Maths Plus NSW Assessment Book 4 Full Digital Sample

NEW SOUTH WALES SYLLABUS

Harry O’Brien

Greg Purcell

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© Harry O’Brien and Greg Purcell 2023

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First published 2023

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ISBN 9780190338206

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Acknowledgements

NSW Mathematics K–6 Syllabus © NSW Education Standards Authority for and on behalf of the Crown in right of the State of New South Wales, 2023. NESA does not endorse model answers prepared by the Publisher and takes no responsibility for errors in the reproduction of the Material supplied by NESA.

Acknowledgement of Country

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Message to teachers

Maths Plus Assessment Book Year 4 is an easy-to-use book for both students and teachers. It provides students and teachers with an assessment book that should easily fit into the whole-school maths assessment policy of most schools.

The book is designed to diagnostically assess students at Year 4 level. Each assessment page is a snapshot of work that addresses the specific outcome from the NESA Syllabus. The book provides students with a variety of opportunities to demonstrate their skills, knowledge and understanding of key concepts in Number and Algebra, Measurement and Geometry, and Statistics and Probability.

The pages in this book can assist with:

• assessing understanding of specific knowledge required by the NESA Syllabus

• diagnosing students’ knowledge to assist with future scaffolding of work

• providing evidence for A–E reporting

• providing meaningful work samples of students’ work and understanding. Supported by discussion, observation, hands-on experiences and teachers’ own observations, these assessment pages can become a useful component in assisting teachers to accurately assess their students.

Answers for the assessment tasks and a Student Book–Assessment Book correlation chart can be found online on the Maths Plus Teacher Dashboard.

Harry O’Brien, Greg Purcell

Place value to tens of thousands

1 Place these numbers in the Place Value House in ascending order.

2 Make the smallest number you can using the number cards above.

3 Make the second largest number you can using the same cards.

Round 88 850 to the nearest 10 thousand and then to the nearest 100 thousand.

Make these numbers larger.

12 Make 32 ten times larger.

13 Make 82 one hundred times larger.

14 Make 36 one thousand times larger.

1 Label the decimals that are missing from the tape.

Draw a line to connect each hundredth to a place on the 100 cm ruler. 2

rulex metre ruler

Short distances and lengths can be measured using metres and centimetres,

height is 147 centimetres, which can be written as 1 metre 47 centimetres or 1.47 metres.

Complete this chart that shows different ways of recording distances, including the dimensions of the storage container.

14 Draw a line to match the fractions to a place on the number line.

Addition strategies

Regroup the addends into tens and ones to add them mentally. The first one has been done for you. 7 36 + 47 becomes +

15 Round each number to the nearest 10 to make an estimate of the answer.

16 Round each number to the nearest 100 to make an estimate of the answer.

Use the jump strategy to answer the questions.

Use any strategies you wish to solve the problems.

Problem

21 Mali walked 560 m, rested for a while and then walked another 306 m. What was the total distance she walked?

22 Goode Cars Pty Ltd sold 643 cars in the first half of the year and 356 in the second half of the year. How many cars were sold during the whole year?

My strategy

Jump strategy Partition the second number into its place-value set to subtract the numbers. For example, 189 56 becomes 189 50 6 =

Use the jump strategy or any strategy you wish to solve the subtractions.

16 Round each number to the nearest 100 to make an estimate of the answer.

Separate the numbers into place value parts in order to subtract.

Solve the problems below.

Problem

19 Mia had a bag of 376 marbles. If she lost 123 of them, how many would be left?

20 There were 4233 buttons in a jar and the owner gave away 516. How many buttons were left in the jar?

21 Alex had 6264 sheep. If she sold 1341, how many would she have left?

Working Answer

Calculate the missing numbers in the number sentences.

Find the missing numbers in these equivalent number sentences.

16 8 – 3 = 21 −

Solve the problems below.

19 Maxwell scored 276 points in the first game and 325 in the second. How many points did he score altogether?

20 Zia had a bag of 375 marbles. If she gave away 150, how many did she have left?

21 How far did Joni travel if her trip to Sydney was 695 km and the flight to Brisbane was 754 km?

22 The sticker book contained 573 stickers. If the teacher used 125 of them, how many are left?

Use your knowledge of addition and subtraction to find the missing digits.

27 Write a problem of your own to match the number sentence provided.

Complete the multiplication facts.

Multiplication strategies and missing values

Multiply the tens, then the ones to solve the following multiplications. For example, 26 × 3 becomes 20 × 3 (60) plus 6 × 3 (18) = 78.

Complete the number sentences that describe the family number facts.

Solve the word problems.

15 Hai saved $35 per month for 7 months. How much did he save?

16 Keira planted 6 rows of trees with 14 seeds in each row. How many seeds did she plant?

17 Waru had 7 boxes of toys with 15 toys in each box. How many toys did he have?

Find the missing numbers in each number sequence.

Represents and uses the structures of multiplicative relations to 10 3 10 to solve problems MA2-MR-01 Completes number sentences involving multiplication and division by finding missing values MA2-MR-02

Division strategies and missing values

This area model is not finished but it can still be used to help identify multiplication facts.

