i see problem solving-lks2

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GARETH METCALFE

I SEE PROBLEM SOLVING - LKS2MATHS TASKS FOR TEACHING

PROBLEM-SOLVING

0 10025 8433

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I SEE PROBLEM-SOLVING – LKS2CONTENTS

I SEE PROBLEM-SOLVING – LKS2

Contents (tasks 1 → 20)Introduction

Task 1, Number and Place Value: Making 3-digit numbers

Task 2, Number and Place Value: Making 4-digit numbers

Task 3, Number and Place Value: Numbers in columns

Task 4, Number and Place Value: 0-100 number line

Task 5, Number and Place Value: 0-1000 number line

Task 6, Number and Place Value: Patterns in Sequences

Task 7, Number and Place Value: Count back through 0

Task 8, Number and Place Value: Rounding to 10 and 100

Task 9, Number and Place Value: Rounding money

Task 10, Number and Place Value: Roman Numerals

Task 11, Addition and Subtraction: Consecutive numbers

Task 12, Addition and Subtraction: Make 24

Task 13, Addition and Subtraction: Number sentences

Task 14, Addition and Subtraction: = and > signs

Task 15, Addition and Subtraction: Bordering 10

Task 16, Addition and Subtraction: Position digits to add

Task 17, Addition and Subtraction: Position digits to subtract

Task 18, Addition and Subtraction: Sum and difference

Task 19, Addition and Subtraction: More boys or girls?

Task 20, Addition and Subtraction: Part/whole word questions



Contents (tasks 21 → 41)Task 21, Addition and Subtraction: Change at the shop

Task 22, Multiplication and Division: × + number sentences

Task 23, Multiplication and Division: Area models

Task 24, Multiplication and Division: Largest product

Task 25, Multiplication and Division: 2-digit product

Task 26, Multiplication and Division: Shapes with matchsticks

Task 27, Multiplication and Division: Division in context

Task 28, Multiplication and Division: Different quotients

Task 29, Multiplication and Division: Finding factors

Task 30, Multiplication and Division: Venn diagrams

Task 31, Mixed Operations: Different answers

Task 32, Mixed Operations: Questions in context

Task 33, Mixed Operations: Combinations

Task 34, Fractions: Estimating fractions

Task 35, Fractions: Fraction of a shape

Task 36, Parts and the whole

Task 37, Fractions: Fractions on a line

Task 38, Fractions: Sharing contexts

Task 39, Fractions: Fraction of a number

Task 40, Measurement: Balancing scales

Task 41, Measurement: Measures of time



Contents (tasks 42 → 54)Task 42, Measurement: Reading clocks

Task 43, Measurement: Combinations of change

Task 44, Measurement: Comparing angles

Task 45, Measurement: Area and perimeter

Task 46, Geometry: Shape properties

Task 47, Geometry: Building shapes

Task 48, Geometry: Lines of symmetry

Task 49, Geometry: Coordinate points

Task 50, Data Handling: After-school clubs

Task 51, Data Handling: Different graph types

Task 52, Data Handling: Making judgements

Task 53, Data Handling: Train timetables

Task 54, Data Handling: Comparing teams

I See Maths Resources

I SEE PROBLEM-SOLVING – LKS2INTRODUCTION

I SEE PROBLEM-SOLVING – LKS2Maths tasks for teaching problem-solving

Introduction

For use by the purchasing institution only. Copyright I See Maths ltd. Circulation is prohibited.

I See Problem-Solving – LKS2 helps all children to learn how to

solve multi-step maths questions.

Tasks start with a Build prompt,

which leads into the main Task question. Each page can be

printed and given to the

children.

There are also Support, Explain

and Extend prompts for most tasks – these provide additional

support for the main task or extra

challenge to take the learning

deeper!

The answers to each task are

shown in the Worked Examplesdocument, which is available for

free on this page as a

PowerPoint or as a PDF file,

modelling solutions step-by-step.

The resource is comprised of 54 tasks, linked to all different

areas of the lower KS2 mathematics curriculum.

I hope that I See Problem-Solving – LKS2 helps all children to develop their maths problem-solving skills!

Gareth Metcalfe

http://www.iseemaths.com/problem-solving-lks2


Task 1 Build: Making 3-digit numbers

BUILD

Teacher notes: Representations of 230 are correct; representations of 203 and 210 incorrect.

100

Is this 230? or Is this 203? or

Is this 230? or

20 + 3

Is this 210? or

100

100 100 10

NUMBER AND PLACE VALUE

10 10

10

1010

10

10

10 10 10 10 10

10 10 10 10 10

BUIL

D100


Is this 230? or

20 + 3

Is this 210? or

100

100 100 10 10 10

10

1010

10

10

10 10 10 10 10

10 10 10 10 10

BUILD

100


Is this 230? or

20 + 3

Is this 210? or

100

100 100 10 10 10

10

1010

10

10

10 10 10 10 10

10 10 10 10 10


Task 1: Making 3-digit numbersTeacher notes: 4 ways: Three 100s and four 10s; two 100s and fourteen 10s; one 100 and twenty-four 10s; thirty-four 10s. Solutions are shown in the Worked Example (download from www.iseemaths.com/problem-solving-LKS2).

TASK

100 10

How can 340 be made using 10 and 100 counters?

Level 1: I can find a way

Level 2: I can find different ways

Level 3: I know how many ways there are

TASK

100 10





TASK

100 10





TASK

100 10





TASK

100 10






http://www.iseemaths.com/problem-solving-LKS2


Task 1 Prompts: Making 3-digit numbers

SUPPORT

EXTEND

Teacher notes: Explain: 4 hundreds 16 tens 46 tens 12 ones 102 onesExtend: Fewest counters is 9 (four 100s, two 10s, three 1s); most counters is 423 (just using 1s).423 with 18 counters: three 100s, twelve 10s, three 1s OR four 100s, one 10, thirteen 1s.

EXPLAIN

Tip 1: 340 can be made with two 100 counters and some 10 counters. How many 10 counters would be needed?

Tip 2: 340 can be made using only 10 counters.

How many 10 counters to make 340?

Remember: ten lots of = 10010

460 can be made with hundreds and 6 tens.

460 can be made with 3 hundreds and tens.

460 can be made with tens.

342 can be made with 3 hundreds, 3 tens and ones.

342 can be made with 2 hundreds, 4 tens and ones.

How can 423 be made using 1, 10 and 100 counters?

What are the fewest counters that can be used?

What are the most counters that can be used?

There are two ways to make 423 using 18 counters. Find them.

10010

1

EXTEND


What are the fewest counters that can be used?

What are the most counters that can be used?

There are two ways to make 423 using 18 counters. Find them.

10010

1



Task 2 Build: Making 4-digit numbers

BUIL

D

426 can be made

with these counters:

counters100

1

10

Teacher notes: 4 100s, 2 10s, 6 1s 4 100s, 1 10s, 16 1s 42 10s, 6 1sNote: for question 1 there are other possibilities e.g. 3 100s, 2 10s, 106 1s

426 can be made


100

1

10

426 can be made


1

10

2 6

4

1counters

counters

counters

counters

counters

counters

counters


BUILD

426 can be made


counters100

1

10

426 can be made


100

1

10

426 can be made


1

10

2 6

4

1counters

counters

counters

counters

counters

counters

counters

BUILD

426 can be made


counters100

1

10

426 can be made


100

1

10

426 can be made


1

10

2 6

4

1counters

counters

counters

counters

counters

counters

counters


Task 2: Making 4-digit numbersTeacher notes: Example ways: Two 1000s, one 100 and five 10s; one 1000, eleven 100s and five 10s; 215 10s. Solutions are shown in the Worked Example (download from www.iseemaths.com/problem-solving-LKS2).

TASK




Level 3: Find 4 or more ways100

101000


TASK





101000

TASK





101000

TASK





101000

TASK





101000



Task 2 Prompts: Making 4-digit numbers

SUPP

ORT

EXTEND

Teacher notes: Explain: 1300 has 2 ways (one 1000 and three 100s; thirteen 100s). 3100 has 4 ways (three 1000s and one 100; two 1000s and eleven 100s; one 1000 and twenty-one 100s). The more thousands, the more ways the number can be made.Extend: Largest = 930, smallest = 129, closest to 200 = 192.

EXPLAIN

Which question can be completed in more ways?

Adding a number’s digits gives the sum of the digits.

Examples:

59 is a 2-digit number. The sum of the digits is 5 + 9 = 14

306 is a 3-digit number. The sum of the digits is 3 + 0 + 6 = 9

I think of a 3-digit number. All the digits are different. The sum of the digits is 12.

What is the largest the number could be?

What is the smallest the number could be?

What is the closest to 200 the number could be?

is the same as lots of 1001000

10is the same as lots of 1000

10150 is the same as one and lots of 100

10150 is the same as lots of

Explain why one of these questions can be answered in more ways.

Question A:

Make 1300 using 100 and 1000counters.

1001000

Question B:

Make 3100 using 100 and 1000counters.

1001000



Task 3 Build: Numbers in columns

BUILD

Teacher notes: 416, made with 11 counters. 537, made with 15 counters.

For this task, 3-digit numbers are made by putting counters in the

hundreds, tens or ones columns.

Example: This is 241

It is made with 7 counters

This is

It is made with counters.

H T O

H T O

This is


H T O draw

537

BUI

LD





This is


H T O

H T O

This is


H T O draw

537

BUILD





This is


H T O

H T O

This is


H T O draw

537



Task 3: Numbers in columns

TASK

Teacher notes: Smallest to largest: 103, 112, 121, 130, 202, 211, 220, 301, 310, 400. A system for finding all solutions is shown in the Worked Example (download from www.iseemaths.com/problem-solving-LKS2).





H T O

How many 3-digit numbers can be made using four counters?

What is the smallest possible number? What is the largest possible number?

TASK





H T O



TASK





H T O






Task 3 Prompts: Numbers in columns

SUPPORT

EXTEND

Teacher notes: Support: Left to right: Incorrect (2-digit number), incorrect (5 counters), correct.Explain: James could have made 500, Zack could have made 499.Extend: 493

EXPLAIN

James makes a 3-digit number by placing 5 counters in the


Zack makes a 3-digit number by placing 22 counters in the


Explain how it is possible for James to make a bigger number than Zack.

James could have made… Zack could have made…

Make the number closest to 500by placing 16 counters in the


H T O

The task: make 3-digit numbers using four counters.

Are these correct or incorrect examples? or

Example A:

H T O

Example B:

H T O

Example C:

H T O

EXTEND

Make the number closest to 500by placing 16 counters in the hundreds, tens or ones columns.

H T O



Task 4 Build: 0-100 number line

BUILD

Teacher notes: Draw out reasoning behind the positioning of the numbers. For example, 8 is slightly nearer 0 than 20; 25 is one-third of the distance between 20→35; the gap between 73→85 is slightly smaller than the gap between 85→100.

0 10020 35 73

Position 8, 25 and 85 on the number line:

BUILD 0 10020 35 73


BUILD 0 10020 35 73


BUILD 0 10020 35 73


BUILD 0 10020 35 73




Task 4: 0-100 number lineTeacher notes: Number lines can be made using masking tape. Example of reasoning: 0→32 is three times the distance of 32→40. Examples of reasoning shown in the Worked Example (download from www.iseemaths.com/problem-solving-LKS2).

TASK

Make a long number line. Put a 0 on the left end and 100 on

the right end of your number line:

Position these numbers on your number line: 32, 40, 59, 84

1000

Tip 1: compare the gap between 0 and 32 with the gap between 32 and 40.



TAS

K

Make a long number line. Put a 0 on the left end and 100 on the right end of your number line:


1000



TASK



1000





Task 4 Prompts: 0-100 number line

SUPPORT

EXT

END

Teacher notes: Support: 13 = red arrow, 38 = green arrow.Explain: Example sentences: The green arrow is approximately three times shorter than the red arrow. The yellow arrow is exactly twice as long as the green arrow.Extend: Number line approximate values: 0-16-56; 0-90-140; 18-37-44; 18, 63, 83.

EXPLAIN

Estimate the value of the missing numbers:

0 5020

Which arrows show the position of 13 and 38 on the number line?

0 10025

Write 4 sentences that compare the lengths of the red, green, blue and orange arrows:

Example sentence stems:

The ______ arrow is approximately ___ times longer than the ______ arrow.

The ______ arrow is exactly ___ times shorter than the ______ arrow.

8433

0 16

0 90

18 63

4437


Explain how you know.


Task 5 Build: 0-1000 number line

BUILD

Teacher notes: Draw out reasoning behind the positioning of the numbers. For example, 200 is nearer 350 than 0; 640 is one-third of the distance between 600→720; the gap between 880→1000 is smaller than the gap between 720→880.

0 1000720350 600



BUILD 0 1000720350 600


BUILD 0 1000720350 600


BUILD 0 1000720350 600


BUILD 0 1000720350 600



Task 5: 0-1000 number lineTeacher notes: Number lines can be made using masking tape. Example reasoning: 790→931 is approximately twice the gap of 931→1000. Reasoning examples are shown in the Worked Example (download from www.iseemaths.com/problem-solving-LKS2).

TASK



10000


Tip 2: which is the biggest gap between the numbers? Which is the smallest gap?


TASK



10000



TASK



10000





Task 5 Prompts: 0-1000 number line

SUPPORT

EXTEND

Teacher notes: Support: 235 = purple arrow, 412 = blue arrow.Explain: Example sentences: The green arrow is exactly four times longer than the red arrow; The blue arrow is approximately three times longer than the yellow arrow.Extend: Number line approximate values: 18-70-122; 100-460-580; 280-490-800; 245, 267, 317.

EXPLAIN

Estimate the value of the missing numbers:

0 500350

Which arrows show the position of 240 and 410 on the number line?

0 40055

Write 3 sentences that compare the lengths of the red, green, blue and orange arrows:

Example sentence stems:

The ______ arrow is approximately ___ times longer than the ______ arrow.

The ______ arrow is exactly ___ times shorter than the ______ arrow.

369275

18 70

100 460

245 267

800490



I SEE PROBLEM-SOLVING – LKS2NUMBER AND PLACE VALUE

Task 6 Build: Patterns in sequences

BUILD

Teacher notes: Pattern for 5 times table: repeating of 5,0… Pattern for 2 times table: repeating of 2,4,6,8,0...

This is the 5 times table: 5, 10, 15, 20, 25, 30, 35, 40…

The pattern in the ones value is…

This is the 2 times table: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20…


BUILD





BUILD





BUILD





This is the times table.


Task 6: Patterns in sequencesTeacher notes: The green task has more clues than the yellow task (same answers). 4 × table, pattern of ones: 4,8,2,6,0... 6 × table, pattern of ones: 6,2,8,4,0... Answers shown in the Worked Example (download from www.iseemaths.com/problem-solving-LKS2).

TASK

For each times table, what is the pattern in the ones value?

1 × =

2 × =

3 × =

4 × =

5 × =

6 × =

7 × =

8 × =

9 × =

10 × =

3

2

2

1

1

0

6

0


1 × =

2 × =

3 × =

4 × =

5 × =

6 × =

7 × =

8 × =

9 × =

10 × =

3

2

1

4

8

2

0

8


TASK

For each times table, what is the pattern in the ones value?

1 × =

2 × =

3 × =

4 × =

5 × =

6 × =

7 × =

8 × =

9 × =

10 × =

3

2

1

0

0


1 × =

2 × =

3 × =

4 × =

5 × =

6 × =

7 × =

8 × =

9 × =

10 × =

1

4

2

0

8



Task 6 Prompts: Patterns in sequences

S

UPPORT

EXTEND

Teacher notes: Support: 3 × 3 = 9, single-digit number. 3 × 8 = 24, incorrect ones value.Explain: 8 × table ones value pattern: 8,6,4,2,0…Extend: Statement 1 is true: to multiply, 14 can be partitioned into 10 and 4. Multiplying by 10 does not affect the ones value. Example: 4 × 7 = 28, 14 × 7 = 98. Statement 2 is false: The pattern that repeats is 3,6,9,2,5,8,1,4,7,0… You have to extend the 3 ×table beyond 10 lots of 3 to expose this repeating pattern.

EXPLAIN

Agree or disagree:

Statement 1: ‘If you multiply any number by 14, the ones value is

the same as when you multiply the number by 4.’

Statement 2: ‘There is not a repeating pattern for the ones value in

the 3 times table.’

Look at these three lines:

The repeating pattern for the ones value

in the 8 times table is…


1

1 × =

2 × =

3 × =

Finish the statement:

‘This can’t be the 3 times

table because…’

Look at these three lines:

Finish the statement:

‘This can’t be the 8 times

table because…’

1

8

1 × =

2 × =

3 × =

EXTEND

Agree or disagree:

Statement 1: ‘If you multiply any number by 14, the ones value is

the same as when you multiply the number by 4.’

Statement 2: ‘There is not a repeating pattern for the ones value in

the 3 times table.’


