Primary Maths for Scotland 2025

The first maths mastery programme developed specifically for Scotland to plan routes through the Es and Os and help raise attainment for maths in Scotland

Twelve write-in practice workbooks to embed and consolidate learning

Primary Maths for Scotland Teacher Guides

Primary Maths for Scotland

Primary Maths for Scotland

1st Level Maths

2nd Level Maths

Teacher Guide

Teacher Guide

Primary Maths for Scotland Teacher Guides Aligned to CfE benchmarks

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Planning and teaching support manuals to accompany Primary Maths for Scotland Textbooks 1st Level Maths Primary Maths for Scotland

Primary Maths for Scotland

Primary Maths for Scotland

2nd Level Maths

2nd Level Maths

Teacher Guide Teacherconceptual Guide ensure pupils develop understanding alongside Assessment Pack

procedural fluency

provide ideas for active learning identify potential misconceptions and how to address them save time, with key vocabulary and resource lists included

Aligned to CfE benchmarks

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Planning and teaching support manuals to to find out more: Contact your local rep today Clairefor • East Scotland • 07557 188 154 • claire.mcauley@harpercollins.co.uk accompany Primary Maths Scotland Textbooks

Christine • West Scotland • 07825 116 401 • christine.stein@harpercollins.co.uk

Textbooks There are three textbooks at First Level and three at Second Level. Engaging and pedagogically rigorous, the Textbooks help pupils master mathematics at their own pace. Clear and simple, they are easy to use and can fit in with teachers’ existing planning, resources and schemes of work.

Let’s practise sections provide opportunities to consolidate conceptual learning and develop procedural fluency

Characters introduce learning outcomes and lead pupils through the maths

Challenge questions give every child the chance to develop their problem solving and investigation skills

Each unit is tightly focused on one objective, following small steps of progression

Practice Workbooks Two write-in practice workbooks per textbook provide plenty of practise questions to help embed and consolidate learning. With support and extension activities, the textbooks support the mastery approach to have all children working on the same topic at the same time.

2.1 Reading and writing numbers

3 How many flowers? Write the number word for each collection.

1 Match the correct numeral to each number word on these t-shirts.

Helps children develop conceptual understanding alongside procedural fluency

thirteen 16 twenty

18 19

eighteen 20

sixteen

13 nineteen

2 Draw the correct number of fruit for each question.

Challenge Isla is writing number words to 20 but is stuck on these numbers.

Can you help her by filling in the missing number words? a) Draw twelve apples

11 eleven

16 sixteen

12

17

13

18 eighteen

14 fourteen

19 ninteen

b) Draw eleven bananas

c) Draw seventeen grapes

d) Draw thirteen strawberries

15

20

2

3

1.3 Using rounding to estimate the answer 1

2

Say whether each answer is reasonable or not. Explain your answer.

Reasonable Yes

No

b) 36 x 18 = 928 Reasonable

A range of questions are provided in context to develop pupils’ understanding of real-life application of the skills they are learning

c) 24 740 + 5 429 = 30 169

Explain your answer

Reasonable Zahid multiplied 48 by 9 and got 432

Not Reasonable

d) 72 375 – 23 862 = 48 513 Reasonable

Alana multiplied 79 by 6 and got 513

Not Reasonable

e) 45 x 21 = 9 540 Reasonable

Marek multiplied 93 by 7 and got 651

Not Reasonable

f) 496 + 816 + 1532 = 2 144 Reasonable

2

Not Reasonable

Amman has worked out these problems. Use rounding and estimating to help you to decide if his answers are reasonable.

Explain your thinking for each one. The first one has been done for you.

Not Reasonable

g) 275 812 – 122 401 = 153 411 Reasonable

Not Reasonable

a) 17 428 – 4 283 = 13 145

Challenge Reasonable

Not Reasonable

Use estimation to help you here. Choose 3 numbers from those shown so that when you add them together the answer is close to 100 000.

Do you think there is a better solution? How can you check?

Rounding to the nearest 1000, this is 17 000 – 4000. 13 000 is a good estimate so 13 145 is reasonable.