Use the model to complete these facts.

1 5 × 6 = 3 30 ÷ 5 =

2 6 × 5 = 4 30 ÷ 6 = Complete these divisions related to the model.

5 30 ÷ 2 = 7 30 ÷ 3 =

6 30 ÷ 4 = 8 30 ÷ 10 =

Kedra has 24 building blocks that she is sorting into groups.

17 How many groups of 2 can she make?

18 How many groups of 3 can she make?

19 How many groups of 4 can she make?

20 How many groups of 6 can she make?

21 How many groups of 8 can she make?

22 What would happen if she tried to make 5 groups?

24 ÷ 5 = groups and a remainder of

Problem

23 $64 was to be shared equally among 4 people. How much did each person receive? ÷ =

24 Navaya’s bracelet was $96. If she is going to pay it off over 4 weeks, how much will she pay each week? ÷ =

Partitioned fractions

Shade then record equivalent fractions for the ones given.

Compare the fractions with related denominators to decide whether the statements are true (t) or false (f).

17 How many eighths equal one whole?

18 How many fifths equal one whole?

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) MA2-PF-01

Fractions greater than one

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) MA2-PF-01

Write the mixed numerals displayed by the shaded shapes below. 1

3

4

Shade the shapes to display the mixed numerals.

Add the missing mixed numerals to the number lines.

Connect each mixed numeral to a place on the number line.

Change these fractions into mixed numerals.

Eight children—Hanny, Kim, Than, Sam, Logan, Mila, Gina and Eliana—put their houses on the map above by putting their initial in their house, e.g. H is Hanny’s house.

Answer true (t) or false (f).

1 Gina’s house can be found at grid reference C3.

2 Eliana’s house can be found at grid reference G3.

3 Than’s house can be found at grid reference D5. 4 The library can be found at grid reference F3. 5 There are three railway stations.

6 There are two schools.

7 A restaurant can be found on the corner of Cook Road and Ocean Road.

8 Mila’s house is south of Logan’s house.

9 Logan’s house is south of Mila’s house.

10 Gina’s house is west of Wharf Street.

11 Ocean Road runs from east to west.

Measure the length of these lines in millimetres. Write the answers on the lines.

5 Measure and record the length and width of each rectangle. Calculate each rectangle’s perimeter and record it on the shape.

Each model has been built with centicubes. Calculate and record the length, width and height of each model in centimetres.

Answer the questions.

1 Does box A contain a straight angle?

2 Which box contains a right angle?

3 Which box contains an acute angle, which is an angle smaller than a right angle?

4 Which box contains an obtuse angle, which is an angle larger than a right angle?

5 A reflex angle is greater than a straight line. It is almost a full circle. Which box shows a reflex angle?

Draw another arm to create an angle that matches the description.

6 Right angle

7 Acute angle

8 Obtuse angle

Acute angles are less than a right angle. Obtuse angles are greater than a right angle.

9 Which of the shapes above are made up of right angles?

10 Which of the shapes above is made up of three acute angles?

11 Which of the shapes above is made up of angles that are all larger than right angles?

Features of 2D shapes

Use the letters on the shapes to answer the questions.

1 Which shape is an octagon?

2 Which shape has 6 sides and 6 angles?

3 Which shape is a rhombus?

4 Which shapes have 4 right angles?

5 Which shape is a trapezium?

6 Polygons are shapes that have 3 or more straight sides and 3 or more angles. Are all the shapes L to S polygons?

7 Which shapes are quadrilaterals?

8 Which shapes are parallelograms?

9 Name each polygon and record the number of sides and angles each shape has.

Name Sides Angles

Name Sides Angles

10 Explain how to tell the difference between a rhombus and a trapezium.

1 equilateral triangles combine to make a .

2 trapeziums combine to make a .

3 combine to make a rhombus.

4

Trace over parts of the hexagon’s diagonals to show how 3 rhombuses can combine to create a hexagon.

What shapes combine to form the following shapes, e.g. squares and triangles?

5 L-shape A _____________________________________________

6 triangle B _____________________________________________

7 trapezium C _____________________________________________

8 trapezium D _____________________________________________

9 hexagon E _______________________________________

10 hexagon F _______________________________________

11 trapezium G _____________________________________

12 hexagon H ______________________________________

13 trapezium I ______________________________________

14 pattern J ________________________________________

15 Draw lines on the star to make it into 4 triangles and a square.

Area/square

centimetres and square metres

A base unit for measuring area is a square centimetre (cm2), which can be viewed as a square with 1 cm sides.

1 Below each shape record the area in square centimetres (cm2). The shapes are drawn on 1 cm grid paper.

cm2 cm2 cm2 cm2 cm2

2 Calculate the area of these right-angle triangles drawn on 1 cm grid paper by following these steps:

• Transform each triangle into a rectangle.

• Calculate the area of the rectangle.

• Halve the rectangle’s area to get the area of the triangle.

cm2 cm2 cm2 cm2

3 Calculate the area of these rectangles in square centimetres (cm2).

Rectangle = 4 cm2

Triangle = 4 cm2

Draw a line to match each object to its net.

Record the number of faces, vertices and edges there are on each 3D object.

