Maths Plus NSW SB 5 Draft Sample Pages

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 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.

Number and Algebra

and Space

Statistics and Probability

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

• blackline masters and investigation pages

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

• assessment tests

• answers for student resources

www.oxfordowl.com.au

Oxford Owl is the home for Oxford Primary professional resources.

NSW Syllabus Outcomes

MA3-RN-01

Applies an understanding of place value and the role of zero to represent the properties of numbers

MA3-RN-02

Compares and orders decimals up to 3 decimal places

MA3-RN-03

Determines percentages of quantities, and finds equivalent fractions and decimals for benchmark percentage values

MA3-AR-01

Selects and applies appropriate strategies to solve addition and subtraction problems

MA3-MR-01

Selects and applies appropriate strategies to solve multiplication and division problems

MA3-MR-02

Constructs and completes number sentences involving multiplicative relations, applying the order of operations to calculations

MA3-RQF-01

Compares and orders fractions with denominators of 2, 3, 4, 5, 6, 8 and 10

MA3-RQF-02

Determines

MA3-GM-01

Locates and describes points on a coordinate plane

MA3-GM-02

MA3-GM-03

of measures and quantities

MEASUREMENT AND SPACE

Selects and uses the appropriate unit and device to measure lengths and distances including perimeters

Measures and constructs angles, and identifies the relationships between angles on a straight line and angles at a point

MA3-2DS-01

Investigates and classifies two-dimensional shapes, including triangles and quadrilaterals, based on their properties

MA3-2DS-02

Selects and uses the appropriate unit to calculate areas, including areas of rectangles

MA3-2DS-03

Combines, splits and rearranges shapes to determine the area of parallelograms and triangles

MA3-3DS-01

Visualises, sketches and constructs three-dimensional objects, including prisms and pyramids, making connections to two-dimensional representations

MA3-3DS-02

Selects and uses the appropriate unit to estimate, measure and calculate volumes and capacities

MA3-NSM-01

Selects and uses the appropriate unit and device to measure the masses of objects

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MA3-NSM-02

Measures and compares duration, using 12- and 24-hour time and am and pm notation

MA3-DATA-01

Constructs graphs using many-to-one scales

MA3-DATA-02

Interprets data displays, including timelines and line graphs

MA3-CHAN-01

Conducts chance experiments and quantifies the probability

MAO-WM-01 Working mathematically

STATISTICS AND PROBABILITY

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

STATISTICS AND PROBABILITY

MA3-DATA-01

MA3-DATA-02

MA3-CHAN-01

MAO-WM-01 Working mathematically

The 4 facts associated with this array are:

4 × 3 = 12

3 × 4 = 12

12 ÷ 3 = 4

12 ÷ 4 = 3

Write 4 facts you can derive from each array. 1

Associative and commutative laws

The commutative law of multiplication tells us that two factors of a multiplication number sentence can be multiplied in reverse and it will not change the answer.

3 × 4 has the same result as 4 × 3.

The associative law states that it does not matter in which order factors are multiplied. 3 × 2 × 4 has the same result as 4 × 2 × 3.

Complete these pairs of number sentences. 2

Write some division number sentences to find out if division is commutative. 3

Addition and subtraction strategies

Last year, the following strategies were taught. Use them to solve the questions on this page.

Use the split strategy to add and subtract these numbers.

Bridge to a decade to calculate the answers.

Estimate an answer to each of the additions and subtractions by rounding each number. The first one is done for you.

Solve these problems using your mental arithmetic skills.

a Jim has 54 m of timber in one pile and 38 m of timber in another. How much timber does he have altogether?

b Sarah had $73 in her bank account but spent $48 on clothes. How much money does she have left in her bank account?

Recognising angles

An angle is the amount of turn between two arms. Angles can be measured and named according to the size of their opening. This common angle is called a right angle.

It is equal to a 1 4 turn of the hands on a clock face.

Angles are classified according to the amount of turn between two arms.

Right angle

Square corner; 90°

Obtuse angle

Acute angle

Straight angle

Reflex angle

Larger than a right angle; greater than 90°

Smaller than a right angle; less than 90°

Can be made from two right angles; 180°

Label the angles either right angle, obtuse, acute, reflex or straight.

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Larger than a straight angle; greater than 180°

A B C

Identify which shape is being described.

a I have four right angles.

b I have one obtuse angle, one acute angle and two right angles.

c I have three acute angles.

d I have three right angles and two obtuse angles.

e I have six obtuse angles.

