Maths Plus NSW SB 4 Draft Sample Pages

STUDENT BOOK

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Harry O’Brien

Greg Purcell

The Maths Plus NSW Syllabus/Australian Curriculum series, Year K to Year 6, is based on the NSW Education Standards Authority 2023 Mathematics K–6 Syllabus for the Australian Curriculum Mathematics (ACARA). Each book after Year K builds upon prior knowledge and works towards an understanding of the achievement standards for the relevant year level and beyond. Maths Plus provides students with opportunities to sequentially develop their skills and knowledge in the three strands of the Australian Curriculum Mathematics: Number, Algebra, Measurement, Space, Statistics and Probability

Series components

Student Books

Student Book features

• All pages are colour coded.

Work towards achieving the relevant outcomes by developing skills and competency in understanding mathematical structures, fluency, reasoning and problem solving.

Mentals and Homework Books

Provide concise, essential revision and consolidation activities that correspond with the concepts and units of work presented in the Student Books.

Assessment Books

Include short post-tests with a simple marking system to assess students’ skills and understanding of the concepts in the Student Books.

• Australian Curriculum Mathematics content descriptions, proficiency strand references and general capabilities appear on each page.

• The Dictionary (Years 2 to 6) features clear and simple explanations of mathematical terms and language.

Diagnostic term reviews

• Diagnostic term reviews (Years 1 to 6) assist in pinpointing students’ strengths and weaknesses, allowing intervention and re-teaching opportunities where required.

• The Find a topic page allows teachers the freedom to address particular topics and student needs as appropriate, providing essential revision and consolidation opportunities.

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Teacher Book and Teacher Dashboard

Provide access to a wealth of resources and support material:

• curricula and planning documents

• interactive teaching tools

• potential difficulties videos

• learning activities

• support and extension activities

• reflection

www.oxfordowl.com.au

Oxford Owl is the home for Oxford Primary professional resources.

• blackline masters and investigation pages

• links to Advanced Primary Maths (Years 3 to 6)

• assessment tests

• answers for student resources

MEASUREMENT AND SPACE

NSW Syllabus Outcomes

Representing numbers using place value

MA2-RN-01 Applies an understanding of place value and the role of zero to represent numbers to at least tens of thousands

MA2-RN-02 Represents and compares decimals up to 2 decimal places using place value

Additive relations

MA2-AR-01 Selects and uses mental and written strategies for addition and subtraction involving 2- and 3-digit numbers

MA2-AR-02 Completes number sentences involving addition and subtraction by finding missing values

Multiplicative relations

MA2-MR-01 Represents and uses the structure of multiplicative relations to 10 x 10 to solve problems

MA2-MR-02 Completes number sentences involving multiplication and division by finding missing values

Partitioned fractions

MA2-PF-01 Represents and compares halves, quarters, thirds and fifths as lengths on a number line and their related fractions formed by halving (eighths, sixths and tenths)

Geometric measure

MA2-GM-01 Uses grid maps and directional language to locate positions and follow routes

MA2-GM-02 Measures and estimates lengths in metres, centimetres and millimetres

MA2-GM-03 Identifies angles and classifies them by comparing to a right angle

Two-dimensional spatial structure

MA2-2DS-01 Compares two-dimensional shapes and describes their features

MA2-2DS-02 Performs transformations by combining and splitting two-dimensional shapes

MA2-2DS-03 Estimates, measures and compares areas using square centimetres and square metres

Three-dimensional spacial structure

MA2-3DS-01 Makes and sketches models and nets of three-dimensional objects including prisms and pyramids

MA2-3DS-02 Estimates, measures and compares capacities (internal volumes) using litres, millilitres and volumes using cubic centimetres

Non-spatial measure

MA2-NSM-01 Estimates, measures and compares the masses of objects using kilograms and grams

MA2-NSM-02 Represents and interprets analog and digital time in hours, minutes and seconds

