...USING THE TASKS I SEE REASONING –Y5 Tasks to inspire mathematical thinking Using the Tasks I...
Transcript of ...USING THE TASKS I SEE REASONING –Y5 Tasks to inspire mathematical thinking Using the Tasks I...
CONTENTS
I SEE REASONING – Y5
Contents
Introduction
Using the Tasks
Place Value
Decimals
Negative Numbers
Rounding
Roman Numerals
Addition
Subtraction
Addition and Subtraction
Multiplication
Division
Multiplication and Division
Fractions
Fractions + – × ÷
Fractions, Decimals, Percentages
Measurement
I SEE REASONING
CONTENTS
I SEE REASONING – Y5
Contents
Perimeter, Area, Volume
Angle
Shape
Position, Direction, Coordinates
Statistics
Answers
I See Maths Resources
I SEE REASONING
INTRODUCTION
I SEE REASONING – Y5Tasks to inspire mathematical thinking
Introduction
For use by the purchasing institution only. Copyright I See Maths ltd. Circulation is prohibited.
I See Reasoning – Y5 helps children build a strong
conceptual understanding of mathematics and gives a
wide range of tasks for deepening and extending
thinking.
Children grasp key concepts and ideas using Part-
Complete Examples and Spot the Mistakes questions.
Mathematical patterns and relationships are
highlighted by sequences of Small Difference Questions
and I know… so… tasks. Rank by Difficulty and Different
Ways prompts open up great debates, whilst
challenges are extended through Multi-Skill and How
Many Ways? questions.
The resource is comprised of 362 varied tasks, linked to
all different areas of England’s Year 5 mathematics
curriculum. This corresponds to US Grade 4 and
Australia Year 5. Screenshots of tasks can be used
within presentations or questions can be printed and
given to children.
I hope that I See Reasoning – Y5 enriches the maths
learning in your classroom, helping all children to build
knowledge and make rich connections. I also hope
that it gives you lots of great classroom moments!
Gareth Metcalfe
I SEE REASONING
USING THE TASKS
I SEE REASONING – Y5Tasks to inspire mathematical thinking
Using the TasksI See Reasoning – Y5 will help teachers to plan coherent
sequences of lessons. Some tasks help children to grasp key
ideas; others break down calculations. There are prompts for
generating discussion and challenges for deepen learning. This
section introduces the most common question types and
considers how they might be used.
Contexts: Context examples are used to connect maths
concepts to real world scenarios. For example, the Negative
Numbers section looks at contexts where negative numbers
are/are not used.
Explain the Mistakes: Common mistakes are shown so children
can understand key differences between correct and incorrect
thinking. For example, in the Angle section, children explain
mistakes when measuring an angle with a protractor.
Which Answer? Agree or Disagree? and Correct or Incorrect:
Here, children have to spot correct responses and explain
mistakes that have been made, like in the Multiplication and
Division example where different ways to complete a number
sentence are shown.
Estimate: These tasks show the thought process behind making
relatively accurate estimates, like in this Multiplication example.
Next Step and Part-Complete Examples: These tasks break
calculation procedures down into small steps. Children’s
attention is drawn to the key next step, like in this Division
example, or to complete the rest of a question like this
Multiplication task.
I SEE REASONING
USING THE TASKS
I SEE REASONING – Y5Tasks to inspire mathematical thinking
Using the TasksSmall Difference Questions and I know… so… In these tasks,
there are small differences between questions in a sequence.
This draws children’s attention to key patterns and ideas. If a
question changes but the answer stays the same, how can this
be explained? This technique is shown in the Rounding section.
Explain: For these prompts, children consider relationships,
explain patterns and make generalisations. Sentence stems may
be used to scaffold responses. This technique is used in the
Roman Numerals section.
Different Ways and Rank by Difficulty: These tasks encourage
children to use different calculation techniques and compare
strategies, deepening conversations. In this Adding Fractions
example, children are encouraged to use a range of methods.
Extend and Multi-Skill: To answer these questions, children have
to work through a range of steps or use knowledge from
different parts of the maths curriculum. This is shown in the Angle
section, with questions involving skills about reading clocks.
How Many Ways? The ultimate challenge on these tasks is for
children to find all the possible answers to the question. For this, a
system is needed to know that every solution has been
identified. There is an example in the Place Value section.
I SEE REASONING
How can 2410 be made using 10, 100 and 1000 counters?
What are the fewest counters that can be used?
What are the most counters that can be used?
Find a way of making 2410 using 16 coins.
PLACE VALUE
True or False?
392
3 hundreds
9 tens
2 ones
Different Ways
1 hundred
29 tens
2 ones
35 tens
32 ones
3 hundreds
7 tens
12 ones
or
Make 534
5 hundreds, tens, 4 ones.
3 hundreds, tens, 4 ones.
4 hundreds, tens, 14 ones.
tens, ones.
10010
1000
Different Ways
Extend: Find other ways of making 392
I SEE REASONING
PLACE VALUE
Which Answer?
Small Difference Questions
Three thousand and four30004
3004
Sixty thousand and two60002
600002
20006Two thousand and six
Twenty thousand and six
50070Fifty thousand and seventy
Five hundred and seventy
Write in words:
35000 ___________________________________________
30500 ___________________________________________
30050 ___________________________________________
3050 ____________________________________________
300005 __________________________________________
OrderIn each number, how many zeros?
Fifty-six thousand and twenty
Three hundred thousand, two hundred and seventy
Thirteen thousand and thirty-one
I SEE REASONING
PLACE VALUE
Spot the Pattern
Small Difference Questions
Fill the gaps:
, 764, 774, 784, ,
963, , 983, ,
, 1206, 1106, ,
999 + 1 = 9999 + 1 =
999 + 100 = 9999 + 1000 =
999 + 10 = 9999 + 100 =
Estimate
Estimate the value of the numbers at the arrows:
0 10000
0 100000
Extend: Design a sequence question with missing numbers.
I SEE REASONING
PLACE VALUE
EstimateEstimate the position of 836 on each number line:
0 1000
800 850
700 1000
0 10000
EstimateEstimate the position of 3280 on each number line:
0 10000
3000 4000
3200 3300
0 5000
your example
your example
I SEE REASONING
PLACE VALUE
Different WaysWhat could the start and end numbers be?
194
Different WaysWhat could the start and end numbers be?
3070
0
Small Difference Questions5
0
500
0
25
I SEE REASONING
PLACE VALUE
How Many Ways?
Agree or Disagree?
A three-digit number is added to a two-digit number.
The sum is a 4-digit number.
Which digit must be in the blue box?
Explain
Jen thinks of a 2-digit number. The sum of its digits is 7.
Molly thinks of a 2-digit number. The sum of its digits is 15.
Jen’s number might be larger than Molly’s number
Example: The sum of the digits for 35 is 8
3 + 5 = 8
I think of an even 4-digit number. It is more than 4000.
The sum of its digits is 8. Each digit is different.
What could the number be?
Level 1: I can find a possible answer.
Level 2: I can find different possible answers.
Level 3: I know how many possible answers there are.
+ =
Different WaysWhich number with a digit sum of 16 is closest to 700?
There are two possible answers.
I SEE REASONING
DECIMALS
Small Difference Questions
Show the position 0.36 on each number line:
0 1
0.3 0.4
0 0.5
Small Difference Questions
Show the position 0.8 on each number line:
0 10
0 1
0.5 1
Agree or Disagree?
0 1
0.77
I SEE REASONING
I SEE REASONING - 5
Different Ways
Compare
Choose different start and end numbers. Position 3.74
on each number line:
Use < = > signs to compare the decimals:
Agree or Disagree?
140 is more than 80 as it has more digits
0.14 is more than 0.8 as it has more digits
0.64 0.52
0.64 0.9
0.64 0.614
0.64 0.644
0.7 0.70
0.55 0.505
0.08 0.088
0.915 0.92
>
DECIMALS
Question 1:
How many ways can 0.42 be made?
Question 2:
How many ways can 0.24 be made?
Explain the Mistakes
CompareComplete with the correct symbol: < = >
0.47 + 0.3 = 0.500.88 + 0.22 = 1
0.25 > 0.2 + 0.08
0.33 0.3 + 0.3
0.33 0.3 + 0.03
0.41 0.4 + 0.004
0.67 0.6 + 0.07
0.87 0.7 + 0.08
How Many Ways?
