

Length, Mass, Area & Volume M 3.1

Kilograms and Grams 2

Mass M 3.5

Length, Mass, Area & Volume M 3.1

Volume 1

Capacity and Volume M 3.4(b)

Length, Mass, Area & Volume M 3.1

Area Calculation 1 Area Calculation 2 Area of a Triangle 1

Circumference 1

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Area of a Triangle 2

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What’s The Time? Help Sheet

Time M 3.7

Time M 3.2

What’s The Time? 1

Time M 3.7

Time M 3.2

What’s The Time? 2

Time M 3.7

Time M 3.2

What’s The Time? 3

Time M 3.7

Time M 3.2

What’s The Time? 4

Time M 3.7

Time M 3.2

Time M 3.7

Time M 3.2

Looking at Calendars 1

Time M 3.7

Time M 3.2

Looking at Calendars 2

Time M 3.7

Time M 3.2

Looking at Timetables 1

Time M 3.7

Time M 3.2

Looking at Timetables 2

Time M 3.7

Time M 3.2

Range, Mode, Median and Mean 1

Number Operations N 3.4 Data Representation S 3.5

Data CD 3.2

Range, Mode, Median and Mean 2

Number Operations N 3.4 Data Representation S 3.5

Data CD 3.2

Bar Graphs 1

Data Representation S 3.5

Data CD 3.2

Bar Graphs 2

Data Representation S 3.5

Data CD 3.2

Venn Diagrams 1

Data Representation S 3.5

Data CD 3.2

Venn Diagrams 2

Data Representation S 3.5

Data CD 3.2

What’s The Time? Estimates

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Length, Mass, Area & Volume M 3.1

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Capacity and Volume M 3.4(b)

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Victoria

Western Australia

Measurement 3.5

Measuring and Estimating 3.3

Indirect Measure M 3.4(a)

Measurement 3.5

Measuring and Estimating 3.3

Indirect Measure M 3.4(a)

Measurement 3.5

Measuring and Estimating 3.3

Indirect Measure M 3.4(a)

Measurement 3.5

Measuring and Estimating 3.3

Indirect Measure M 3.4(a)

Measurement 3.5

Measuring and Estimating 3.3

Indirect Measure M 3.4(a)

Measurement 3.5

Measuring and Estimating 3.3

Indirect Measure M 3.4(a)

Measurement 3.5

Measuring and Estimating 3.3

Indirect Measure M 3.4(a)

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South Australia

Measurement 3.5

Measuring and Estimating 3.3

Indirect Measure M 3.4(a)

Measurement 3.5

Measuring and Estimating 3.3

Indirect Measure M 3.4(a)

Measurement 3.5

Measuring and Estimating 3.3

Indirect Measure M 3.4(a)

Measurement 3.5

Measuring and Estimating 3.3

Indirect Measure M 3.4(a)

Measurement 3.5

Measuring and Estimating 3.3

Indirect Measure M 3.4(a)

Measurement 3.5

Measuring and Estimating 3.3

Indirect Measure M 3.4(a)

Measurement 3.5

Measuring and Estimating 3.3

Indirect Measure M 3.4(a)

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Measurement 3.5

Time 3.1, 3.2

Direct Measure M 3.2

Measurement 3.5

Time 3.1, 3.2

Direct Measure M 3.2

Measurement 3.5

Time 3.1, 3.2

Direct Measure M 3.2

Measurement 3.5

Time 3.1, 3.2

Direct Measure M 3.2

Measurement 3.5

Time 3.1, 3.2

Direct Measure M 3.2

Time 3.1, 3.2

Direct Measure M 3.2

Measurement 3.5

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Measuring and Estimating 3.3

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Measurement 3.5

Time 3.1, 3.2

Measurement 3.5

Time 3.1, 3.2

Direct Measure M 3.2

Measurement 3.5

Time 3.1, 3.2

Direct Measure M 3.2

Measurement 3.5

Time 3.1, 3.2

Direct Measure M 3.2

Exploring, Analysing

Summarising & Presenting Data 3.1

Interpret Data C&D 3.4

Summarising & Presenting Data 3.1

Interpret Data C&D 3.4

Data 3.1

Summarising & Presenting Data 3.2, 3.3

Summarise and Represent Data C&D 3.3

Data 3.1

Summarising & Presenting Data 3.2, 3.3

Summarise and Represent Data C&D 3.3

Data 3.1

Summarising & Presenting Data 3.2, 3.3

Summarise and Represent Data C&D 3.3

Data 3.1

Summarising & Presenting Data 3.2, 3.3

Summarise and Represent Data C&D 3.3

& Modelling Data

3.3

Exploring, Analysing & Modelling Data

Direct Measure M 3.2

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3.3

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Curriculum Links - National Document Activities in this book mainly address the following outcomes in the Measurement Strand, with some content from Chance and Data. Measurement

Chance & Data

Choosing Measuring Estimating Units

Activity

Time

Space

Using Organising Display & Interpreting Relations. Data Summarise Data

3.18 4.18 3.19 4.19 3.20 4.20 3.21 4.21 3.22 4.22 3.25 4.25 3.26 4.26 3.27 4.27

Measuring Perimeter 1 Measuring Perimeter 2 Area 1

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Area Calculation 1 Area Calculation 2

Area of a Triangle 2

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Circumference 1

Circumference 2

Litres & Millilitres 1

Litres & Millilitres 2

Kilograms & Grams 1

Kilograms & Grams 2

Volume 1

What’s The Time? 1

What’s The Time? 2

What’s The Time? 3

What’s The Time? 4

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What’s The Time? Help Sheet

What’s The Time? Estimates

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Looking at Calendars 1 Looking at Calendars 2

Looking at Timetables 1 Looking at Timetables 2 Looking at Timetables 3

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Area of a Triangle 1

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Range, Mode, Median & Mean 1

Range, Mode, Median & Mean 2

Bar Graphs 1

Bar Graphs 2

Venn Diagrams 1

Venn Diagrams 2 Page 6

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Specific Learning Difficulties (SLDs) What are Specific Learning Difficulties? Specific Learning Difficulties ARE: • A range of conditions including dyslexia, dyscalculia, dyspraxia and dysgraphia. • Significant difficulties in one or a few areas of learning, whilst demonstrating average to above average abilities in most or all other areas. Specific Learning Difficulties ARE NOT: • A result of global low intelligence, physical conditions such as visual or hearing impairments, or a lack of appropriate parenting or teaching. • Attention difficulties (or behavioural disorders) such as Attention Deficit Disorder (ADD) and Attention Deficit Hyperactivity Disorder (ADHD). Specific Learning Difficulties are founded on a reduced capacity to learn, and attention difficulties stem from a reduced capacity to concentrate and attend to tasks when learning. Specific Learning Difficulties CAN: • Appear to overlap, as learning areas often merge. For example, a person with reading difficulties may struggle in maths in the presence of lengthy word problems or poorly set-out activities (www.dyslexia-speld.com).

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Descriptions of the Types of Specific Learning Difficulties

(www.dyslexia-speld.com)

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Dyslexia is the most commonly recognised and well-researched SLD, characterised by difficulties in: • Recognising, reading and spelling words; • Comprehension of written information; • Relating new written concepts to stored ideas and existing knowledge; • Phonological coding, the process of associating sounds with letter groups; • Producing written work (sequencing letters, recognising letter reversals).

Dyscalculia describes significant difficulties in the area of mathematics. People with dyscalculia may possess average to above average linguistic skills but struggle with: • Mental recall of basic facts; • Accurate calculation; • Understanding and applying mathematical concepts, rules and formulas; • Awareness of time, direction (such as spatial and mapping skills) and sequence; • The ability to estimate and recognise errors in maths work; • Money and budgeting; • Games that involve strategic planning or complex scoring.

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Dysgraphia outlines difficulties with the production of written language which may occur in isolation or in conjunction with other SLDs. Underlying causes include difficulties with sequencing and ordering of letters and words, attention difficulties leading to poor fine motor and organisational skills and reduced auditory processing. (www.ldonline.org) Dyspraxia describes difficulties in the ability to plan and execute new or unfamiliar movements in a coordinated manner. During early childhood, many new tasks are being learned, so this is a time where dyspraxia can significantly impact upon daily living. Problems can appear with performing fine and gross motor tasks (Motor Dyspraxia) and / or speech-related tasks (Verbal or oral Dyspraxia). (www.dyspraxiafoundation.org.uk)

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Associated Difficulties

Visual and Visual-Perceptual Difficulties (Source: www.children-special-needs.org)

These difficulties may occur in conjunction with, or as a result of, other learning or attention difficulties. The problems listed below can also place a considerable strain on the reading process for a child, and can often go unnoticed until the child is in primary school, where the he / she spends longer periods of time focusing on print. Myopia (short-sightedness) - may lead to difficulties in reading information written on the blackboard or on charts around the classroom, if not rectified with glasses or contact lenses. Binocular coordination - the action of both eyes moving together, a process required to read effectively. Convergence - the movement of both eyes inwards, reaching an accurate point of focus. Fixation - where the eyes meet on a specific point so that the image is clear. Pursuit - smoothly tracking across an image or follow a moving object. Saccades - a “jump” from one point of focus to another without losing place. This is particularly important as skilled reading involves a series of fixations on words across a line rather than one continuous movement. • Children who have difficulty with any of the above may show signs such as skipping or re-reading lines, misreading small words, using their finger or moving their head as they read.