Task 7 Build: Count back through 0

BU

ILD

Teacher notes: The number line can be used to count steps. Answers: -1, -2, -2

0


-1-2-3-4 21 3 4 5 6 7 8 9 10

Question 1: I start counting from 10.

I count back in steps of 1. The first negative number I say is





BUILD

0-1-2-3-4 21 3 4 5 6 7 8 9 10







BUILD

0-1-2-3-4 21 3 4 5 6 7 8 9 10








Task 7: Count back through zero

TASK

Teacher notes: The Task prompt can be printed and laminated. Create different questions using this format by giving children one or two of the numbers. Example Question: Start from 9, first negative number -3. Possible answers: count back in steps of 3,6,12. Example Question: Count back in steps of 4. Answer 1: start from 13, first negative -3. Answer 2: start from 22, first negative -2. Example questions and answers are shown in the Worked Example (download from www.iseemaths.com/problem-solving-LKS2).


Start counting from

Count back in steps of

The first negative number is

TASK

Start counting from


The first negative number is



Task 7 Questions: Count back through 0

PRAC

TISE

Teacher notes: Green questions: Q1: -2 Q2: -2 Q3: -1 Q4: 2 OR 5 Q5: 2 or 7 or any other number adding a multiple of 5 to 7. Yellow questions: Q1: -2 Q2: -4 Q3: 7 or 12 any other number adding a multiple of 5 to 12 Q4: 6, 9 or 18 Q5: -4Extend: 3, 4, 6, 8, 12 or 24

1. Start from 14. Count back in 2s. The first negative number is

5. Start from . Count back in 5s. The first negative number is -3.

4. Start from 9. Count back in s . The first negative number is -1.



PRACTISE


4. Start from 14. Count back in s . The first negative number is -4.


EXTEND

Start from 21


The first negative number is -3

3. Start from . Count back in 5s. The first negative number is -3.


Which of these questions can be answered in different ways?

Level 1: I can find an answer

Level 2: I can find different answers

Level 3: I can find all the answers


Task 8 Build: Rounding to 10 and 100

BUILD

1

Q1. Which of these numbers, rounded to the nearest 10, are 50?

47 58 149 42 54

BUILD

2

Teacher notes: Build 1: Q1: 47, 54 Q2: 147, 149, 154 Q3: 247, 158, 196Build 2: Mistake 1: 351 to the nearest 10 is 350. Mistake 2: 351 should round up to 400. Mistake 3: should round up to 240. Mistake 4: Answer does not include the 2 hundreds.



147 158 149 142 154


247 158 149 196 254

Explain the mistakes:

Round 351 to the nearest 100.

Mistake 1: 350

Mistake 2: 300


Mistake 3: 230

Mistake 4: 40

BUILD

1


47 58 149 42 54

BUILD

2


147 158 149 142 154


247 158 149 196 254



Mistake 1: 350

Mistake 2: 300


Mistake 3: 230

Mistake 4: 40


Task 8: Rounding to 10 and 100Teacher notes: 5 answers: 350, 351, 352, 353, 354. Solutions are shown using a number line in the Worked Example (download from www.iseemaths.com/problem-solving-LKS2).

TASK

Rounded to the nearest 10, my number is 350.


What could my number be?





330 340 350 360 370

200 300 400 500 600

TASK







330 340 350 360 370

200 300 400 500 600

TASK







330 340 350 360 370

200 300 400 500 600

TAS

K







330 340 350 360 370

200 300 400 500 600


To the nearest 10, numbers in the blue space round to 350.

To the nearest 100, numbers in red space round to 400.


Task 8 Prompts: Rounding to 10 and 100

SUPPORT

EXTEND

Teacher notes: Support: 342 in neither, 347 in blue only, 354 in both, 358 in red only.Explain: 64 because 64 is larger than 59 and 65 rounds to 70.Extend: 396, 399, 402

EXPL

AIN

What is the largest whole number that, rounded to the

nearest 10, is 60?

(a) 65

(b) 59

(c) 64


My number is a multiple of 3.


There are different possible answers.

EX

TEND


My number is a multiple of 3.



340 360350

300 500400

Which of these numbers go in the red and blue spaces: 342, 347, 354, 358


Task 9 Build: Rounding money

BUILD

1

Position these numbers on the number line:

7 18 22 26 34

BUILD

2

Teacher notes: Build 2 answers: Lisa has 24p, Rachel has 25p

For each number, which is the closest 10?

0 10 20 30 40

Rounded to the nearest 10p, Lisa has 20p.

Rounded to the nearest 10p, Rachel has 30p.

Rachel has 1p more than Lisa.

Lisa has Rachel hasp p


BUILD

1

Position these numbers on the number line:

7 18 22 26 34

BUILD

2

For each number, which is the closest 10?

0 10 20 30 40

Rounded to the nearest 10p, Lisa has 20p.

Rounded to the nearest 10p, Rachel has 30p.

Rachel has 1p more than Lisa.

Lisa has Rachel hasp p


Task 9: Rounding money

TASK

Rounded to the nearest 10p, Max has 50p.

Rounded to the nearest 10p, Ben has 80p.

Teacher notes: Green Task: Q1: True Q2: 75p Q3: Possible, e.g. Max has 51p, Ben has 76p.Yellow task: Smallest difference: Max 54p, Ben 75p, difference = 21p. Largest difference: Max 45p, Ben 84p, difference = 39p Example solutions are shown in the Worked Example (download from www.iseemaths.com/problem-solving-LKS2).


Q1: True or false: Max could have 54p.

Q2: What is the smallest amount of money Ben could have?

Q3: Possible impossible: Ben could have 25p more than Max.

TASK



What is the smallest possible difference between the amount of

money Max and Ben have?

What is the largest possible difference between the amount of


TASK



Q1: True or false: Max could have 54p.

Q2: What is the smallest amount of money Ben could have?

Q3: Possible or impossible: Ben could have 25p more than Max.

TASK



What is the smallest possible difference between the amount of


What is the largest possible difference between the amount of




Task 9 Prompts: Rounding money

SUPPORT

EXTEND

Teacher notes: Explain: Joy has between £1.65 and £1.74, Simona has between £1.50 and £2.49. Simone may, therefore, have less money than Joy.Extend: The least Stan has is £2.45, the most Gavin has is £4.49, largest possible difference £2.04

EXPLAIN

40p 50p 60p 70p 80p 90p

Max Ben

The smallest amount of money Max could have.

The largest amount of money Max could have.

The smallest amount of money Ben could have.

The largest amount of money Ben could have.

Rounded to the nearest 10p, Joy has £1.70

Rounded to the nearest £1, Simona has £2

Agree or disagree:

‘Simona may have less money than Beth.’

Rounded to the nearest £1, Gavin has £4

Rounded to the nearest 10p, Stan has £2.50

What is the largest possible difference between the

amount of money Gavin and Stan have?

EXTEND

Rounded to the nearest £1, Gavin has £4

Rounded to the nearest 10p, Stan has £2.50

What is the largest possible difference between the

amount of money Gavin and Stan have?


Task 10 Build: Roman Numerals

BUILD

Teacher notes: IX = 9 XIX = 19 VIII = 8 XI = 11. Leftover numbers: 13 = XIII 21 = XXINote potential misconceptions, for example confusing 9 and 11 or interpreting VIII as 13.

Match the Roman Numerals to the correct number.

IX XIX

VIII XI

13

19

21

8

11

9

Note: some of the numbers will be left over.

Write the Roman Numerals for the leftover numbers.

BUILD


IX XIX

VIII XI

13

19

21

8

11

9



BUILD


IX XIX

VIII XI

13

19

21

8

11

9




Task 10: Roman NumeralsTeacher notes: Part 1: XVII (17). The answer to part 1 is shown in the Worked Example (download from www.iseemaths.com/problem-solving-LKS2).

TASK

Part 1: My Roman Numeral is less than 20.

It has 4 symbols. 3 of the symbols are different.

What is my Roman Numeral?


Part 2: Design your own question.

My Roman Numeral is less than…

It has... symbols and… of the

symbols are different.

Example: XII = 12

3 symbols 2 different symbols (X and I)

TASK








Example: XII = 12


TASK








Example: XII = 12


TASK








Example: XII = 12



Example Roman Numerals:

I = 1 V = 5 (1 less than 5) X = 10

I I = 2 IV = 4 (1 less than 5) IX = 9 (1 less than 10)

I I I = 3 VI = 6 (1 more than 5) XI = 11 (1 more than 10)

VIII = 8 (3 more than 5) XVIII = 18 (3 more than 10)


Task 10 Prompts: Roman Numerals

SUPPORT

EXTEND

Teacher notes: Explain: Key ideas are that we have a place value system meaning that we don’t need any more symbols for larger numbers. Roman Numerals involves adding and subtracting symbols which can make numbers hard to read, e.g. 18 = XVIII, 5 symbols used.

Extend: Smallest to largest: XXVII (27), XXIX (29), XXX (30), XL (40), L (50). For these Roman Numerals, the numbers with the most symbols are the smallest and vice versa.

EXPLAIN

To write all our numbers, we use ten symbols: 0,1,2,3,4,5,6,7,8,9.

To write the numbers between 1→30 in Roman Numerals, you only need to use three symbols (I, V and X).

Agree or disagree:

‘Roman Numerals are easier to use than our numbers because you don’t need as many symbols.’

Order the numbers from smallest to largest:

What do you notice?

XXVIILXLXXX XXIX

L = 50X = 10V = 5I = 10

EXTE

ND

Order the numbers from smallest to largest:

What do you notice?

XXVIILXLXXX XXIX

L = 50X = 10V = 5I = 10

I SEE PROBLEM-SOLVING – LKS2ADDITION AND SUBTRACTION

Task 11 Build: Consecutive numbers

BUILD

‘Say three consecutive numbers.’

4, 5, 7 2, 3, 4, 59, 10, 11

Circle the number sentences that are equal to 15:

1 + 3 + 5 + 7

6 + 5 + 4 1 + 2 + 3 + 4 + 5

2 + 3 + 4 + 5 2 + 3 + 5 + 3 + 2

Teacher notes: Draw attention to efficient calculation strategies e.g. for 6+5+4, do 6+4 then add 5. Make the connection between 2+3+5+3+2 and 3 lots of 5 (two lots of 2+3, one 5).

or

BUILD


4, 5, 7 2, 3, 4, 59, 10, 11


1 + 3 + 5 + 7

6 + 5 + 4 1 + 2 + 3 + 4 + 5

2 + 3 + 4 + 5 2 + 3 + 5 + 3 + 2

or

BUILD


4, 5, 7 2, 3, 4, 59, 10, 11


1 + 3 + 5 + 7

6 + 5 + 4 1 + 2 + 3 + 4 + 5

2 + 3 + 4 + 5 2 + 3 + 5 + 3 + 2

or


Task 11: Consecutive numbers

Think of three consecutive numbers. These are your numbers.

Add your numbers.

Multiply your middle number by 3.

What do you notice? Explain.

TASK


Add your numbers.



TASK

Teacher notes: The sum of three consecutive numbers is the same as the middle number multiplied by 3. Examples: 3 + 4+ 5 = 3 × 4; 20 +21+ 22 = 3 ×21. Once children find this pattern with one example, they see if the pattern works for other examples. Explain the pattern using visual representations e.g. 10-frames. An example solution is shown in the Worked Example (download from www.iseemaths.com/problem-solving-LKS2).


Add your numbers.



TASK


Add your numbers.



TASK

http://www.iseemaths.com/problem-solving-KS1


Task 11 Prompts: Consecutive numbers

This picture shows 5 + 6 + 7

SUPPORT

Examples: these consecutive numbers add up to make 18:

5, 6, 7 3, 4, 5, 6

Q1: Which consecutive numbers add up to make 30?

There are 3 possible answers.

Q2: I think of a number. It is less than 20. I can make this

number by adding two, three or five consecutive numbers.

What is my number?

EXTEND

Teacher notes: Explain: True. When you have two consecutive numbers, one number is always odd and the other number is always even. Odd + even = odd.Extend: Q1: 9, 10, 11 6, 7, 8, 9 4, 5, 6, 7, 8 Q2: 15

This picture shows 3 × 6

Explain why 5 + 6 + 7 gives the same answer as 3 × 6.

Agree or disagree:

‘When I add two consecutive numbers, the answer is

never in the two times tables.’

Explain.

EXPLAIN


Task 12 Build: Make 24

BUILD

Teacher notes: Red: 2 is less than 3. Green: two 6s. Blue: sum is 16.

I think of three different whole numbers.

Each number is 3 or more. The numbers add to make 15.

What could the three numbers be?

+ + = 15

Spot the mistakes:

8 + 5 + 2 4 + 5 + 76 + 6 + 3

BUILD




+ + = 15

Spot the mistakes:

8 + 5 + 2 4 + 5 + 76 + 6 + 3

BUILD




+ + = 15

Spot the mistakes:

8 + 5 + 2 4 + 5 + 76 + 6 + 3


Task 12: Make 24

TASK

Teacher notes: This task can be modelled practically using 24 counters (see Support prompt).Answers: 6, 7, 11 6, 8, 10 7, 8, 9 All possible solutions are shown in the Worked Example (download from www.iseemaths.com/problem-solving-LKS2).


Each number is more than 5. The numbers add to make 24.


There are different possible answers!

+ + = 24

TA

SK





+ + = 24

TASK





+ + = 24

TASK





+ + = 24



Task 12 Prompts: Make 24

SUPP

ORT

EXTEND

Teacher notes: Explain: If one number is 12, the sum of the other two numbers is 12. This is not possible using two different whole numbers that are more than 5.Extend: Two possible answers: 6, 7, 8, 11 6, 7, 9, 10

Explain why one of the numbers cannot be 12.

If one of the numbers is 12, then the other two numbers…

The three numbers have to be… but…

EXPLAIN

Tip: Share 24 counters between three whiteboards.

Each whiteboard represents one of the numbers.

There must be more than 5 counters on each whiteboard.

There must be a different number of counters on each whiteboard.

I think of four different whole numbers.


What could the four numbers be?

+ + = 32+



Level 3: I know how many answers there are

10 – = 6

10 = – 6

10 = + 6

6 + = 10


Task 13 Build: Number sentences

BUILD

Teacher notes: The bar model can be used to help discern whether a part or the whole needs to be calculated. 6 + 10 = ____ 6 + ____ = 10

6 + 10 =

– 10 = 6

36 – = 12

36 – 12 =

36 = 12 +

12 + = 36

12 + 36 =

– 36 = 12

106

10

6

10 – = 6

10 = – 6

10 = + 6

6 + = 10BUILD

6 + 10 =

– 10 = 6

36 – = 12

36 – 12 =

36 = 12 +

12 + = 36

12 + 36 =

– 36 = 12


Task 13: Number sentencesTeacher notes: Green Task: 16 number sentences (4+3=7, 3+4=7, 7=4+3, 7=3+4, 7-4=3, 7-3=4, 4=7-3,

3=7-4, 7+4=11, 4+7=11, 11=7+4, 11=4+7, 11-7=4, 11-4=7, 7=11-4, 4=11-7)

Yellow Task: 16 number sentences (19+15=34, 15+19=34, 34=19+15, 34=15+19, 34-19=15, 34-15=19,

19=34-15, 15=34-19, 34+19=53, 19+34=53, 53=34+19, 53=19+34, 53-34=19, 53-19=34, 34=53-19, 19=53-34)

A systematic approach for finding all possible number sentences for the green task is shown in the Worked Example (download from www.iseemaths.com/problem-solving-LKS2).

TASK

TASK

34

+=

– 19

How many number sentences can you make using these

numbers and symbols?

7

+=

– 4


numbers and symbols? You choose this number. You can make it different for different number sentences.

You choose this

number. You can make it different for different number sentences.

TASK

7

+=

– 4



TASK

34

+=

– 19





Task 13 Prompts: Number sentences

SUPPORT

EXTEND

Teacher notes: Explain: The calculations have been presented in a systematic order. This system would continue with 6+11=17, 17=11+6, 17=6+11.Extend: Compare the difficulty in choosing the correct operation and in performing the calculation. Example: when calculating 57+24, there is a 10 to carry when adding the ones.

Kate is trying to make every + and – number sentence

using the numbers 11 and 17. She is writing her number

sentences in an order.

Kate has written these number sentences so far:

EXPLAIN

Tip: put the = sign in different positions.

14

9 5

Examples:

9 + 5 = 14 14 – 9 = 5

14 = 9 + 5 5 = 14 – 9

17 + 11 = 28 11 + 6 = 17

11 + 17 = 28

28 = 17 + 11

28 = 11 + 17

How has Kate ordered her number

sentences?

Which number sentences will come next?

Fill in the boxes:

– 57 = 2457 – 24 =

57 = – 24

+ 24 = 57

Which question did you find easiest? Hardest?

Explain why.