D E

Find two acute angles and two obtuse angles in your classroom.

Longer distances are measured in kilometres. There are 1000 metres in 1 kilometre. Trundle wheels are often used to measure long distances because each revolution equals 1 metre.

How many times would a trundle wheel click when measuring 1 kilometre?

Measuring 1 kilometre

You will need a trundle wheel and about 11 traffic cones. With your teacher, select an area that you think is about 1 kilometre long. Mark your starting point with a traffic cone and begin walking in a straight line, counting the clicks of the trundle wheel as you go. At the count of every 100 metres, place a cone until you have covered 1000 metres.

Mark out a 1 kilometre cross-country course

11 12 13

In your school, mark out a cross-country course that is about 1 kilometre. You may need to write some distances in chalk on the ground or mark distances with markers. It can zigzag or go around buildings a number of times.

Use a stopwatch to record how long it takes your group members to run your course.

Use the map of New South Wales and the distances from Sydney to calculate the distances between these places.

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10 × 100 m equals 1 km.

Use a street directory or online map to help you name locations about 1 2 a km from school, about 1 km from school and about 2 km from school.

Learning to trade in an addition sum

PROCESS Hund Tens Ones

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

Add 1 hundred plus 1 hundred equals 2 hundreds. Add 1 ten plus 3 tens plus 1 ten equals 5 tens. Trade the 10 ones for a ten.

Complete each addition algorithm.

Solve the problems.

a At Kingsland primary school there are 248 girls on the school roll and 249 boys. How many children attend the school?

b Ms Green, the garden shop owner, banked $389 on Monday and $456 on Tuesday. What was her total banking for the two days?

Selects and applies appropriate strategies to solve addition and subtraction problems PROBLEM SOLVING, COMMUNICATING L N CCT MP_NSW_SB5_38343_TXT_PPS_NG.indb 6 30-Aug-23 08:58:37 SAMPLEPAGES

2 3

Thirds and sixths 2

The numerator shows us how many parts out of the whole (the fractional part).

The denominator shows us how many parts are in the whole.

What fraction of each shape is shaded? The first one has been done for you.

Label the fractions on the number lines.

Which fraction is larger:

or

?

A polygon is a shape made up of three or more straight sides.

Give a clear description of each shape by recording its properties.

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A parallelogram is a four-sided shape with two pairs of parallel sides. Opposite sides and angles are equal. A square and a rectangle are examples of a parallelogram.

Circle the parallelogram.

9632 4569 8741

Calculating area 2

Martha wanted to know what the area of her bank card was, so she divided it exactly into square centimetres and counted them up.

a Find a quicker way for finding the area using the square centimetres Martha drew on the card.

b Explain what it is.

Apply the formula ‘Area = length × width’ to find the area of these shapes. 11

12

Calculate the areas of this ticket.

a What is the area of the smaller section of the ticket? cm2

b What is the area of the larger section of the ticket? cm2

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Subtract 1 hundred from 2 hundreds to give 1 hundred.

1 ten

Trade a ten for 10 ones.

9 ones from 3 ones can’t be done. Trade a ten from the tens column to the ones column to make 13 ones.

4 tens becomes 3 tens. 9 ones from 13 ones equals 4 ones.

Complete these subtractions without trading.

2 Complete these subtractions with trading in the ones.

Complete these subtractions with trading in the tens.

Crack this secret code by matching shapes with their numbers.

Probability using fractions 3

Fractions can be used to describe chance. For example, the chance of a dice landing on 6 is one out of 6, or 1 6 .

Write the fraction to describe the chance of a dice:

a landing on a five

b landing on a one

c landing on an even number

d landing on a number less than five

8 9

Write the fraction to describe the chance of these spinners landing on blue.

b c

Lena put 20 different-coloured marbles in a bag. Write true or false to answer the questions about marbles being drawn from the bag first go.

a The chance of blue being drawn is 4 20 .

b The chance of red being drawn is 5 20 .

c The chance of green being drawn is 3 20 .

d The chance of yellow being drawn is 5 20

e The chance of purple being drawn is 1 20 .

f The chance of orange being drawn is 5 20

10 11

Make up a bag of different-coloured marbles or counters yourself and write the chances, as fractions, of drawing a colour from the bag.

Which objects above are most suitable for packing or stacking?

Explain why.

A base unit for measuring volume is the cubic centimetre. It can be shown by a cube measuring 1 cm long, 1 cm wide and 1 cm high. A centicube or MAB one are good examples of a cubic centimetre (cm3).