Data

MA2-DATA-01 Collects discrete data and constructs graphs using a given scale

MA2-DATA-02 Interprets data in tables, dot plots and column graphs

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MEASUREMENT AND SPACE

STATISTICS AND PROBABILITY

Chance

MA2-CHAN-01 Records and compares the results of chance experiments

MA0-WM-01 working mathematically

Develops understanding and fluency in mathematics through exploring and connecting mathematical concepts, choosing and applying mathematical techniques to solve problems, and communicating their thinking and reasoning coherently and clearly

Representing numbers using place value

Additive relations

Multiplicative relations

Partitioned fractions

Geometric measure

Two-dimensional spatial structure

Three-dimensional spacial structure

Non-spatial measure

Data

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STATISTICS AND PROBABILITY

Chance

MA0-WM-01 working mathematically

Extending addition facts

We know that 8 + 6 = 14, so 8 tens plus 6 tens must equal 140.

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b Josh has one bag of 50 potatoes and another of 70 potatoes. How many potatoes does he have altogether?

c Hans has $60 in one bank account and $80 in another. How much money does Hans have in total in both accounts?

d Mary had $150 but spent $60. How much does she have left?

e Zara had 180 books but lost 70. How many does she have left?

Multiplication facts, times 3

Write a multiplication fact to describe each array.

Skip count to complete the table of threes and other related facts.

Use the multiplication facts of 3 to answer the divisions.

To solve 21 ÷ 3 think 3 × = 21

Write a problem to match this number sentence: 8 × 3 = 24.

Represents and uses the structure of multiplicative relations to 10 × 10 to solve problems Completes number sentences involving multiplication and division by finding missing values

Revision of three-dimensional objects

Prisms have two parallel faces that are congruent. All the other faces on a prism are rectangular if the faces are square to the ends.

vertex base

Place the letters in the correct position on the grid to identify the cylinders, cones, spheres, prisms and pyramids.

A B C E G U Z H N

Cylinders Cones Spheres Prisms

Pyramids

Find two items in your school that are:

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a prisms

8 9 10

b cylinders

c cones

BLOCK

d spheres

Explain why this object is a prism.

Makes and sketches models and nets of three-dimensional objects including prisms and pyramids

Length can be measured in centimetres. A centimetre is one-hundredth of a metre.

Use a ruler to measure the length of these lines in centimetres.

How many centimetres are in a metre ruler?

and measure the length of each pencil.

Convert each metre measurement into centimetres.

2- and 3-digit subtraction

Learning to trade in a subtraction

4 ones from 2 ones can’t be done. Trade a ten from the tens column to the ones column to make 12 ones. 6 tens becomes 5 tens. 4 ones from 12 ones equals 8 ones.

Selects and uses mental and written strategies for addition and subtraction involving 2- and 3-digit numbers Completes number sentences involving addition and subtraction by finding missing values

3 Write how many pieces of each Base 10 material would be needed to make the numbers, then record the numbers on the numeral expanders.

4 Write the place value of each bold number. thousands, hundreds, tens, ones

5 Write the number one less and one more than the shaded number on each line.

6 Order the following numbers from smallest to largest.

a 46, 247, 56, 474

b 357, 323, 531, 784

c 2374, 7423, 3724, 2743

d 2701, 2671, 2761, 3017

e 8603, 3806, 6803, 6380

Decide whether each shape has symmetry by answering yes or no, then draw as many lines of symmetry as you can on the shapes. The first one has been done for you.

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Draw the other half of each shape by using its line of symmetry as a starting point.

Compares two-dimensional shapes and describes their features Performs transformations by combining and splitting two-dimensional shapes

The square centimetre

Small areas are measured using square centimetres

1 cm 1 cm 1 square centimetre

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2- and 3-digit addition

9 ones plus 3 ones equals 12 ones. Exchange 10 ones for 1 ten. Record 2 in the ones column. Add 1 ten + 3 tens plus 1 ten equals 5 tens.

1 Complete each addition algorithm.

a Space City to Launch Pad.

b Space City to Moon Town.

c Rocket Hill to Blast Off.

d Centre Town to Launch Pad.

e Rocket Hill to Retro City.

f Launch Pad to Rocket Hill.

g Moon Town to Launch Pad.

h Blast Off to Space City.