4

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2C

2

ok 1

ook 2

Workbook

2B

Practice

2B

kbo Practice Wor

1C

Practice Workb

Practice Workbook 1

1C

2

ok 1

ook 2

Workbook

1B

Practice

kbo Practice Wor

1B

Practice Workb

Practice Workbook 1

Gives teachers high-quality questions to set as and when they see fit

69 416 71 829 25 980 9817 81 904 38 055 17 356 4203

2C

Teacher Guides The Teacher Guides contain teaching ideas and activities that add breadth, depth and challenge to the textbook resource. They can be used to introduce a topic prior to pupils practising new skills or as part of reinforcement of learning.

Provides an explanation of the key content of the topic, and the conceptual Estimation and rounding 2A and rounding 2A Estimation learning which should take place

Shows the coverage of the CfE 1 Estimation and rounding 1 Estimation and rounding and Benchmarks within this section Estimation and rounding 2A Estimation and rounding 2A

ConceptualConceptual content content

Section overview Section overview Textbook 2A units

Textbook 2A Review units units

Prior learning Review units

Unit 1.1 Rounding whole numbers to the nearest 10

1C Unit 1.1 units 1.1, 1.2whole Rounding and 1.6 to the numbers

2-01a • 1C I can read and write numbers withand upwrite MNU • I can read numbers with up

MNU 2-01a

1.6 • place Rounds whole • and I understand that the• place of a digitthat the I understand of a digit

• Rounds whole

Unit 1.2 Rounding whole numbers to the nearest 100

1C Unit 1.2 units 1.1, 1.2whole Rounding and 1.6 to the numbers

Unit 1.3 Rounding decimal fractions to the nearest whole number

1C Unit 1.3 units 1.1, 1.2 Rounding and 1.6 fractions decimal

Unit 1.4 Estimating the answer using rounding

nearest 10

nearest 100

to the nearest whole number

1C Unit 1.4 units 1.1, 1.2 the Estimating and 1.6 using answer rounding

to 4 digits units 1.1, 1.2

Prior learning

Benchmarks/ Es&Os

Benchmarks/ Es&Os

to 4 digits

numbers to the within a number showswithin its value a number shows its value nearest 1000, • I know the meaning •of Ieach digit know thein meaning of10 each 000digit and in the ones, tens, hundreds theand ones, tens, hundreds 100and 000. thousands columns thousands columns • Rounds decimal fractions to the • 1C I can read and write numbers withand up write numbers • I can read with up nearest whole to 4 digits units 1.1, 1.2 to 4 digits number, to one and 1.6 • I understand that the• place of a digitthat the place of a digit I understand decimal place within a number showswithin its value a number showsand its two value decimal • I know the meaning •of Ieach digit know thein meaning ofplaces. each digit in the ones, tens, hundreds and the ones, tens, hundreds and thousands columns thousands columns • Applies knowledge • 1C I can read and write decimal fractions of rounding to • I can read and write decimal fractions to one decimal units 1.1, 1.2 place to one decimal place give an estimate to a calculation • and I can1.6 count in decimal amounts to one • I can count in decimal appropriate amounts to one to decimal place forwardsdecimal and backwards place forwards and backwards the context.

• I understand the value each digit the value of each digit • Iofunderstand in decimal fractions up in todecimal one decimal fractions up to one decimal place place • I can round whole numbers the whole numbers to the • I can to round nearest ten and the nearest hundred nearest ten and the nearest hundred

numbers to the nearest 1000, 10 000 and 100 000.

• Rounds decimal

fractions to the nearest whole number, to one decimal place and two decimal places.

knowledge of rounding to give an estimate to a calculation appropriate to the context.

Children need to learnChildren to identify multiples on either of side, find theonhalfway pointfind the halfway point need to learnof tohundred identify multiples hundred either side, between them and use this understanding decide whether toto round up whether or down.to round up or down. between them and usetothis understanding decide

Resources Resources

to 4 digits

within a number showswithin its value a number shows its value

Round

•

Estimate

• Money - £10, £100• notes and Money - £10, £100 notes and

• I can round numbers•toI the can nearest round numbers to the nearest

£1 coins

ten or hundred

2

£1 coins

Promotes use of 3 3 mathematical language and provides definitions in the online glossary

A wide range of resources are provided online Estimation and rounding

Misconceptions Potential misconception

Addressing the misconception

The pupil might not understand which digit in the number to look at to determine whether to round up or down.