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Directionality - A convention of the English language is that information is written from left to right. Some children confuse or reverse this direction and may also confuse letters that are the same shape in a different direction, such as d and b, or p and q. Visual Figure-Ground is the ability to distinguish certain forms, words or features amongst irrelevant visual information such as reading print on a cluttered page, successfully scanning for key words within a block of text and editing work for errors. Visual Discrimination relates to the distinction of similar words. Some children, for example, may consistently confuse similar words such as bad and bed, through and thorough. Visual Form Constancy describes the recognition of the same object image or word in a different form, for example, being able to read the same sentence correctly in a variety of fonts, or understanding that a word is the same whether it is represented in capital or lower case letters. Visual Closure can be demonstrated by mentally or physically completing “gaps” in visual images, such as writing the end of a word where only part of it is given or doing “dot-to-dot” and jigsaw puzzles. Visual Memory aids in both reading and writing, as familiar words can be recognised, pronounced and spelt more automatically once they are retained. Students with poor visual memory take longer to learn new words. Visual Sequential Memory refers to the recall of a sequence of shapes, images or words, and the ability to apply what is recalled. For example, looking up at the board to remember and write down a list of spelling words. Visual Motor Integration is the process of integrating visual input with motor output – the coordination of “seeing, planning and doing”. In the classroom context, this skill is used in accurate copying of images and words, staying on the lines when writing and correctly aligning maths calculations, to name a few examples.

Auditory Processing

Auditory processing problems affect the learner’s ability to interpret auditory information. Often under the broad category of Central Auditory Processing Disorder (CAPD), this group of disorders are caused by a dysfunction of the brain, rather than of the ear, and include symptoms such as: • A slower rate of processing auditory information due to a perceived distortion of the incoming sounds; • A sensitivity to excessive noise or background noise – inability to concentrate and distractibility; • Difficulty locating directionality of sound; • Confusion of similar words or sounds; • Poor memory of verbal instructions; • Difficulty interpreting intonation such as jokes, sarcasm, questions, etc.; • Apparent hearing loss, e.g. saying “What?” often despite normal results on hearing tests; • Poor reading and/or writing as a result of some of the above problems. There are several subgroups, which more specifically describe auditory processing disorders and like visual perceptual problems, these can exist in conjunction with other learning or attention difficulties.

Attention Deficit Disorder

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Attention Deficit Disorder or ADD is a neurological disorder that has been a focus of media attention over the last decade. There are two types that are commonly recognised: Attention Deficit Hyperactivity Disorder (ADHD) is characterized by: • Constant fidgeting or moving about in a seat; • Having trouble waiting a turn; • Impulsivity; • Difficulty listening to and following instructions. Attention Deficit Disorder (ADD) is evident in individuals who: • Are quiet, withdrawn and sluggish; • Demonstrate low self-esteem; • Are often described as “daydreamers”; • Need constant prompting to remain on task. Both types tend to be: • Easily distracted • Forgetful • Disorganised As previously mentioned, Attention Deficit Disorder is a separate entity to Specific Learning Difficulties and each requires some unique strategies to best approach the difficulties. There are, however, instances where an individual may experience both conditions to a certain degree. Initially, it may be difficult for the untrained individual to pinpoint the “cause”. A student with attention difficulties may appear dyslexic because their distractibility leads them to constantly lose their place when reading. Conversely, a student with a specific learning difficulty may become so frustrated that they avoid work or give up easily, appearing to “lose concentration”.

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Source: http://add.about.com

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How are Individuals With Specific Learning Difficulties Affected? Some of the obstacles that students with SLDs can face are: • Being branded as “lazy” because they are capable in most areas, and their difficulties often do not correspond with expectations based on their intelligence; • Becoming frustrated that they understand a concept, but are not able to read or write about it; • Developing a low self-esteem as they struggle to keep up with their peers; • Missing out on educational support and resources during the time it takes to identify their problems. On the positive side, having a SLD can also mean that the individual: • Is constantly seeking out alternative ways of thinking and learning, thus becoming a creative and innovative thinker or a strong leader; • Is an intelligent, capable individual, who can be educated at any level if approached with understanding and a willingness to provide appropriate learning opportunities and strategies; • Can overcome learning difficulties to become successful in their chosen fields. Some examples of these people can be found at: www.nald.ca and www.dyslexiaonline.com

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General Strategies for the Classroom

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Below are some ideas that may be of assistance with any of the areas of difficulty listed above. They are not intended to be specific strategies for any one area. These suggestions are provided as a guide only and it is recommended that teachers and parents seek specialised, individualised assessment and intervention for students who have SLDs. Location - Seat the student where they can: • Read the board; • Hear instructions clearly; • Easily access teacher assistance; • Locate reference charts; • Find personal belongings; • Be free from potential distractions. Organisation - Encourage a desk that: • Is clear of “clutter”; • Contains daily work items in a clear pencil case or a tin (contains only the “essentials” such as pencils, ruler, eraser, scissors, glue and a calculator). A daily or weekly checklist to ensure that all stationery is available may help the student to keep track of when things need to be tidied or replaced. Collaboration - A peer tutor needs to know how to: • Prompt and set good examples for the student; • Help without “spoon-feeding” them with the answers; • Avoid distractions. Support Success - Building self-esteem by: • Drawing attention to any success, even if partial, e.g. “Well done! You are using the formula correctly, you just might like to check your final calculation again”. • Drawing on student’s strengths, e.g. asking them to dictate answers verbally if extended writing is difficult. Break It Down - Aid learning by breaking tasks down into manageable components. • Help the student to plan each stage of a task with a familiar “plan of attack” can be helpful. For example, when approaching a word problem, asking “What sort of sum is this”, then “What numbers will be in the sum”, then “Write the sum”, etc. Allow Extra Time - allowing students additional time in situations such as tests is a fair means of compensating for their difficulties. Additional time can also be given to a student by spending a few minutes explaining a new concept in advance before introducing it to the class, so that the information is consolidated, rather than lost in a panic. Easy On Eyes - Try some of the following and ask the student what they prefer. • Font: simple, clear font with no serifs, such as “Arial”. (This book is typeset in Arial.) • Size: Medium to larger size, for example 14 point. • Line Length: 45 - 75 characters including spaces and punctuation. • Paragraphing: wide margins (1.5 - 2.0 cm), 1.5 or double spacing, short, clearly separated paragraphs. • Alignment: Do not justify - it leads to uneven spacing on the line. • Emphasis: simple headings, using bold instead of italics. Use boxes to highlight information. • Points: Use bullets or numbers to identify a list. • Paper: Use matt paper, and try cream or other pastel colours, as many students with SLDs find white paper harder to read from. • Limit irrelevant pictures, background print and borders. • Additional space for ease of working out. • Guiding lines, boxes and cues to assist students with setting out their work. • Simple pictures, only used to reinforce concepts or problems, not as additional decoration on the page.

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Multisensory Learning - Students with SLDs often learn more successfully if provided with a variety of sensory experiences. To consolidate a concept use some of these – it will help ALL students learn: Look at it; write it in six different colours; write it in the air; trace it on sandpaper; show classmates on the blackboard; sing it or make it into a rhyme; say it to a partner; draw it; act it out; use counters, MAB blocks and plastic money or other real objects.

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1x9 bend first finger down

4x9 3 9

• Reversals, e.g. 6 + 4 = 4 + 6 • “Tens pairs” (pairs of numbers adding up to 10) e.g. 1 + 9, 2 + 8, 3 + 7, 4 + 6, 5 + 5 …

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Keep On Track - To avoid “losing track of time”: • Issue regular warnings about how much time is left; • Try a timer on the student’s desk (if this does not cause additional stress); • Highlight a number of items that they should aim to complete before the next time you pass by their desk. Room To Move - Provide an outlet for excess energy by: • A small “fidget toy” such as a palm sized squeeze ball; • Asking the student to take messages to other classrooms. Memory Strategies • Reference charts; • Mnemonics, poems; • Visualising in pictures; • The “9 x table finger” technique, i.e.

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General Strategies for the Home Some of the strategies below may be of assistance when supporting your child in their mathematics homework. • Short and Sweet - Shorter, more frequent sessions of homework minimise the risk of your child losing concentration. Practising a task over a number of days will help to reinforce the concept, so try 10 - 15 minutes of homework each day rather than one hour, once a week.

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• A Friendly Place - Create an environment that is consistent, quiet, comfortable and well lit, with plenty of space for both you and your child to work together. Have a glass of water for your child to drink. Some students also work best if they have small snacks to nibble on whilst they work. • The Right Stuff - Make sure your child has all the necessary equipment before starting. Some handy things to have include highlighters (to emphasise important parts of the homework or examples), eraser (so that mistakes can easily be corrected and there is no mess of scribbling out), sharpener (so that writing is clear and easy to read), lined scrap paper (with relevant sized lines and plenty of space for working out and examples).

• Write it Big - A whiteboard may be a useful way of working out problems. It is easy to see, easy to rub out, and another way of introducing a different sensory experience to the child.

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learners. Classical (Baroque) music has been researched quite extensively and may be of assistance.

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• Check it Off - Using a checklist to tick off tasks that have been done give your child a sense of achievement as well as helping them to keep their place.

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• Charts are not Cheating - A chart with rules, formulas, definitions and basic maths facts can help your child enormously. Remember that integrating several concepts at once can be overwhelming, and it is best to “isolate” the new skill being learned until your child is confident. For example, if your child is learning how to calculate area, a multiplication chart may be useful until he / she has learned how to use the length x width formula.

o c . che e r o t r s super • Success is the Best Foundation - Remember that every time your child gets something correct, even if it is just one part of a larger task, praising them for their success is the most effective way to increase their self esteem and to motivate them to continue. Vary your positive comments, make them specific: “Good work for writing the 3 in the correct column!” and give them small rewards for reaching their goals: “You finished the whole page! Let’s go and kick the footy!”