3 km

Make up a journey on the map and record its distance.

Selects and uses mental and written strategies for addition and subtraction involving 2- and 3-digit numbers Completes number sentences involving addition and subtraction by finding missing values

2 Calculate the shortest distance from:

Terms in number patterns

4 Continue the patterns that are modelled by the dice until the seventh term. Then record what you think would be the tenth term in the patterns. a Tenth term

3 6 9 12 b Tenth term

4 8 12 16

Tenth term

5 10 15 20

Tenth term

6 12 18 24

5 Complete the number patterns then write a rule for each.

c 21 31 41 51

f 100 95 90 85 Rule Rule

6

Write two number patterns of your own.

7 Understanding position.

a Which book is on the far right of the top row?

b Which book is in the centre of the bottom row?

c Which book is second from the left in the middle row?

d Which book is fourth from the right in the bottom row?

e Which book is in the centre of the bookshelf?

f Which book is in the top row and third from the right?

g Describe the position of book D.

8 What shapes can be found at these grid references?

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Book Y is in the middle row, second from the right.

Ms Wills graphed the number of times her best spellers achieved no mistakes in spelling during Term 1.

a Who scored the highest?

b Who scored the lowest?

c Who scored six less than Wang Shu?

d How many more did Aimee score than Zlatco?

e Whose scores were the same?

f Who scored four fewer than Wang Shu?

g Who scored four more than Angel?

h What was the total number of times that all of the best spellers achieved

A dot plot is a graphical display that uses dots to record the frequency of events. For example, in this survey six people selected C.

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Use the number line to help you answer the questions.

Take away the tens part then the ones part to solve the subtractions.

4 Write as many subtraction number sentences as you can that have an answer of 17. 4

Solve the table facts using the arrays if you need them.

Calculate the cost of each family’s shopping.

4 Write a multiplication problem based on the items above.

8 Colour each object and matching description the same colour.

a I am a prism that has 6 rectangular faces.

b I am a pyramid that the Ancient Egyptians built. I have a square base.

c I am a pyramid that has 5 triangular faces and a pentagon as a base.

d I am a pyramid that has a six-sided shape as a base.

e I am an object with 2 circles as bases.

f I am a prism that has 2 pentagonal faces and 5 rectangular faces.

9 Model some of these objects from materials like matchsticks, toothpicks, modelling clay and playdough.

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10 Describe the difference between a prism and a pyramid.

10

Choosing length units

Length can be measured in metres. There are 100 centimetres in each metre. The way of writing metre is m

Estimate within a range then use a metre ruler, trundle wheel or tape measure to measure each distance to the nearest metre.

a The width of your classroom

b The length of your classroom

c The length of a handball court

d The distance between your classroom and the canteen

e The distance between your classroom and the office door

Choose the correct unit to measure, and write cm or m after each measurement.

a The length of a match

b The length of a glue stick

c The length of a car

d The length of a house

e The length of a paper clip

f The length of this page

g The length of a stapler

h The length of your classroom

Convert each centimetre measurement into metres.

We know that 4 × 3 = 12 so 4 × 3 tens must equal 12 tens. For example: 4 × 30 = 120.

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Another strategy used to multiply by a multiple of 10 is to use repeated addition. For example: 4 × 20 = becomes 20 + 20 + 20 + 20 = 80.

3 x 90 = 270 90 + 90 + 90 = 270

3 × 30 is 3 groups of 3 tens, which equals 9 tens. 9 tens is 90.

Rounding off numbers allows us to make quick estimates. It also allows us to check the reasonableness of our answers.