0.1
0.01
You have a pile of 0.1 and 0.01 counters.
Spot the PatternContinue the sequences:
0.37, 0.38, 0.39, ,
0.07, 0.08, 0.09, ,
40, 40, 4, ,
8, 4, 2, 1, ,
DECIMALS I SEE REASONING
Small Difference QuestionsOn each number line, which number is half-way?
20 21
2 2.1
800 810
0.8 0.81
Which Answer?
What is 53.48 to the nearest whole number?
Explain the mistakes.
(a) 54
(b) 53.5
(c) 53
38 39 40 41
Position 38.42, 39.08, 39.6, 40.27 and 40.82 on the number
line:
For each decimal, which is the nearest whole number?
Number Lines
23.5 23.6 23.7 23.8
Position 23.555, 23.64, 23.708 and 23.78 on the number
line:
For each decimal, which is the nearest tenth?
DECIMALS I SEE REASONING
Different Ways
3.5 is half-way between…
3.5
Use 1 decimal place numbers:
3.5
Use 3 decimal place numbers:3.5
Use 2 decimal place numbers:
Small Difference Questions
30 ÷ = 1
30 ÷ = 0.3
30 ÷ = 0.1
40 ÷ = 0.4
40 ÷ = 1
40 ÷ = 0.5
Different Ways2 = 0.2
2 = 0.2
0.8 = 80
0.8 = 80
= 0.1
= 0.1
= 0.1
Complete using different
symbols +
–
×
÷
DECIMALS I SEE REASONING
0.05, , 0.15,
0.15, , 0.45,
Spot the Pattern
Different Ways
Small Difference Questions
Continue the sequences:
0, 0.3, 0.6, 0.9, ,
0.02, 0.04, 0.06, ,
× = 3
× = 3
× = 3
× = 3
6 × 5 = 30
× = 2.4
× = 2.4
× = 2.4
× = 2.4
10 × 2.4 = 24
2 × = 6 0.2 × = 4 0.2 × = 2
4 × = 6 0.1 × = 4 0.25 × = 2
12 × = 6 0.5 × = 4 0.5 × = 2
× = 6 × = 4 × = 2
DECIMALS I SEE REASONING
NEGATIVE NUMBERS
ContextsFor each example, are the negative numbers used
correctly?
There are 30 children. I
have 20 sweets. Each
child has a sweet. There
are -10 sweets left.
I was at level 8 in the car
park. I go down 10 levels
in the lift. Now I’m on
level -2.
I spent £15 on face paints
for the school fair. I made
£20 doing face paints.
Overall, the stall made -£5.
The temperature was 4˚c on
Monday. It was 7˚c colder on
Tuesday. The temperature on
Tuesday was -3˚c.
Think of other examples where negative numbers are used.
Question Number Sentence
I spent £6 on ribbon to make bracelets.
I made £4 at my stall selling bracelets.
What was my profit?
I was 2 floors below ground level at the
hotel. I got the lift. It took us 5 floors up.
Which floor am I on now?
5 – 7 = -2
Contexts
I SEE REASONING
Explain the Mistake
-2 -1 0 1 2 3
The difference
between -2 and 3
is 6. I counted all the numbers.
Different Ways
This question can be answered in two ways:
The difference between -20 and is 50
The difference between -20 and is 50
Show both answers on the number line:
-20 0
EstimatePosition the numbers on the number line: -8 -14 17 -3
-10 0-20 10 20
NEGATIVE NUMBERS
Position the numbers on the number line: -34 -58 65 -80
-50 0-100 50 100
Answer in two ways:
The difference between -17 and is 25
The difference between -17 and is 25
I SEE REASONING
Estimate
EstimatePosition 0 on each number line:
020
0
20
8
0
-10 10
-10 20
-20 40
-10 40
NEGATIVE NUMBERS
your own example
0
I SEE REASONING
Small Difference QuestionsOn each number line, which number is half-way?
2 10
-3 5 -5 7
-5 3
How are the questions similar? How are they different?
Small Difference Questions
Half-way between -3 and 7 is
Half-way between -7 and 3 is
Half-way between -6 and -2 is
Half-way between -6 and is -2
Half-way between -6 and is 2
Small Difference Questions
Half-way between 7 and 15 is
Half-way between -7 and 15 is
Half-way between -11 and is -4
Half-way between -11 and is 4
NEGATIVE NUMBERS I SEE REASONING
Which Answer?
What are the next 3 numbers in this sequence:
21, 16, 11, 6…
Explain the mistake
1, -6, -11 1, -4, -9
Rank by Difficulty
How Many Ways?
Different Ways
What is the first negative number in each sequence?
231, 229, 227…
120, 114, 108…
80, 73, 66…
There are 5 numbers in a sequence. 3 of the numbers are positive and 2 of the numbers are negative.
-5 and 7 are two of the numbers in the sequence.
What could the sequence be? Do in different ways.
The first number in the sequence is 17
The first negative number in the sequence is -3
To get the next number in the sequence subtract
Level 1: I can find a possible answer.
Level 2: I can find different possible answers.
Level 3: I know how many possible answers there are.
NEGATIVE NUMBERS I SEE REASONING
ROUNDING
Explain
Here are two examples where we use rounding:
To say how many people live in Scotland.
Why do we use rounding in these situations?
Think of other examples where we use rounding.
To give the time
of the day.
Explain
Would you use the exact number? Or the rounded number?
204 children in the school.
OR
200 children in the school.
Which Method?
Which questions would you use rounding to calculate?
198 – 57
You need 296g of flour.
OR
You need 300g of flour.
400m race time: 52.84 seconds
OR
400m race time: 53 seconds
59 × 4
249 + 148
49 × 49
503 + 246
Are there any questions where you would round
both numbers?
I SEE REASONING
Number Lines
Position the numbers on both number lines: 437, 446, 453
430 440 450 460
400 500
The closest 10 to 437 is The closest 100 to 437 is
The closest 10 to 446 is The closest 100 to 446 is
The closest 10 to 453 is The closest 100 to 453 is
Number Lines
Position 376, 419, 438 and 471 on the number line:
350 400 450 500
For each number, which is the nearest 50?
600 680 700620 640 660
Position 607, 632, 668 and 685 on the number line:
For each number, which is the nearest 20?
ROUNDING I SEE REASONING
Small Difference Questions
Small Difference Questions
245 rounded to the nearest 10 is
245 rounded to the nearest 100 is
250 rounded to the nearest 100 is
496 rounded to the nearest 10 is
496 rounded to the nearest 100 is
568 rounded to the nearest 10 =
568 rounded to the nearest = 600
568 rounded to the nearest 50 =
568 rounded to the nearest = 560
Agree or Disagree?
569 always rounds to a
bigger number because each digit is 5 or more
ROUNDING
Extend: round 534 to different numbers, getting as many different answers as possible.
I SEE REASONING
Explain the Mistakes
5082 is nearer to
6000 than 5000 as the 8 rounds up
4273 to the nearest 100 is 300
Which Answer?
The nearest 10 is 400
But 400 is not a 10, the nearest 10 is 410
What is 403 to the nearest 10?
Which Answer?
What is the largest whole number that, when rounded to the nearest 100, is 1500?
14991504 1549
Explain
Give examples to show that this statement is true:
‘Numbers can be close together but round to
different numbers.’
ROUNDING I SEE REASONING
Different Ways
Multi-Skill
Question 1:
To the nearest 10, my number is 250. My number
is a multiple of 3. What could my number be?
Question 2:
To the nearest 10, my number is 300. My number
is a multiple of 7. What could my number be?
Extend: Design your own question.Your question must have two possible answers.
The nearest 10 is 250
Put two numbers in each section of the Venn diagram:
The nearest 100 is 300
258
Multi-StepTo the nearest 10p Tim has £1.50
To the nearest 50p Kam has £2.50
What is the largest possible difference between the
amount of money that Tim and Kam have?
ROUNDING I SEE REASONING
ROMAN NUMERALS
Compare Questions
Rank by Difficulty
Write each number in Roman Numerals.
LXVI
LXIV
XLVI
XLIV
44
66
46
64
Draw lines to match numbers to Roman Numerals:
Which numbers were easiest/hardest
to write in Roman Numerals?
33 =
I = 1
V = 5
X = 10
L = 50
65 = 49 =
I = 1
V = 5
X = 10
L = 50
Compare Questions
Write each number in Roman Numerals.