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Internet References The following can be used as alternatives for parents who wish their child to practise basic mathematics online. http://www.math.com - Go to “Homework Help” for a range of explanations on a variety of maths skills. http://schooldiscovery.com - Visit sections such as “Parents”, “Brain Boosters” and “Webmath” for a range of activities.

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www.discover.tased.edu.au - A Tasmanian education site with links to mathematics activities.

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www.kevinsplayroom.co.uk - Visit the “Maths” section and explore activities such as the Maths Dictionary, A-Plus Math (including online flash cards), Curious and Useful Maths with interesting tricks and puzzles, and Math Baseball. www.yahooligans.com - Follow the links from School Bell > Math > Real World Math to discover activities for sites such as Math in Daily Life, Cadbury Learning Zone, Cool Math and Figure This.

www.awesomelibrary.org - Follow the links from Maths > Elementary School for a range of activity and article sites.

© ReadyEdPubl i cat i ons Sites with more information on learning difficulties: • f o r r e v i e w p u r p o s e s o nl y• www.dyslexia-speld.com - Western Australian organisation for people with learning difficulties.

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www.ldonline.org - Contains many links for a range of informative sites. www.interdys.org - International Dyslexia Association website.

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www.bda-dyslexia.org.uk - British Dyslexia Association website with ideas for parents and educators.

o c . www.dyscalculia.org c - Information of dyscalculia (specific learning difficulties e her r in maths). o t s s r u e p Contact your local organisation that caters for people with dyslexia and specific learning difficulties, or ask your local Child Development Centre or Child Health service for more information.

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Ready-Ed Publications

Parent Power

Maths W ords Words

o Here are some meanings for words that you might read in maths work. Examples are underneath. Addition - Plus, add or “what is the sum of?” e.g. 2 + 4 = 6 Subtraction - Minus, take away or “how much is left?” e.g. 5 - 2 = 3

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Multiplication / Multiplied by - Times, “lots of” or “what is the product of?” e.g. 3 x 5 = 15

Whole Number - 0, 1, 2, 3, 4 … (counting numbers as well as zero) Even Numbers - 2, 4, 6, 8, 10 … (numbers divisible by 2) Odd Numbers - 1, 3, 5, 7, 9 … (numbers not divisible by 2)

Prime Numbers - A number that can only be divided by 1 and itself. e.g. 1, 3, 5, 7, 11, 13, 17, 19, 23, 29

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Division / Divided by - Shared into groups or “how many times does x go into y?” e.g. 10 ÷ 2 = 5 or 10 shared into groups of 2 = 5 groups

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Rounding - Finding the closest 10, 100 or 1000 for the number. e.g. Round 46 to the nearest 10 = 50 Round 530 to the nearest 100 = 500 Round 2978 to the nearest 1000 = 3000

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Composite Numbers - Numbers that have more than 2 numbers (factors) that divide into it. e.g. 2, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18. e.g. Factors of 16 are 1, 2, 4, 8 and 16 so it is a composite number.

[ If the number to be rounded is “in the middle”, e.g. 35 is in between 30 and 40, most sources agree that it is best to round up, i.e. round 35 to 40. It is best to check with individual teachers on what they expect and why.

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Parent Power Measurement o Learn these to help you understand measurement Kilo = One thousand = 1000

Centi = One hundredth

Milli = One thousandth

1 kilogram (kg) = 1000 grams (g)

100 centimetres (cm) = 1 metre

1000 millimetres (mm) = 1 metre

1 kilometre (km) = 1000 metres (m)

$6.55 = 655 cents

1000 millilitres (mL) = 1 litre

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Length (How LONG is it?) • Kilometres = km Metres = m

Centimetres = cm

My house to school

1 km

1000 m

100 000 cm

100 cm

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My desk

My fingernail

1 cm

An ant

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Example

Millimetres = mm

1 000 000 mm 1000 mm 10 mm 2 mm

•

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Multiply length x width. Units are squared mm, cm or km e.g. Area = 4 m x 6 m = 24 m² My neighbourhood block = 1 km² = 1000 000 m² My bedroom window = 1 m² = 10 000 cm² My computer key (1 letter) = 1 cm² = 100 mm² 10000 m² = 1 hectare (ha)

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Volume (How much is it FILLED up?) • Litres = L Millilitres = mL Small water tank or outdoor spa = 1 kL (kilolitre) = 1000 L (litres) Carton of milk = 1 L (litre) = 1000 mL (millilitres)

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© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y• Area (How much SPACE does it take up?) Perimeter (How LONG is it AROUND the OUTSIDE?) • Add the lengths of all the sides: My classroom = 8 m + 8 m + 8 m + 8 m = 24 m

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Mass (Often called weight - how much does it WEIGH?) • Tonne = t Kilograms = kg Grams = g Total mass of a class of children = 1 t = 1000 kg = 1000 000 g Bag of rice = 1 kg = 1000 g

When are length, perimeter and area used? • •

Page 14

Making models, craft work, clothes, etc., e.g. measuring a 3 cm hem. House and garden plans, renovating, working out amounts of material required, e.g. ordering enough paving to cover 5 m² or checking the length of a wall to make sure a new couch will fit along it. Book 2

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Parent Power • •

Distances in sporting events, e.g. 100 m sprint, jumping 1.5 m in the long jump. Distances between places, e.g. I live 5 km from school, shop or park. Mum jogs 2 km each day.

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When are liquid and mass measurements used? • •

•

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o Activities at Home: • Buy model or craft kits which require measuring for your child. These will produce a more pleasing result if measurements are accurate, whilst many projects still allow for a certain degree of flexibility. • Sewing is another excellent way to practise measurements. • Encourage your child to estimate distances, using pacing out, etc. e.g. ”If you step really widely, that is about 1 m. How many metres across is your bedroom using this trick?” • Keep a height chart of your child and siblings, and ask questions each time you measure, e.g. “How many cm have you grown in the last 6 months?” “How much taller than you is Joe?”, “What is your height in mm?”. • Ask your children to estimate how large something is with their hands, e.g. “This brochure says that the TV is 60 cm wide - show me how big you think that is with your hands.” “I caught a fish that was this big - how many cm do you think that is?” Showing amounts of products on their packaging, e.g. a 250 g packet of chips, a 2 L bottle of soft drink. Providing measurements in the kitchen, laundry or outdoors, e.g. 6 g of butter in the recipe, 10 mL of medicine for a chest cold, 50 mL of washing liquid, 10 mL of pool chemicals. Keeping a record of body weight on the bathroom scales.

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o Activities at Home: • Use a variety of containers to show the same amount of liquid, e.g. pour water from a narrow measuring jug into a wide bowl to see how different it appears. • During cooking, familiarise your child with the different types of measuring tools that they can use, including cups, tablespoons and teaspoons. Note: although these are names of everyday items, they also represent specific measurements. Not all plastic cups = 1 cup! • Plan a birthday party, and estimate the number of drink bottles required, based on a trial measurement of 1 glass of drink. The same can be done with food portions.

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Parent Power Time 1 year = 365 days = 52 weeks 10 years = 1 decade 100 years = 1 century 1000 years = 1 millennium

= 12 months

1 month 30 days = April, June, September, November 31 days = January, March, May, July, August, October, December February has 28 days or 29 days in a leap year (every 4 years)

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1 week = 7 days 1 fortnight = 14 days

1 hour = 60 minutes = 3600 seconds 1 minute = 60 seconds Clock face 11

Words

3:00

Three o’clock

3:15

Three fifteen OR Quarter past three

2 3

9 8

4 5

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1 2

10 9

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3:30

Three thirty OR Half past three

3.45

Three forty five OR Quarter to four

4 7

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Digital

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1 day = 24 hours

Morning = am Afternoon / Night = pm 12:00 pm (daytime) = noon 12:00 am (night time) = midnight Page 16

Book 2

Ready-Ed Publications

Parent Power When do we need to tell the time? •

All the time! Making sure you are not late, keeping appointments, social visits, knowing what time to turn on the TV for a favourite show, going to bed at the right time.

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o Activities at Home: • Frequently ask your child to tell you the time, staring with simple hourly times such as 3 o’clock and gradually introducing terminology such as “quarter past” etc. • Keep a variety of clocks at home, with different faces, roman numerals, number-less faces as well as digital clocks to accustom your child to reading the time in a variety of contexts. • Buy your child a watch from a young age. If they ask the time, they can have the question put back to them. • Make clocks using a paper plate, split pins and cardboard for the hands and black marker for the numbers. Use this to practise telling the time. • Keep a clock near where your child is doing homework so that they can keep track of how long they have been working. • Teach your child how to use a stopwatch and time activities such as siblings racing, the time it takes to complete a puzzle, etc. • Show your child how to set their own bedside alarm. Point out the difference between am and pm. • Encourage use of the oven timer or microwave time settings when cooking with your child. • Ask your child to help you set the video recorder to tape their favourite show. • Talk about a 24 hour clock - relate this to real-life examples such as flight times when going on holidays, using some timers such as video recorders, on some television programs such as “army” shows. • Relate daily activities back to time by mentioning in everyday conversation: “Go and spend five minutes brushing your teeth.” “Dinner should be ready in half an hour when ‘The Simpsons’ has finished.” “We are running late - it takes ten minutes to get to school and it is already 8:30!”