Task 14 Build: = and > signs

BUILD

1

Is each number sentence correct or not correct? or

8 – 3 = 5

5 = 3 – 8

6 + 2 = 8 – 3

3 + 2 = 8 – 3

4 + 3 > 6

4 + 3 > 6 + 2

BUILD

2

Use these digits to complete the number sentences:

12 – = 3

2 6

48

9

14 = +

5 + = 7 +

Teacher notes: Build 2 answers: 14 = 8 + 6 5 + 4 = 7 + 2 12 – 9 = 3

You can only use each digit once.

BUI

LD

1

Is each number sentence correct or not correct? or

8 – 3 = 5

5 = 3 – 8

6 + 2 = 8 – 3

3 + 2 = 8 – 3

4 + 3 > 6

4 + 3 > 6 + 2

BUILD

2

Use these digits to complete the number sentences:

12 – = 3

2 6

48

9

14 = +

5 + = 7 +

You can only use each digit once.

3 + > 10

20 – = 8 +


Task 14: = and > signsTeacher notes: 20 – 7 = 8 + 5 9 – 3 = 6 3 + 8 > 10 Solutions are shown in the Worked Example (download from www.iseemaths.com/problem-solving-LKS2).

TASK

Use these digits to complete the number sentences: You can only use each digit once.

3 7

5 8

9

– = 6

3 + > 10

20 – = 8 +TASK


3 7

5 8

9

– = 6

3 + > 10

20 – = 8 +TASK


3 7

5 8

9

– = 6


15 – = 6 +


Task 14 Prompts: = and > signsTeacher notes: Explain: blue number sentence one answer (21 – 15 = 6); red and green different answers; purple one answer (6 × 1 = 10 – 4).Extend: There are different possible answers. Example: 2 + 1 = 7 – 4 6 < 9 – 0 5 + 3 = 8

SUPPOR

T

EXPL

AIN

EXTEND

3 + > 10

20 – = 8 +

– = 6 Tip: fill in this line first

this side is more

this side is less

Which number sentences have only one answer?

Which number sentences have different answers?

6 × = 10 –

6 × = 10 + – 15 = 6

+ =

+ = –

Complete the number sentences using the digits 0 to 9: Use each digit once.

3

7

58

9< –

0 2

1

4

6


Task 15 Build: Bordering 10

BUILD

Teacher notes: The digit in the blue box must be 1 less than the digit in the red box. The two ones values must add to 10 or more. Example answers can be shown using 10-frames. Example: 17 + 5 = 22

Fill the gaps. The digit in the blue box must be different to the digit in the red box.

One example has been done. Answer in 3 different ways.

What is the difference between the digit in the blue box and the

digit in the red box?

3 7 4 25+ =

+ =

+ =

+ =

BUILD

Fill the gaps. The digit in the blue box must be different to the digit in the red box.

One example has been done. Answer in 3 different ways.

What is the difference between the digit in

the blue box and the

digit in the red box?

3 7 4 25+ =

+ =

+ =

+ =


Task 15: Bordering 10Teacher notes: 8 ways: 16+7=23 17+6=23 17+9=26 19+7=26 27+9=36 29+7=36 63+9=72 69+3=72. Solutions are shown in the Worked Example (download from www.iseemaths.com/problem-solving-LKS2).

TASK

Use the digits to complete the number sentence.

You can only use each digit once in each number sentence.

+ =



Level 3: I know how many ways it can be done

1 2

3

6

79

Example: 16 + 3 = 19 is not an answer because it uses 1 twice.

TASK



+ =




1 2

3

6

79


TASK



+ =




1 2

3

6

79




Task 15 Prompts: Bordering 10

SUPPORT

EXTEND

Teacher notes: Explain: The digits in the ones place can be swapped e.g. 27 + 9 = 36Extend: Impossible because there are no consecutive numbers. If you add a single-digit number, the answer in the tens column either stays the same or becomes one ten more. With these digits, you can’t make one more 10.

EXPLAIN

Tip: try positioning the digits like this.

Finish each example.

1 9 2+ =

2 39+ =

6 7 2+ =

29 + 7 = 36

‘You can move two of these digits to make a new number sentence.’

Explain.

Is it possible to use these digits to complete the number

sentence? You can only use each digit once in a number sentence.

+ =0

2

4

6

8

Clue: think about how the tens value changes when you add a single-digit number to a 2-digit number.


Task 16 Build: Position digits to add

BUILD

Spot the mistake for each column addition calculation:

Teacher notes: Example 1: Hundreds value incorrect. Example 2: Incorrect alignment of 74. Example 3: Error in ones value calculation (subtraction rather than addition).

8 9 3

+

Example 1:

7 4 1

5 2

9 5 3

+

Example 2:

2 1 3

7 4

8 0 3

+

Example 3:

7 1 5

9 2

BUILD


8 9 3

+

Example 1:

7 4 1

5 2

9 5 3

+

Example 2:

2 1 3

7 4

8 0 3

+

Example 3:

7 1 5

9 2

BUILD


8 9 3

+

Example 1:

7 4 1

5 2

9 5 3

+

Example 2:

2 1 3

7 4

8 0 3

+

Example 3:

7 1 5

9 2


Task 16: Position digits to add

TA

SK

Use the digits 0-9 to complete the calculation.You can use each digit only once. There will be two digits left.

7

64

8

9

Teacher notes: Example answers: 613 + 92 = 705 468 + 71 = 539 Note that the hundreds value in the answer is always one hundred more that the hundreds value of the 3-digit addend. Example answers are shown in the Worked Example (download from www.iseemaths.com/problem-solving-LKS2).

+5

3

2

1

0

TASK


7

64

8

9

+5

3

2

1

0

TASK


7

64

8

9

+5

3

2

1

0



Task 16 Prompts: Position digits to add

SUPPORT

It is impossible to complete these examples with the digits

positioned as shown. Explain why.

EXTEND

Teacher notes: Support example: 834 + 71 = 905.Explain: 1 less. You have to use different digits. The number in the red box can’t increase by more than one hundred when the number being added is less than 100.Extend: Example 1: The position of the 0 means only two identical digits can fill the gaps. Example 2: The tens values add to less than 100, so only two identical digits can fill the gaps. Example 3: two consecutive digits are needed to fill the gaps; none of the remaining digits are consecutive.

‘The digit in the blue box must be

less than the digit in the red box.’

Explain why.

EXPLAIN

+

4

7

0 5

Tip: try positioning the digits

0, 4, 5 and 7 as shown. Then,

complete the calculation with the other digits.

+

6

+

3

8 0

7 1

Example 1:

+

5 1

4 2

9 3

Example 2:

+

7 2

8 4

5 6

Example 3:


Task 17 Build: Position digits to subtract

BUILD

Teacher notes: Example answers: 32 – 7 = 25 91 – 7 = 84 Note the tens value in the answer is one ten less than the tens value of the minuend.

Use the digits 0-9 to complete the calculation.You can only use each digit once. There will be five digits left.

7

64

8

9

53

2

1

0– =

BUILD


7

64

8

9

53

2

1

0– =

BU

ILD


7

64

8

9

53

2

1

0– =

BUILD


7

64

8

9

53

2

1

0– =


Task 17: Position digits to subtract

TAS

K

Use the digits 0-9 to complete the calculation.You can only use each digit once. There will be four digits left.

76

4

8

9

Teacher notes: Answers: 105-8=97, 105-7=98, 104-8=96, 104-6=98, 103-8=95, 103-7=96, 103-6=97, 103-5=98, 102-8=94, 102-7=95, 102-5=97, 102-4=98. Two solutions are shown in the Worked Example (download from www.iseemaths.com/problem-solving-LKS2).

5

32

1

0– =


Level 2: I can find three different answers

TASK


76

4

8

9

5

32

1

0– =



TASK


76

4

8

9

5

32

1

0– =



TASK


76

4

8

9

5

32

1

0– =





Task 17 Prompts: Position digits to subtract

SUPPORT

EXTEND

Teacher notes: Support: 102 – 4 = 98Explain: Red box digit = 1, Blue box digit = 0, Purple box digit = 9Extend: Possible answers: 106 – 47 = 59, 136 – 47 = 89

EXPLAIN

Tip: position the digits 0, 4 and 9 as shown:

7

6

45

32

1–0 2 4 9=

– =

The digit in the red box must be

The digit in the blue box must be

The digit in the purple box must be

Use the digits 0-9 to complete the calculation.You can only use each digit once. There will be three digits left.

764 8 953210

There are two

possible answers.– =

EXTEND

Use the digits 0-9 to complete the calculation.You can only use each digit once. There will be three digits left.

764 8 953210

There are two

possible answers.– =


Task 18 Build: Sum and difference

BUILD

Sum =

Difference =

Teacher notes: counters or bar models can be used to model, e.g. 7 & 4: sum = 11, difference = 3

and10 5

5

Sum =

Difference =

and6 4

10

Sum =

Difference =

and7

11 Sum =

Difference =

and

5

1

7

43 3

11 11

BUILD

Sum =

Difference =

and10 5

5

Sum =

Difference =

and6 4

10

Sum =

Difference =

and7

11 Sum =

Difference =

and

5

1


Task 18: Sum and difference

TASK

TASK

Teacher notes: Counters or bar models can be used to model. Green Task: 7 & 3 Yellow Task: 17 & 13

7

34 4

10 10

I think of two numbers.

The sum of my numbers is 10.

The difference between my numbers is 4.

What are my numbers?





Example solutions and likely misconceptions are shown in the Worked Example (download from www.iseemaths.com/problem-solving-LKS2).

TASK





TASK







Task 18 Questions: Sum and difference

PRACTISE

Question 1:Tim thinks of two numbers. The sum of his numbers is 7. The difference between his numbers is 1. What are Tim’s numbers?

Question 2:Zara thinks of two numbers. The sum of her numbers is 7. The difference between her numbers is 3. What are Zara’s numbers?

Question 3:Jen thinks of two numbers. The sum of her numbers is 9. The difference between her numbers is 3. What are Jen’s numbers?

Teacher notes: Draw out the connections between the questions, noting similarities and differences. For example, the sums for Q1 and Q2 are the same but the difference increases.Green questions: Q1: 4 & 3 Q2: 5 & 2 Q3: 6 & 3Yellow questions: Q1: 11 & 9 Q2: 12 & 8 Q3: 11 & 7Extend: 5, 7, 8

PRACTI

SE

I think of three numbers.

The sum of the three numbers is 20.

The difference between the largest and smallest number is 3.

What are the three numbers?

EXTEND

Question 1:Harry thinks of two numbers. The sum of his numbers is 20. The difference between his numbers is 2. What are Harry’s numbers?

Question 2:Amy thinks of two numbers. The sum of her numbers is 20. The difference between her numbers is 4. What are Amy’s numbers?

Question 3:Sam thinks of two numbers. The sum of his numbers is 18. The difference between his numbers is 4. What are Sam’s numbers?


Task 19: More boys or girls?

BUILD

children

girls6 2

4

boys

more girls than boys

children

girls5

13

3

boys

more boys than girls

children

girls6 3

9

boys


children

girls 4

3

boys


BUILD

children

girls6 2

4

boys


children

girls5

13

3

boys


children

girls6 3

9

boys


children

girls 4

3

boys



Task 19: More boys or girls?

There are 8 children at the park.

There are more boys than girls at the park.

Talk: how many girls could be at the park?

Next step: your teacher will tell you the number in the red box.

Answer: There are girls at the park.

TASK

1

Teacher notes: Children start by generating different possible answers. Then choose an even number for the red box to create a question (repeat for task 2). Example: 8 children, 2 more boys than girls = 5 boys & 3 girls. Double-sided counters can be used. Example solutions are shown in the Worked Example (download from www.iseemaths.com/problem-solving-LKS2).

There are 14 children at the party.

There are more girls than boys at the party.

Talk: how many boys could be at the party?


Answer: There are boys at the party.

TASK

2

There are 8 children at the park.

There are more boys than girls at the park.

Talk: how many girls could be at the park?


Answer: There are girls at the park.

TASK

1

There are 14 children at the party.

There are more girls than boys at the party.

Talk: how many boys could be at the party?


Answer: There are boys at the party.

TASK

2



Task 19 Questions: More boys or girls?

PRACTISE

Question 1: There are 9 children at the party. There are 7 boys.

How many girls are at the party?

Question 2: There are 9 children at the park. There are more girls than boys. How many boys could be at the park?

Question 3: There are 9 children at the park. There are 3 more girls than boys. How many girls are at the park?

Question 4: There are 11 children at the party. There are 3 more girls than boys. How many girls are at the party?

Challenge: Create your own version of this type of question.

PRACTISE

Question 1: There are 9 children at the park. There are 5 more girls than boys. How many girls are at the park?

Question 2: There are 13 children at the party. There are 5 more girls than boys. How many boys are at the party?

Question 3: Tim and Sam have £13 in total. Tim has £5 more than Sam. How much money does Tim have?

Question 4: Jen and Zara have £17 in total. Jen has £5 more than Zara. How much money does Zara have?

Challenge: Create your own version of this type of question.

Teacher notes: Draw out the connections between Q3 and Q4 on each task.Green questions: Q1: 2 girls Q2: 4 boys or less Q3: 6 girls Q4: 7 girlsYellow questions: Q1: 7 girls Q2: 4 boys Q3: £9 Q4: £6

EXPLAIN

8 children at the park. 2 more boys than girls. How many girls?

Spot the mistakes:

Mistake 1:

B

G 2 girls

B

G

BB BB

Mistake 2:

B

G 4 girls

B

G

BB BB

GG


Task 19 Extend: More boys or girls?Teacher notes: Question A: 3 men. Question B has no answer (4 boys & 2 girls = 6 children; 5 boys & 3 girls = 8 children). Question C: Ben has £2.50. Note that questions B and C are similar but question B can’t be answered because it’s impossible to have half of a child!

EXTEND

At least one of these questions is incorrect (there’s no possible answer).

Which question(s) can’t be answered?

Question B: There are 7 children at the park. There are 2 more boys than girls. How many girls are there at the park?

Question A: There are 8 adults at the party. There are 2 more women than men. How many men are at the party?

Question C: Kam and Ben have £7 in total. Kam has £2 more than Ben. How much money does Ben have?

EXTEND






EXTEND






The children ate 16 grapes. Liz ate the most grapes.

Jack ate 5 grapes. Omar ate grapes.

Jen has £16. Zara has £ .

They have £ in total.


Task 20 Build: Part/whole word questions

BUILD

Teacher notes: Example answers: Tim 10 stickers, Sam 6 stickers. Zara £4, £20 in total. Omar could have 1→5 grapes. Bar models can be used to show the whole and the parts for each example. Children have to discern between the whole and the parts in each context.

For each question, fill in the boxes to give a possible answer:

Tim has stickers. Sam has stickers.

They have 16 stickers in total.

The children ate 16 grapes. Liz ate the most grapes.

Jack ate 5 grapes. Omar ate grapes.

Jen has £16. Zara has £ .

They have £ in total.

BUILD

For each question, fill in the boxes to give a possible answer:

Tim has stickers. Sam has stickers.

They have 16 stickers in total.


Task 20: Part/whole word questions

TASK

Teacher notes: Green Task: Dan = 14, Joy = 7, Adam = 6. Yellow Task: Mo = 14, Vicky = 9, Matt = 7. Solutions shown in the Worked Example (download from www.iseemaths.com/problem-solving-LKS2).

Dan has 14 stickers. Joy has stickers.

Adam has stickers. They have 27 stickers in total.

Joy has one more sticker than Adam.

Mo has stickers. Vicky has stickers.

Matt has stickers. They have 30 stickers in total.

Mo has twice as many stickers as Matt.

Vicky has more stickers than Matt but less than Mo.

TASK

TASK

Dan has 14 stickers. Joy has stickers.

Adam has stickers. They have 27 stickers in total.

Joy has one more sticker than Adam.

Mo has stickers. Vicky has stickers.

Matt has stickers. They have 30 stickers in total.

Mo has twice as many stickers as Matt.

Vicky has more stickers than Matt but less than Mo.

TASK



Task 20 Practise: Part/whole word questions

PRACTISE

Question 1:Tom and James have £20 in total. James has £6.

How much money does Tom have?

Question 2:Lucy, Sophie and Molly eat 20 grapes in total. Molly eats 6 grapes. Lucy and Sophie share the rest.

How many grapes does Sophie eat?

Question 3:Kim, Ben and Emily have 30 stickers in total. Kim has 12 stickers.

Ben and Emily have the same number of stickers.

How many stickers does Ben have?

Question 4:Three friends eat 23 sweets. Jim eats 12 sweets. Sam eats one more sweet than Harry.

How many sweets does Harry eat?

Teacher notes: Help children to see the connections between the questions.Green questions: Q1: £14 Q2: 7 grapes Q3: 9 stickers Q4: 5 sweetsYellow questions: Q1: 5 grapes Q2: £7 Q3: 4 stickers (Ruth has 3, Dom has 8)

PRACTISE

Question 1:Ethan, Joe and Raja eat 17 grapes. Ethan eats one more grape than Raja. Joe eats 8 grapes.