• Show number on a number line and ask them

e.g. 829 rounded to the nearest 100 is 900 (pupil is using last digit to round incorrectly)

!

which multiple of 10 the number is between and how they decide which multiple is nearer to the number.

Ask them which digit helps them decide.

• • •

• Refer back to Place Value Units

•

The pupil might not understand the convention for rounding up if a digit is five or more.

• Show number on a number line and allow them to

•

The pupil always rounds up, e.g. 62 rounded to the nearest ten is 70.

• Show number on a number line and ask them which

The pupil thinks rounding is just changing the numbers to zero, e.g. 587 rounded to the nearest 100 is 500

• Show number on a number line and ask them which

be cubes, arrow cards, counters or money.

explore which multiple is nearer on either side.

Explain that we usually round up when the digit is five or more.

multiples the number is between and how they decide which multiple is nearer to the number. Ask them which digit helps them decide.

multiples the number is between and how they decide which multiple is nearer to the number. Ask them which digit helps them decide.

Teaching ideas Unit 1. Rounding whole numbers to the nearest 10 • • • • • •

4

• • •

• Use materials to represent the amounts. This could

The pupil might not understand what each digit in a number represents

Lists the pre-requisite knowledge required to embark on the unit

Helps you identify and address misconceptions associated with the units

•

numbers such as cubes or place numbers such as cubes or place value sticks value sticks

the ones, tens, hundreds theand ones, tens, hundreds and thousands columns thousands columns

Signposts units to review if children do not possess pre-requisite knowledge and skills

Key vocabulary Key vocabulary

• Number lines 0 -100, 0 - 1000lines in 0 -100, 0 - 1000 • in Round • Number • Numeral cards 0 -• 100 Numeral cards 0 - 100 • Decimats • Decimats • Arrow cards • Arrow cards • Physical materials• toPhysical represent materials to represent

• I know the meaning •of Ieach digit know thein meaning of each digit in

2

For example, if we want round 382 towant the nearest hundred: Forto example, if we to round 382 to the nearest hundred: ________________________________________________________382________________ ________________________________________________________382________________

a range of increments – ones, a range of increments – ones, • Estimate tens, hundreds, tenths tens, hundreds, tenths

1.6 • and I understand that the• place of a digitthat the place of a digit I understand

ten or hundred

It is important that the children to use number lines, (as wellnumber as a range of other materials to of other materials to It is important that the children to use lines, (as well as a range represent numbers visually if needed) to visually allow them to explore howthem and why we round represent numbers if needed) to allow to explore howupand why we round up or down. In this way, or they can also learn to visualise these materials to help them make an down. In this way, they can also learn to visualise these materials to help them make an active decision on rounding for themselves, ratherfor than simply following a rule. active decision on rounding themselves, rather than simply following a rule.

• Applies

• 1C I can read and write numbers withand up write numbers with up • I can read to 4 digits units 1.1, 1.2

In daily life we oftenInround to allow usnumbers to easily to work with andwork to check daily numbers life we often round allow us them to easily with them and to check answers. It is important that pupils have a clear of theunderstanding numerals theyofare answers.

It is important thatunderstanding pupils have a clear the numerals they are working with and their value to be and abletheir to estimate They also need to They also need to working with value toand be round able toeffectively. estimate and round effectively. understand why we round and estimate through a wide rangethrough of contexts relevant understand why weproblems round and estimate problems a wide range of contexts relevant to daily life. to daily life.

Take a pack of numeral cards to 100 and shuffle them.

Ask a child to pick one and tell you the number.

Find the numeral on a number line to 100.

Then ask what multiples are on either side of the number – can they find them on the number line?

For example, if you picked 32, the multiples of 30 and 40 are the multiples of ten either side.

Which is nearer to the number?

In this case 32 is nearer to 30, so we round down.

Repeat with lots of different examples, rounding u Discuss what happens if we have a number ending w in this case, although it depends on the particular co For instance if we were measuring materials to bu we would always round down to make sure the between posts.

Or if we wanted to buy tickets that cost £10 each an round down to the nearest ten because we can’t u So there may be some particular contexts where w up, but otherwise the rule is that for numbers 5 an Ask for examples why we might round to the money, directions.

Extend to 3 digit and 4 digit numbers once confide

Unit 2. Rounding whole numbers to the • •

Check understanding of rounding to the nearest 10 Ask questions such as “What is 88 rounded to the nea do I look at to decide? If I think of a number and round numbers be?”