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When are calendars used? •

Keeping track of day-to-day events, remembering birthdays and other special events, making and keeping social arrangements, looking forward to see what day of the week dates fall on.

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o Activities at Home: • Record family members’ birthdays on a calendar that is easily seen by the child. Ask them questions like “What day of the week does grandma’s birthday fall on?”, “How many weeks and days until your birthday?”, “What is the date two weeks before Christmas?” • Send unique cards to relatives “Happy two-decade birthday”, “Congratulations on reaching 2920 days on earth” by working out years in different ways on a calculator. • Find out about leap years and when they are. • Use computer programs such as Publisher to make personalised calendars for the home and as presents. • Your child can decorate special days on the family calendar at home.

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Book 2

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Parent Power o When are timetables used? • Public transport timetables • School - daily schedules • Television guides • Entertainment - cinema and other events

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o Activities at Home: • Allow your child to watch a certain amount of television each day. They can use the TV guide to work out when they would like to watch and how much time they will be watching each program for. • Work with your child to devise a timetable for a special family day during the holidays. Use public transport timetables including connecting services, cinema schedules; allow times for travel and lunch, etc. • Work with your child to write a timetable of their school week, and keep it in their room so that they can always be prepared for sport, library, etc. • Devise a homework timetable with your child and try to stick to it, so that it becomes a routine. Tick each week off and set goals with rewards for your child sticking to the timetable.

o When are tallies and graphs used? • Keeping records of observations, such as how many cards of each type in a collection. • Games and sports scores, e.g. a tally of points in each half of a game. • Scientific records, such as growth of a plant over a year, or rainfall over a month. • Surveys, such as recording the favourite song for a class item.

• •

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•

Draw your child’s attention to graphs used in the media, such as cricket scores on the television and water usage in the newspaper, and ask them questions about the graphs: “In which over did Australia score the most runs?” “What would be your estimate for the score in the first 3 overs?” “Are we using more or less water this month?” “How much less water did we use in November compared to December?” Join a local volunteer group that records items in tallies, such as counting cars and passengers or numbers of birds at a wildlife reserve. Find out if your child can keep score in their local sports team, if they are unable to play one week. Your child can keep a bar graph of their growth in height over one year.

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Book 2

Ready-Ed Publications

Progress Chart

What Can I Do? l Colour the lines in as you learn something new: Encourage your child to use their own judgement for colouring in. The first square can be coloured in straightaway. Getting some right: Approx 4/10; Getting most right: Approx 6/10 to 8/10; I can do this: Consistently getting more than 8/10 and confidently trying more complex problems

Measuring Length and Perimeter

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Starting to learn

Getting some right Getting most right

I can do this!!

Getting some right Getting most right

I can do this!!

Measuring Area

Measuring Litres and Millilitres Starting to learn

Getting some right Getting most right

Measuring Kilograms and Grams

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Starting to learn

I can do this!!

Starting to learn

Getting some right Getting most right

Looking at Calendars and Timetables

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Starting to learn

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Mapping Skills

Starting to learn

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Getting some right Getting most right

I can do this!!

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Starting to learn

I can do this!!

o c . che e r o t r s super Getting some right Getting most right

Book 2

I can do this!!

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How To Use The Following Activity Pages

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Each topic will focus on a single maths concept with a choice of two separate activity sheets. The teacher is able to introduce and explain the sheet to the whole class and then select which worksheet is assigned to each student. As both worksheets focus on the same content, only differing by the level of complexity, there is no need to isolate students by giving them separate instructions. Teachers may also choose to give all students the first sheet, and then follow up with the second sheet if the student is able to complete the first with minimal difficulties. Some topics in this book have 3 or 4 sheets. These should be completed in sequential order. Note: Although the second worksheet is designed for the more “able” students in the classroom, this certainly does not discount students with learning difficulties. Research shows that many students with Specific Learning Difficulties can work at an average to above average level, provided that their needs are taken into consideration. With this in mind, both worksheets have been designed so that ALL students have the opportunity to be extended.

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Book 2

Ready-Ed Publications

Learning Outcome: Students will calculate perimeter by adding the length of all sides of an object.

Name:

Measuring Perimeter 1 Perimeter is the distance around an object. l Look at this shape:

6 cm 3 cm

3 cm

To work out the perimeter, add up all the sides.

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3 + 3 + 3 + 3 + 6 + 6 = 24cm

3 cm

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6 cm

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l Work out the perimeter of these shapes by measuring with your ruler.

_____ + _____ + _____ = _____ mm

_____ _____ +l _____ _____ _____ mm © ReadyEd+P ub i ca+t i on=s •f orr evi ew pur posesonl y•

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_____ + _____ + _____ + _____ = _____ mm

o c . c e he r l Look at how the missing parts are figured out and then work out the o t r s s uper perimeter. Hint: The top and bottom are equal, the sides are equal. 4 km

5 km

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_____ + _____ + _____ + _____ = _____ km

Book 2

Page 21

Learning Outcome: Students will calculate perimeter by working out the length of all sides of an object and adding these together.

Name:

Measuring Perimeter 2 Perimeter is the distance around an object. l Look at how the missing parts are figured out and then work out the perimeter: 5 + 2 = 7 km

8 km

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8 km

5 km

2 km

5 km

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2 km

_______ + _______ + _______ + _______ = _______ km

l Use the same idea to work out the perimeter of the shapes below. 10 km

6 km

2 km

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______ + ______ + ______ + ______ + ______ + ______ = ______ km

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4 km

2 cm

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4 cm

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______ + ______ + ______ +_______ + ______ + ______ = ______ cm

2 cm

8 cm 4 cm 2 cm

_______ + _______ + _______ + _______ = _______ cm

6 cm Page 22

Book 2

Ready-Ed Publications

Learning Outcome: Students will work out the area of the shapes in a grid by counting the number of squares for each shape.

Name:

Area 1 Here is one square cm (1cm²). Area is the amount of space taken up on a flat surface. 1cm²

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l Work out the area of the shapes in this grid by counting the number of squares for each shape.

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Some shapes have half squares. Add two half squares to make a whole one.

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o c . e Which shape has thec biggest area? A B C her r o t sB C su Aer Which shape has the smallest area? p A: ______ cm²

B: ______ cm²

C: ______ cm²

On the grid, draw a rectangle that has an area of 12 cm².

l Challenge: Draw a triangle that has an area of about 9 cm².

Ready-Ed Publications

Book 2

Page 23

Learning Outcome: Students will use the formula Area = Length x Width to work out the area of squares and rectangles.

Name:

Area Calculation 1 Area of a square or rectangle can be worked out by using: Area = Length × Width

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l Use the formula to work out the area of these shapes.

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5 cm

8 cm

6 cm 4 cm

Area =l _____ ×t _____ =s _____ cm² © ReadyEdP ub i ca i on 7 cm •f orr evi ew pur posesonl y•

5 = _____ 20 cm² 4 Area = _____ × _____

6 cm

3 cm

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2 cm

Area = _____ × _____ = _____ cm²

. te o c l Measure these shapes and then work out the area to the nearest mm². . che e r o t r s super _____ mm

_____ mm

Area = _____ × _____ = _____ mm² Page 24

Area = _____ × _____ = _____ mm² Book 2

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Learning Outcome: Students will recognise how two or more rectangles can be “broken up” and then use the formula Area = Length x Width to work out the area of each.

Name:

Area Calculation 2 Area of a square or rectangle can be worked out by using: Area = Length × Width

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l Shapes that combine two or more rectangles can be “broken up” and then use the formula to work out the area. Area 2

Area 1 = _____ × _____ = _____ cm²

3 cm

2 cm

Area 1

Total area (add two areas) = _____ + _____ = _____ cm²

4 cm

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Area 2 = _____ × _____ = _____ cm²

4 cm

l Try these.

3 cm

Area 1

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Area 1 = _____ × _____ = _____ cm²

2 cm

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4 cm

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Total area (add two areas) = _____ + _____ = _____ cm²

4 cm

1 cm

3 cm

Area 2 = _____ × _____ = _____ cm²

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2 cm

3 cm

6 cm

Area 1 = _____ × _____ = _____ cm² Area 2 = _____ × _____ = _____ cm²

3 cm

Total area (add two areas) = _____ + _____ = _____ cm²

3 cm

4 cm

Ready-Ed Publications

Book 2

Page 25

Learning Outcome: Students will use the formula Area = Length x Width ÷ 2 to find out the area of a triangle.

Name:

Area of a TTriangle riangle 1 Area of a triangle can be worked out by using:

You divide the square formula in half because a triangle is HALF a square.

Area = Length × Height ÷ 2

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l Finish this question to find out the area of the triangle.

3 cm

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Area = _____ 4 × _____ 3 = _____ 12 cm²

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Divide by 2 (you may use a calculator) = _____ cm²

4 cm

l Now try these. Area = _____ × _____ = _____ cm²

3 cm

Divide by 2 = _____ cm²

Area = _____ × _____ = _____ cm² Divide by 2 = _____ cm²

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4 cm

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7 cm

o c . Divide by 2 = _____ cm² che e r o t r s super 12 cm

Area = _____ × _____ = _____ cm²

10 cm

l Measure this triangle to the nearest mm and work out the area on your calculator. height

Area = _____ × _____ = _____ mm² Divide by 2 = _____ mm² length Page 26

Book 2

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Learning Outcome: Students will use the formula Area = Length x Width ÷ 2 to find out the area of a triangle.

Name:

Area of a TTriangle riangle 2 Area of a triangle can be worked out by using: Area = Length × Height ÷ 2

You divide the square formula in half because a triangle is HALF a square!