How many grapes does Ethan eat?

Question 2:Lara, Rachel and Karen have £25 in total. Karen has £8. Lara has £3 more than Rachel.

How much money does Rachel have?

Question 3:Dom, Zack and Ruth have 15 stickers. Ruth has the fewest stickers. Dom has got twice as many stickers as Zack.

How many stickers does Zack have?

Extension: design your own question using a whole and three parts.


Task 21 Build: Change at the shop

BUILD

Question 1: How much do two sandwiches

and a drink cost?

Question 2: How much does a sandwich

and two drinks cost?

Question 3: Kim buys a sandwich and two drinks. She pays the

shopkeeper £3. How much change does Kim get?

Question 4: Paul has £5. How many sandwiches can he afford?

Sandwich: £1.80

Drink: 30p

BUILD


and a drink cost?






Sandwich: £1.80

Drink: 30p

BUIL

D


and a drink cost?






Sandwich: £1.80

Drink: 30p

BUILD


and a drink cost?






Sandwich: £1.80

Drink: 30p


Task 21: Change at the shop

TASK

1

Teacher notes: Two solutions to Task 1 are shown in the Worked Example (download from www.iseemaths.com/problem-solving-LKS2).

I buy sandwich(es) and drink(s).

I pay with a £5 note. I get change.

Find 3 different possible answers:Sandwich: £1.80

Drink: 30p





TASK

1



Find 3 different possible answers:Sandwich: £1.80

Drink: 30p







Task 21: Change at the shop

TASK

2

Question 1:

I buy sandwiches and drinks.

I pay with a £5 note. I get 20p change.

Sandwich: £1.80

Drink: 30p

Question 2:


I pay with a £10 note. I get £1.90 change.

Question 3:

I buy 6 sandwiches and drinks.


Explore:

Do any of

these questions

have different

possible

answers?

Teacher notes: Q1: 2 sandwiches & 4 drinks OR 0 sandwiches & 18 drinks. Q2: 4 sandwiches & 3 drinks OR 2 sandwiches & 15 drinks OR 0 sandwiches & 27 drinks. Q3: 8 drinks.

TASK

2

Question 1:


I pay with a £5 note. I get 20p change.

Sandwich: £1.80

Drink: 30p

Question 2:



Question 3:

I buy 6 sandwiches and drinks.


Explore:

Do any of

these questions

have different

possible

answers?

Question 1: Harry buys 3 apples and 2 oranges. He pays with a £2 coin.

How much change does Harry get?

Question 2: Mel buys some apples and an orange.She pays with a £2 coin and gets 15p change.

How many apples does Mel buy?

Question 3: Kate buys 8 apples and some oranges. She pays with a £5 note and gets 80p change.

How many oranges does Kate buy?

Question 4: Hugo buys apples and oranges. He pays with a £2 coin and gets 5p change.

How many apples and oranges does Hugo buy?


Task 21 Prompts: Change at the shopTeacher notes: Practise: Q1: 30p Q2: 4 apples Q3: 4 oranges Q4: 3 apples & 3 oranges Extend: 4 ways: pays 50p, buys 1 apple; pays £1, buys 6 plums; pays £2, buys an apple and 10 plums; pays £2, buys 4 apples and 2 plums.

Apples: 40p

Oranges: 25pPRA

CTISE

EXTEND

Apples: 40p

Plums: 15p

Stan buys some fruit.

He pays with one coin.

He gets 10p change.

Which fruits did Stan buy?

Find all possible answers.

EXTEND

Apples: 40p

Plums: 15p

Stan buys some fruit.

He pays with one coin.

He gets 10p change.

Which fruits did Stan buy?

Find all possible answers.

I SEE PROBLEM-SOLVING – LKS2MULTIPLICATION AND DIVISION

Task 22 Build: × + number sentences

BUILD

Teacher notes: 5 + 5 + 5 = 3 × 5 20 + 20 = 8 × 5 5 + 10 + 20 = 7 × 5 4 × 5 + 5 = 5 × 5Use visual representations to show the connection between these number sentences and their multiplication equivalences e.g. showing that there are 4 lots of 5 in 20.

For each number sentence, how many 5s?

5 + 10 + 15 3 × 5 + 5

6 lots of 54 lots of 5

5 + 5 + 5 5 + 10 + 20 4 × 5 + 520 + 20

B

UILD


5 + 10 + 15 3 × 5 + 5


5 + 5 + 5 5 + 10 + 20 4 × 5 + 520 + 20

BUILD


5 + 10 + 15 3 × 5 + 5


5 + 5 + 5 5 + 10 + 20 4 × 5 + 520 + 20


Task 22: × + number sentencesTeacher notes: Print and cut out for each pair/group. Matching images/number sentences shown in the Worked Example (download from www.iseemaths.com/problem-solving-LKS2).

TASK

6 × 3 6 × 5 + 5

6 × 6 double 3 × 3

6 × 5 5 × 6 + 6

7 × 5 4 × 5 + 10

Match the number sentences and pictures that are the same:

5 5 5 5 5 5 5

+6 +6 +6 +6 +6 +6

60 3630241812

TASK

6 × 3 6 × 5 + 5

6 × 6 double 3 × 3

6 × 5 5 × 6 + 6

7 × 5 4 × 5 + 10

Match the number sentences and pictures that are the same:

5 5 5 5 5 5 5

+6 +6 +6 +6 +6 +6

60 3630241812



Task 22 Practise: × + number sentences

PRAC

TISE

Teacher notes: Green questions: 5×3=15 5+5+5+5=20 4+4+8=16 same as 4×4=1630+10+5=45, same as 9×5=45. True statements: 3+6+6 and 3+3+3+6Yellow questions: 3+6+9=18, same as 6×3=18 4+4+4+4+4+4=24 6+6+24=36, same as 6×6=36 9+15=24, same as 8×3=24. True statements: 16+8+12 and 4+28+4

+ number sentence × number sentence

4 + 4 + 4 = 12 3 × 4 = 12

3 + 3 + 3 + 3 + 3 = 15 × = 15

4 × 5 = 20

4 + 4 + 8 = 16 × 4 = 12

30 + 10 + 5 = 45 × 5 =

Which number sentences show 5 lots of 3?

3 + 6 + 9 5 + 5 + 5 3 + 6 + 6 3 + 3 + 3 + 6

PRACTISE

+ number sentence × number sentence

4 + 4 + 12 = 20 5 × 4 = 20

3 + 6 + 9 = 15 × 3 = 15

6 × 4 = 24

6 + 6 + 24 = 16 × =2

9 + 15 = 45 × =2

Which number sentences show 9 lots of 4?

4 + 12 + 16 16 + 8 + 12 4 + 28 + 4 4 + 4 + 32


Task 22 Extend: × + number sentences

EXTEND

Teacher notes: Answers, Extend: 6+12+30=48, same as 8×6=48 and 24×2=48; 24+16+16=56, same as 7×8=56 and 14×4=56 and 28×2=56; 27+18=45, same as 5×9=45 and 15×3=45

+ number sentence × number sentence × number sentence

6 + 12 + 30 = 48 × 6 = × 2 =

24 + 16 + 16 = 52 × =0 × =0

27 + 18 = 16 × =0 × =0

For each addition number sentence, write two multiplication number sentences:

EXTEND


6 + 12 + 30 = 48 × 6 = × 2 =

24 + 16 + 16 = 52 × =0 × =0

27 + 18 = 16 × =0 × =0


EXTEND


6 + 12 + 30 = 48 × 6 = × 2 =

24 + 16 + 16 = 52 × =0 × =0

27 + 18 = 16 × =0 × =0



Task 23 Build: Area models

BUILD

This shape is split into two rectangles.

The sections have 20 squares and 12 squares.

There are 32 squares in the whole shape.

This shape is split into three identical rectangles.

There are squares in each section.

In the whole shape there are squares.

This shape is split into two identical rectangles.



BUI

LD

This shape is split into two rectangles.

The sections have 20 squares and 12 squares.

There are 32 squares in the whole shape.

This shape is split into three identical rectangles.



This shape is split into two identical rectangles.




Task 23: Area models

TASK

Teacher notes: Part 1 example: a vertical line splits the shape into sections of 5 × 6 = 30 and 4 × 6 = 24. Part 2 answer: a horizontal line splits the shape into two sections of 3 × 9 = 27. Part 3 answer: three vertical lines split the shape into three sections of 3 × 6 = 18 or two horizontal lines split the shape into three sections of 2 × 9 = 18 . Solutions to the task are shown in the Worked Example (download from www.iseemaths.com/problem-solving-LKS2).

Part 1: Split this shape

into two different

rectangles. Work out

how many squares in

each rectangle, and

how many squares in

the whole shape.


into two identical


how many squares in

each rectangle, and

how many squares in

the whole shape.


into three identical


how many squares in

each rectangle, and

how many squares in

the whole shape.



Task 23: Area models

TASK

Teacher notes: Part 1 example: a vertical line splits the shape into sections of 10 × 8 = 80 and 5 × 8 = 40. Part 2 answer: a horizontal line splits the shape into two sections of 4 × 15 = 60. Part 3 answer: two vertical lines split the shape into three sections of 5 × 8 = 40. Solutions to the task are shown in the Worked Example (download from www.iseemaths.com/problem-solving-LKS2).


into two different


how many squares in

each rectangle, and

how many squares in

the whole shape.


into two identical


how many squares in

each rectangle, and

how many squares in

the whole shape.


into three identical


how many squares in

each rectangle, and

how many squares in

the whole shape.



Task 23 Prompts: Area models

SUPPORT

EXTEND

Teacher notes: Extend: There are multiple possible answer e.g. partition the 14 into 7 & 7, partition the 9 into 3 & 3 & 3. Encourage children to answer in many different ways. Also, note that 14 × 9 is 9 less than 14 × 10.

These diagrams show two different ways to split up the rectangle:

Area model 1: 13 × 7 calculated

by partitioning 13 into 8 and 5:

56 + 35 = 91

Area model 2: 13 × 7 calculated

by partitioning 13 into 8 and 5:

65 + 26 = 91

8 5

75

2

13

8 × 7 = 56 5 × 7= 35

13 × 5 = 65

13 × 2 = 26

Calculate 14 × 9 using an area model. Do in different ways.

Show your first two methods by labelling the rectangle below:

MULTIPLICATION AND DIVISION

How many squares in each section? How many squares in total?


Task 24 Build: Largest product

BUILD

Teacher notes: 13×2 is the smallest as the largest digit (3) is in the ones position. 21×3 is larger than 31×2. To explain, note that 20×3 is the same as 30×2 but 1×3 is larger than 1×2.

Step 1 - Predict: Which calculation do you think will give

the largest product? Which will give the smallest product?

21 × 3 12 × 3 13 × 2 31 × 2

Step 2 – Calculate: What do you find? Is this what you

predicted?

BUILD



21 × 3 12 × 3 13 × 2 31 × 2


predicted?

BUILD



21 × 3 12 × 3 13 × 2 31 × 2


predicted?

BUILD



21 × 3 12 × 3 13 × 2 31 × 2


predicted?


Task 24: Largest productTeacher notes: 43×5=215, largest possible product. Note 53×4 is smaller: 40×5 is the same as 50×4 but 3×5 is larger than 3×4. The solution, and other answers, are compared in the Worked Example (download from www.iseemaths.com/problem-solving-LKS2).

TASK

Position the digits 3, 4 and 5 to make the product as large

as possible.

× =3 4 5

TASK


as possible.

× =3 4 5

TASK


as possible.

× =3 4 5

TASK


as possible.

× =3 4 5

TASK


as possible.

× =3 4 5



Task 24 Prompts: Largest product

SUPPORT

EXTEND

Teacher notes: Explain: note that 40×5 is the same as 50×4 but 6×5 is larger than 6×4Extend: largest is 543×6 smallest is 456×3

EXP

LAIN

Useful multiplication facts:

3 × 4 = 12

30 × 4 = 120

40 × 3 = 120

3 × 5 = 15

30 × 5 = 150

50 × 3 = 150

4 × 5 = 20

40 × 5 = 200

50 × 4 = 200

Complete the calculations:

What’s the same? What’s different?

46 × 5

40 6

5

56 × 4

50 6

4

Position the digits 3, 4, 5 and 6 to make the product as large as possible. Do it again to make the product as small as possible.

× =34

5 6

EXTEND

Position the digits 3, 4, 5 and 6 to make the product as large as possible. Do it again to make the product as small as possible.

× =34

5 6


Task 25 Build: 2-digit product

BUILD

Teacher notes: 47 × 2 23 × 4 14 × 7 Make connections with known facts relating to 100. For example, 25 × 4 = 100 so 23 × 4 must be less than 100, therefore a 2-digit number.

Which calculations give a 2-digit product?

47 × 2 21 × 5 18 × 6

13 × 8 23 × 4 14 × 7


BUILD


47 × 2 21 × 5 18 × 6

13 × 8 23 × 4 14 × 7

BUILD


47 × 2 21 × 5 18 × 6

13 × 8 23 × 4 14 × 7

BU

ILD


47 × 2 21 × 5 18 × 6

13 × 8 23 × 4 14 × 7

BUILD


47 × 2 21 × 5 18 × 6

13 × 8 23 × 4 14 × 7


Task 25: 2-digit productTeacher notes: Answers: 43×2 13×4 13×6 All possible solutions are shown in the Worked Example (download from www.iseemaths.com/problem-solving-LKS2).

TASK

Use the digits 1-9 to complete the number sentence.

Position the digit 3 as shown:You can only use each digit once in each number sentence.




1 2 4

6 7 9

× =35

8


TASK






1 2 4

6 7 9

× =35

8

TASK






1 2 4

6 7 9

× =35

8



Task 25 Prompts: 2-digit product

SUPPORT

EXT

END

Teacher notes: Support: Digit in the red box less than 5. One possible answer: 43 × 2 = 86Explain: Sometimes: smallest possible 10×10=100; largest possible 99×99=9801Extend: One possible answer: 12×8=96. Other numbers will give 3-digit product (e.g. 13×8=104) or use two or more of the same digit (e.g. 11×8=88).

EXPLAIN

Tip 1: finish the statement:

‘A 2-digit number multiplied by a 2-digit number

gives a 3-digit product’

Always, sometimes or never?

Positioning the digit 8 as shown, is it possible to complete

this number sentence using the digits 1-8?You can only use each digit once in a number sentence.

1

2 4 6

7

This is impossible because…

The only possible answer is… There are no other answers

because…

There are different possible answers, like…

× =3

Tip 2: there is one possible answer when you position the

digit 2 as shown:

× =3 2

× =83 5

‘The digit in the red box is less than…’



Task 26 Build: Shapes with matchsticks

BUILD

Teacher notes: 2 pentagons, 0 left over 2 squares, 2 left over 3 triangles, 1 left over. To reflect the thought-process of division (e.g. ‘How many 4s in 10?’), ensure children make separate shapes. Use matchsticks to represent practically.

With 10 matchsticks I can make pentagons.

There will be matchstick(s) left over.

With 10 matchsticks I can make squares.


With 10 matchsticks I can make triangles.


Idea: try this task with a different number of matchsticks.

BUILD

With 10 matchsticks I can make pentagons.








Task 26: Shapes with matchsticksTeacher notes: 6 triangles, 1 left over 4 squares, 3 left over 3 pentagons and 4 left over OR 3 hexagons and 1 left over. To reflect the thought-process of division (e.g. ‘How many 3s in 19?’), ensure children make separate shapes. Use matchsticks to represent practically. Solutions are shown in the Worked Example (download from www.iseemaths.com/problem-solving-LKS2).

TASK





With 19 matchsticks I can make 3

There will be matchstick(s) left over. name

the shape


TASK





With 19 matchsticks I can make 3

There will be matchstick(s) left over. name

the shape




Task 26 Prompts: Shapes with matchsticks

SUPPORT

EXTEND

Teacher notes: Explain: Tim: if you have 3+ matchsticks left you can make another triangle. Fran: with 23 matchsticks you can make 7 triangles and 2 matchsticks will be left over.Extend: If the original number of matchsticks leaves two leftover sticks, doubling the number of matchsticks will more than double the number of triangles made. Example: 14 matchsticks makes 4 triangles; 28 matchsticks makes 9 triangles.

EXP

LAIN

‘The number of matchsticks I am given is doubled.

Now I can make more than double the number of

triangles.’

Give an example that shows that this can be true.

With 14 matchsticks you can make…

4 triangles (4×3 =12)

2 left over

4 squares (3×4 =12)

2 left over

2 pentagons (2×5 =10)

4 left over


Tim: ‘With 20 matchsticks you can make 5 triangles.

5 matchsticks are left over.’

Fran: ‘With 23 matchsticks you can make 7 triangles.

1 matchstick is left over.’

EXTEND

‘The number of matchsticks I am given is doubled.