Which of these questions are similar?
40 =
Writing 40 in Roman Numerals is similar to writing… because…
9 =
80 = 13 =
I = 1
V = 5
X = 10
L = 50
I SEE REASONING
ROMAN NUMERALS
Rank by Difficulty
Write each number in Roman Numerals.
Which numbers were easiest/hardest
to write in Roman Numerals?
230 = 780 =
490 =
I = 1
V = 5
X = 10
L = 50
C = 100
D = 500
Explain
Explain why both statements are sometimes true.
Order
Order from smallest to largest:
What do you notice?
I = 1
X = 10
C = 100
D = 500
M = 1000
DXX M DIII CM
I = 1
V = 5
X = 10
L = 50
C = 100
In Roman Numerals, numbers above 200 have more symbols than numbers below 20.
With Roman Numerals, adding another symbol increases the size of the number.
This is true for examples like…
However, if you compare the Roman Numerals… and…
I SEE REASONING
ROMAN NUMERALS
Spot the Pattern
These sequences increase in steps of 10.
Fill the gaps:
80 90 100 110 120
LXXX CX
Small Difference Questions
210 220 230 240 250
CCX CCXX CCL
560 570 580 590 600
DLX DLXXX
I = 1
V = 5
X = 10
L = 50
1 less than XLIII is
1 more than XLIII is
10 more than XLIII is
10 less than XLIII is
1 less than XXX is
10 more than XXX is
50 more than XXX is
XLIII is 43
XXX is 30
I SEE REASONING
ROMAN NUMERALS
Extend
I think of a Roman Numeral.
It has 3 symbols. They are all different.
It is less than 60.
What is my Roman Numeral?
How Many Ways?
I think of a Roman Numeral.
It has 3 symbols. They are all different.
It is more than 400 and less than 700.
What is my Roman Numeral?
I = 1
V = 5
X = 10
L = 50
C = 100
D = 500Level 1: I can find a possible answer.
Level 2: I can find different possible answers.
Level 3: I know how many possible answers there are.
I = 1
V = 5
X = 10
L = 50Level 1: I can find a possible answer.
Level 2: I can find different possible answers.
Level 3: I know how many possible answers there are.
How Many Ways?
I = 1
V = 5
X = 10
L = 50
What is the smallest number that can
be made using four different Roman
Numeral symbols?
Example: LXI is 61. It uses three
different symbols.
I SEE REASONING
ADDITION
Simplify
Small Difference Questions
Mental or Written Method?
494 + 238 = 500 + 396 + 189 = 600 –
785 + 145 = 800 +
Extend: Create your own ‘simplify’ addition questions.
615 + 283 = 900 –
Simplify
2645 + 3978 = 4000 + 4950 + 1850 = 7000 –
2975 + 2060 = 5000 +
Extend: Create your own ‘simplify’ addition questions.
910 + 1200 = 2000 –
375 + 145 =
345 + 175 =
345 + 157 =
353 + 149 =
684 + 347 =
674 + 357 =
686 + 342 =
646 + 372 =
4731 + 5268 = 895 + 385 =
2480 + 2520 =463 + 278 =
I SEE REASONING
ADDITION
Explain the Mistakes
Correct or Incorrect?
Rank by Difficulty
Different Ways
In this calculation, two digits are hidden.
Circle the possible answers:
1523
2 6 5 5
+ 7 2 8 0
9 9 3 51
2 6 5 5
+ 7 2 8
3 4 8 311
2 6 5 5
+ 7 2 8
2 3 7 311
1 3.6
+ 6.7 2
8.0 81
8 3 9 5
+ 7 2 3 7
1 5 6 3 21 1
8 4 6 9
+ 78 3 7
9 2 9 61 1
4065 + 3205 =
744 + 579 =
2996 + 2995 =
473.6 + 516.2 =
3509 + 3444 =
16521442 1532
1 6 6 7
+ 78 3 5
I SEE REASONING
ADDITION
Which Answer?
6 1 8
+ 3 5
7 6 9
1 8 2 5
+ 7 3 6
1 6 6 4
Different Ways
Level 1: Answer each question.
Level 2: Spot the question(s) with more than one answer.
Level 3: Find all possible answers.
Extend: Design a question with one answer. Design a question with 2 or 3 answers.
1 2 4 5
+ 2 3 6
2 6 7 9
1 2 2 5
+ 1 3 8
2 6 8 6
How Many Ways?
As there are two blank
boxes in the tens
column, this question
can be answered in
different ways
This question
can only be
answered in
one way
Level 1: Complete using digits 0→9 (no repeated digits).
Level 2: Complete using digits 0, 1, 2, 4, 6, 7, 8
Level 3: I know how many ways it can be completed
using the digits 0, 1, 2, 4, 6, 7, 8
+ =
I SEE REASONING
SUBTRACTION
Simplify
525 – 384 = – 400 815 – 568 = 799 –
706 – 268 = – 261
Extend: Create your own ‘simplify’ subtraction questions.
732 – 475 = 757 –
Rank by Difficulty
43.2 – 16.8 =
601 – 337 =
869 – 321 =
845 – 297 =
Simplify
7127 – 2850 = – 3000 5362 – 3485 = 4999 –
3824 – 2476 = – 2451
Extend: Create your own ‘simplify’ subtraction questions.
4260 – 1790 = 4470 –
Rank by Difficulty
8765 – 2543 =
5432 – 2543 =
6672 – 3994 =
7002 – 3497 =
I SEE REASONING
SUBTRACTION
Different Methods
3728 – 1465 =
3012 – 2994 =
900 – 452 =
3000 – 30 =
764 – 296 =
Small Difference Questions
50 – 35 =
500 – 35 =
5000 – 35 =
50000 – 35 =
Small Difference Questions
558 – 233 =
564 – 239 =
584 – 219 =
600 – 235 =
6000 – 235 =
800 – 75 =
8000 – 75 =
8000 – 750 =
80000 – 750 =
5685 – 1675 =
5658 – 1675 =
5658 – 1995 =
5618 – 1965 =
5648 – 1961 =
I SEE REASONING
SUBTRACTION
Explain the Mistakes
Correct or Incorrect?
6 0 5.8
– 3 2 8.5
3 2 3.3
Rank by Difficulty
Explain
14 2 5.6
– 2 7.2 5
1 5 3.1
31
6 0 4 4
– 2 0 8 1
3 0 6 3
5
8 9 0 3
– 3 2 6 7
5 6 3 6
81
9
1 5 8 0
– 8 5 7
7 3 3
011
2 6 3.0
– 4 4.8
2 1 8.2
125 1
Explain, using examples, why this statement is incorrect:
6 6 5
–72 3 4
1
The digit in the red box must be 4
Complete these calculations using the column method:
For each pair, which question is harder? Easier?
23.65 – 12.8 =
23.8 – 12.65 =
4600 – 1280 =
4006 – 1280 =
I SEE REASONING
SUBTRACTION
Explain
7 3– =5
Fill the gaps:
What do you notice?
5 3– =7
Difference between the digits in blue boxes =
Difference between the digits in red boxes =
How Many Ways?
Different Ways
Level 1: Answer each question.
Level 2: Spot the question(s) with more than one answer.
Level 3: Find all possible answers.
Extend: Design a question with 2 or 3 possible answers.
6 0 2
– 2 3 7
3 6 5
Level 1: I can find an answer.
Level 2: I can find different answers.
Level 3: I know how many answers there are.
Extend: Change one digit to create two
more possible answers.
8 3 9
– 2 8 5
5 5 4
9 1 6
– 1 6 0
7 5 6
4 7 9
– 1 8 6
2 9 3
I SEE REASONING
ADDITION AND SUBTRACTION
Broken Calculator‘The 7 and 5 keys on my calculator are broken!’
How can I use my calculator to work out:
750 + 850 =
505 – 367 =
866 – 597 =
Contexts
Question Which method?
Kara is 6 years old. Her Dad is 30 years old. How old will Kara’s Dad be
on her 18th birthday?
(a) 30 + 18
(b) 30 + 12
(c) 30 × 3
Ben and Tom meet. Then, Ben drives 15 miles south and Tom drives 7 miles
north. How far apart are they?
(a) 15 + 7
(b) 15 – 7
Max is given some money. He spends £15 and has £25 left. How
much money was Max given?