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l Finish this question to find out the area of the triangle. A = _____ 3 = _____ 12 cm² 4 × _____

3 cm

4 cm

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Teac he r

Divide by 2 (you may use a calculator) = _____ cm²

l Measure these triangles to the nearest mm and work out the area on your calculator.

A = _____ × _____ = _____ ÷ 2 = _____ mm²

height

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l Now try writing the formula on your own and work out the area of these triangles.

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height

length

height length length

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height

Book 2

Page 27

Learning Outcome: Students will use the formula C = 3 x D to work out the circumference for a given circle.

Name:

Circumference 1 Circumference is the distance around the outside of a circle (in other words, the perimeter of a circle). mferen ce rc u i C l Look at this circle to learn the parts.

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Circumference (C) = the distance around the circle.

Diameter

Diameter (D) = the length from one side to the other.

Not this:

Rule: Circumference is about 3 × D

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Diameter passes exactly though the centre of the circle.

l Using the formula C = 3 × D, work out the circumference for these circles.

7 cm

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4 cm

C = 3 × _____ = _____ cm

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o c . che e r o t r s s r u e p C = 3 × _____ = _____ cm C = 3 × _____ = _____ cm 50 cm

3 cm

27 cm

This is half the diameter, called the radius.

What would the full diameter be?

C = 3 × _____ = _____ cm Page 28

5 cm

C = 3 × _____ = _____ cm Book 2

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Name:

Learning Outcome: Students will use the formula C = 3.14 x D to work out the circumference for these circles on the calculator.

Circumference 2 Circumference (C) = the distance around the outside of a circle. Diameter (D) = the length from one side to the other. Diameter passes exactly though the centre of the circle.

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You may have learned that C = 3 × D. Now you will be working with more exact numbers. A special number, called pi (say “pie”), is the number that multiplies by the D to give the C. and is equal to about 3.14.

Rule: C = π × D or 3.14 × D

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Pi is shown on your calculator like this:

l Using the formula C = 3.14 × D, work out the circumference for these circles on your calculator.

7 cm

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3 cm

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C = _______ × _____ = _______ cm

Make sure you double the radius to find the diameter.

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C = 3.14 × _____ = _______ cm

20 cm

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C = _______ × _____ = _______ cm

l Measure the diameter to the nearest mm and work out the circumference.

C = _______ × _____ = _______ mm Ready-Ed Publications

C = _______ × _____ = _______ mm Book 2

Page 29

Learning Outcome: Students will order everyday amounts of liquid from the least to the most amount of liquid and using the equation 1 L (litre) = 1000 mL (millilitres), write the conversions for given amounts.

Name:

Litres and Millilitres 1 Liquids are usually measured in litres (L), such as 1L cartons of milk, or in mL, such as a 375 mL can of soft drink.

___________

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___________

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l Order these from the least to the most amount of liquid by writing numbers 1 - 5 underneath.

___________

= 5000 mL

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l Write the conversions for these amounts.

10L = ________ mL

. te o c 0.5L = ________ mL . che e r o t r s super 3.5L = ________ mL

l Add up these amounts of liquid.

2 mL + 8 mL + 25 mL = ________ mL 160 mL + 320 mL + 400 mL = ________ mL 500 mL + 225 mL + 600 mL = ________ mL l Place a tick next to the one that equals more than 1L (1000 mL). Page 30

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Learning Outcome: Students will order everyday amounts of liquid from the least to the most amount of liquid and using the equation 1L (litre) = 1000 mL (millilitres), write the conversions for given amounts.

Name:

Litres and Millilitres 2 Rule: 1L (litre) = 1000 mL (millilitres) A regular carton of milk is 1L, a cup of water is 250 mL, 1 teaspoon is 5 mL. Write an estimate for these things.

___________

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

___________

= ________ mL

= ________ L

3.75L = ________ mL

10 mL

= ________ L

0.05L = ________ mL

4000 mL = ________ L

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365 mL

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l Add up these amounts of liquid and convert to litres.

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15L

___________

l Write the conversions for these amounts. 5L

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Choose from these measures: 375 mL; 1 L; 500 mL; 250 mL; 50 mL; 2 L.

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230 mL + 800 mL + 250 mL = ________ mL = ________ L 460 mL + 320 mL + 500 mL = ________ mL = ________ L

800 mL + 325 mL + 1 200 mL = ________ mL = ________ L

l Some of these measurements are in mL, some are in L. Make them all into mL and then add them up, then convert the final amount to L. 5 mL + 25 mL + 0.5 L + 1 L = 5 + 25 + 500 + 1000 = 1530 mL = 1.53 L 10 mL + 0.25 L + 2000 mL + 3 L = _______________________ = ________ mL = ________ L 15 mL + 0.05 L + 300 mL + 2 L = ________________________ = ________ mL = ________ L Ready-Ed Publications

Book 2

Page 31

Learning Outcome: Students will order everyday amounts of mass from the least to the most amount of mass and using the equation 1 kg) = 1000g, write the conversions for given amounts.

Name:

Kilograms and Grams 1 The proper name for weight is mass. Mass is measured in kilograms (kg), such as with people, or grams (g), such as with packages of food.

___________

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___________

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l Order these from the least to the most by writing numbers 1 - 5 underneath.

___________

= 8000 g

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8 kg

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l Write the conversions for these amounts.

12 kg = ________ g

. te o c 0.6 kg = ________ g . che e r o t r s super 6.4 kg = ________ g

l Add up these masses.

3 g + 5 g + 18 g = ________ g 475 g + 180 g + 300 g = ________ g 700 g + 187 g + 698 g = ________ g l Place a tick next to the one that equals more than 1 kg (1000g). Page 32

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Learning Outcome: Students will estimate everyday amounts of mass from given examples and using the equation 1 kg) = 1000g, write the conversions for given amounts.

Name:

Kilograms and Grams 2 Rule: 1L (litre) = 1000 mL (millilitres)

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250 g

5 kg

20 kg

900 g

5 kg

35 kg

100 kg

500 g

1 kg

5 kg

40 kg

13 g

100 g

1 kg

6 kg

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A medium bag of carrots weighs about 1 kg and an 11-year-old child can weigh about 36 kg. Circle your estimate for these things.

l Write the conversions for these amounts.

17 kg

= ________ g

4300 g = ________ kg = ________ kg

0.03 kg = ________ g

500 g

= ________ kg

. te

l Add up these amounts and convert to kilograms.

m . u

25 g

w ww

5.98 kg = ________ g

o c . che e r o t r s super

570 g + 400 g + 350 g = ________ g = ________ kg 382 g + 506 g + 230 g = ________ g = ________ kg

420 g + 222 g + 1500 g = ________ g = ________ kg

l Some of these measurements are in g, some are in kg. Make them all into g, add them up, and then convert the final amount to kg. e.g. 2 g + 10 g + 0.6 kg + 2 kg = 2 + 10 + 600 + 2000 = 2612 g = 2.612 kg 15 g + 0.75 kg + 5000 g + 2 kg =_________________________ = ________ g = ________ kg 12 g + 0.04 g + 200 g + 5 kg = __________________________ = ________ g = ________ kg Ready-Ed Publications

Book 2

Page 33

Name:

Learning Outcome: Students will count the number of cubes inside the length, width and height of given shapes, and multiply them for the volume.

Volume 1 Volume is the amount of space taken up inside a container, such as the space inside a removalist’s truck. Volume of an object can be worked out by counting the number of cm cubes that can fit inside it.

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

If you can’t see all the cubes in a shape, an easy way of counting them is to multiply the number of cubes going lengthways, widthways and in height.

ew i ev Pr

Teac he r

Rule: Cube Length × Cube Width × Cube Height

l Count the number of cubes for the length, width and height of these shapes, and multiply them for the volume. This unit is measured in cm3 because you are multiplying 3 dimensions (length, width and height).

w ww

2 cm

. te

m 2c

7 cm

m 3c

m . u

4 cm

o c . che e r o t r s super

Volume = _____ × _____ × _____ = _____ cm³

3 cm

m 5c 3 cm

Volume = _____ × _____ × _____ = _____ cm³ Page 34

Book 2

Ready-Ed Publications

Name:

Learning Outcome: Students will use the formula Volume = Length x Width x Height with a calculator to work out the volume of drawn shapes.

Volume 2 Volume is the amount of space taken up inside a container, such as the space inside a removalist’s truck. Volume of a square or rectangular-based object can be worked out by using:

r o e t s Bo r e p ok u S Volume = Length × Width × Height

Teac he r

Volume is expressed in cubic units, e.g. 10 cm³, because there are three dimensions being measured.

8 cm

ew i ev Pr

l Use the formula and your calculator to work out the volume of these shapes.

Volume = ______ × ______ × ______ = ______ cm³

4 cm

w ww

2 cm

. te

m . u

5 cm

o c . che e r o t r s super 2 cm

8 cm

Volume = ______ × ______ × ______ = ______ cm³

l Measure this shape and then work out the volume to the nearest mm³.

height

Volume = ______ × ______ × ______ = ______ cm³ width length

Ready-Ed Publications

Book 2

Page 35

Name:

What’s the Time? Help Sheet Here are some examples of times after 2:00.

Teac he r

Time Digital Time 5 past 2 2:05 10 past 2 2:10 Quarter past 2 2:15 20 past 2 2:20 25 past 2 2:25 Half past 2 2:30 25 to 3 2:35 20 to 3 2:40 Quarter to 3 2:45 10 to 3 2:50 5 to 3 2:55 3 o’clock 3:00

Examples 2:15

Examples 2:30

r o e t s Bo r e p ok u S 11

9 8

4 7

1 2 3

9 8

4 7

3:00

2:45

ew i ev Pr

Big Hand 1 2 3 4 5 6 7 8 9 10 11 12

We can also tell the time in seconds.