Draw an empty number line on the whiteboard, e.g Ask children what the multiples of 100 on either si Ask them to write them in on the number line.

Which multiple of 100 is nearer to 379?

Discuss how they know.

Explain that we round to the nearest 100 by findin Repeat with different examples.

Discuss what happens when a number ends in 50 this case, although it depends on the particular co Extend to 4 digit numbers once confident.

Each unit •offers ideas, • advice and guidance • • for teaching the topic • • • • •

Early Level Record Book The Early Level Record Book is a pupil-facing write-in booklet that can be used to assess achievement of the Early Level benchmarks or as evidence of completion of Early Level.

More or fewer?

Contents Curriculum organiser

Curriculum coverage

Page name

Page

Estimation and rounding

MNU 0-01a

More or fewer?

3

Colour match

4

Regular patterns

5

MNU 0-02a

Join me up

6

MNU 0-04

Me first!

7

Higher and faster

8

Collections

9

How many?

10

Party time

11

Colour the facts

12

Finding totals

13

Something is missing

14

Double up

15

Farm calculations

16

The bigger half?

17

Fair sharing

18

Number and number processes

Tick box contents page to easily identify what has been mastered

Fractions, decimal fractions and percentages

MNU 0-07a

Money

MNU 0-09a

Show me the money

19

Time

MNU 0-10a

What is going on?

20

Tick tock

21

Measure me

22

How many?

23

Dancing patterns

24

Carry on please

25

Measurement

MNU 0-11a

Patterns and relationships MTH 0-13a

Properties of 2D shapes and 3D objects

MTH 0-16a

Shape shift

26

Angle, symmetry and transformation

MTH 0-17a

This way

27

MTH 0-19a

Symmetry

28

Data and analysis

MNU 0-20a

Sorting toys

29

MNU 0-20b

Data drop

30

MNU 0-20c

Data drop

31

Date completed

Objective

Completed

I have developed a sense of comparing collections.

1)

2)

Write-in workbook helps support children moving into a more formal setting and beginning First Level

3)

Teacher’s notes 1) Tick which collection has the most in it.

2) Are there more bananas or apples?

3) Circle which collection has ‘fewer than’ the other collection?

2

3

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Something is missing

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Double up

Date completed

You need

Objective

I can solve simple missing number problems.

Coloured pencils

I can double numbers to a total of ten mentally.

10

3 5 3

9 6

6 2

Coloured question boxes for easy navigation

Date completed

Objective

1)

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1)

8 5 7

1 2) Double 5

2)

7+

Double 0 3 plus 3 Two groups of 4 1 add 1 Double 2

=10

0

Primary Maths for Scotland

Early Level Maths Record Book

Teacher’s notes

Teacher’s notes

1) Write in the missing numbers to complete the bar diagrams.

1) Show me all the doubles facts you know to 10 by drawing red and green circles on each string.

Write the double fact for each string in the box.

2) Draw red and green apples into the ten frame to complete the missing number calculation – There are ten apples. 7 are green. How many are red?

2) Match each question to the correct answer.

14

15

Aligned to CfE benchmarks

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Early Level Digital Pack

The primary maths mastery programme for Scotland

The Digital Pack can be used with the whole class to demonstrate concepts, to embed knowledge and to practice key skills or can be set up on tablets, computers or whiteboards for group work, as invitations to play or as part of a learning carousel.

Assessment Packs The Assessment Packs contain questions to assess mental agility, procedural fluency and conceptual understanding of the key numeracy and mathematical ideas in each level. They are photocopiable resources that can be used both as a diagnostic tool to identify children requiring more support or challenge and to record and report children’s attainment. Supporting resources are available to download online.

End of early level assessment 1

Yearly progress check 2: end of P1

Dinosaurs

Teacher instructions

Context

Yearly progress checks help identify areas for improvement

Context

Investigating Dinosaurs is a very popular topic in the Early Years. This assessment is suitable for use with children who have carried out class-based topic work relating to dinosaurs. Resources and materials previously used within the topic (concrete, pictorial and in story form) will provide familiar contexts and enable children to demonstrate their understanding and apply their knowledge. However, some of the tasks could be used without prior knowledge of dinosaurs.