(a) £25 - £15
(b) £15 + £25
Three friends have 200 stickers. Kim has 55, Zara has 85. How many
stickers does Jen have?
(a) 200 – (55 + 85)
(b) 200 + 55 + 85
(c) 55 + 85 – 200
For each question, choose the correct method:
Extend: design your own ‘Broken Calculator’ questions.
7.5 – 5.5 =
63.5 + 79.5 =
1.4 – 0.7 =
I SEE REASONING
ADDITION AND SUBTRACTION
Building QuestionsDraw lines to join the blue information
to matching the red question.
Mo has £2.
How many oranges can he afford?
BananasApples
25p
Oranges
35p 15p
Ben has £2. He wants four oranges and three apples.
How much more money does he need?
Matt has £2. He wants four oranges and three bananas.
How much change does he get?
How much does it cost him?
Raja buys three apples and three bananas.
Which Bar Model?
Circle the bar model which correctly
shows the information in the question:
Apples Oranges
25p 35p
Sam buys four oranges and two apples. He pays with a £2 coin. How much change does he get?
35p 35p 35p 35p
£2
25p25p 35p 35p 35p 35p
£2
25p 25p
change
change
Explain
What is the largest number
that can go in the blue box?
Adam buys three apples and oranges.
He pays with a £2 coin and gets some change.
Apples Oranges
25p 35p
I SEE REASONING
ADDITION AND SUBTRACTION
Small Difference Questions
Building Questions
Information Question Answer
How much
change did
she get?
75p
How much
more money
does he need?
15p
How many
melons can
she afford?
For each question, give the missing
information:
1. Zack bought a sandwich, an apple and a drink.
How much did it cost?
2. Nada wants a sandwich, an apple and a drink. She has £2.
How much more money does she need?
3. Jen bought a sandwich, an apple and a drink. She paid £3.
How much change did she get?
4. Tom has £2.
How many apples can he afford?
5. Joy has £2.
How many oranges can she afford?
6. Andy spent £2 on 3 items. He got 80p
change. What does he buy?
Sandwiches: £1.80
Oranges: 35p
Apples: 25p
Drinks: 50p
Melons: 90p
Pineapples: 75p
Mangoes: 55p
5 melons
I SEE REASONING
ADDITION AND SUBTRACTION
Multi-StepJohn bought 4 pieces of fruit and paid
with a £2 coin. He got 60p change.
What did he buy?
Oranges: 35p
Apples: 25p
Bananas: 20p
Kelly bought 5 pieces of fruit and paid with a £5 note.
She got £3.60 change. What did she buy?
Ben bought 6 pieces of fruit and paid with a £10 note.
He got £8.60 change. What did he buy?
Which Bar Model?A piece of cake and a drink costs £2. The cake costs 30p more than the drink. How much does the cake cost?
30pcake
85pdrink
85p
Cake = 85p
30pcake
85pdrink
85p
Cake = £1.15
£1.30
30p
cake
70pdrink
Cake = £1.30
cake
£2drink
Cake = £2.30
30p£2
Agree or Disagree?There are 30 children in the class.
There are 4 more boys than girls.
11 girls in the class 17 boys in the class
34 boys in the class
I SEE REASONING
ADDITION AND SUBTRACTION
Small Difference Questions
Small Difference Questions
1. There are 18 children at the park. There are 8 more boys
than girls. How many girls are there at the park?
2. There are 22 children at the park. There are 8 more boys
than girls. How many boys are there at the park?
3. Lisa and Kate have £22 in total. Lisa has £10 more than
Kate. How much money does Lisa have?
4. Kevin and Sam have £22 in total. Kevin has £9 more than
Sam. How much money does Kevin have?
1. A bucket and a spade cost 80p in total. The bucket costs
20p more than the spade. How much does the spade cost?
2. 80 people go to running club. There are 20 more women
than men. How many women are there at running club?
3. In total, Gavin and James have £80. Gavin has £30 more
than James. How much money does James have?
4. An apple and a kiwi weigh 240g. The apple weighs 90g
more than the kiwi. How much does the kiwi weigh?
5. I think of two numbers. The numbers have a sum of 240
and a difference of 70. What are my numbers?
Rank by Difficulty
A pear and an orange weigh 300g.
The pear is 60g lighter than the orange.
How much does the orange weigh?
There are 30 children in the class. There
are 6 more girls than boys.
How many boys are there in the class?
+ = 30
– = 5
=
=
I SEE REASONING
ADDITION AND SUBTRACTION
How Many Ways?
The sum of two numbers is more than 50 and less than 60.
The difference between the numbers is 8.
What could the numbers be?
Level 1: I can find an answer.
Level 2: I can find different answers.
Level 3: I know how many answers there are.
Small Difference QuestionsComplete with the correct symbol: < = >
55 + 45 < 100
75 + 45 < 120 – 10
75 + 65 < 150 – 10
85 + 75 < 160 – 20
85 + 75 < 160 + 20
95 + 85 < 155 + 25
230 – 165 < 83 – 8
230 – 165 < 83 – 18
230 – 165 < 93 – 28
230 – 185 < 93 – 48
230 – 85 < 93 + 48
230 – 85 < 103 + 48
= <
Which Answer?
275 + 165 = – 45
440
Explain the mistakes.
485395
I SEE REASONING
ADDITION AND SUBTRACTION
Agree or Disagree?
+ = –
The number in the green box is equal to the sum
of the numbers in the blue, purple and red boxes
The smallest number
must be the number
in the red box
Multi-SkillThe missing numbers are all multiples of 6.
Complete using the largest possible number:
90 – > 50
30 + < 70
– 20 < 30
Extend: Design your own ‘largest/smallest possible number’ questions.
Complete using the smallest possible number:
90 – < 50
30 + > 80
– 30 > 40
Multi-Step
>
+ = –
+ < 35
Complete using digits 1→9.
Position 5 and 3 as shown.
I started with… because…
The only digit that can go… is…
I SEE REASONING
ADDITION AND SUBTRACTION
Agree or Disagree?
Explore
Extend
You can calculate the
value of these shapes
+ = 32
= 45
You can’t calculate the
value of these shapes
+ = 40
+ = 35++
The shape I calculated first was… because…
35
38
39
35 32 45
19
25
16 12 16
The numbers show the sum for the columns and rows.
42
33
38
28 22 31 32
The numbers show the sum for the columns and rows.
Extend: design your own shape puzzle.
Use three different
shapes.
=
=
=
=
=
=
=
=
=
I SEE REASONING
MULTIPLICATION
Different Ways 14 × 9
Find 3 ways to calculate 15 × 8:
14
97×9= 63
7×9= 63
14
910×9= 90
14
9
14×3=42
14×3=42
14×3=42
63 × 2 = 126 42 × 3 = 126
4×9= 36
90 + 36 = 126
15
8
15
8
15
8
Small Difference Questions
15 × 6 = 90
15 × 8 =
30 × 4 =
34 × 4 =
34 × 14 =
33 × 14 =
33 × 7 =
6 × 7 = 42
12 × 7 =
12 × 9 =
24 × 9 =
36 × 9 =
35 × 9 =
70 × 9 =
16 × 4 = 64
16 × 6 =
16 × 8 =
16 × 7 =
18 × 7 =
18 × 6 =
9 × 12 =
I SEE REASONING
Matching Number Sentences
+ or - number sentence × number sentence
4 + 8 + 12 4 × 6
6 + 18 + 30
24 + 32
24 + 36
12 + 18 + 27
Matching Number Sentences
+ or - number sentence × number sentence
27 + 15 3 ×
63 + 18 9 ×
72 + 48
49 + 35
I know… so…
24 × 18 = 432
24 × 19 =
30 × 15 = 450
40 × 15 =
35 × 12 = 420
38 × 12 =
MULTIPLICATION I SEE REASONING
Small Difference Questions
25 × 6 =
23 × 6 =
18 × 6 =
18 × 12 =
36 × 24 =
41 × 24 =
21 × 30 =
21 × 15 =
21 × 16 =
26 × 16 =
39 × 16 =
39 × 24 =
Rank by Difficulty
37 × 6 =
804 × 6 =
45 × 6 =
MULTIPLICATION
98 × 6 =
To answer, did you use the same method?
Or different methods?
Rank by Difficulty
32 × 50 =
409 × 6 =
46 × 7 =
99 × 4 =
To answer, did you use the same method?