1 2

w ww

3 4

. te 6

10 9

3 4

8 7

Three forty seven and thirty five seconds

o c . oh eight and thirty che 11:08:31 Elevenone e r seconds o t r s super

1 2

9 8

1:57:05

4 7

Page 36

3:47:35

m . u

One fifty seven and five seconds

Book 2

Ready-Ed Publications

Name:

Learning Outcome: Students will tell the time on clock faces to the nearest minute and express in digital form.

What’s the Time? 1 l Tell the time on these clocks to the nearest minute. 12

11 2

9 8

4 7

Teac he r

8 6

4 7

1 2 3

9 8

4 7

8: 11

4 7

. te 3

9 8

4 6

Ready-Ed Publications

4 6

11 2

9 8

4 7

Book 2

2 3

4 7

o c . che e r o t r s super 2

w ww 12

8 7

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

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3:07 11

m . u

4 6

1 2

10 9

4 7

Page 37

Name:

Learning Outcome: Students will tell the time on clock faces to the nearest second and express in digital and written form.

What’s the Time? 2 l Tell the time on these clocks to the nearest second. Clock 12

Time 1

Digital Time

r o e t s Bo r e p ok u S 2

10 9

3:05:27

5 past 3 and 27 seconds

ew i ev Pr

Teac he r

2 3

w ww

m . u

. te

o c . che e r o t r s super

l Draw the time on these clocks. 4:45:25

8 6

1 2 3

9 8

4 7

11 10

Page 38

9:05:55

4 7

Book 2

Ready-Ed Publications

Learning Outcome: Students will use simple formulas (multiplication) to convert from minutes to seconds, hours to minutes and days to hours (using calculators for more difficult calculations).

Name:

What’s the Time? 3 Remember: 60 seconds = 1 minute 60 minutes = 1 hour

r o e t s Bo r e p ok u S 24 hours = 1 day

l Convert from minutes to seconds. (Multiply by 60.)

5 min = _______ seconds

8 min = _______ seconds 2 min = _______ seconds 4 min 5 seconds

ew i ev Pr

Teac he r

3 min = (3 × 60 = 180 or 3 × 6 = 18 with 0 on the end) = 180 seconds

= (4 × 60 = 240 + 5 = 245) = 245 seconds

w ww

m . u

l Convert from hours to minutes. 2 hours = (2 × 60) = _______ min

. t= _______ min o 7 hours 56 mine c . che e r o t r s super l Convert from days to hours. (You may use a calculator.) 4 hours 5 min = (4 × 60 = _______ + 5 = _______ ) = _______ min

3 days = (3 × 24) = _______ hours 4 days 8 hours = (4 × 24 = _______ + 8 = _______ ) = _______ hours

Ready-Ed Publications

Book 2

Page 39

Learning Outcome: Students will convert from minutes to seconds, from seconds to minutes and seconds and from minutes to hours and minutes using conversion procedures such as division or multiplication.

Name:

What’s the Time? 4 Remember: 60 seconds = 1 minute 60 minutes = 1 hour

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

l Convert from minutes to seconds.

= (4 × 60 = 240 + 5 = 245) = 245 seconds

6 min 49 seconds = _______ seconds

ew i ev Pr

Teac he r

4 min 5 seconds

l Convert from seconds to minutes and seconds, e.g. for 230 seconds.

Count by 60 (like counting by 6 with a 0 on the end) until you reach the largest number under 230:

This gives you 180 seconds.

w ww

m . u

How many more seconds do you need to reach 230 seconds? (230 – 180) You need 50 more seconds.

. te

Answer = 3 min 50 seconds.

o c . ch l Convert from minutes to hours and minutes, e.g. for 560e minutes. r e o t r s s r p8e 5 × 60 = 300; 6 × 60 = 360; 7 × 60 =u 420; × 60 = 480; 9 × 60 = _______; How many more minutes do you need to reach 560 minutes? (560 – _______ = _______ ) You need _______ more minutes. Answer = _______ hours _______ minutes Page 40

Book 2

Ready-Ed Publications

Learning Outcome: Students will estimate the time taken to perform everyday tasks, to the nearest second or minute.

Name:

What’s the Time? Estimates l Circle the best estimate for these times. [ Brushing your teeth 2 minutes

10 seconds

8 minutes

1 hour

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

[ Counting the students in your class 4 seconds

1 minute

3 minutes

17 seconds

8 minutes

14 minutes

6 hours

9 hours

30 seconds

3 minutes

[ Time spent at school in one day 5 hours

8 hours

l Write your best estimate for these times.

ew i ev Pr

Teac he r

[ One song on the radio

Eating breakfast = ______ minutes

w ww

m . u

Watching a movie = __________ Making a cake = ___________

. tethen time yourself doing the following, using a clock o l Estimate and with a c . second hand or ac stopwatch. Look at the example. e her r o t s Estimate Real Time r upe Activity Estimate Reals Time Activity Clap 100 times

40 secs

32 secs

Recite the alphabet

Tie both shoelaces

Make your bed

Wash your hands

Count the words on this page

Ready-Ed Publications

Book 2

Page 41

Name:

Learning Outcome: Students will use calendars to answer simple questions about time between certain days, and periods of time within the month.

Looking at Calendars 1 l Use this calendar to answer the questions underneath. January

February

March

April

S M TW T F S

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

1 2 3 4 5 6 7 9 16 23 30

10 11 12 13 14 17 18 19 20 21 24 25 26 27 28 31

May

S M TW T F S

7 14 21 28

1 8 15 22 29

2 9 16 23 30

3 10 17 24 31

4 11 18 25

5 12 19 26

6 13 20 27

5 12 19 26

6 13 20 27

7 8 9 10 11 14 15 16 17 18 21 22 23 24 25 28

1 2 3 4

5 12 19 26

6 13 20 27

7 14 21 28

8 15 22 29

9 16 23 30

10 11 17 18 24 25 31

June

July

S M TW T F S

4 11 18 25

5 12 19 26

6 13 20 27

7 14 21 28

1 8 15 22 29

2 9 16 23 30

3 10 17 24

1 2 9 16 23 30

3 10 17 24 31

4 11 18 25

5 12 19 26

6 13 20 27

7 14 21 28

8 15 22 29

2 9 16 23 30

3 10 17 24

1 4 11 18 25

5 12 19 26

6 13 20 27

7 14 21 28

8 15 22 29

ew i ev Pr

Teac he r

8 15 22 29

1 2 3 4

August

S M TW T F S 6 13 20 27

7 14 21 28

1 8 15 22 29

2 9 16 23 30

3 10 17 24 31

4 11 18 25

5 12 19 26

6 13 20 27

7 14 21 28

2 9 16 23 30

1 8 15 22 29

2 9 16 23 30

3 10 17 24 31

4 11 18 25

5 12 19 26

6 13 20 27

7 14 21 28

5 12 19 26

6 13 20 27

7 14 21 28

1 8 15 22 29

2 9 16 23 30

3 10 17 24

4 11 18 25

. te

3 10 17 24 31

4 11 18 25

5 12 19 26

6 13 20 27

7 14 21 28

1 8 15 22 29

m . u

4 11 18 25

w ww

3 10 17 24

1 8 15 22 29

2 9 16 23 30

o c . cish Circle October 13. What the date two weeks later? _____________________ e r e o t r s s r upe How long between February 3 and February 26? _______ weeks _______ days. What is the date of the third Sunday in November? _______________________

Joe’s birthday is March 6. Jan’s birthday is November 29. Between these two dates there are ____ months, ____ weeks and ____ days. Circle and label 5 special days on this calendar.

Page 42

Book 2

Ready-Ed Publications

Name:

Learning Outcome: Students will use calendars to answer simple questions about time between certain days, and periods of time within the month.

Looking at Calendars 2 l Use this calendar to answer the questions underneath. January

February

March

S M TW T F S

1 8 15 22 29

1 5 6 7 8 12 13 14 15 19 20 21 22 26 27 28

3 10 17 24 31

4 11 18 25

5 12 19 26

6 13 20 27

7 14 21 28

3 10 17 24 31

4 11 18 25

5 12 19 26

4 11 18 25

S M TW T F S 5 12 19 26

6 13 20 27

June

S M TW T F S 2 9 16 23 30

3 10 17 24

1 8 15 22 29

2 9 16 23 30

3 10 17 24 31

4 11 18 25

S M TW T F S

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

May

1 8 15 22 29

2 9 16 23

6 13 20 27

July

S M TW T F S 4 11 18 25

5 12 19 26

6 13 20 27

7 14 21 28

1 8 15 22 29

7 14 21 28

2 9 16 23 30

3 10 17 24

S M TW T F S 2 9 16 23 30

3 10 17 24 31

4 11 18 25

5 12 19 26

6 13 20 27

7 14 21 28

1 8 15 22 29

2 9 16 23 30

3 10 17 24

4 11 18 25

5 12 19 26

6 13 20 27

7 14 21 28

1 8 15 22 29

August

ew i ev Pr

Teac he r

2 9 16 23 30

April

S M TW T F S 6 13 20 27

7 14 21 28

1 8 15 22 29

2 9 16 23 30

3 10 17 24 31

4 11 18 25

5 12 19 26

6 13 20 27

7 14 21 28

8 15 22 29

9 16 23 30

. te

9 16 23 30

10 11 12 13 14 17 18 19 20 21 24 25 26 27 28 31

5 12 19 26

6 13 20 27

7 14 21 28

1 8 15 22 29

2 9 16 23 30

3 10 17 24

4 11 18 25

1 2

3 10 17 24 31

4 11 18 25

5 12 19 26

6 13 20 27

7 14 21 28

8 15 22 29

9 16 23 30

m . u

4 11 18 25

1 2 3 4 5 6 7

w ww

3 10 17 24

1 2

What is the date of the fourth Wednesday in September? ________________

o c . che e r o t r s super

Circle Christmas Day. What is the date two weeks later? ________________ How long between April 4 and June 8? _______ weeks _______ days Write your birthday ________________

Write a parent’s birthday ________________

Between these two dates there are _______ months, _______ weeks and _______ days. Using this calendar, on what day of the week is: Christmas Day? ______________________________________________ Australia Day? _______________________________________________ The first day of spring? ________________________________________ Ready-Ed Publications

Book 2

Page 43

Name:

Learning Outcome: Students will use a simple timetable, such as a performance schedule, to answer questions relating to performance times.