Now I can make more than double the number of

triangles.’

Give an example that shows that this can be true.


BUILD

2

Teacher notes: To create questions, give children numbers in some of the boxes; they fill in the remaining boxes to give answers/possible answers. Example: tell children 14 people go camping. They complete the two other boxes to find a possible answer. The Build tasks can be printed and laminated for children to use.

Bill has eggs.

He packs them in boxes of

There are full boxes.

boxes are needed for allthe eggs.

BUILD

1

people go camping.

people in each tent.

tents in total.

Task 27 Build: Division in context


Task 27 Practise: Division in context

Question 1: 14 people go camping. 4 people fit in each tent.

How many tents are needed?





Question 4: Kelly has 16 eggs. She packs them in boxes of 6.

How many boxes can she fill?

Question 5: Kelly has 16 eggs. She packs them in boxes of 6.

How many boxes does she need for all the eggs?

Question 6: Matt packs his eggs in boxes of 6. He fills 2 boxes. 2 eggs

are left over. How many eggs does Matt have?

Question 7: Sam has some eggs. He packs them in boxes of 6. He

needs 2 boxes to hold all the eggs. How many eggs could Sam have?

Teacher notes: Green questions: Q1: 4 tents Q2: 7 tents Q3: 7 tents Q4: 2 boxes Q5: 3 boxes Q6: 14 eggs Q7: 7 to 12 eggs. Yellow questions: Q1: 4 tents Q2: 7 tents Q3: 7 tents Q4: 4 boxes Q5: 7 boxes Q6: 62 eggs Q7: 31 to 36 eggs. Solutions to questions 1, 2 and 3 are shown in the Worked Example (download from www.iseemaths.com/problem-solving-LKS2).

PRACTISE







Question 4: Grace has 29 eggs. She packs them in boxes of 6.

How many boxes can she fill?

Question 5: Elen has 39 eggs. She packs them in boxes of 6.

How many boxes does she need for all the eggs?

Question 6: Matt packs his eggs in boxes of 12. He fills 5 boxes. 2 eggs

are left over. How many eggs does Matt have?

Question 7: Sam has some eggs. He packs them in boxes of 6. He

needs 6 boxes to hold all the eggs. How many eggs could Sam have?

PRACTISE



Task 27 Extend: Division in contextTeacher notes: 14 eggs or 44 eggs

EX

TEND

A farmer has less than 50 eggs.

When the eggs are packed in boxes of 10, there are 4 eggs left over.


How many eggs does the farmer have?

There are two possible answers.

E

XTEND






EXTEND






EXTEND






EXTEN

D







Task 28 Build: Different quotients

BUILD

Which calculations give a 2-digit answer?

36 ÷ 4 36 ÷ 3 40 ÷ 5

60 ÷ 6 80 ÷ 5

BUILD


36 ÷ 4 36 ÷ 3 40 ÷ 5

60 ÷ 6 80 ÷ 5

BUILD


36 ÷ 4 36 ÷ 3 40 ÷ 5

60 ÷ 6 80 ÷ 5

BUILD


36 ÷ 4 36 ÷ 3 40 ÷ 5

60 ÷ 6 80 ÷ 5

BUILD


36 ÷ 4 36 ÷ 3 40 ÷ 5

60 ÷ 6 80 ÷ 5


Task 28: Different quotientsTeacher notes: 12 ÷4 = 3 20 ÷ 4 =5 28 ÷ 4 = 7 32 ÷4 = 8 36 ÷4 = 9 Dividing a number that is 40→ 399 gives a 2-digit quotient. All possible solutions are shown in the Worked Example (download from www.iseemaths.com/problem-solving-LKS2).

TASK



4÷ =




1 23

6 7

9

58

0

TASK



4÷ =




1 23

6 7

9

58

0

TASK



4÷ =




1 23

6 7

9

58

0



Task 28: Different quotientsTeacher notes: 52 ÷4 = 13 60 ÷ 4 = 15 68 ÷ 4 =17 72 ÷ 4 = 18 76 ÷4 = 19All possible solutions are shown in the Worked Example (download from www.iseemaths.com/problem-solving-LKS2).

TASK



4÷ =




1 23

6 7

9

58

0

TASK



4÷ =




1 23

6 7

9

58

0

TASK



4÷ =




1 23

6 7

9

58

0



Task 28 Prompts: Different quotients

SUPPORT

EXTEND

Teacher notes: Explain: ÷ 3 has more possible answers (more multiples of 3 between 30 and 99 than multiples of 7 between 70 and 99). The smaller the divisor, the more possible answers. Extend: Children describe the link between the first number fact and the following questions. 84 ÷6 =14 84 ÷ 3 = 28 72 ÷3 = 24 81 ÷ 3 =27 64 ÷ 4 = 16 64 ÷8 =8

EXPLAIN

Which question has more possible answers? Why?

I know… so…

78 ÷ 6 = 13

84 ÷ 6 =

84 ÷ 3 =

4÷ =

Tip 2: partitioning

‘To give a 2-digit answer, this

number must be or more’

Tip 1: size of numbers

For 56 ÷ 4, partition 56 into 40 and 16.

40 ÷ 4 = 10

16 ÷ 4 = 4

56 ÷ 4 = 14

3÷ =

Question A:

7÷ =

Question B:

75 ÷ 3 = 25

72 ÷ 3 =

84 ÷ 3 = 27

32 ÷ 4 = 8

64 ÷ 4 =

64 ÷ 8 =

I know 96 ÷ 8 = 12 so… Think of related number facts.

The number that you divide by is called the divisor.


Task 29 Build: Finding factors

BUILD

Teacher notes: Factors of 20: 4 & 10 factors of 100: 1, 2, 4 & 5

Circle the factors of 20:

0.5 4 6 10 40


1 2 3 4 5 6

BUILD


0.5 4 6 10 40


1 2 3 4 5 6

BUILD


0.5 4 6 10 40


1 2 3 4 5 6

BUILD


0.5 4 6 10 40


1 2 3 4 5 6

BUILD


0.5 4 6 10 40


1 2 3 4 5 6


Task 29: Finding factorsTeacher notes: 1, 2, 3, 4, 6, 7. Answers are shown in the Worked Example (download from www.iseemaths.com/problem-solving-LKS2).

TASK

Which of the digits from 1 to 9 are factors of 84?

Sentence stems:

Numbers ending in the digit… always/never have… as a factor.

I split 84 into… and…

To work out that… is a factor of 84 I multiplied/divided…

TASK


Sentence stems:




T

ASK


Sentence stems:




TASK


Sentence stems:






Task 29 Prompts: Finding factors

SUPPORT

EXTEND

Teacher notes: Explain: the first statement is true, all multiples of 6 are multiples of 3. The second statement is false, for example 4 is a factor of 28 but 8 is not a factor of 28. Similarly, 4 is a factor of 52 but 8 is not a factor of 52.Extend: 96 has 12 factors (1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96), 100 has 9 factors (1, 2, 4, 5, 10, 20, 25, 50, 100). Factors of both numbers: 1, 2, 4.

EXPLAIN

Agree or disagree:

‘6 is a factor of 42 so 3 must also be a factor of 42.’

‘4 is a factor of 52 so 8 must also be a factor of 52.’

Explain.

Which has more factors: 96 or 100?

Which numbers are factors of 96 and 100?

For each sentence, choose is or is not.

‘I know that 8×10 = 80. This means that 8 is/is not a factor of 84.’



EXTEND

Which has more factors: 96 or 100?

Which numbers are factors of 96 and 100?


Task 30 Build: Venn diagrams

BUILD

1

multiples of 3 odd numbers

Position these numbers in the Venn Diagram:

9 10 11 12

Write another number in each section of the Venn diagram.

BUILD

2

multiples of 3 multiples of 5

These numbers have been positioned in the Venn diagram:

12

9 15

60

25

10118


Position the same numbers in this Venn diagram:

Numbers:

8 9 10

11 12 15

25 60

even numbers

Teacher notes: Build 1: 12 left oval; 9 middle; 11 odd number; 10 outside.Build 2: 8 even; 9 multiple of 3; 10 even multiple of 5; 11 outside (in none of the groups); 12 even multiple of 3; 15 multiple of 3 and 5; 25 multiple of 5; 60 middle (in all of the groups).



Task 30: Venn diagrams

TASK

Teacher notes: Green Task: 404 left oval; 120 & 40 middle; 15 right oval; 99 outside.Yellow Task: 404 multiple of 4; 120 multiple of 4 and 5; 15 multiple of 5 and less than 50; 40 middle; 99 outside. Solutions for the green and yellow tasks are shown in the Worked Example (download from www.iseemaths.com/problem-solving-LKS2).


Position these numbers in the correct section of the Venn diagram: 15 40 99 120 404


TASK

Position these numbers in the correct section of the Venn diagram: 15 40 99 120 404


numbers less than 50





Task 30 Extend: Venn diagramsTeacher notes: 4 less than 10; 7 less than 10 & odd; 12 multiple of 3; 14 outside. Two numbers in middle (3 & 9). Multiple of 3, less than 10, not odd, only answer = 6

EXTEND

Part 1: Position these numbers in the correct section of the Venn diagram: 4 7 12 14

Part 2: How many numbers can go in the middle section?

Part 3: Find the section with only one possible answer.



EXTEND

Part 1: Position these numbers in the correct section of the Venn diagram: 4 7 12 14

Part 2: How many numbers can go in the middle section?

Part 3: Find the section with only one possible answer.




I SEE PROBLEM-SOLVING – LKS2MIXED OPERATIONS

Task 31 Build: Different answers

BUILD

Teacher notes: True statements: 4×6=20+4 4×10=20+20 15-3>10

Question: 4 × = 20 +

For each example, or

4 × = 20 +

4 × = 20 +

4 × = 20 +

Question: 15 – 6 > 10


15 – 6 > 10

15 – 6 > 10

15 – 6 > 10

45

46

10 20

12

3

5

more > less

BUIL

D



4 × = 20 +

4 × = 20 +

4 × = 20 +

Question: 15 – 6 > 10


15 – 6 > 10

15 – 6 > 10

15 – 6 > 10

45

46

10 20

12

3

5

more > less

BUILD



4 × = 20 +

4 × = 20 +

4 × = 20 +

Question: 15 – 6 > 10


15 – 6 > 10

15 – 6 > 10

15 – 6 > 10

45

46

10 20

12

3

5

more > less


Task 31: Different answersTeacher notes: 40 ÷ 2 = 20 (1 way); ___ - 11 > 8 infinite ways (20 or more); 20 - ___ = 5 × ___ three ways (20 - 15 = 5 × 1 20 - 10 = 5 × 2 20 - 5 = 5 × 3); 11 - ___ > 8 two ways (11 - 1 > 8 11 - 2 > 8); 24 - 6 = 18 (one way); ___ × 5 = 26 + ___ infinite ways (multiply by more, add more). Solutions are shown in the Worked Example (download from www.iseemaths.com/problem-solving-LKS2).

Fill the gaps. Some of the questions can be answered in different ways.

TASK

For this task, only whole numbers greater than 0 are used.

Which two questions can be answered in only one way?

Which question can be answered in two ways? Which in three ways?

Which two questions can be answered in an infinite number of ways?

÷ 2 = 20

× 5 = 26 +

– 11 > 8

11 – > 8

24 – = 18

20 – = 5 ×

TASK

÷ 2 = 20

× 5 = 26 +

– 11 > 8

11 – > 8

24 – = 18

20 – = 5 ×

Fill the gaps. Some of the questions can be answered in different ways.

TASK

÷ 2 = 20

× 5 = 26 +

– 11 > 8

11 – > 8

24 – = 18

20 – = 5 ×



Task 31 Prompts: Different answers

SUPPORT

EXTEND

Teacher notes: Explain: 5 × 6 = 30 (one way); 5 × ___ = 30 - ___ five ways (5 × 1 = 30 - 255 × 2 = 30 - 20 5 × 3 = 30 - 15 5 × 4 = 30 - 10 5 × 5 = 30 - 5); 5 × ___ = 20 + ___ infinite ways.Extend: Example answers: 8 - ___ > 4 30 - 26 > ___ 10 × ___ = 40 - ___ 8 × ___ = 31 - ___

EXPLAIN

Design questions that can be answered in exactly three ways when using whole numbers greater than 0.

Tip: Use these structures:

Order the questions from fewest to most possible answers:

Use the bar models to find an answer to four of the questions:

20 20

÷ 2 = 20 20 – = 5 ×

20

5 5

– 11 > 8 × 5 = 26 +

5 5 5 5 5 5

2611 8

For this task, only whole numbers greater than 0 are used.

5 × = 30

Question A:

5 × = 30 +

Question B:

5 × = 30 –

Question C:

× = –– >


Task 32 Build: Questions in context

BUILD

6 friends share 3 pizzas.

How much pizza each?6 + 3 = 9

Tom is 3 years older than

Alex. Alex is 6 years old.

How old is Tom?6 ÷ 3 = 2

Mr Holt has 3 pairs of

trousers and 6 shirts. How

many ways can he dress?3 ÷ 6 =

𝟏

𝟐

6 cookies are shared

between 3 friends. How

many cookies each?6 × 3 = 18

Match the question to the correct bar model and calculation:

6

3

36

Teacher notes: print and cut out for each pair/small group.

BUILD

6 friends share 3 pizzas.

How much pizza each?6 + 3 = 9

Tom is 3 years older than

Alex. Alex is 6 years old.

How old is Tom?6 ÷ 3 = 2

Mr Holt has 3 pairs of

trousers and 6 shirts. How

many ways can he dress?3 ÷ 6 =

𝟏

𝟐

6 cookies are shared

between 3 friends. How

many cookies each?6 × 3 = 18

Match the question to the correct bar model and calculation:

6

3

36


Task 32: Questions in context

TASK

Questions Which answer?

Question 1: A jug can fill 2 bottles. A bottle can fill 3

cups . How many cups can you fill with a jug?

(a) 5 cups

(b) 6 cups

Question 2: To make a sandwich you can use white or

brown bread. You can have chicken, ham, tuna or

cheese. How many different types of sandwich can you

make?

(a) 8 types

(b) 6 types

Question 3: John and two friends get the train. The total

cost is £12. How much does John’s train ticket cost?

(a) £36

(b) £4

(c) £6

Question 4: Mum and Dad are blowing up balloons.

Dad starts first. They blow them up at the same speed

as each other. When Mum has blown up 3 balloons,

Dad has blown up 5 balloons. How many balloons has

Dad blown up when Mum has blown up 9 balloons?

(a) 15 balloons

(b) 11 balloons

(c) 8 balloons

Choose the correct answer. Explain your choice.

Teacher notes: Green and Yellow Task Answers: 6 cups, 8 types of sandwich, £4, 11 balloons.Solutions are shown in the Worked Example (download from www.iseemaths.com/problem-solving-LKS2).

TASK

Question 1: A jug can fill 2 bottles. A bottle can fill 3 cups.

How many cups can you fill with a jug?

Question 2: To make a sandwich you can use white or brown bread.

You can have chicken, ham, tuna or cheese.

How many different types of sandwich can you make?

Question 3: John and two friends get the train. The total cost is £12.

How much does John’s train ticket cost?

Question 4: Mum and Dad are blowing up balloons. Dad starts first.

They blow them up at the same speed as each other. When Mum has

blown up 3 balloons, Dad has blown up 5 balloons.

How many balloons has Dad blown up when Mum has blown up 9

balloons?



Task 32 Extend: Questions in contextTeacher notes: Q1: 50 lengths (if they keep swimming at the same speed). Q2: 34 lengths. Note that Q1 is a multiplicative context and Q2 is an additive context: the girls swim at the same speed so Liz has always done 4 more lengths than Kim.

EX

TEND

Question 2: Liz starts swimming before Kim.

Liz and Kim swim at the same speed as each other.

When Liz had swam 10 lengths, Kim had swam 6 lengths.

In total, Kim swam 30 lengths. How many lengths did Liz swim?

Question 1: Jason and Adam start swimming at the same time.

Jason is a faster swimmer than Adam.

When Jason had swam 10 lengths, Adam had swam 6 lengths.

In total, Adam swam 30 lengths. How many lengths did Jason swim?

EXTEND









EXTEND










Task 33 Build: Combinations

BUILD

Teacher notes: Question A: 5 + 3 = 8. Questions B and D: 5 × 3 = 15 (note that despite the same calculation being used, the visual representations for these two questions are likely to be different). Question C: 9 + 2 = 11 (the difference between the children’s ages stays the same).

For each question, 5 + 3 = 8 OR 5 × 3 = 15 OR other?

Question C:

Tim is 3 years old. Sam is 5 years old.

When Tim is 9, how old will Sam be?

Question B:

Kay earns £5 per hour. She works for 3 hours.

How much does she earn in total?

Question A:

Saj walks 3 miles east. Ray walks 5 miles west.

How far apart are Saj and Ray?

Question D:

There are 5 main meals and 3 puddings on the menu.