Or different methods?
I SEE REASONING
Different Methods
Different Ways
‘The 8 key on my calculator is broken!’
How can I use my calculator to work out:
26 × 8
80 × 15
Broken Calculator
Ways to calculate 24 × 8:
less than 24 × 10
less than 25 × 8
Double ×
Double one number, halve the other number, the product
is the same. Example: 8 × 12 = 96 16 × 6 = 96
Which of these questions are made easier by a
doubling and halving strategy?
26 × 24 14 × 25
80 × 60 5 × 18
1.5 × 6
MULTIPLICATION I SEE REASONING
Estimation
293 × 4
The answer will be odd/even.
The answer will be a - digit number.
Of these numbers, the answer will be closest to:
800 950 1100 1300
Checking Possible AnswersDo not calculate the answer to the question.
Which numbers cannot be the answer to 493 × 6?
Explain how you know.
29413028 2958
369 × 7
The answer will be odd/even.
300 × 7 = 2100 400 × 7 = 2800
Estimate for 369 × 7 is
Estimation
MULTIPLICATION
Estimation584 × 9
The answer will be odd/even.
500 × 9 = 4500 600 × 9 = 5400
Estimate for 584 × 9 is
I SEE REASONING
Explain the Mistakes
Part-Complete Examples
2 6 1 × 4
8 2 4 4
Different Methods
500 20 7
6 3000 120
3 0 0 0
1 2 0
4 2
3 1 6 2
Two ways of calculating 527 × 6:
What’s the same? What’s different?
3
4 1 7 × 5
2 0 5 5
1
8 4 3 × 6
4 4 5 8
2
4 8 9 × 5
8 2 4 5
1
7 2 3 × 4
2 0 5 2
2
4 6 3 × 8
4 4 5 4
44
4
5 2 7
× 6
3 1 6 2
1
42
MULTIPLICATION I SEE REASONING
Estimation
53 × 19 The answer will be odd/even.
The answer will be a - digit number.
Of these numbers, the answer will be closest to:
900 1000 1100 1200
Checking Possible AnswersDo not calculate the answer to the question.
Which numbers cannot be the answer to 39 × 38?
Explain how you know.
14821602 1543
29 × 26
The answer will be odd/even.
20 × 20 = 400 30 × 30 = 900
Estimation for 29 × 26 is
Estimation
MULTIPLICATION
Estimation89 × 43
The answer will be odd/even.
90 × 40 = 3600 90 × 50 = 4500
Estimation for 89 × 43 is
I SEE REASONING
Part-Complete Examples
Different Methods
Explain the Mistakes
50
3
2000
What is the same? Different?
40
2
150 6
80
2000
150
80
+ 6
2236
1 5 62 0 8 0
2 2 3 6
5 2
× 4 3
61 5 0
8 02 0 0 0
2 2 3 6
5 2
× 4 3
2 1 62 8 8
5 0 4
7 2 × 4 3
1 6 84 0 2 0 0
4 0 3 6 8
8 4 × 5 2
1
1
1 8 9
0 2 5 0
4 3 6 9
6 3
× 5 3
1
4
2 4 0
2 4
× 1 6
2
4 8 6
0 2
4 3 6
8 1
× 4 6
3
8 21 2 3 0
1 3 1 2
4 1 × 2 3
11 1
MULTIPLICATION I SEE REASONING
Missing Digits
8 2 5
× 6
2 5 6 8
How Many Ways?
Level 1: I can find a way
Level 2: I can find different ways
Level 3: I know how many ways there are
× =
Complete using digits 0-9.
The digit in the box with a border must be odd.
5 2 4
× 6
4 1 9 2
8 9 5
× 5
3 4 7 5
Different Answers
8 3 5
× 6
3 7 2 4
8 3 5
× 6
3 7 2 4
This question can be answered in
two ways.
MULTIPLICATION
Tip: think about which digits can and cannot be used in the ones columns.
I SEE REASONING
DIVISION
Different MethodsWhat is different about how you answer each question?
480 ÷ 240 =
480 ÷ 10 =
480 ÷ 6 =480 ÷ 4 =
480 ÷ 20 =
I know… so…
72 ÷ 3 = 24
78 ÷ 3 =
98 ÷ 7 = 14
91 ÷ 7 =
72 ÷ 4 = 18
144 ÷ 8 =
84 ÷ 6 = 14
168 ÷ 6 =
112 ÷ 4 = 28
192 ÷ 4 =
48 ÷ 6 = 8
108 ÷ 6 =
Small Difference Questions
48 ÷ 3 = 16
54 ÷ 3 =
108 ÷ 3 =
108 ÷ 6 =
216 ÷ 12 =
64 ÷ 8 = 8
64 ÷ 4 =
104 ÷ 4 =
144 ÷ 4 =
144 ÷ 8 =
I SEE REASONING
Small Difference Questions
56 ÷ 4 = 14
112 ÷ 4 =
224 ÷ 8 =
304 ÷ 8 =
344 ÷ 8 =
108 ÷ 3 = 36
216 ÷ 6 =
216 ÷ 3 =
246 ÷ 3 =
261 ÷ 3 =
Which Operation?
For each question, do you multiply or divide to find
the missing number?
100 ÷ = 20
÷ 100 = 20
40 × = 200
4 = ÷ 20
= 20 ÷ 4
Contexts
Question number sentence
16 children share some sweets. They get 4 sweets each. How many sweets?
90 eggs are packed into 15 boxes. How many eggs in each box?
÷ 16 = 4
Write a question for and 60 ÷ = 5÷ 5 = 60
DIVISION I SEE REASONING
Estimate
165 ÷ 6
Whole number answer?
Yes Possibly No
120 ÷ 6 = 20 180 ÷ 6 = 30
Estimate for 165 ÷ 6
344 ÷ 8
Whole number answer?
Yes Possibly No
320 ÷ 8 = 40 400 ÷ 8 = 50
Estimate for 344 ÷ 8
Estimate
705 ÷ 3
Whole number answer?
Yes Possibly No
600 ÷ 3 = 200 900 ÷ 3 = 300
Estimate for 705 ÷ 3
ExplainFor this task, do not work out the answers to the questions.
For each question, the answer has how many digits?
70 ÷ 5
digit(s)
435 ÷ 5
digit(s)
3000 ÷ 4
digit(s)
3075 ÷ 3
digit(s)
615 ÷ 5
digit(s)
719 ÷ 4
Whole number answer?
Yes Possibly No
400 ÷ 4 = 100 800 ÷ 4 = 200
Estimate for 719 ÷ 4
DIVISION
Explain how you know.
I SEE REASONING
Which Answer?
Next StepIn each calculation, what’s the remainder? 8 46
1 42
Next StepIn each calculation, what’s the remainder? 5 8 23
1 9 42 1
8 6 44
2 1
9 6 44
2 41
6 6 44
1 62
2 6 13
0
6 7 53
2 2
7 7 43
2 51
92 ÷ 4 = To answer, split 92
into 90 and 2
To answer, split 92
into 80 and 12 To answer, split 92
into 88 and 4
4 53
1
5 53
1
6 53
2
7 53
2
7 64
1
8 64
2
9 64
2
9 68
1
DIVISION I SEE REASONING
Part-Complete Examples
The calculations have been started. Finish them:
5 24
11
9 24
2
8 9 24
2
8 9 28
1
4 9 28
04
7 9 24
1
Part-Complete Examples
The calculations have been started. Finish them:
8 5 23
22
8 6 23
22
7 6 23
2
4 4 86
04
8 4 86
12
8 3 86
1
Which Answer?
745 ÷ 4
Find the correct calculation.
Spot the mistakes.
7 4 543 2
1 9 6 r 1
7 4 543 2
1 8 5 r 5
7 4 543 2
1 8 6 r 1
DIVISION I SEE REASONING
Explain the Mistakes 5258 ÷ 6
5 2 5 865 4
0 8 8 6 r 23
5 2 5 865 4
0 8 7 63
5 2 5 865 4
0 8 7 31
Question Answer
Eggs are put in boxes of 6. The farmer has 51
eggs. How many boxes does he need for all
the eggs?9 boxes
A sunflower grows to a height of 51cm in 6
weeks. On average, how many centimetres
does it grow each week?
51 children turn up for a 6-a-side football
tournament. How many teams can be made?Teams can have substitutes.