Explain to the children they are going on a space adventure with lots of maths problems to solve. The questions can be done in the suggested groupings or all together. Work with a small group of children at a time so that you can observe the strategies each child uses. Questions 7, 8 and 10 need to be done one-to-one and recorded on the child’s answer sheet. Resource sheets are provided.

Suggested grouping of questions

Resources

1–7 • 8–12 • 13–16 • 17–18 • 19–20 • 21–23 • 24–26 • 27–29

Resources provided online: A range of 2D shapes • Pictures of dinosaurs • Dinosaur wrapping paper Resources needed and available in the setting: 3D toy dinosaurs • Selection of fiction and non-fiction books pertaining to dinosaurs • Word bank of dinosaur names

Resources Resources provided online: Dot cards 1–10 Alien pictures • Gem resource sheet

Tasks

Es & Os

Benchmarks

Task 1 Dinosaur sort

MNU 0-20b I can match objects, and sort using my own criteria, sharing my ideas with others.

•

Uses knowledge of colour, shape, size and other properties to match and sort items in a variety of different ways.

Task 2 Describe and design a dinosaur

MNU 0-02a I have explored numbers, understanding that they repesent quantities, and I can use them to count, create sequences and describe order.

•

Uses one-to-one correspondence to count a given number of objects to 20.

Asks simple questions to collect data for a specific purpose.

Collects and organises objects for a specific purpose.

Applies counting skills to ask and answer questions and make relevant choices and decisions based on the data.

Contributes to concrete or pictorial displays where one object or drawing represents one data value, using digital technologies as appropriate.

Recognises, describes and sorts common 2D shapes and 3D objects according to various criteria; for example, straight, round, flat and curved.

• •

MNU 0-16a I enjoy investigating objects and shapes • and can sort, describe and be creative with them.

•

•

Questions 1. Look at the numbers in the rockets. Write in the missing numbers.

2. Look at the numbers in the spaceships. Write in the missing numbers.

3. Write the following numbers in the moons – thirteen, zero, twenty, twelve, eight.

4. Look at the numbers on the aliens. Rewrite the numbers in order from the biggest to the smallest.

5. Look at the planets. Write in the missing numbers before, after or in-between the given numbers.

6. Count how many aliens there are, write the total in the box.

7. The astronaut can count up to thirty. Can you count up to thirty? Please start at fourteen.

8. a Give the child 18 aliens (toys or cut outs from the resources bank). Count the aliens. How many aliens are there? Now write the total in the box. b Now move the aliens into a circle. How many aliens are there?

9. Count each alien’s treasure and write the total in the box. Discuss why the third alien might be looking glum. Can the child explain that zero means there are none?

10. Show the children some dot cards to 10; regular dot patterns (five-wise ten-frames; pair-wise ten-frames; domino patterns) and irregular dot patterns (see resource pack). Show each card for a couple of seconds and ask How many dots are there? How do you know? How did you see the 7? etc.

11. Ask the child Look at the space coins here. Point to pile A. How many coins do you think there are (without counting)? Now look at these space coins. Point to pile B. Do you think there are more coins or less coins? Circle the correct answer. Ask the child to explain their thinking. Now count the coins in each pile to check your guess. Discuss how accurate their estimates were.

End-of-level assessments check that pupils have mastered one level before moving to another

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Yearly progress check 2: marking guidance Topic benchmarks/ Es & Os

Question Answers and marking guidance

Number – order and place value MNU 0-02a

1

Number – order and place value MNU 0-02a

Number – order and place value MNU 0-02a

Number – order and place value MNU 0-02a

2

3

4

Answers and marking guidance is given

Early level yearly progress check 2: record sheet •

Answer: 5, 6, 7, 8, 9, 10, 11, 12 and 22, 23, 24, 25, 26, 27, 28, 29 On track • The child writes each missing number correctly and completes the forward sequence accurately and confidently.

Further learning required • The child omits a number or numbers, especially when crossing a decade or in the early teens.

• They mix up the number sequence.

• They reverse the digits when writing some numbers from 12 to 30; for example, the child writes 15 as 51.

• They require a visual support – for example, a number track – to help them complete the task.

On track • The child writes each missing number correctly and completes the backwards sequence accurately and confidently.

Further learning required • The child omits a number or numbers, for example when bridging 10.