How many different meals can be ordered?

BUILD

For each question, 5 + 3 = 8 OR 5 × 3 = 15 OR other?

Question C:

Tim is 3 years old. Sam is 5 years old.

When Tim is 9, how old will Sam be?

Question B:

Kay earns £5 per hour. She works for 3 hours.

How much does she earn in total?

Question A:

Saj walks 3 miles east. Ray walks 5 miles west.

How far apart are Saj and Ray?

Question D:

There are 5 main meals and 3 puddings on the menu.

How many different meals can be ordered?


Task 33: Combinations

TASK

Teacher notes: 3 shirts and 5 ties. The solution is shown in the Worked Example (download from www.iseemaths.com/problem-solving-LKS2).

Mr Harris is choosing his clothes for the day. He will wear a pair of trousers, a shirt and a tie.

He has two pairs of trousers (black and grey). He has more ties than shirts.

He can make 30 different possible outfits.

How many shirts does he have? How many ties does he have?

Example outfit 1: Grey trousers, white shirt, blue tie.

Example outfit 2: Black trousers, pink shirt, blue tie.

TASK







TASK









Task 33 Prompts: Combinations

SUPPORT

EXTEND

Teacher notes: Build: Children have laminated copy of build prompt, use to explore questions using this structure with smaller quantities e.g. 2 shirts, 3 ties, 2 pairs of trousers.Explain: Disagree: He would have 15 new outfits (3 × 5 × 3 = 45).Extend: Disagree: 30 outfits before (3 × 5 × 2 = 30); 24 outfits after (2 × 6 × 2 = 24) so different.

E

XPLAIN

True or false:

‘If Mr Harris buys another pair of trousers he would

have one more possible outfit.’

Mr Harris lost a shirt and he bought a tie.

True or false:

‘Mr Harris still has the same number of possible outfits.’

shirts. ties.

pairs of trousers.

possible outfits.

I SEE PROBLEM-SOLVING – LKS2FRACTIONS

Task 34 Build: Estimating fractions

BUILD

Teacher notes: Examples: a large part of a tree is the trunk; a tree is part of a forest. A small part of a school day is register time; a school day is part of a term. Encourage children to compare the relative size of the part in comparison to the whole.

Finish the sentences:

A small part of a tree is…

A large part of a tree is…

A tree is part of…

A small part of the school day is…

A large part of the school day is…

A school day is part of…

Think of part/whole sentences about a classroom, an arm or a wheel.

BUILD









BUILD









BUILD










Task 34: Estimating fractions

TASK

Teacher notes: Smallest to largest fractions: a fingernail as a part of a human; a fin as a part of a shark; a trunk as a part of an elephant; the wings as a part of a butterfly. Answers are shown in the Worked Example (download from www.iseemaths.com/problem-solving-LKS2).

Order these fractions from smallest to largest:

The wings as

a fraction of

a butterfly.

The trunk as a

fraction of an

elephant.

A fingernail

as a fraction

of a human.

The fin as a

fraction of

a shark.

TASK


The wings as

a fraction of

a butterfly.

The trunk as a

fraction of an

elephant.

A fingernail

as a fraction

of a human.

The fin as a

fraction of

a shark.

TASK


The wings as

a fraction of

a butterfly.

The trunk as a

fraction of an

elephant.

A fingernail

as a fraction

of a human.

The fin as a

fraction of

a shark.



Task 34 Prompts: Estimating fractions

SUPPORT

EXTEND

Teacher notes: Support: The trunk of an elephant is smaller relative to the size of an elephant than the wings of a butterfly relative to the size of a butterfly.

Extend: By distance, 5

100by car. By time,

20

100by car. The car travel is relatively slower.

EXPLAIN

Explain the mistake:

‘The trunk of an elephant is a bigger fraction than the

wings of a butterfly. This is because a trunk of an elephant

is bigger than the wings of a butterfly.’

Sometimes, a part is less than half of a whole:

Megan took part in six races. She won two of the races.

The bedroom is part of the house.

Sometimes, a part is more than half of a whole:

More than half the people in the classroom are children.

In summer, it is light for more than half of the day.

Think of real-world examples of fractions that are less than half and fractions that are more than half.

I am travelling to visit my friend. I drive 5 miles to my nearest train station. It is a 20-minute drive.

The train journey takes 1 hour and 20 minutes. It is 95 miles long.

What fraction of the journey is done by car?

This answer can be given in different ways.

EXTEND

I am travelling to visit my friend. I drive 5 miles to my nearest train station. It is a 20-minute drive.

The train journey takes 1 hour and 20 minutes. It is 95 miles long.

What fraction of the journey is done by car?

This answer can be given in different ways.


Task 35 Build: Fraction of a shape

BUILD

Teacher notes: Blue parts are the same size but different shapes so both shapes are half blue. Yellow parts are the same size but for the right-hand shape the whole is larger so the fraction yellow for the right-hand shape is smaller. Both of the bottom shapes are half purple as the parts/whole are identical – it’s harder to identify the right-hand shape as being half purple as the white half is split in two differently sized sections.

For each pair of shapes, what is the same? What is different?

The same… different… The same… different…

The same… different…

BUILD

For each pair of shapes, what is the same? What is different?

The same… different… The same… different…

The same… different…


Task 35: Fraction of a shapeTeacher notes: Print off and cut out the shapes for each pair/small group. Top row (left to

right): 1

2, 1

3, 1

2. Middle row (left to right):

1

3, 1

4, 1

4. Bottom row (left to right):

1

4, 1

4, 1

2. Solutions are

shown in the Worked Example (download from www.iseemaths.com/problem-solving-LKS2).

TASK

Sort the shapes into three groups: 𝟏

𝟐blue

𝟏

𝟑blue

𝟏

𝟒blue

TASK

Sort the shapes into three groups: 𝟏

𝟐blue

𝟏

𝟑blue

𝟏

𝟒blue



Task 35 Prompts: Fraction of a shape

EXTEND

Teacher notes: Explain: Shape A is 3

4shaded. Despite having a larger shaded part, shape B is

less than 3

4shaded. The white part of shape B is more than

1

4of the shape.

Extend: Children might attempt this by estimating the correct position of the lines. They could measure the length of each rectangle and use this to calculate the exact position of the lines.

EXPLAIN

SUPPORT

Example 1

This shape is 1

4blue. This dotted line

shows the four equally sized parts.

Example 2

Both squares are 1

2yellow. The squares

and the yellow parts are the same size

in both shapes.

Shape A Shape B

The dotted line splits the rectangle into a part of 1

4and a part of

3

4

Which shape has the

larger fraction shaded?

Explain.

Draw one line to split the

rectangle into parts of 1

3and

2

3

Draw one line to split the

rectangle into parts of 2

5and

3

5

Explain how you estimated where to position these lines.


Task 36 Build: Parts and the whole

BUILD

Teacher notes: Example answers:

Shade 1

4of the shape: This is

1

4of a shape. Draw the whole

shape:

This is 1

2of a shape: This is the whole shape:

BUILD

Shade 1

4of the shape: This is

1

4of a shape. Draw the whole

shape:

This is 1

2of a shape: This is the whole shape:


Task 36: Parts and the wholeTeacher notes: Possible answers shown here. Different solutions are shown in the Worked Example (download from www.iseemaths.com/problem-solving-LKS2).

TASK

This is 1

4of a symmetrical shape. Draw the whole shape.

This is 3


Answer in two ways.

Answer in three ways.

TASK

This is 1


This is 3


Answer in two ways.

Answer in three ways.



Task 36 Prompts: Parts and the whole

EXTEND

Teacher notes: Explain: The diagrams show each shape split into quarters:

EXPLA

IN

SUPPORT

1

4of a shape.

1

2of the shape. This is

3

4of a shape.

One more 1

4is

needed to

make the whole shape.

Shade 𝟑

𝟒of each shape:

Which shape was easiest? Which shape was hardest?

This is 3

4of a rectangle.

Draw the whole rectangle.

This is 2

3of a rectangle.

Draw the whole rectangle.

Teacher notes: Extend:


Task 37 Build: Fractions on a line

BUILD

Position 1 on each number line. One example has been done.

𝟏

𝟑0 1

𝟏

𝟐0

𝟏

𝟒0

𝟑

𝟒0

BUILD

Position 1 on each number line. One example has been done.

𝟏

𝟑0 1

𝟏

𝟐0

𝟏

𝟒0

𝟑

𝟒0


Task 37: Fractions on a lineTeacher notes: Answers are shown in the Worked Example (download from www.iseemaths.com/problem-solving-LKS2).

TASK

Position 𝟏

𝟐and

𝟏

𝟒on each number line:

0 1

0 2

0 𝟑

𝟒

0 𝟏

𝟖

TASK

Position 𝟏

𝟐and

𝟏

𝟒on each number line:

0 1

0 2

0 𝟑

𝟒

0 𝟏

𝟖



Task 37 Prompts: Fractions on a line

SUPPORT

EX

TEND

Teacher notes: Explain: the red number line. Three-tenths is the smallest fraction, so the distance left to 1 is longer.

EXPLAIN


0 2

‘One-quarter goes here.

I split the line into four parts.’𝟏

𝟒

0 𝟏

𝟖

𝟏

𝟒

‘One-quarter goes here.

4 is half of 8.’

1𝟏

𝟐

Think of some fractions that are more than 𝟏

𝟐and less than 1.

Position them on the number line:

0 𝟑

𝟏𝟎

0 𝟒

𝟏𝟎

0 𝟒

𝟓1 will be furthest along on which number line? Explain why.


Task 38 Build: Sharing contexts

BU

ILD

Teacher notes: Each child gets 3

4bar. Note different methods of sharing e.g. splitting the first

two chocolate bars in half and the fourth bar into quarters; splitting each bar into quarters.

4 children share 3 chocolate bars.

How much chocolate each?

BUILD



BUILD



BUILD




Task 38: Sharing contextsTeacher notes: The girls each have 1

1

4of a pizza, the boys each have 1

1

6of a pizza. Therefore

the girls have more pizza each. The solution is shown in the Worked Example (download from www.iseemaths.com/problem-solving-LKS2).

TASK

4 girls share 5 pizzas equally.

6 boys share 7 pizzas equally.

All the pizzas are the same size.

Which statement do you agree with:

Rachel: ‘Each girls gets more pizza than each boy.’

Paul: ‘Each boy gets more pizza than each girl.’

Sam: ‘Each child gets the same amount of pizza.’

TASK








TASK










Task 38 Prompts: Sharing contexts

SUPP

ORT

EXTEND

Teacher notes: Explain: here, Rose’s suggestion shares the books equally, Jenny’s suggestion shares the books equally based on the proportion of children in each class.Extend: If there were 4 pizzas before Harry came, each child would still get one pizza each. If there were more than 4 pizzas, each child would now get less pizza each. If there were less than 4 pizzas before Harry came, each child would get more pizza.

EXPLAIN

There are two classes in the nursery school. The Caterpillar class has 12 children. The Butterfly class 18 children.

The school are given 20 books to share between the classes.

Rose says ‘Each class should be given 10 books.’

Jenny says ‘Caterpillar class should get 8 books and Butterfly class should get 12 books.’

Which is the fairest way to share the books? Explain why.

4 children are about to share some pizzas.

Then Harry joins them. He brings another pizza to share.

Now that Harry has come, will each child have more, less or

the same amount of pizza?


The girls each get a whole

pizza. Then they share the one

last pizza.

Show how the girls will share the

last pizza:


The boys each get a whole

pizza. Then they share the one

last pizza.

Show how the boys will share

the last pizza:

of = 3


Task 39 Build: Fraction of a number

BUILD

Fill the gaps. Use the bar models to help.

2of 6 = 3

1

3of 9 = 3

1

3

6

3

9

3

33

4

1

of = 35

1

3 33 3

3 33 3 3

of = 3

BUILD

Fill the gaps. Use the bar models to help.

2of 6 = 3

1

3of 9 = 3

1

3

6

3

9

3

33

4

1

of = 35

1

3 33 3

3 33 3 3


Task 39: Fraction of a numberTeacher notes: Example answers:

1

2of 12 = 6

1

3of 18 = 6

1

4of 24 = 6. Note the link between the

three numbers. For example, 1

2of 12 = 6 which links to the multiplication fact 6 × 2 = 12

Example answers are shown in the Worked Example (download from www.iseemaths.com/problem-solving-LKS2).

TASK


Level 2: I can find three different

answers

1of 6=

TASK



answers

1of 6=

TASK



answers

1of 6=

TASK



answers

1of 6=

TASK



answers

1of 6=



Task 39 Prompts: Fraction of a number

SUPPO

RT

EXTEND

Teacher notes: Explain: the red number multiplied by the blue number gives the green number.Extend: there are an infinite number of answers for question A. There are a limited number of answers for question B: the denominator must be 12 or less.

EXPLAIN

Use the bar models to help:

Which question can be answered in more ways?

Question can be answered in more ways. This is because…

1of 6=

6

1of 6=

6

1

2of 10 = 5

1

3of 15 = 5

1

4of 20 = 5

1

9of 45 = 5

Every time, I have seen that…

When you multiply… by…

The pattern is…

Here is another example…

Look at these examples. What do you notice?

Question A:

1of = 12

Question B:

1of 12 =

The numbers in

the boxes are

positive whole numbers.

I SEE PROBLEM-SOLVING – LKS2MEASUREMENT

Task 40 Build: Balancing scalesTeacher notes: A strawberry is heavier (1 strawberry = 1.5 cherries). When scales balance, the side with fewer items must have heavier items. This principle can be explored practically with balancing scales.

BUILD

strawberries cherriesWhich is heavier:

or

BUILD


or

BUILD


or

BUIL

D


or


Task 40 Part 1: Balancing scales

TASK

1

Teacher notes: Lightest to heaviest: lemon, pear, apple. Apples are heaviest (same weight as lemon and pear). 1 pear = 2 lemons so lemons are lighter than pears. Answers are shown in the Worked Example (download from www.iseemaths.com/problem-solving-LKS2).

Apple: Lemon: Pear:

Order the fruits from lightest to heaviest. Explain how you know.

TASK

1

Apple: Lemon: Pear:


TASK

1

Apple: Lemon: Pear:




Task 40 Part 2: Balancing scales

TASK

2

Teacher notes: Lightest to heaviest: pear, banana, orange. 2 pears = 1 orange so oranges heavier than pears. 2 bananas = 1 orange + 1 pear so for scales to balance a banana must be lighter than an orange and heavier than a pear. Answers are shown in the Worked Example (download from www.iseemaths.com/problem-solving-LKS2).

Banana: Orange: Pear:


TA

SK

2



TASK

2





Task 40 Part 3: Balancing scalesTeacher notes: 1 cherry = 2 grapes. Therefore, 3 cherries = 6 grapes. If you swapped the 3 cherries for 6 grapes on the right-hand scale it would still balance. This means 2 strawberries = 6 grapes. Therefore, 1 strawberry = 3 grapes. The solution is shown in the Worked Example (download from www.iseemaths.com/problem-solving-LKS2).

Strawberry: Cherry: Grape:

A strawberry is the same weight as how many grapes?

TASK

3



TASK

3



TA

SK

3



Task 41 Build: Measures of timeTeacher notes: Discuss examples of time periods that could be measured in different units, for example the length of a tennis match could be measured in hours or in minutes.

BUILD

1

Which unit of time would you use to measure…

(a) The time it takes to eat a meal?

(b) The time it takes a sunflower to grow 20cm taller?

(c) The time it takes for a child to grow 20cm taller?

(d) The time it takes to run a 100 metre race?

(e) The length of time until Christmas?

seconds minutes hours days

weeks months years

BUILD

2

Dan fell off his bike. He broke his arm and grazed his knee.

Fill in the gaps to show what the doctor said to him:

Your current heart rate is 70 beats per .

You need to get 8 of sleep per night.

Your knee will be better in a few .

It will take 6-8 for your arm to heal.

seconds minutes hours days

weeks months years

Challenge: think of your own sentences using these time words.

BUILD

3

Would you rather…

Finish a race in a time of 3 minutes or a time of 200 seconds?

Go on a two week holiday or a 10 day holiday?

Have 100 days or 3 months until your next birthday?

Have a party that is 2 hours or 100 minutes long?


Task 41: Measures of timeTeacher notes: Q1: (shortest to longest) 600 seconds (10 minutes),

1

4hour (15 minutes),

20 minutes. Q2: 5 weeks (35 days), 50 days, 2 months (58-62 days). Solutions are shown in the Worked Example (download from www.iseemaths.com/problem-solving-LKS2).

TASK

Question 1: Order these times from shortest to longest:

600 seconds 20 minutes 𝟏

𝟒hour


50 days 5 weeks 2 months

TASK



𝟒hour



TASK



𝟒hour



TASK



𝟒hour





Task 41 Extend: Measures of timeTeacher notes: Task answers: 4 months 13 hours

EXT

END

months is more than 100 days and less than 18 weeks.

hours is more than 1

2day and less than 800 minutes.