7

Draw a line to match the views to a model.

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

Volume – cubic centimetres

Calculate the volume of each model built with cubic centimetres.

Start by working out how many are in the bottom layer and then multiply that number by how many layers there are.

Record the volume of each object made from cubic centimetres.

12 Which model had the smallest volume?

13 Which model had the greatest volume?

14 Which models had the same volume?

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

Colour the measuring beakers to the level that matches the capacity of the containers.

1 2 3

200 mL 250 mL 350 mL 500 mL 280 mL 600 mL

4 Place the containers on the grid in ascending order.

Name Millilitres

Use millilitres and then litres and millilitres to show two different ways of recording how much is in the sets of measuring beakers.

5

Convert these millilitres into litres.

7 2000 mL = L

8 5000 mL = L

Convert these litres into millilitres.

6

9 2250 mL = L

10 5750 mL = L

Mass/kilograms and grams

200 g 50 g 250 g 500 g 100 g

1 Place the grocery items in ascending order.

Use a scaled measuring device like kitchen scales to measure these items.

Change the fractions of a kilogram into grams.

DRAFT

Convert these grams into kilograms.

9 4000 g = kg 10 6000 g = kg 11 9000 g = kg

Convert these kilograms into grams.

12 5 kg = g 13 7 kg = g 14 2.5 kg = g

Answer true or false.

15 1 kg 200 g is heavier than 11 2 kg

16 1 kg 600 g is less than 2 kg

Apple Atrawberry Potato Pineapple Tomato

Draw the hands on the clock faces to display the matching time. 1

7 o’clock half past 2 a quarter to 3 : :

Write the digital time using am or pm for the following clocks, e.g. 2:35 pm.

6 7 8 9

Place these race times in order from shortest to longest.

10 54 sec 48 sec 39 sec 50 sec

11 41 sec 52 sec 29 sec 38 sec

12 65 sec 57 sec 60 sec 58 sec

Calculate how long it is until the next hour.

15 If the time is 2:52 am how many minutes is it to 3 am? minutes

16 If the time is 8:45 pm how many minutes is it to 9 pm? minutes

17 If the time is 9:25 am how many minutes is it to 10 am? minutes

18 If the time is 6:15 am how many minutes is it to 7 am? minutes

19 If the time is 10:10 pm how many minutes is it to 11 pm? minutes

Answer true or false.

seconds

minute

Data/graphs

Sam said that most children in his class liked the colour green the best.

The children held up signs naming their favourite colours to see if Sam was correct.

1 Use tally marks to show favourite colours.

Blue Red Green Yellow Black Orange Pink

2 Construct a column graph showing the tally results.

3 Which colour is the most popular?

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4 Which colour is the least popular?

5 Which colours were equally popular?

6 How many more children like red than green?

7 Class 4P collected data about the types of pets they have. Use the data shown on the tally mark grid to create a dot plot that displays that data.

Fish Birds Dogs Cats Rabbits Horses

Our class pets Fish Birds Dogs Cats Rabbits Horses

1 Conduct a survey to find: Which is the most popular sports team among Year 4 students? Predict 6 teams you think might be mentioned.

2 Conduct your survey and record the results on the grid using tally marks. Team Tally

3 Show how your data could be displayed on a column graph. Most Popular Sports Team

Numbers

Teams

4 How accurate were your predictions?

5 Which game was represented the most?

6 Was there a result that surprised you? What was it?

7 If a new sports store was to open near your school, what merchandise would you recommend they stock?

Here are the contents of Catherine’s marble bag.

R = red, B = blue, G = green, Y = yellow, P = pink, O = orange

Write yes or no to answer the questions below.

1 Is Catherine more likely to pick a red marble than an orange marble?

2 Is Catherine more likely to pick a yellow marble than a blue marble?

3 Is Catherine less likely to pick a yellow marble than a green one?

4 What is the most likely colour that Catherine will pick out of the bag?

impossible certain H H T H H ? DRAFT

5 Circle the label above that best describes the chance of the dice landing on 2.

6 Will the next toss of the coin above definitely be a head?

7 Explain why or why not.

A bag of 10 red marbles and 1 yellow marble

8 What is the most likely colour to be drawn from the bag?

One marble was drawn from the bag and not returned.

9 Is it certain that you could still draw a yellow marble from the bag?

10 Explain why.

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ASSESSMENT BOOK PRACTISE, MASTER, ASSESS

Maths Plus NESA Syllabus / Australian Curriculum Edition, Year K to 6 is a whole-school program based on the NSW Education Standards Authority Mathematics K–6 Syllabus for the Australian Curriculum.

Maths Plus follows a graded and spiralling approach, allowing teachers to revisit concepts throughout the year. It provides students with opportunities to sequentially develop, practise and master their skills and knowledge in the content strands of the Australian Curriculum: Mathematics:

• Number

• Measurement

• Statistics

• Algebra

• Space

• Probability

The Assessment Books feature post-tests to assess the concepts and skills developed in the Student Books and Mentals and Homework Books. Answers can be found online on the Maths Plus Teacher Dashboard.

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ISBN 978-0-19-033820-6

9 780190 338206