• They mix up the number sequence.

• They reverse the digits when writing some numbers from 20–10; for example, the child writes 15 as 51.

• They require a visual support – for example, a number track – to complete the task.

On track • The child will immediately link each oral number word with its corresponding numeral and write it correctly.

Further learning required • The child may be able to connect the oral number word with its symbol for one-digit numbers but find two-digit numbers more challenging, most commonly reversing digits; for example, writing 13 as 31.

• They require a visual support – for example, a number track – to complete the task.

On track • The child understands that the numbers symbolise quantities and can use this knowledge to confidently order the numbers.

Further learning required • The child regards each digit in the numbers 12 and 19 as separate and so orders the numbers as follows: 1, 1, 2, 5, 8, 9.

• They disregard the ‘ones’ digit in 2-digit numbers and so believe that 12 and 19 have the same value and are both ‘the smallest number’.

• They need to use the 0–20 counting sequence to order the numbers.

• They require a visual support – for example, a number track – to complete the task.

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Primary Maths for Scotland

2nd Level Maths Assessment Pack

Aligned to CfE benchmarks

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Add the names of the children in the group/class to the top of columns 3-12. Use multiple sheets depending on the size of your class.

Mark each child as they complete their early level yearly progress check. Suggested coding is: A. Chose an appropriate strategy/method and used it correctly

•

B. Chose an appropriate strategy/method but used it incorrectly or made an error in calculation C. Chose an inappropriate strategy/method or did not attempt the question Question

Domain

1

MNU 0-02a

2

MNU 0-02a

3

MNU 0-02a

4

MNU 0-02a

5

MNU 0-02a

6

MNU 0-02a

7

MNU 0-02a

8a

MNU 0-02a

8b

MNU 0-02a

9

MNU 0-02a

10

MNU 0-01a

11

MNU 0-01a

12

MNU 0-03a

13

MNU 0-03a

14

MNU 0-03a

15a

MNU 0-07a

15b

MNU 0-07a

16

MNU 0-03a

17

MNU 0-13a

18

MNU 0-13a

19

MNU 0-02a

20

MNU 0-03a

21

MNU 0-16a

22a

MNU 0-09a

22b

MNU 0-09a

23

MNU 0-10a

24a

MNU 0-11a

24b

MNU 0-11a

24c

MNU 0-11a

25a,b,c

MNU 0-17a MNU 0-19a

26

MNU 0-17a MNU 0-19a

27

MNU 0-20a MNU 0-20b

28

MNU 0-20a MNU 0-20b

29a, b, c

MNU 0-20a MNU 0-20b

Record sheets allow teachers to monitor progress

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Problem Solving Packs Problem Solving Packs are ready-made banks of rich problem-solving activities and resource sheets, with enabling prompts to stimulate thinking or simplify problems and extension activities to stretch pupils.

Number, Money and Measure

Number, Money and Measure

Cuttings

Let’s go!

Experiences and Outcomes •

I can use my knowledge of the sizes of familiar objects or places to assist me when making an estimate of measure. (MNU 2-11a)

•

I can use the common units of measure, convert between related units of the metric system and carry out calculations when solving problems. (MNU 2-11b)

•

I can explain how different methods can be used to find the perimeter and area of a simple 2D shape or volume of a simple 3D object. (MNU 2-11c)

Resources •

Centimetre square paper and scissors

•

Some pre-cut 6 cm by 4 cm rectangles and the outline of a 22 cm by 10 cm rectangle drawn on centimetre square paper.

Before they start...

•

Pupils need to be able to work with dimensions given in centimetres.

•

Pupils need to know how to calculate the area of a rectangle.

4 cm

10 cm

6 cm

4 cm

6 cm

Let’s Go gives pupils working below age-related What is the maximum number of 6 cm by 4 cm rectangles that can be cut from the 22 cm by 10 cm expectations an enabling piece of plastic? Show how this can be done. prompt. There is an Enabling prompt Pupils who are struggling to make a start on the problem may be encouraged to draw a 22 cm by 10 cm extension activity for those rectangle, or be given the rectangle already drawn on centimetre square paper. They can also be given some pre-cut 6 cm by 4 cm rectangles. The following prompts will help pupils to get started on the work above age-related problem, with the teacher pointing to pupils’ diagrams as appropriate: • I wonder how many of these small rectangles can be fitted into the large one? expectations • If we turn these ones around I wonder if we can fit in any more?