Numbers ending in 1, 2, 3 and 4 are rounded down to the closest ten. 32 becomes 30 Numbers ending in 5, 6, 7, 8 and 9 are rounded up to the closest ten. 48 becomes 50 The number 5

the middle but is always rounded up to the nearest ten. 35 becomes

Estimate the purchases by rounding off to the nearest 10.

a A baseball bat and a soccer ball $

b A book and a toy car $

c Four toy cars $

d A baseball bat, a teddy and a soccer ball $

e Three soccer balls $

Applies an understanding of place value and the role of zero to represent numbers to at least tens of thousands Completes number sentences involving addition and subtraction by finding missing values

Polygons are closed shapes with 3 or more angles and straight sides.

9 Put a cross on the shapes which are not polygons. Match each polygon with its name by colouring them the same colour. Remember, shapes are not always the same. Both of these are pentagons. Name

Record the number of sides and angles of each polygon.

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Compares two-dimensional shapes and describes their features

Time units

Complete and learn these facts.

a 60 seconds = f 52 weeks =

b 60 minutes = g 12 months =

c 24 hours = h 365 days =

d 7 days = i 366 days =

e 2 weeks =

Would you use seconds, minutes, hours, days, weeks, months or years to measure these periods of time?

a Lunch time f Cricket match

b Football match g Your favourite song

c TV advertisement h Spring

d Christmas holidays i Recess

e Walk 10 metres j Your life

Use the greater than or less than symbols to make these sentences true.

a 5 days is one week. e 90 seconds is 1 hour.

b 75 minutes is 1 hour. f 13 days is 2 weeks.

c 12 hours is 1 day. g 130 minutes is 2 hours.

d 59 seconds is 1 minute. h 17 days is 2 weeks.

Place these swimming times in order for the judges.

1 min 18 sec 1 min 19 sec 1 min 20 sec 1 min 12 sec 1 min 56 sec fourth

16 Why are there more minutes than hours in a day?

> is the greater than symbol.

< is the less than symbol.

Expanding and ordering numbers

Write the numbers on the place value chart.

c 2307

d 60

e 5207

f 1406

g 6237

Place each set of numbers in descending order.

a 8507, 7503, 5073, 3057

b 2645, 3658, 1999, 2500

c 2907, 8436, 3541, 2657

d 3524, 5234, 2453, 4532

e 837, 238, 1438, 2745

Descending order means from the highest to the lowest.

Write the largest number you can using the digits supplied.

Expand each number. The first one has been done for you.

a 4527 = 4000 + 500 + 20 + 7

Multiplication facts, times 6

Write a multiplication fact to describe each area model.

Skip count the area model to complete the table of sixes and other related facts.

Revise your multiplication facts by solving the problems.

a Willow saved $4 per week for 6 weeks. How much did she save?

b Arjun trains 5 days a week running 6 km per day. How far does he run each week?

c How much for 9 tickets at $6 each?

d Jack put 7 chocolates in each of 6 bags. How many chocolates did he have?

8 Write the missing numbers to make the number sentences equivalent.

Waru, Jarrah and Alinta paddled across the water in their canoe to a deserted island. Because nobody knew the name of the island, Waru called it Monday Island. Jarrah drew a map of the island. Alinta added a grid to the map to make it easier to identify places on the island.

Use the children’s map above to answer these questions.

a What can be found at B3?

b What can be found at E2?

c What can be found at D4?

d What can be found at G4?

e What can be found at F2?

f What can be found at F5?

The children have not finished the map. Add these items to the map.

a Waru found a broken spear at G3. Draw a spear on the map.

b Alinta saw lots of fish at E2. Draw some fish on the map.

c Jarrah found a very tall tree at C4. Draw a tall tree on the map.

d Waru named the bay at D1 Explorers Bay. Label Explorers Bay on the map.

Make a grid map of your classroom.

How tall are students in Year 4?

On this page you will compare the heights of six students in class 4B at another school with six students in your class.

Use the information in the table to create a column graph showing the heights of the class. Names

Column graphs 6

Class heights of 4B

Measure and graph the height of six people in your class.

The horizontal axis gives the names of the children whilst the vertical axis gives their heights.

Compare the heights of the students in your class with those in 4B and explain what you noticed.

Centimetres

Names

Heights of my class

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Centimetres

Names

Ava Eli Sam Kia Priya Ali