An artist works on a masterpiece for 51 hours
over 6 days. On average, how long does she
work each day?
Form of Answer 5 16
0 8 r 35
Form of Answer
Jess sleeps for 29 hours over 4 nights.
On average, how long is she asleep each night?
7 hours 10 minutes
7.1 hours
7 hours 15 minutes
DIVISION I SEE REASONING
Mental or Written?
320 ÷ 3 =
Which questions use the same/different calculation
methods?
320 ÷ 6 = 320 ÷ 9 =
320 ÷ 5 = 320 ÷ 8 = 320 ÷ 10 =
Mental or Written?
540 ÷ 4 =
Which questions use the same/different calculation
methods?
540 ÷ 6 = 540 ÷ 7 =
550 ÷ 55 = 550 ÷ 25 = 550 ÷ 15 =
Small Difference Questions
560 ÷ 4 =
560 ÷ 8 =
560 ÷ 7 =
560 ÷ 9 =
567 ÷ 9 =
1134 ÷ 9 =
441 ÷ 3 =
4410 ÷ 30 =
441 ÷ 6 =
501 ÷ 6 =
501 ÷ 3 =
1503 ÷ 9 =
DIVISION I SEE REASONING
Rank by Difficulty340 ÷ 20 =
550 ÷ 30 =
425 ÷ 5 =
546 ÷ 6 =
500 ÷ 3 =
How Many Ways?
‘The 6 and 8 keys on my calculator are broken!’
How can I use my calculator to work out:
522 ÷ 6 =
624 ÷ 8 =
Broken Calculator
Level 1: I can find a way
Level 2: I can find different ways
Level 3: I know how many ways there are
6 ÷ =
Complete using digits 0-9.
Position the digit 6 as shown.
DIVISION
My system for knowing I have found all of the answers is…
I SEE REASONING
MULTIPLICATION AND DIVISION
Contexts
Which operation(s) does each question involve?
addition subtraction multiplication division
(a) Tim is years old. Jack is years old.
When Tim is , how old will Jack be?
(b) Zara has t-shirts, pairs of trousers and hats.
How many different outfits can Zara wear?
(c) Holly is saving for a bike that costs £ . She has £ .
Holly earns £ per week.
How many weeks will Holly need to save up for?
Extend
At work, Mr James wears a pair of trousers and a shirt. Sometimes he wears a tie.
He has 4 pairs of trousers, 5 shirts and 8 ties.
How many combinations of outfits does Mr James have?
Agree or Disagree?
Kam has 3 pairs of jeans, 6 t-shirts and 2 caps.
Pete has 3 pairs of jeans, 5 t-shirts and 3 caps.
Kam and Pete have the same number of outfits as they own the
same amount of clothing
I SEE REASONING
MULTIPLICATION AND DIVISION
Spot the Difference
What’s the same? What’s different?
(a) Ruth earns £15 each day delivering newspapers. How much money does Ruth earn each week?
(b) Kate plays the piano for 15 minutes every day. How long, in hours and minutes, does Kate spend playing the piano each week?
Answer the questions:
Explore
At the market, apples cost 25p each.
At the shop, it costs £1.10 for a bag of 6 apples.
Using this information, think of a question that involves:
(a) Multiplication
(b) Multiplication and addition
(c) Multiplication and subtraction
(d) Division
Explore
1500 people are travelling from Sheffield to Leeds to
go to the match. They travel by car or by coach.
200 people fit in a coach. 5 people fit in a car.
Using this information, think of a question with the answer:
(a) 6 coaches
(b) 140 cars
I SEE REASONING
MULTIPLICATION AND DIVISION
Small Difference Questions
Explore
(a) 18 people camping. Each tent fits 3 people.
How many tents are needed?
(b) 36 people camping. Each tent fits 6 people.
How many tents are needed?
(c) 31 people camping. Each tent fits 6 people.
How many tents are needed?
(d) 25 people camping. They use 7 tents.
How many people fit in each tent?
(e) Some people camping. They use 8 tents that fit 4 people.
How many people could be camping?
(f) Some people camping. They use 4 tents that fit 8 people.
How many people could be camping?
There are children in the class.
The teacher has 2-litre bottles of orange juice.
Add information to create a question with the answer:
(a) 250ml each
(b) 1 litre left
(c) 12 children
Extend
Adam is seven times as old as his daughter, Lara.
Next year, Adam will be six times as old as Lara.
How old is Adam? Explain how you know.
I SEE REASONING
MULTIPLICATION AND DIVISION
Explain the Mistakes
480 ÷ 100 = _____48
Correct or Incorrect?
I know… so…
7.6 × 10 = _____7.60
3600 ÷ 36 = _____10 3.05 × 1000 = ______3005
360 ÷ ______ = 3.61000 0.34 ÷ 10 = _____3.4
1200 ÷ 12 = _____100 3.02 × ______ = 30201000
17 × 6 = 102
17 × 60 =
170 × 60 =
42 ÷ 6 = 7
420 ÷ 60 =
420 ÷ 6 =
160 ÷ 10 = 16
160 ÷ 16 =
1600 ÷ 16 =
Correct or Incorrect?
1050 ÷ ______ = 10105 400 ÷ 50 = _____80
60 × 70 = _____420 320 ÷ _____ = 1032
403 ÷ 100 = _____4.3 90 × _____ = 450050
I SEE REASONING
MULTIPLICATION AND DIVISION
Which Answers?
Circle the factors of 12
4 36 60 0.5 6
Circle the multiples of 30
90 6 200 15 120
Which Answers?Circle the prime numbers:
21 31 41 51 61 71
Spot the Mistakes
Which Answers?
Circle the prime number(s):
87 121 137 375
Which numbers do you immediately know are not prime?
5cm × 5cm × 5cm
= 125cm²9cm × 9cm =
81cm³
Which Answers?
Circle the square numbers.
Underline the cube numbers:
24 27 36 64 121
I SEE REASONING
MULTIPLICATION AND DIVISION
Mental or Written Calculation?
Spot the Pattern
Which of the digits from 1 to 9 are factors of 128?
1 2 3 4 5 6 7 8 9
Which digits could you work out mentally?
Which written calculations did you do?
Mental or Written Calculation?
Which of the digits from 1 to 9 are factors of 624?
1 2 3 4 5 6 7 8 9
Which digits could you work out mentally?
Which written calculations did you do?
Complete using positive whole numbers greater than 1:
× = 420
× × = 420
× × × = 420
× × × × = 420
Example:
12 × 5 = 60
6 × 5 × 5 = 60
6 × 5 × 5 × 5 = 60
Extend: Create your own example.
I SEE REASONING
MULTIPLICATION AND DIVISION
I know… so…
360 ÷ 15 = 24
List different factors of 360
How does the calculation help you to find lots of
other single-digit factors of 360?
Order
Order from the number with the least factors
to the number with the most factors:
35 36 45
Explain the Mistake
Small Difference Questions
Every multiple of is also a multiple of 4
Every multiple of is also a multiple of 6
Every multiple of 15 is also a multiple of
Every multiple of 5 is also
a multiple of 10
Change the statement to make it correct.
The number… has more factors because…
I SEE REASONING
MULTIPLICATION AND DIVISION
Different Answers
multiples of 4 multiples of 6
Put two numbers in each section of the Venn diagram:
Different Answers
multiples of 4 factors of 24
Put two numbers in each section of the Venn diagram:
Which Answers?
Circle the common
factors of 18 and 42:
2 3 6 7 9
Circle the common
factors of 27 and 45:
3 5 7 9 90
I SEE REASONING
MULTIPLICATION AND DIVISION
How Many Ways? Level 1: I can find a way
Level 2: I can find different ways
Level 3: I know how many ways
there are
60 ÷ = 3 ×
Correct or Incorrect?
Small Difference QuestionsComplete with the correct symbol: < = >
6 × 32 < 200
6 × 32 < 200 – 20
6 × 36 < 200 + 20
<
4 and 320
Which pairs of numbers can go in the boxes?
80 × = ÷ 2
5 and 800
3 and 480
6 and 240
Different Ways Answer in 4 different ways:
20 × = × 4 20 × = × 4
20 × = × 4 20 × = × 4
What’s the relationship between the numbers in the red
and blue boxes?
6 × 40 < 240 ÷ 4
6 × 20 < 240 ÷ 2
12 × 20 < 120 × 2
I SEE REASONING
FRACTIONS
Read the Picture
Which fractions do you see?