Use centicubes or MAB ones to build each prism, then record the volume of each.

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Challenge!

Daya has constructed a shape that has a volume of 24 cm3. Construct a shape of your own that has the same volume, then sketch it in the box.

Addition and subtraction strategies

Last year the following strategies were taught. Use them to answer the questions on this page.

Use your knowledge of number facts to extend these additions and subtractions.

2 Use the jump strategy to add and subtract these numbers.

Add the numbers mentally using the compensation strategy.

Subtract the numbers mentally using the compensation strategy.

Use the strategies above to write addition and subtraction number sentences that have an answer of 54.

Reading numbers

When we read numbers, we read them in groups of hundreds, tens and ones. The following chart best illustrates this concept.

Write these numbers in numerals. The first one is done for you.

a Two hundred and sixteen thousand, four hundred and twenty-six.

b Three hundred and twenty-one thousand, two hundred and sixteen.

c Four hundred and thirty-five thousand, five hundred and sixty.

d One million, five hundred and eighteen thousand, six hundred and twenty.

e Twelve million, two hundred and seventy thousand, four hundred and eighty.

f Twenty-eight million, three hundred and seventy-eight thousand, nine hundred and ninety-nine.

The table below shows the areas of each state and territory of Australia.

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a List the states and territories in order of their areas. ACT,

b Which state has an area closest to 1 000 000 km2?

c Which state has an area closest to 3 000 000 km2?

d Which states are more than double the area of NSW?

e Which state is more than double the area of SA?

f Which state is closest to the area of NSW?

Coordinates are used to locate position on a number plane. The order of the numbers is very important.

The first number is the reading on the x axis

The second number is the reading on the y axis

The number plane, on the left, shows the point (3,2).

8

Plot the coordinates, then connect them to make a polygon.

a Plot these points: (2,1), (1,3), (3,5), (5,3) and (4,1).

b Join (2,1) to (1,3).

c Join (1,3) to (3,5).

d Join (3,5) to (5,3).

e Join (5,3) to (4,1).

f Join (4,1) to (2,1).

What shape did you make?

Remember! Read the horizontal before the vertical, e.g. (9,3) Port Macquarie

Find the closest coordinate for each place.

Estimate the mass of each object in grams, then measure them using standard masses.

Object Estimate Mass

a Pencil case

b Textbook

c Basketball

11 12

This cardboard box can hold a mass of 3 kg. How many of each item could be packed into a box of this type?

250 g 750 g 150 g 50 g 2 3 0 +

+ =

-

% C / 4 5 6 7 8 9 a b c d

Masses can be recorded using decimal notation. 300 g = 0.3 kg 250 g = 0.25 kg 258 g = 0.258 kg

13

Write the masses as decimals.

a 500 g = kg

b 250 g = kg

c 275 g = kg

d 376 g = kg

e 459 g = kg

f 674 g = kg

g 1 kg and 632 g = kg

h 1 kg and 347 g = kg

i 1 kg and 250 g = kg

j 2 kg and 374 g = kg

k 2 kg and 500 g = kg

l 3 kg and 200 g = kg

Draw a line from each object to the most suitable measuring device. 14

d e a b Dictionary Dictionary

5.25 kg

c

Bathroom scales

Weighbridge

Electronic scale

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5

Complete the multiplication facts using your knowledge of place value.

Use your knowledge of place value to multiply by tens. For example, 50 × 60 equals 5 tens × 6 tens which equals 30 hundreds (3000).

a 20 × 50 =

b 30 × 40 =

c 40 × 40 =

d

e

Mentally calculate the products of these multiplications.

The product is the result of multiplying.

Use mental computation skills to solve the problems.

a Mary bought 6 games. How much did she spend?

b Thomas bought 3 watches. How much did he spend?

c Sarah bought 5 T-shirts. How much did she spend?

d How much would 5 books cost?

e How much would 4 dresses cost?

If you had $150 to spend on the above items, how might you spend it? 5

Problem solving 5

Discuss with a friend what strategies you would use to solve these problems. Solve them, then check your solutions with other groups in the class.