Looking at Timetables 1 l Here are some examples to help with reading timetables. 9:00 am

9:30 am

10:00 10:30 11:00 11:30 12:00 12:30 am am am am pm pm

1:00 pm

1:30 pm

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

Remember am = morning

pm = afternoon or evening

15 minutes = quarter of an hour

Teac he r

30 minutes = half an hour

ew i ev Pr

60 minutes = 1 hour

l Here is the program for the school fete. Use it to answer the questions. Event

Times

What is the last event before closing?

Sally’s dancing 10:05 - 10:30 am troupe 1:05 - 1:30 pm Spun every hour, on the hour

w ww

Auction

Raffle draw

Pet parade

2:30 - 3:00 pm

Close Page 44

Ann is in the choir and in the dancing troupe. Can she do all the performances?

11:15 am and . 4:00 pm te If you watch the karate demonstration, o how much of the first dance performance c . e 11:00 c - 11:30 heamr do you miss?st r super o

Karate 10:00 - 10:15 pm demonstration School choir

m . u

Chocolate Wheel

9:30 - 10:00 am 3:30 - 4:00 pm

How long do most events last for?

If a student takes their pet in the parade, which raffle draw should they enter?

5:00 pm Book 2

Ready-Ed Publications

Learning Outcome: Students will use a simple timetable, such as a bus timetable, to answer questions relating to travel time.

Name:

Looking at Timetables 2 l Here are some examples to help with reading timetables. 9:00 am

9:30 am

10:00 am

10:30 am

11:00 am

11:30 am

12:00 pm

12:30 pm

1:00 pm

1:30 pm

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

Remember am = morning

pm = afternoon or evening

15 minutes = quarter of an hour 30 minutes = half an hour

Depart City

Smart Street

Rush Road

Mill Street

8:30 am

8:46

8:50

9:05

10:00 am

10:13

10:17

10:32

12:00 pm

12:13

12:17

12:32

ew i ev Pr

Teac he r

60 minutes = 1 hour

Sunset Beach 9:13 am

10:40 am 12:40 pm

4:02

9:30 am

9:38

9:53

9:57

10:10 am

11:00 am

11:08

11:23

11:27

11:40 am

1:30 pm

1:38

1:53

1:57

5:00 pm

5:08

5:23

5:27

. te

4:10 pm

m . u

3:43

w ww

3:30 pm

2:10 pm 5:40 pm

o c . che e r o t r s super

How long does the 8:30 am trip from the city take to Sunset Beach? How long do all of the other trips take?

Why do you think there is a difference?

If I leave the city at 10:00 am and I want to spend at least 2 hours at the beach, what time do I go back to the city? If I travel from the city to Mill St at 10:00 am, and then catch a bus from Mill St to Smart St at 1:38 pm, how many minutes do I spend travelling in total?

Ready-Ed Publications

Book 2

Page 45

Learning Outcome: Students will fill in a timetable for a day’s activities, including time for travelling between places, and lunch breaks.

Name:

Looking at Timetables 3 l Fill in this timetable for a day out with visitors to your city or town. Make sure you include time for travelling between places, and allow an hour for lunch. Time

Activity

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

ew i ev Pr

Teac he r

9:00 am -

w ww

. te

6:00 pm

m . u

12:00 pm - 1:00 pm

o c . che e r o t r s super Arrive Home

What activity did you do for the longest? _______________________________ What took you the shortest time? _____________________________________ How much travel time in total did you use? ______________________________ Page 46

Book 2

Ready-Ed Publications

Name:

Learning Outcome: Students will demonstrate understanding of range, mode, mean and median by completing simple steps in an explanation of these concepts.

Range, Mode, Median and Mean 1 l Finish this tally chart. Day of Week

Hours Slept

Monday

IIII III

Tuesday

Total

r o e t s Bo r e p ok u S 11

Wednesday

IIII IIII

Friday

Saturday

IIII IIII I

Sunday

IIII III

Tuesday Wednesday Thursday Friday Saturday Sunday © R e a d y E d P u b l i c a t i o ns 8 11 8 10 7 11 •f orr evi ew pur posesonl y•

Monday 8

IIII = 5

ew i ev Pr

Teac he r

Thursday

Remember:

Highest = 11 Lowest = 7

Range = 11 – 7 = ______ hours

w ww

Mode = The amount or score that appears the most often.

m . u

Range = The difference between the lowest and highest amounts.

. te o Mode = ______ hours c . che e r o t r su per Mean = Also called average. Total of amounts ÷s Number of amounts

The number of hours that appears most often is ______ hours.

Total of amounts = 8 + 11 + 8 + 10 + 7 + 11 + 8 = 61

Number of amounts = 7

Mean = 63 ÷ 7 = ______ hours Median = The middle amount. Write amounts in order and find the middle one. 7

Ready-Ed Publications

11 Book 2

Median = ______ hours Page 47

Learning Outcome: Students will demonstrate understanding of range, mode, mean and median by completing simple steps in an explanation of these concepts, i.e. working out the answer for each given a set of scores.

Name:

Range, Mode, Median and Mean 2 l Year Seven Spelling Test Scores (out of 40) 28

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

Range = The difference between the lowest and highest score. Lowest = _______

Range = _______ – _______ = _______

ew i ev Pr

Teac he r

Highest = _______

Mode = The amount or score that appears the most often. The score that appears most often is _______ Mode = _______ Mean = Also called average. Total of scores ÷ Number of scores.

© ReadyEdPubl i cat i ons Number of scores (number of students that took the test) = _______ •f orr evi ew pur posesonl y• Mean = _______ ÷ _______ = _________ (round the decimal places up or down) Total of scores (add up all scores on the calculator) = _______

w ww

m . u

Median = The middle amount. Write amounts in order and find the middle one.

19, 20, 21, 22, 23, 25, 26, 27, 28, 28, 29, 29, 30, 31, 32, 32, 33, 34,

34,

. te 34,

Median = _______

34,

35,

36,

37,

38,

39,

40,

o c . che e r o t r s super

There are two middle scores when the number of scores is even. If they are both the same, you can say that the median is that number. If they are different, you need to find the average, or the number in between these two numbers. For example: 13, Median = 17, _______ , 19

Page 48

14,

16,

17,

19,

20,

22,

25:

Median = _______

Book 2

Ready-Ed Publications

Name:

Learning Outcome: Students will interpret simple bar graphs and line graphs by answering questions pertaining to highest, lowest, range and total, etc.

Bar Graphs and Line Graphs 1 Bar Graphs A bar graph usually shows amounts that belong to different groups, e.g. a number of children (see below). It lets you compare how they performed. Number of Runs in a Cricket Game

r o e t s Bo r e p ok u S 9

_______ runs

_______ – _______ = _______ runs

What was the total number of runs for this team? _______ runs

7 6

ew i ev Pr

Teac he r

What is the range of run scores?

Number of Cricket Runs

What was the highest run score?

5 4 3 2

m . u

w ww

Line Graphs A line graph usually shows how something changes over time. In the example below information about the height of a plant can be plotted. Plant Growth Over Six Weeks

. te o measured? _______ cm c . che e r o t r s super Between which two weeks did the 7

At what height was the plant first

Height cm

plant grow the most?

5 4 3

Week _______ and Week _______ 2 1

Draw what you think the rest of the graph would look like.

1 Ready-Ed Publications

Book 2

3 4 Week

Page 49

Name:

Learning Outcome: Students will interpret simple bar graphs and line graphs by answering questions pertaining to highest, lowest, range and total, etc.

Bar Graphs and Line Graphs 2 Bar Graphs A bar graph usually shows amounts that belong to different groups, e.g. a number of children (see below). In this case it lets you compare the number of tickets students sold. 35

Number of Raffle Tickets Sold by Students

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

Who sold the most tickets? _______________ What was the range of tickets sold?

Teac he r

_______ – _______ = _______ tickets

What was the total number of all tickets sold? _______ tickets

25 20 15 10 5

What was the mean (average number of tickets) sold? _______ ÷ _______ = _______ tickets

Bill

ew i ev Pr

Number of Tickets Sold

Fred Sally Sam Children

Line Graphs A line graph usually shows how something changes over a given time. In the example below information about water usage over a week can be plotted. On what day was the most water used?

Water Usage Per Week

_______________

w ww

600 550

What was the mean amount of water

. te

500

used this week? _______________

watered the garden? _____________ Could you predict how the rest of

Why / why not?