Read the PictureMatch the pictures to the fractions.
𝟏
𝟒
𝟏
𝟑
𝟏
𝟓
ExplainWhich is the larger fraction?
Explain how you know.
I SEE REASONING
FRACTIONS
Explain
For each pair, circle the larger fraction:
True or False?
EstimateFor each rectangle, estimate the fraction that is blue.
The fingers as a fraction of a hand
The hands as a fraction of the body
OR
The toes as a fraction of a foot
The fingers as a fraction of a hand
OR
The brain as a fraction of the head
The bones as a fraction of the body
OR
or
𝟏
𝟓
𝟓
𝟖𝟑
𝟖
I SEE REASONING
FRACTIONS
Context Question8 children share 5 pizzas equally.
Show the amount of pizza that each child gets.
Which Answer?9 boiled eggs shared between 4 people.
How many eggs each?
Context Question4 people share 11 pieces of toast equally.
Show the amount of toast that each person gets.
(a) 2 eggs each
(b)𝟒
𝟗of an egg each
(c) 2𝟏
𝟒eggs each
Explain your choice.
I SEE REASONING
FRACTIONS
What Fraction?
Different Number Lines
0 1
0 1
0 2
0 1
2
1
Draw arrows to show the position of 𝟑
𝟒on each line
0 2
0 1
1
1
2
1
4
I SEE REASONING
FRACTIONS
Explain
0 1
0 1
0 1
Which equivalent fractions are shown by the number lines?
Agree or Disagree?
0 1
0 1
These number lines show that thirds and sixths are equivalent
Read the Picture
0 1
0 1
0 1
Use the number lines to order these fractions: 4
5
5
6
6
8
I SEE REASONING
FRACTIONS
Which Answer?
Odd One Out
0 1
0 1
0 1
0 1
Odd One Out
0 1
6
(a)𝟏
𝟏𝟐
(b)𝟏
𝟑
The fraction at the
red arrow is…
I SEE REASONING
FRACTIONS
Agree or Disagree?
Small Difference Questions
+4
3
4=
8
+47To make equivalent
fractions, do the same
thing to the denominator
and the numerator.
Explain the Mistake
Both shapes
are 𝟏
𝟔blue
=
21 4
Complete each question by positioning the digits:
8
Digits:
=
21 4
8
Digits:
<
21 4
8
Digits:
Do in different ways.
I SEE REASONING
FRACTIONS
How Many Ways?
Explain the Mistake
2
1 3
Make equivalent fractions using these numbers:
=
Rank by Difficulty
Level 1: I can find a way
Level 2: I can find different ways
Level 3: I know how many ways there are
6
4 12
Note:
𝟏
𝟐= 𝟐
𝟒is not an
answer because
2 is used twice.
I know 𝟑
𝟒is more than
𝟓
𝟔because
quarters are bigger than sixths
For each pair, circle the larger fraction.
Which question was hardest? Which was easiest?
𝟏
𝟒or
𝟏
𝟓
𝟑
𝟔or
𝟒
𝟔
𝟑
𝟒or
𝟓
𝟖
𝟑
𝟒or
𝟗
𝟏𝟎
I SEE REASONING
FRACTIONS
Read the Pictures
Which is more?
Explain
Order the improper fractions from smallest to largest:
What do you notice?
𝟏𝟎
𝟑
Finish the Pictures
3𝟏
𝟐=
23𝟏
𝟐=
4
𝟏𝟎
𝟒
𝟏𝟏
𝟓
𝟏𝟖
𝟔
Finish the pictures. Fill in the missing numbers:
I SEE REASONING
FRACTIONS
Small Difference Questions
Different WaysAnswer this question in two different ways:
11= 2
11= 2
4 =
54 𝟑
𝟓=
55 𝟑
𝟓=
5
4
12=
4
15=
4
19=
Agree or Disagree?
𝟖
𝟑is equivalent to
𝟏𝟔
𝟔
Extend: Design your own question by changing the denominator and the whole number. Your question must have 2 possible answers.
I SEE REASONING
FRACTIONS
Explain the Mistakes
Mistake A:
𝟑
𝟒𝐨𝐟 𝟑𝟔 =
36
10 10 10 6
30
Mistake B:
𝟐
𝟑𝐨𝐟 𝟐𝟒 =
24
9 9 9
18
Mistake C:
𝟑
𝟓𝐨𝐟 𝟐𝟎 =
20
4 4 4 4 416
Finish the Pictures
𝟐
𝟑𝐨𝐟 =
There are different possible answers.
𝟑
𝟒𝐨𝐟 =
𝟑
𝟓𝐨𝐟 =
I SEE REASONING
FRACTIONS
Two WaysAnswer each question in two different ways:
1of 45 =
1of 45 =
2of 24 =
2of 24 =
I know… so…𝟑
𝟒𝐨𝐟 𝟐𝟒𝟎 = 1801
4of 240 =
3
4of 248 =
I know… so…𝟐
𝟑𝐨𝐟 𝟏𝟒𝟒 = 961
3of 144 =
2
3of 288 =
4
6of 144 =
3
8of 480 =
3
8of 240 =
2
9of 144 =
Give other examples
Give other examples
3of 60 =
3of 60 =
I SEE REASONING
FRACTIONS
Small Difference Questions𝟏
𝟑𝐨𝐟 𝟒𝟓 =
𝟐
𝟑𝐨𝐟 𝟒𝟓 =
𝟐
𝟑𝐨𝐟 𝟒𝟖 =
𝟐
𝟑𝐨𝐟 𝟗𝟔 =
𝟏
𝟓𝐨𝐟 𝟒𝟎 =
𝟏
𝟓𝐨𝐟 𝟖𝟎 =
𝟒
𝟓𝐨𝐟 𝟖𝟎 =
𝟒
𝟓𝐨𝐟 𝟖𝟓 =
Small Difference Questions𝟏
𝟐𝐨𝐟 𝟑𝟐 =
𝟏
𝟒𝐨𝐟 𝟑𝟐 =
𝟑
𝟒𝐨𝐟 𝟑𝟐 =
𝟑
𝟒𝐨𝐟 𝟔𝟒 =
𝟑
𝟖𝐨𝐟 𝟔𝟒 =
𝟏
𝟒𝐨𝐟 𝟐𝟒 =
𝟏
𝟔𝐨𝐟 𝟐𝟒 =
𝟏
𝟑𝐨𝐟 𝟐𝟒 =
𝟐
𝟔𝐨𝐟 𝟐𝟒 =
𝟐
𝟑𝐨𝐟 𝟐𝟒 =
Small Difference Questions𝟑
𝟖𝐨𝐟 𝟏𝟐𝟎 =
𝟔
𝟖𝐨𝐟 𝟐𝟒𝟎 =
𝟓
𝟖𝐨𝐟 𝟐𝟒𝟎 =
𝟓
𝟖𝐨𝐟 𝟐𝟖𝟎 =
𝟐
𝟑𝐨𝐟 𝟏𝟖𝟎 =
𝟒
𝟔𝐨𝐟 𝟏𝟖𝟎 =
𝟐
𝟔𝐨𝐟 𝟑𝟔𝟎 =
𝟓
𝟔𝐨𝐟 𝟑𝟔𝟎 =
I SEE REASONING
FRACTIONS + – ×
Explain the Mistakes
1
4=+
3
8
4
12
Mistake A:
1
4=+
3
8
4
8
Mistake B:
Small StepsFor each calculation, choose a common denominator:
𝟑
𝟓+
𝟑
𝟓Common denominator:
𝟐
𝟑+
𝟓
𝟏𝟐Common denominator:
𝟓
𝟏𝟎+
𝟐
𝟒Common denominator:
ExplainCircle the calculations where the sum is a mixed number:
𝟑
𝟒+
𝟐
𝟖
Explain how you know.