4 cm

22 cm

6 cm

!

•

Can you fit any more rectangles into this space?

Extension activity Let’s go!

Amman and Isla have a different rectangular piece of plastic. It measures 28 cm by 22 cm. They are going to cut out smaller rectangles measuring 10 cm by 6 cm from their piece of plastic so that some larger rips can be repaired.

When introducing the problem, the teacher can pose the question “Why do Findlay and Nuria want to cut the maximum number of rectangles?”. This will generate some discussion of reducing waste.

6 cm

Finlay and Nuria are repairing some small rips in the plastic covering of the school polytunnel.

They have a rectangular piece of plastic measuring 22 cm by 10 cm which they intend to cut into smaller rectangles to use as patches. The smaller rectangles will each measure 6 cm by 4 cm. Finlay and Nuria want to cut the maximum number of 6 cm by 4 cm rectangles from the larger 22 cm by 10 cm rectangle.

10 cm

22 cm

6 cm

28 cm

Before They Start sections ensure pupils have the prerequisite knowledge and skills they need before completing the problem

10 cm

6 cm

10 cm

What is the maximum number of 10 cm by 6 cm rectangles that can be cut from the 28 cm by 22 cm piece of plastic? Show how this can be done.

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Let’s Check gives solutions to the problem

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Number, Money and Measure

Number, Money and Measure

Let’s discuss!

Let’s check!

When a range of solutions have been offered, the teacher should begin to facilitate discussion of these using prompts like: • Do all of the rectangles need to be lying the same way?

•

✔

9 smaller rectangles can be cut out in this way:

If you arrange the rectangles in a different way, can you cut more out?

Using a visualiser, or similar, to display different solutions for discussion will be useful. The teacher can use a number of pre-cut 6 cm by 4 cm rectangles and the outline of a 22 cm by 10 cm rectangle to model different solutions and to demonstrate how moving the smaller rectangles around within the outline of the larger rectangle can result in different solutions.

Some pupils may see the relationship between the dimensions of the smaller rectangle and the larger rectangle and use this as they decide where to place the smaller rectangles within the larger rectangle. Some pupils may work with areas immediately, using number facts to calculate the area of the large rectangle and the area of the small rectangle then dividing. This would provide an opportunity to discuss the real-life context and emphasise the importance of showing how the smaller rectangles can be cut out.

Note that rotations of this solution might be offered. Two examples are shown below. This provides valuable opportunities to discuss the real-life context.

If the most efficient solution (fig. 1) is not reached, it is likely that solutions like fig. 2 will be offered as the ‘best’ way to cut out the rectangles.

In the extension activity, 10 smaller rectangles can be cut out as shown here. Note that this is the same solution rotated.

Let’s Discuss gives pupils different strategies to solve the problem independently, in pairs or groups.

There are prompts for teachers as well as methods pupils may use

Fig. 1

Fig. 2

For some pupils this might be a reasonable conclusion to the problem. For others though the teacher might direct the discussion towards the area ‘left over’ to encourage pupils to see that there may be a more efficient solution. Prompts like these may be useful: •

Do you think there is enough plastic left over to make another rectangle? How can you check this?

•

It is interesting that 6 cm and 4 cm added together make 10 cm (and/or 6 cm + 6 cm + 6 cm + 4 cm makes 22 cm and/or 6 cm + 4 cm + 4 cm + 4 cm + 4 cm makes 22 cm)

Some pupils might ask if the unused pieces of plastic can be collected and used to repair a rip.

The teacher might use this as an opportunity to ask the pupils to consider how strong the smaller pieces might be and also how efficient this would be in terms of the work involved.

Let’s reflect!

After pupils have had an opportunity to grapple with the problem they should be brought together and given an opportunity to share their strategies and discuss their progress towards a solution.

It is likely that pupils will share approaches that involve them ‘having a go’, evaluating their solution, breaking down one attempt in order to look for a better solution, and so on.

Teacher Guide Reference • •

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Let’s Reflect offers an opportunity to discuss different strategies and methods as a class, to consolidate learning

Unit 8, 1st Level Teacher Guide Unit 9, 2nd Level Teacher Guide

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