Write a sentence that compares three different lengths of time. Use three different measures of time in your sentence.

Example: 50 hours is more than… minutes and less than… days.

EXTEND






EXTEND







Task 42 Build: Reading clocksTeacher notes: 13:50 1:50am 1:50pm Note misconceptions of identifying the hour as 2 o’clock (or 14h) and the minutes as 10 minutes.

BUILD

1212

3

4

5678

9

1011

Circle the times that this clock could be showing:

13:50

1:50pm

1:50am

2:10am 14:10

2:50pm

14:50

BUILD

1212

3

4

5678

9

1011


13:50

1:50pm

1:50am

2:10am 14:10

2:50pm

14:50

B

UILD

1212

3

4

5678

9

1011


13:50

1:50pm

1:50am

2:10am 14:10

2:50pm

14:50

BUILD

1212

3

4

5678

9

1011


13:50

1:50pm

1:50am

2:10am 14:10

2:50pm

14:50


Task 42: Reading clocksTeacher notes: Print off and cut out times and clocks for each pair/small group. Missing time is 3:40, time to draw is 17:10. Solutions are shown in the Worked Example (download from www.iseemaths.com/problem-solving-LKS2).

TASK

5:20

4:50

20:05

missing time:

17:10

Match each clock with the correct time.

Complete the clock face with

no hands. Fill in the missing time.

12 12

3

4567

8

9

10

11

12 12

3

4567

8

9

10

11

12 12

3

4567

8

9

10

11

12 12

3

4567

8

9

10

11

12 12

3

4567

8

9

10

11

TASK

5:20

4:50

20:05

missing time:

17:10

Match each clock with the correct time.

Complete the clock face with

no hands. Fill in the missing time.

12 12

3

4567

8

9

10

11

12 12

3

4567

8

9

10

11

12 12

3

4567

8

9

10

11

12 12

3

4567

8

9

10

11

12 12

3

4567

8

9

10

11



Task 42 Practice: Reading clocksTeacher notes: Check that children draw the hour hand shorter and the minute hand longer. Also, look at the accuracy with which children position the hour hand. For example, at 7:45 when correctly positioned the hour hand points ¾ of the distance between 7 and 8.

PR

ACTISE

For each clock, draw the missing hand:

12 12

3

4567

8

9

10

11

6:00

12 12

3

4567

8

9

10

11

10:1012 1

2

3

4567

8

9

10

11

5:40

12 12

3

4567

8

9

10

11

3:30

12 12

3

4567

8

9

10

11

5:0512 1

2

3

4567

8

9

10

11

7:45

PRACTISE

For each clock, draw the missing hand(s):

12 12

3

4567

8

9

10

11

22:00

12 12

3

4567

8

9

10

11

15:20

12 12

3

4567

8

9

10

11

5:40

12 12

3

4567

8

9

10

11

20:30

12 12

3

4567

8

9

10

11

5:05

12 12

3

4567

8

9

10

11

19:45


Task 43 Build: Combinations of change

BUILD

Teacher notes: Ella gets two 2p coins change (the fewest coins possible). Jess gets three 5p coins change (can also be done with 2 coins, 10p and 5p).

Ella buys an apple for 36p.

She pays with these coins:

She gets these 2 coins change:

20p2p1p 5p 10p

20p 20p

Jess buys an orange for 35p.

She pays with this coin:


50p

50p

For each example, what are the fewest coins in change that can be

given? What are the most coins in change that can be given?

BUI

LD

Ella buys an apple for 36p.

She pays with these coins:


20p2p1p 5p 10p

20p 20p

Jess buys an orange for 35p.

She pays with this coin:


50p

50p

For each example, what are the fewest coins in change that can be

given? What are the most coins in change that can be given?


Task 43: Combinations of changeTeacher notes: Paid with 50p, 20p, 10p; 2p, 2p, 1p change. Paid with 50p, 20p & 20p; 3 × 5p change. Kam could have paid £1.10 ( £1, 2 × 5p ) and got 35p change (20p, 10p, 5p). Practically, though, you wouldn’t give more than a £1 coin to pay 75p. Solutions are shown in the Worked Example (download from www.iseemaths.com/problem-solving-LKS2).

TASK

Kam bought a toy that costs 75p. He paid with 3 coins.

He was given 3 coins change.

Which coins could have been used?


Answer 1

Kam paid using these coins:

He got these coins in change:

Answer 1



20p

2p1p

5p

10p

50p

TASK



Which coins could have been used?


Answer 1



Answer 1



20p

2p1p

5p

10p

50p



Task 43 Prompts: Combinations of change

EXTEND

Teacher notes: Support: Mistake 1: paid less than 75p. Mistake 2: 15p change should be given.Explain: 47p 4 coins (2 × 20p, 5p, 2p). 38p 5 coins (20p, 10p, 5p, 2p, 1p). 6 coins: 88p, 89p, 98p, 99p.Extend: 4 possible answers. Paid 50p, 5p, 5p, 5p. Paid 50p, 10p, 10p; change 5p. Paid 50p, 20p, 5p; change 10p. Paid £1; change 20p, 10p, 5p.

EXPLAIN

SUPPORT

Mistake 1






20p

5p 10p

50p

Mistake 2



5p 5p

20p 20p 20p 20p

10p 5p

To make 47p you need to use at least coins.

To make 38p you need to use at least coins.

To make you need to use at least 6 coins.

Amy bought some stickers that cost 65p.

4 coins were exchanged with the shopkeeper.

Which coins were exchanged?


Amy gave the shopkeeper…

The coins she got in change were…

p


Task 44 Build: Comparing angles

BUILD

Make each angle in different ways. Examples: with a pair of scissors,

with a pipe cleaner, with the hands of a clock.

Can you think of any other ways to show these angles?

BUILD




BUILD





Task 44: Comparing anglesTeacher notes: Smallest to largest angles: blue, green, purple, red. Children may be able to order the blue and red angles without needing to measure. Note the possible error of thinking the blue angle is biggest because the lines are longer. Draw out different ways of comparing angles (using a right-angle, a pipe cleaner, tracing paper etc). Answers are shown in the Worked Example (download from www.iseemaths.com/problem-solving-LKS2).

TASK

Order the angles from smallest to largest:

Think of ways to compare the angles without using a protractor.

TASK



TASK





Task 44 Prompts: Comparing angles

SUPPORT

E

XTEND

Teacher notes: Explain: green is a right-angle (lines 3 along, 1 up & 3 up and one along), blue is a right-angle (lines cut diagonally through squares), purple is an obtuse angle (line straight & 3 along, 1 down), red is an acute angle (lines 3 up, 1 along & 4 along, 1 down).Extend: 9:00 right-angle; 3:30 and 11:50 acute; 2:50, 12:45 and 7:00 obtuse; 6:00 (straight line) and 12:00 (no angle) something else. Note that reflex angles are also created.

EXPLAIN

Explain the mistake:

Angles are created between the hands of a clock at different times.

Example: at 8:00 an obtuse angle is made.

Say if each angle is acute, obtuse or a right-angle.

The red angle is the biggest because the lines are longer

How do the squares help you to answer

this question?

12 12

3

4567

8

9

10

11

For the following times, is the angle between the hands acute,

obtuse, a right-angle or something else?

9:00

6:00

3:30

11:50

2:50

12:00

7:00

12:45


Task 45 Build: Area and perimeter

BUILD

Teacher notes: Area (smallest to largest) B, D, A, C. Perimeter (smallest to largest) A, C, B, D. Note that shapes with a larger area only sometimes have a larger perimeter and that thinner rectangles have a relatively larger perimeter and smaller area.

Order the shapes from smallest to largest area.

Order the shapes from smallest to largest perimeter.

Shape D

Shape BShape C

Shape A

Agree or disagree: ‘The shape with the largest area has the largest perimeter.’

BUILD

Order the shapes from smallest to largest area.

Order the shapes from smallest to largest perimeter.

Shape D

Shape BShape C

Shape A

Agree or disagree: ‘The shape with the largest area has the largest perimeter.’


Task 45: Area and perimeterTeacher notes: An answer is any different rectangle with an area of 24 squares. Identify the pattern: the thinner rectangles have a greater perimeter. Example solutions are shown in the Worked Example (download from www.iseemaths.com/problem-solving-LKS2).

TASK

Draw two more rectangles on the grid. Make all three rectangles have the same area and different perimeters.

Challenge: Draw a shape on the grid that is not a rectangle. It must have the same area as the other rectangles.

TASK

Draw two more rectangles on the grid. Make all three rectangles have the same area and different perimeters.

Challenge: Draw a shape on the grid that is not a rectangle. It must have the same area as the other rectangles.



Task 45 Prompts: Area and perimeter

EXTEND

Teacher notes: Explain: The shapes have the same perimeter. The right-hand side of both shapes is still 6 squares long, and the top length on both shapes is 5 squares long.Extend: Possible rectangle dimensions: 4 × 5 (area 20, perimeter 18) 3 × 6 (area 18, perimeter 18)

EXPLAIN

SUPPORT

1 2 3 4

5 6 7 8

9

The perimeter of

this shape is 14cm.

To calculate the

perimeter, start at

the dot and add

the lengths of

each side.

The area of this

shape is 12cm

squares. To

calculate the

area, count the

number of squares

that fit inside the

shape.’

These two shapes

have the same

perimeter

Agree or disagree:

10 11 12

Draw a rectangle on the grid. It must have a larger area and a smaller perimeter than the green rectangle.

I SEE PROBLEM-SOLVING – LKS2GEOMETRY

Task 46 Build: Shape properties

BUIL

D

Teacher notes: Draw out a range of similarities and differences relating to angles and sides e.g. number of acute angles, pairs of opposite/adjacent sides the same length.

For each pair of shapes, what’s the same? What’s different?

BUILD

For each pair of shapes, what’s the same? What’s different?


Task 46: Shape propertiesTeacher notes: Example answers: All shapes at least one pair of parallel lines. Four of the shapes have two pairs of equal length sides (A, B, D and E). Four of the shapes are irregular quadrilaterals (B, C, D and E). Three of the shapes have at least one right-angle (A, B and C). Three of the shapes have at least one acute angle (C, D and E). Two of the shapes have four right-angles (A and B). Two of the shapes have two acute angles (D and E). One of the shapes has four lines of symmetry (A). Example explanations are shown in the Worked Example (download from www.iseemaths.com/problem-solving-LKS2).

TASK

Write five sentences using each of the sentence stems to describe what is the same about the shapes:

Sentence stems:

All of the shapes…

Four of the shapes…

Three of the shapes…

Two of the shapes…

One of the shapes…

D

AB

C

E

TASK

Write five sentences using each of the sentence stems to describe what is the same about the shapes:

Sentence stems:

All of the shapes…

Four of the shapes…

Three of the shapes…

Two of the shapes…

One of the shapes…

D

AB

C

E



Task 46 Prompts: Shape properties

EXTEND

Teacher notes: Explain: Left box: two acute angles. Right box: one line of symmetry.Extend: Heading A: at least one right-angle. Heading B: quadrilaterals.

EXPLAIN

SUPPORT 2 acute angles

2 obtuse angles

No right-angles.

Opposite angles different.

No lines of symmetry.

One pair of parallel lines

Example shape:

What is the same about these shapes?

What is the same about these shapes?

The headings for each section of the Venn diagram have been hidden. What could each heading be?

Draw other shapes in each section of the Venn diagram.

Heading A Heading B


Task 47 Build: Building shapes

BUILD

Teacher notes: Top left = hexagon; bottom left = rectangle; top right = pentagon; bottom right = octagon.

These shapes have been made with right-angles triangles and squares.

Draw lines to match each shape with the correct shape name:

Rectangle

Pentagon

Hexagon

Octagon

B

UILD



Rectangle

Pentagon

Hexagon

Octagon

BUILD



Rectangle

Pentagon

Hexagon

Octagon


Task 47: Building shapes

TASK

Use the square and all four right-angles triangles to make:

A square, a rectangle, a trapezium, a parallelogram, a pentagon and a hexagon.

The shapes need to be cut out.

TASK

Use the square and all four right-angles triangles to make:

A square, a rectangle, a trapezium, a parallelogram, a pentagon and a hexagon.

The shapes need to be cut out.

Teacher notes: Square: Rectangle: Trapezium:

Parallelogram: Pentagon: Hexagon:

Answers are shown in the Worked Example (download from www.iseemaths.com/problem-solving-LKS2).



Task 47 Support: Building shapes

SUPP

ORT

Fit the five shapes inside these shape outlines:

Trapezium:

Hexagon:

Parallelogram:


Task 47 Extend: Building shapesTeacher notes: Explain:

Extend: 16 triangles 4 squares9 small triangles 3 squares made with 2 triangles4 triangles made by 2 small triangles 1 square made with 4 triangles2 triangles made by 4 small triangles1 triangle made by 9 small triangles

EXPLAIN

EXTEND

How many triangles? How many squares?

Note: Some of the shapes are different sizes!

This hexagon is made with eight identical triangles:

It is possible to add one more triangle to this shape to make it into a pentagon.

This can be done in different ways.

Explain/draw.

EXTEND

How many triangles? How many squares?

Note: Some of the shapes are different sizes!


Task 48 Build: Lines of symmetryTeacher notes: Correct lines of symmetry: equilateral triangle and quarter circle.

BUILD

Which of the dotted lines are lines of symmetry?

or

BU

ILD


or

BUILD


or


Task 48: Lines of symmetryTeacher notes: Answers (lines of symmetry in brackets): parallelogram (0), triangle (1), rectangle (2), cross (4), hexagon (6). Answers are shown in the Worked Example (download from www.iseemaths.com/problem-solving-LKS2).

TASK

Order the shapes from fewest to most lines of symmetry:

Rectangle: Parallelogram:

Cross:

Hexagon:

Triangle:

TASK



Cross:

Hexagon:

Triangle:

T

ASK



Cross:

Hexagon:

Triangle:



Task 48 Support: Lines of symmetryTeacher notes: Shapes may need cutting out for the children.

SUPPORT

Cut out the shapes. Fold them to find lines of symmetry:


Task 48 Prompts: Lines of symmetry

EXTEND

Teacher notes: Explain: Lines of symmetry split a shape in two halves that are mirror images. This line splits the shape into half but not into a mirror image.

Extend: Three shapes have a line of symmetry:

EXPLAIN

Explain why this statement is incorrect:

Some of these shapes have one line of symmetry.

Draw the lines of symmetry on the shapes:

The red line is a line

of symmetry

because it splits the

rectangle in half.

Circle the shapes with no lines of symmetry.


Task 49 Build: Coordinate points

B

UILD

Teacher notes: (4,3) outside (3,4) bottom edge (5,8) top edge (8,5) inside.

Plot these points on the coordinate grid:

(4,3) (3,4) (5,8) (8,5)

Look at each coordinate point. Is it inside, on the edge or outside of the

rectangle?

321 4 5 6 7 8 9 100

2

0

1

3

4

5

6

7

8

9

BUILD


(4,3) (3,4) (5,8) (8,5)

Look at each coordinate point. Is it inside, on the

edge or outside of the

rectangle?

321 4 5 6 7 8 9 100

2

0

1

3

4

5

6

7

8

9

BUILD


(4,3) (3,4) (5,8) (8,5)

Look at each coordinate point. Is it inside, on the edge or outside of the

rectangle?

321 4 5 6 7 8 9 100

2

0

1

3

4

5

6

7

8

9


Task 49: Coordinate points

TASK

Teacher notes: (6,4) inside (4,4) left edge (5,7) outside (6,1) bottom edge (1,6) outsideAnswers are the same for the green and yellow task. Answers are shown in the Worked Example (download from www.iseemaths.com/problem-solving-LKS2).

For each coordinate point, say whether it is inside, on the edge or outside of the rectangle:

(6,4) (4,4) (5,7) (6,1) (1,6)

Challenge: Think of different

coordinate points that are inside,

on the edge or outside of the

rectangle.

321 4 5 6 7 80

2

0

1

3

4

5

6

7

(4,1)

(4,5) (7,5)

(7,1)

TASK


(6,4) (4,4) (5,7) (6,1) (1,6)




rectangle.

321 4 5 6 7 80

2

0

1

3

4

5

6

7

(4,1)

(4,5) (7,5)

(7,1)

TASK


(6,4) (4,4) (5,7) (6,1) (1,6)




rectangle.

(4,1)

(4,5) (7,5)

(7,1)



Task 49 Prompts: Coordinate points

EXTEND

Teacher notes: Support: (6,1) is red and (1,6) is blueExplain: (6,2) purple (3,2) green (2,5) yellowExtend: Six possible answers: (0,2) (0.6) (8,2) (8,6) (2,4) (6,4)

EXP

LAIN

SUPPORT

321 4 5 6 7 80

2

0

1

3

4

5

6

7

Which coordinate point is (6,1)?