Problem Strategies Answer

a A farmer planted 78 trees in 6 paddocks. If the trees were shared equally, how many trees would there be in each paddock?

b A teacher shared 96 counters among 6 students. How many did each student receive?

c Mabel bought 5 tins of beans for 79c per tin and a can of dog food for 96c. How much did she spend on her purchases?

d Samuel saved $35 per week for 9 weeks from his weekly wages. How much did he save altogether?

e Huan planted 100 flowers but only 1 4 of them sprouted. How many flowers sprouted?

f A bicycle wheel has a circumference of 2 m. How many times will it need to turn to cover a distance of 528 m?

g The cake stall collected $296 at the fete. If $20 was spent hiring a tent and $70 was spent on ingredients, what was the cake stall profit?

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h The cost of a camp was $40 per student plus $15 each for the bus. How much money did the teacher collect from 30 students?

Think about the strategies you used to solve question 6g, then write another method you could use in the future to solve a problem like it.

Baked Beans

Chance experiments 5

Dice-rolling experiment

a If you rolled two dice and totalled the scores, what do you think would be the most common score?

b Roll two dice 40 times, recording the total of each roll in the table below.

c Which total was most frequent?

d Which total was least frequent?

Use the data in the table above to order the scores from least to most.

Do you think 7 would usually have more responses than 12?

Explain why.

Mr Carson put 30 of his favourite-coloured round lollies in a bag.

a How many of each lolly are there? R Y G O

b Which is the most likely colour to be drawn out of the bag?

c How would you describe the chance of red being drawn out of the bag?

d Which is the least likely colour to be drawn out of the bag?

e Is it more likely that an orange lolly would be drawn than a green one?

f Is it more likely that a yellow lolly would be drawn than a green one?

Naming prisms and pyramids

Prisms have two bases that are the same shape and size. All other faces on a prism are rectangular. Prisms are named from the shape of their bases.

Pentagonal prism

Draw a line to join each object to its name.

Pyramids have only one base, with all other faces being triangles. The triangular faces meet at a common apex. Pyramids are named from the shape of their base.

apex

rectangular prism

rectangular pyramid

square pyramid

triangular pyramid cube

hexagonal prism

triangular prism

pentagonal prism

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pentagonal pyramid

octagonal prism

hexagonal pyramid

octagonal pyramid

Visualises, sketches and constructs three-dimensional objects, including prisms and pyramids, making connections to two-dimensional representations

Pentagonal pyramid

Another way of recording division is by using the division symbol. ÷ The quotient is the result of a division.

means

12

Find the quotients of these divisions.

An example of division that leaves a remainder: Tina wanted to share 26 icy-pole sticks among 5 people. She knows that it will not work out equally and that there must be a remainder.

Solve these divisions that have remainders. The first one is done for you.

There are 72 students in Year 5 who need to be transported to the Sports Carnival. How many trips would each vehicle below make if it was the only vehicle available to transport the students? (Working paper may be needed.)

trips

3 passengers

4 passengers c trips

trips

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trips

5 passengers 12 passengers

How many trips would the whole fleet of vehicles need to make if they transported the students together? trips

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Continue

Write a rule for each number pattern, then use it to predict the next two terms in the pattern.

You must look closely at the previous terms in the pattern.

Continue to make the pattern of square numbers and record the numbers. 4 9 16

Look for a rule or a pattern in the square numbers, then extend the table to the twelfth square number.

Square numbers 4 9 16

A column graph is a graph that uses columns to record the frequency of events. For example, in this survey six people selected C.

Ashton threw a set of three dice forty times and recorded the totals on a column graph. Use his graph to answer the questions.

a Which score occurred most frequently?

b What was the frequency of the second most frequent score?

c Which scores occurred 2 times?

d Which scores did not appear at all in this sample?

e Explain why the scores 10, 11 and 12 account for 50% of the results.

Class 5G were given a Quick Quiz about Australia. Madeleine and Grace recorded the scores on this column graph.

9 10

Answer true or false to these statements.

a 13 correct answers was the most common score.

b Most scores were between 11 and 16.

c 8 was a score apart from the main cluster.

d 30 people participated in the quiz.

am and pm time

am is an abbreviation for ante meridiem which means “before midday”. pm is an abbreviation for post meridiem which means “after midday”.

Write a digital label for each clock using “am and pm” notation.

Calculate the

Solve these problems.

a A soldier commenced duty at 1:30 pm. She finished 8 hours later. When did she finish work?

b Jim started work at 6:30 am and finished at 4:30 pm. How long did he work if he had an hour off for lunch?

c The lamb started cooking at 3 pm. We ate it 2 hours 15 minutes later. When did we have dinner?

If I go to bed at 9 pm and wake up 12 hours later, it will be 9 am.