Water Usage (Litres)

o c . che e r o t r s super

On what days do you think the family

the graph looks? _______

m . u

650

450 400 350 300 250 200 150 100

50 Mon

Page 50

Book 2

Tues

Wed Thurs Fri Days of the Week

Sat

Sun

Ready-Ed Publications

Name:

Learning Outcome: Students will interpret simple Venn diagrams by answering simple questions and use a set of data to draw a simple Venn diagram with two categories.

Venn Diagrams 1 A Venn diagram can show information that overlaps, e.g. students that like red apples, students that like green apples, and students that like both. l Count the number of stars.

Preferred Apples of Students

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

How many like red only? ______

Both

How many like both colours? ______

Green

l Use this data to draw your own Venn diagram. Students in the class with brothers or sisters

ew i ev Pr

Teac he r

How many do not like apples? ______

Red

Neither

w ww

. te

Both

m . u

o c . che e r o t r s super

1 or More Brothers

1 or More Sisters Neither

Ready-Ed Publications

Book 2

Page 51

Name:

Learning Outcome: Students will interpret simple Venn diagrams by answering simple questions and use a set of data to draw a simple Venn diagram with three categories.

Venn Diagrams 2 A Venn diagram can show information that overlaps.

Preferred Sports of Students

How many like swimming only? _______

Both

How many like swimming altogether? (number who like only swimming plus

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

number who like both) _______

How many like both activities? _______

Swimming

How many people were surveyed altogether? _______

l Use this data to draw your own Venn diagram. Cat 34

Dog

Fish

Cat & Fish

Dog & Fish

Cat & Dog

Cycling Neither

ew i ev Pr

Teac he r

How many do not like these activities? _______

All Three

None

w ww

. te

m . u

Title: ____________________________________________

o c . che e r o t r s super

l On the back of this sheet, think of some questions about this Venn Diagram, and then write the answers. Page 52

Book 2

Ready-Ed Publications

ANSWERS

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

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N.B. Measurements will vary due to effects of printing and photocopying. Page 21 - Measuring Perimeter 1 Measurements should be accurate to within a few mm: 60mm, 100mm, 100mm, 80mm; Parallelogram at the bottom is 18 km in perimeter. Page 22 - Measuring Perimeter 2 30 km, 32 km, 28 cm, 14 cm Page 23 - Area 1 A = 10 cm², B = 13 ½ cm², C = 12 cm²; Biggest = B, Smallest = A Check shapes by counting number of squares. Page 24 - Area Calculation 1 21 cm², 48 cm², 12 cm² Check area measurement (200mm²; 80mm²). Page 25 - Area Calculation 2 Area 1 = 12 cm², Area 2 = 4 cm², Total Area = 16 cm²; Area 1 = 12 cm², Area 2 = 16 cm², Total Area = 28 cm²; Area 1 = 6 cm², Area 2 = 3 cm², Total Area = 9 cm²; Area 1 = 18 cm², Area 2 = 12 cm², Total Area = 30 cm² Page 26 - Area of a Triangle 1 6 cm², Areas of triangles are: 7.5 cm², 14 cm², 60 cm², Check measurements & subsequent calculation (80mm²). Page 27 - Area of a Triangle 2 6 cm², Check measurements and subsequent calculation of other triangles. (80mm², 45mm², 30mm², 10mm².) Page 28 - Circumference 1 3 × 4 = 12cm, 3 × 7 = 21 cm, 3 × 50 = 150 cm, 3 × 27 = 81 cm, 3 × 6 = 18cm, 3 × 10 = 30cm Page 29 - Circumference 2 3.14 × 7 = 21.98 cm, 3.14 × 4 = 12.56 cm, 3.14 × 6 = 18.84 cm, 3.14 × 40 = 125.60 cm; (94.2, 62.8) Check measurements and calculations for other circles. Page 30 - Litres and Millilitres 1 1 = medicine cup, 2 = small juice carton, 3 = can, 4 = milk, 5 = soft drink bottle. 10L = 10 000mL, 3.5L = 3 500mL, 0.5 L = 500mL; 35mL, 880mL, 1325mL (this one is more than 1L) Page 31 - Litres and Millilitres 2 Medicine cup = 50 mL, small juice carton = 250 mL, can = 375 mL, milk = 1L, bottle = 2L. Conversions: 15L = 15 000 mL; 3.75L = 3750 mL; 0.05L = 50 mL; 365 mL = 0.365L; 10 mL = 0.01L; 4000 mL=4L. 1280 mL = 1.28L; 1280 mL = 1.28L; 2325 mL = 2.325L. 10 + 250 + 2000 + 3000 = 5260mL = 5.26L; 15 + 50 + 300 + 2000 = 2365mL = 2.365L Page 32 - Kilograms and Grams 1 1 = pencil, 2 = apple, 3 = shoes, 4 = chair, 5 = person; 12kg = 12 000g, 6.4kg = 6400g, 0.6kg = 600g; 26g, 955g, 1585g (this one is equal to more than 1kg) Page 33 - Kilograms and Grams 2 Cereal = 250g, Child = 35 kg, Stereo = 5kg, Pencil = 13g; 17kg = 17000g, 5.98kg = 5980g, 0.03kg = 30g; 4300g = 4.3kg, 25g = 0.025kg, 500g = 0.5kg; 1320g = 1.32kg; 1118g = 1.118kg; 2142g = 2.142kg. 15 + 750 + 5000 + 2000 = 7765g = 7.765kg; 12 + 0.04 + 200 + 5000 = 5212.04 g = 5.21204kg Page 34 - Volume 1 4 × 3 × 4 = 48cm³; 7 × 2 × 2 = 28 cm³, 3 × 5 × 3 = 45 cm³ Page 35 - Volume 2 5 × 4 × 8 = 160 cm³; 8 × 2 × 2 = 32 cm³; Check measurements and calculation in mm³ Page 37 - What’s the Time 1

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3:07, 4:35, 6:17, 8:49, 7:23, 1:07, 9:58, 2:21, 8:20, 11:43, 12:37, 2:01, 4:18, 10:10, 1:15, 3:36, 7:00, 5:51, 8:02, 12:39

Page 38 - What’s the Time 2 16 past 8 and 52 seconds, 8:16:32; 47 past 11 and 2 seconds, 11:47:02; 5 past 3 and 40 seconds, 3:05:40; 10 to 8 and 0 seconds Page 39 - What’s the Time 3 5 min = 300 sec, 8 min = 480 sec, 2 min = 120 sec, 3 min 24 sec = 204 sec, 2 min 45 sec = 165 sec; 2 hours = 120 min, 4 hours 5 min = 245 min, 7 hours 56 min = 476 min; 3 days = 72 hours, 4 days 8 hours = 104 hours Page 40 - What’s the Time 4 6 min 49 sec = 409 sec; 9 × 60 = 540, 560 – 540 = 20 (you need 20 more minutes) 560 min = 9 hours 20 minutes

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Page 41 - What’s the Time? Estimates Brushing teeth – 2 min, Counting the students in class – 17 seconds, One song on the radio – 3 minutes, Time spent at school each day – 6 hours; Mark all reasonable estimates as correct (examples: Walking to the office – 1 min, Having a shower = 5 min, Eating Breakfast - 5 – 10 min, Watching a movie = 2 hours, Making a cake = 40 min – 90 min. Page 42 - Looking at Calendars 1 November 19 or 19/11/0(any year), October 27 or 27/10/0(any year), 3 weeks and 2 days, 8 months, 3 weeks, 2 days. Page 43 - Looking at Calendars 2 September 27 or 27/9/0(any year), January 8, 200(any year) or 8/01/0(any year), 9 weeks and 2 days. Answers will vary. Christmas Day - Monday; Australia Day - Thursday; 1st day of spring - Friday. Page 44 - Looking at Timetables 1 Raffle Draw, 5 and a half hours, Yes, 10 minutes, half an hour, The second raffle draw. Page 45 - Looking at Timetables 2 43 minutes, 40 minutes, morning peak hour traffic in the city, 1:30 pm, 32 + 19 = 51 minutes travelling in total Page 46 - Looking at Timetables 3 Answers will vary. Check for travelling time, an hour for lunch, and appropriate allocation of time for each event. Page 47 - Range, Mode, Median & Mean 1 Day of Week Hours Slept Total Monday IIII III 8 Tuesday IIII IIII I 11 Wednesday IIII III 8 Thursday IIII IIII 10 Friday IIII II 7 Saturday IIII IIII I 11 Sunday IIII III 8 Range = 4 hours, Mode = 8 hours, Mean = 9 hours, Median = 8 hours Page 48 - Range, Mode, Median & Mean 2 Highest = 40, Lowest = 19, Range = 40 – 19 = 21; Mode = 34; Mean = 29; Median = 32; Median = 18 Page 49 - Bar Graphs & Line Graphs 1 Highest = 9 runs, Range = 9 – 1 = 8 runs, Total Number = 25 runs; First measures = 1 cm, Most growth = Week 3 and Week 4 Page 50 - Bar Graphs & Line Graphs 2 Most tickets = Jo, Range = 35 – 5 = 30 tickets, Total Number = 90 tickets, Mean = 90 / 5 = 18 tickets; Most Water = Sunday, Mean Water = 366 L (Approx.: allow for +/- 10L) , Watering days = Wednesday and Sunday, Answers for the final question will vary. Page 51 - Venn Diagrams 1 Red Only = 10, Both = 7, No apples = 4; Check diagram is accurate Page 52 - Venn Diagrams 2 Swimming Only = 14, Swimming altogether = 22, Both = 8, Neither = 4, Surveyed = 36, Check diagram is accurate and labelled

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