Which coordinate point is (1,6)?

Which dot is at (6,2)?




321 4 5 6 7 80

2

0

1

3

4

5

6

7

(4,2)

(4,6)A third point can be drawn to make

an isosceles right-angled triangle.

What are the coordinates of this

third point?

Level 1: I can find one possible

coordinate point

Level 2: I can find different possible

coordinate points

Level 3: I know how many possible

coordinate points there are

I SEE PROBLEM-SOLVING – LKS2DATA HANDLING

Task 50 Part 1: After-school clubs

TASK

1

Teacher notes: Suggestions: make question 1 less ambiguous (hard to define ‘a lot of exercise’). Question 2 could list the different sports clubs. Question 3 could look at a broader range of sports e.g. dancing, martial arts. Question 4 could offer possible options.

Bridge Green Primary School want their children to be active and play sports. They will send out a questionnaire to find out which sports children play and which new sports clubs the school could run.

Joy has designed this questionnaire. How can it be improved?

Name: ________________

Year group: ______ boy/girl

1. Do you do a lot of exercise? (tick)

yes some no

2. Do you go to a school sports club? (tick)

yes no

3. Which sports do you like? (tick)

football rugby tennis

rounders running hockey

4. Are there any new sports clubs you would join?

_______________________________________

_______________________________________

_______________________________________


Task 50 Part 2: After-school clubs

TASK

2

Teacher notes: There are the same number of KS1 and KS2 clubs, yet there are more KS2 children. Not as many KS2 boys attend clubs. Consider introducing non-team sports in KS2 and possibly an indoor sport e.g. gymnastics, martial arts or table tennis. Key facts are shown in the Worked Example (download from www.iseemaths.com/problem-solving-LKS2).

Here are some of the questions that the teachers at Bridge Green

Primary asked before choosing their next after-school sports club:

There are 56 children in KS1 and 119 children in KS2. This graph shows how many children go to each of the after-school sports clubs:

What does this graph show? Give suggestions to Bridge Green Primary School about their next sports club.

SUPPORT

Are there different clubs for

children in each year group?

Some children don’t enjoy sports like

football or netball. What might they prefer?

At the moment, are there more

boys or girls at our sports clubs?

Football(KS2)

Running(KS1)

Netball(KS2)

Dance(KS1)

Hockey(KS2)

Could we have

another indoor club?

10

20

15

5

0Football

(KS1)

boys

girls

Things to investigate:

Are there more boys or girls who go to the school sports clubs?

How many children go to KS1 clubs?

How many children go to KS2 clubs?

Are there different types of sports clubs for children to take part in?

Which are the most or least popular sports clubs?



Task 50 Explain: After-school clubs

EXPLAIN

Teacher notes: For Fran’s statement, fewer boys than girls go to hockey club. Maybe hockey just doesn’t interest the boys. It could be argued that there should be more KS2 clubs as there are nearly double the number of KS2 children. Tom may be correct, equally maybe the children who don’t choose to go to football club would also not choose to play a similar sport like rugby.

Agree or disagree?

The school should

encourage more

boys to play hockey

KS2 football is the most popular club, so the school should run another similar club like rugby

There are three KS1 clubs and

three KS2 clubs, which is fair

Tom

Kim

Fran

EXPLAIN

Agree or disagree?

The school should

encourage more

boys to play hockey




Tom

Kim

Fran

EXPLAIN

Agree or disagree?

The school should

encourage more

boys to play hockey




Tom

Kim

Fran


Task 51 Build: Different graph types

BUILD

Teacher notes: Line graph for height of sunflower (in-between readings have meaning for measurement over time). Bar chart for eye colour (eye colours are discrete groups).

Which type of

graph is best to

show the height of a sunflower?

Which type of

graph is best to

show the eye

colour of the

children in the class?

3m

2m

1m

Apr May Jun JulMar

3m

2m

1m

Apr May Jun JulMar

10

brown green grey hazelblue

5

10


5

BUILD

Which type of

graph is best to

show the height of a sunflower?

Which type of

graph is best to

show the eye

colour of the

children in the class?

3m

2m

1m

Apr May Jun JulMar

3m

2m

1m

Apr May Jun JulMar

10


5

10


5

Graph to show rainfall

over a year.

Graph to show whether

children are having a

packed lunch or school

dinners.

Graph to show favourite

football teams for

children in class.

Graph to show the height

of a child since birth.

Graph to show number

of brothers or sisters for

each child in the class.


Task 51: Different graph typesTeacher notes: Print and cut out. Rainfall is the undulating line graph; school lunches is the pictogram; football team is the randomly distributed bar graph; height is the steadily rising line graph; siblings is bar graph with reducing sized bars. Answers are shown in the Worked Example (download from www.iseemaths.com/problem-solving-LKS2).

TASK

There are no labels on the graphs. Match the graph to the correct heading:

= 5 children



Task 51 Prompts: Different graph types

EXPLAIN

Teacher notes: Explain: Note pictograms and bar charts can represent the same discrete data. Bar graphs have scales on both axis and can present data with greater accuracy.Extend: Shoe size is the graph with higher middle values (a normal distribution), with fewer children having smaller/larger feet. Favourite fruit is the graph with a random distribution. Age of children in Y4 is the graph with two values (children aged 8 or 9). How many pets is the graph with bars of descending size as most households have no pets or few pets.

EXTEND

Draw lines to match the heading to the correct graph.

These two graphs show how children travel to Minton Primary School:

What’s the same? What’s different? Which graph is best?

100

Bike/Scoot

Car Walk

How Children Travel to School

50

25

75

Bike/Scoot

Car

Walk

How Children Travel to School

= 10 children

Number of Pets Owned Per Child

Shoe Size for Children in Class

Children’s Favourite Fruit

Age of Children in Y4 Class

Explain your choices.


Task 52 Part 1: Making judgements

TASK

1

Teacher notes: Discern between answers that retrieve one piece of information (e.g. 23 girls in year 5 read 4+ times per week), answers that use different pieces of information (e.g. 47 children in Y3 read 4+ times per week) and answers that look at the general pattern (e.g. fewer boys read 4+ times per week in Y6 than in Y3). Note the pattern of boys reading decreasing in KS2. Observations are shown in the Worked Example (download from www.iseemaths.com/problem-solving-LKS2).

This table shows the number of

children who read 4 or more

times per week in the KS2

classes at Darlow Primary School.

Y3 Y4 Y5 Y6

Boys 23 26 18 16

Girls 24 23 21 24

What does this table show?

…boys in year… read 4

or more times per week.The children read most often in year…

…children in year… read 4 or

more times per week.

TASK

1





Y3 Y4 Y5 Y6

Boys 23 26 18 16

Girls 24 23 21 24






TAS

K

1





Y3 Y4 Y5 Y6

Boys 23 26 18 16

Girls 24 23 21 24









TASK

2

Teacher notes: Note that the graph represents the same information as the table in part 1, but the visual representation of the graph can make it easier to see patterns in data. Girls reading stays consistent but boys reading decreases through KS2. Also, note that children may read more when they get older but less frequently. We don’t know whether most children read as we don’t know how many children there are in total. Observations are shown in the Worked Example (download from www.iseemaths.com/problem-solving-LKS2).

This graph shows the number of children who read 4 or more times per week in the KS2 classes at Darlow Primary School.

Agree or disagree:

Is it better to see the information in a graph or in a table?

All the children

read less as they

get older

0

5

10

15

20

25

30

Y3 Y4 Y5 Y6

Children Reading 4+ Times Per Week

girls boys

Most children

read 4 or more

times per week

TASK

2

This graph shows the number of children who read 4 or more times per week in the KS2 classes at Darlow Primary School.

Agree or disagree:

Is it better to see the information in a graph or in a table?

All the children

read less as they

get older

0

5

10

15

20

25

30

Y3 Y4 Y5 Y6

Children Reading 4+ Times Per Week

girls boys

Most children

read 4 or more

times per week




TASK

2

Teacher notes: Q1: Swansea – note that a lower % of trains late means more trains arriving on time. Q2: January – maybe winter weather causes more train delays. Observations are shown in the Worked Example (download from www.iseemaths.com/problem-solving-LKS2).

This graph shows the percentage of trains that arrive late at different train stations for the first 3 months of the year:

0%

1%

2%

3%

4%

5%

6%

7%

8%

9%

Cardiff Bristol Swansea Newport

% of Trains Arriving Late

January February March

Q1: Which train

station has most

trains arriving on

time?

Q2: In which

month are the

trains least likely

to arrive on time?

TA

SK

2

This graph shows the percentage of trains that arrive late at different train stations for the first 3 months of the year:

0%

1%

2%

3%

4%

5%

6%

7%

8%

9%

Cardiff Bristol Swansea Newport

% of Trains Arriving Late

January February March

Q1: Which train

station has most

trains arriving on

time?

Q2: In which

month are the

trains least likely

to arrive on time?



Task 53 Information: Train timetablesTeacher notes: This timetable is used for all the questions in the ‘Train timetables’ task.

Tinford 6:20 7:40 9:05 10:32

Denley 6:42 8:03 9:27 10:54

Garbury 7:25 8:47 10:08 11:37

Penfield 7:54 9:15 10:36 12:04

This timetable shows the times of the morning trains from Tinford to Penfield:

Tinford 6:20 7:40 9:05 10:32

Denley 6:42 8:03 9:27 10:54

Garbury 7:25 8:47 10:08 11:37

Penfield 7:54 9:15 10:36 12:04


Tinford 6:20 7:40 9:05 10:32

Denley 6:42 8:03 9:27 10:54

Garbury 7:25 8:47 10:08 11:37

Penfield 7:54 9:15 10:36 12:04


Tinford 6:20 7:40 9:05 10:32

Denley 6:42 8:03 9:27 10:54

Garbury 7:25 8:47 10:08 11:37

Penfield 7:54 9:15 10:36 12:04


Tinford 6:20 7:40 9:05 10:32

Denley 6:42 8:03 9:27 10:54

Garbury 7:25 8:47 10:08 11:37

Penfield 7:54 9:15 10:36 12:04


Tinford 6:20 7:40 9:05 10:32

Denley 6:42 8:03 9:27 10:54

Garbury 7:25 8:47 10:08 11:37

Penfield 7:54 9:15 10:36 12:04



Task 53 Part 1: Train timetables

TASK

1

Teacher notes: Q1: 7:54 Q2: 9:05 Q3: 1 hour 35 minutes Note the columns show the times for each train and the rows show the times of the trains at each station. Answers are shown in the Worked Example (download from www.iseemaths.com/problem-solving-LKS2).

Q1: At what time does the first train finish its journey?

7:54 OR 10:32

Q2: At what time does the third train of the day leave Tinford?

7:25 OR 9:05

Q3: How long does the second train take to get from Tinford to Penfield?

9:15 OR 1 hour 35 minutes

Write your own questions based on the timetable. Use the sentence stems:

What time is the first train from… I arrive at… at 9:15. When is the next train?

How long does the third train take to get from… to…

TASK

1


7:54 OR 10:32


7:25 OR 9:05






TASK

1


7:54 OR 10:32


7:25 OR 9:05









TASK

2

Teacher notes: Red statement is false. Example: the first train takes 1 hour 34 minutes; the last train takes 1 hour 32 minutes. Blue statement is true: for all of the trains the journey from Tinford to Denley is the shortest part of the journey. Answers are shown in the Worked Example (download from www.iseemaths.com/problem-solving-LKS2).

Agree or disagree:

All the train journeys

take the same

length of time

The shortest part of

the journey is

always between

Tinford and Denley

TASK

2

Agree or disagree:


take the same

length of time


the journey is

always between

Tinford and Denley

TASK

2

Agree or disagree:


take the same

length of time


the journey is

always between

Tinford and Denley

TASK

2

Agree or disagree:


take the same

length of time


the journey is

always between

Tinford and Denley




T

ASK

3

Teacher notes: The 8:03 train arrives at 8:47, with a 10-minute walk Mrs Patel would arrive at 8:57am. However, this is only 3 minutes before her interview is due to start. Therefore, it may be advisable to get the 6:42 train. Note that a different context may lead to her choosing a different train, e.g. meeting a friend at 9:00am. Answers are shown in the Worked Example (download from www.iseemaths.com/problem-solving-LKS2).

Mrs Patel is a teacher. She lives in Denley.

Mrs Patel has a job interview at a school which is a 10-minute walk from Garbury train station. The interview starts at 9:00am.

Which train should Mrs Patel catch from Denley train station?

TASK

3




TASK

3




TASK

3




TASK

3






Task 54 Build: Comparing teams

BUILD

Teacher notes: 1st row: played 3, won 3, drawn 0. 2nd row: Peel Lane, points 4, goals for 11. 3rd row: Hinley, goals against 8. 4th row: played 3, won 0, drawn 1, lost 2, goals for 3.

Played Points Won Drawn Lost Goals

for

Goals

against

St Johns 9 0 10 5

3 1 1 1 7

3 2 0 2 1 6

Crowford 1 10

There are 4 teams in a school football league. You get 3 points for a win and 1 point for a draw. So far these are the results from their matches:

Fill in the gaps in the league table:

Hinley 1 – 3 St Johns Peel Lane 5 – 0 Crowford

Peel Lane 4 – 4 Hinley Crowford 2 – 4 St Johns

Hinley 1 – 1 Crowford St Johns 3 – 2 Peel Lane

BUILD


for

Goals

against

St Johns 9 0 10 5

3 1 1 1 7

3 2 0 2 1 6

Crowford 1 10

There are 4 teams in a school football league. You get 3 points for a win and 1 point for a draw. So far these are the results from their matches:

Fill in the gaps in the league table:

Hinley 1 – 3 St Johns Peel Lane 5 – 0 Crowford

Peel Lane 4 – 4 Hinley Crowford 2 – 4 St Johns

Hinley 1 – 1 Crowford St Johns 3 – 2 Peel Lane


Task 54: Comparing teamsTeacher notes: League table shows Keyton had 3 more wins; Tanbury had more draws. Tanbury scored relatively few goals and conceded relatively few goals. The scorers graph showed Tanbury had the top scorer but Keyton had more players who scored 10+ goals. Tanbury made most tackles but less shots or passes than Keyton. Overall, their attack needs to improve. The teams had similar numbers of red and yellow cards. Key points shown in the Worked Example (download from www.iseemaths.com/problem-solving-LKS2).

TASK

Last season, football team Tanbury Rovers finished second in the league to

Keyton Town. The manager of Tanbury Rovers wants to find out how the

team can improve. Here is some information from last season’s matches:


for

Goals

against

Keyton Town 28 60 18 6 4 68 34

Tanbury Rovers 28 55 15 10 3 53 25

Denfield F.C. 28 49 14 7 7 59 41

Conley Athletic 28 48 15 3 10 60 49

League Table (top 4 teams):

Top scorers: Keyton Town Top scorers: Tanbury Rovers

20

Passes per

match

Shots per

match

Tackles per

match

Total yellow/

red cards

Keyton Town 317 13 23 18 Y 2 R

Tanbury Rovers 251 10 29 21 Y 1 R

Denfield F.C. 247 11 21 14 Y 0 R

Conley Athletic 276 14 19 26 Y 3 R

Write a report for the manager of Tanbury Rovers. Compared to the other teams, what are Tanbury’s strengths? How can they improve?

Match statistics (top 4 teams):

10

15

5

Meyer

Banks

Olson

Fox

Names of scorers in bars

Rose

20

10

15

5Cox

Garcia D

iaz

Shaw

Lee

Names of scorers in bars

Lawson



Task 54 Prompts: Comparing teams

EXT

END

Teacher notes: Explain: Denfield were the only team to score all their penalties but they only had one penalty. For teams with 4+ penalties, Tanbury scored the highest proportion. Keytonscored the most but missed the most. Colney scored the lowest proportion of penalties.Extend: It can be argued that both statements are true. Garcia scored more goals but Meyer scored with a higher proportion of shots.

EXPLAIN

SUPPORT

Example sentences from a report about Conley Athletic:

Conley Athletic were the 2nd top scorers. They had more shots per match

than any other team. You have a good attack.

Conley Athletic had 49 goals against, which is a lot more than the top 3

teams. The defence can improve.

The team did not make as many tackles as the other teams – 19 per

match, the other teams all had 21 or more. They also had more yellow

cards and red cards. Try to improve the team’s tackling.

Keyton Town had 8 penalties. They scored 5 and missed 3.

Tanbury Rovers had 4 penalties. They scored 3 and missed 1.

Denfield F.C. had 1 penalty, which they scored.

Conley Athletic had 4 penalties. They scored 2 and missed 2.

Order the teams from best to worst at taking penalties.

This graph shows how many shots were taken and how many goals scored by the league’s two top scorers – Garcia and Meyer.

60

30

50

Garcia Meyer

40

20

10

Shots taken

Goals scored

This graph shows that Garcia

is better at scoring goals

This graph shows that Meyer

is a better at shooting

Agree or disagree:

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