𝟓
𝟏𝟎+
𝟑
𝟒
𝟏
𝟐+
𝟑
𝟖
𝟕
𝟏𝟎+
𝟐
𝟓
𝟕
𝟏𝟎+
𝟏𝟎
𝟐𝟓Common denominator:
𝟕
𝟐𝟎+
𝟑
𝟓
𝟓
𝟗+
𝟑
𝟔
𝟏
𝟒+
𝟏
𝟔Common denominator:
I SEE REASONING
Small Difference Questions
𝟏
𝟑+
𝟏
𝟔=
Rank by Difficulty
𝟏
𝟑+
𝟑
𝟔=
𝟐
𝟑+
𝟑
𝟗=
𝟐
𝟒+
𝟏𝟎
𝟐𝟎
𝟏
𝟑+
𝟏
𝟏𝟐
𝟒
𝟓+
𝟑
𝟓
𝟗
𝟐𝟎+
𝟕
𝟐𝟎
𝟏
𝟑+
𝟓
𝟏𝟐
Small Difference Questions
𝟏
𝟑+
𝟐
𝟗=
𝟏
𝟑+
𝟑
𝟗=
𝟐
𝟑+
𝟐
𝟗=
𝟑
𝟏𝟎+
𝟑
𝟐𝟎=
𝟑
𝟓+
𝟑
𝟐𝟎=
𝟐
𝟓+
𝟑
𝟏𝟎=
𝟑
𝟒+
𝟏
𝟖=
𝟑
𝟒+
𝟏
𝟏𝟔=
𝟑
𝟖+
𝟕
𝟏𝟔=
FRACTIONS + – ×
𝟏
𝟔+
𝟏
𝟗
𝟐
𝟓+
𝟏𝟑
𝟐𝟎=
𝟐
𝟓+
𝟏𝟑
𝟒𝟎=
𝟑
𝟓+
𝟏𝟐
𝟒𝟎=
𝟐
𝟒+
𝟔
𝟏𝟐=
𝟏
𝟒+
𝟓
𝟏𝟐=
𝟏
𝟒+
𝟓
𝟏𝟔=
𝟐
𝟑+
𝟐
𝟔=
𝟐
𝟓+
𝟑
𝟒𝟎=
𝟑
𝟒+
𝟑
𝟏𝟔=
I SEE REASONING
Different Ways
How Many Ways?
Different Ways
Level 1: I can find a way
Level 2: I can find different ways
Level 3: I know how many ways
there are
4
3=+
8
Find different possible answers.
6=+
3
1
Ways to calculate 𝟑
𝟒+
𝟓
𝟖
Convert 𝟑
𝟒into
Split 𝟓
𝟖into and
8 8
4 8+++
2
1
2
1
The answer is a proper fraction
FRACTIONS + – × I SEE REASONING
FRACTIONS + – ×
Explain the Mistakes
7
10=–
1
2
6
8
Mistake A:
7
10=–
1
2
6
10
Mistake B:
Small Difference Questions
𝟓
𝟔−
𝟏
𝟔=
𝟓
𝟔−
𝟏
𝟐=
𝟓
𝟔−
𝟏
𝟏𝟐=
𝟕
𝟖−
𝟏
𝟒=
𝟕
𝟖−
𝟑
𝟒=
𝟕
𝟖−
𝟏𝟐
𝟏𝟔=
Small Difference Questions
𝟏 −𝟏
𝟖=
𝟏𝟏
𝟒−
𝟏
𝟖=
𝟏𝟏
𝟒−
𝟑
𝟖=
𝟏𝟏
𝟐−
𝟑
𝟖=
𝟏𝟑
𝟖−
𝟏
𝟐=
𝟐𝟑
𝟖− 𝟏
𝟏
𝟐=
I SEE REASONING
FRACTIONS + – ×
ExplainCircle the calculations where the answer is a
mixed number:
Explain how you know.
𝟏𝟑
𝟏𝟎−
𝟏
𝟓 𝟏𝟏
𝟖−
𝟏
𝟒
How Many Ways?Level 1: I can find a way
Level 2: I can find different ways
Level 3: I know how many ways
there are4=–
8
1
Extend
=+2
1–
4
1Fill the gaps.
1
Different Methods
𝟑𝟑
𝟖− 𝟏
𝟑
𝟒 𝟐𝟐
𝟔− 𝟏
𝟏
𝟑
𝟏𝟑
𝟓−
𝟕
𝟏𝟎𝟏𝟏
𝟐−
𝟑
𝟒𝟏𝟏
𝟑−
𝟓
𝟔
Answer these questions using different methods:
Example methods: find the difference, take away,
using knowledge about halves
I SEE REASONING
FRACTIONS + – ×
Which Answer?
2
3=× 6
12
18
Answer A:
2
3=× 6
12
3
Answer B:
2
3=× 6
2
18
Answer C:
Different Methods
as an
improper
fraction
less than 310
Ways to calculate7
10× 3
as a
mixed
number
Spot the Pattern
Fill the gaps using single-digit numbers.
What do you notice?
2
5=×
3
8=×
Explain the mistakes.
I SEE REASONING
FRACTIONS + – ×
I know… so…
Rank by Difficulty
Different WaysAnswer each question in three different ways.
× = 1𝟏
𝟐× = 1
𝟏
𝟐× = 1
𝟏
𝟐
× = 3𝟏
𝟑× = 3
𝟏
𝟑× = 3
𝟏
𝟑
𝟑
𝟒× 𝟒 = 𝟑
3
4× 6 =
𝟒
𝟓× 𝟔 = 𝟒
𝟒
𝟓
4
5× 7 =
𝟐
𝟕× 𝟏𝟐 = 𝟑
𝟑
𝟕
2
7× 14 =
𝟓
𝟔× 𝟔
𝟏𝟏
𝟒× 𝟕
𝟓
𝟕× 𝟒
𝟐𝟑
𝟒× 𝟑
I SEE REASONING
FRACTIONS, DECIMALS, PERCENTAGES
True or False?
Which Answers?
Which fractions have been positioned correctly?
0 0.1 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.2
𝟏
𝟓𝟓
𝟏𝟎𝟎𝟎
𝟔𝟓
𝟏𝟎𝟎
𝟏
𝟒
0.05 is the same as… circle the correct answers
𝟓𝟎
𝟏𝟎𝟎𝟓
𝟏𝟎𝟎
𝟏
𝟓𝟎
Five thousandths Five hundredths
Odd One Out
0.77
10
25
1000.4
0.006 is the same as… circle the correct answers
𝟔
𝟏𝟎𝟎𝟎𝟔
𝟏𝟎𝟎
𝟔𝟎𝟎
𝟏𝟎𝟎𝟎
Six thousandths Six hundredths
1
7
1
4
I SEE REASONING
FRACTIONS, DECIMALS, PERCENTAGES
Two WaysFor each arrow, give the fraction and the decimal:
0 1
𝟎. 𝟖 𝐨𝐫𝟖
𝟏𝟎
How Many Ways?
0
0.010
1
10
Level 1: I can find a way
Level 2: I can find different ways
Level 3: I know how many ways there are
0 0.50.25 1
Make all the fractions that are more than 0.25
and less than 0.5 using these numbers:
1 2 3 4 5 10
My system for knowing I have found all of the answers is…
I SEE REASONING
FRACTIONS, DECIMALS, PERCENTAGES
Explain
I know… so…
The green section is 20%,
the blue section is 40%
and the red section is 30%
of the square
Explain why this statement must be incorrect.
Estimate: % green % blue % red
1= 25%
1= 50%
1= 5%
1= 10%
1= %
50
1= %
25
1= %
5
50 × 2 = 100
25 × 4 = 100
20 × 5 = 100
10 × 10 = 100
Agree or Disagree? or
1= 20%
20
1= 10%
10= 5%
1
5
I SEE REASONING
Odd One Out
Different Ways
1= %
539
= %50
0.52 = %
0.6 = %
Rank by Difficulty
4= %
8
6= %
107
= %25
36= %
50
Make fractions that are more than 50% and less
than 75% using the digits 1, 2, 3, 4 and 5.
1
2
3
4
5
FRACTIONS, DECIMALS, PERCENTAGES
Rank by Difficulty
30%3
10
1
205%
1
3
1
5
I SEE REASONING
Contexts
MEASUREMENT
Match what is being measured with the correct type of measure and the appropriate unit of measure:
Measuring: Type: Unit:
flour for baking
adult footprint
water in cup
skipping rope
football pitch
length
weight
volume
area
Centimetres (cm)
Metres (m)
Square centimetres (cm²)
Square metres (m²)
Grams (g)
Millilitres (ml)
Litres (l)
Which Answer?
Light years measure time
Light years measure length
Which Answer?For each item, circle the appropriate unit(s) of measure:
Size of a carpet cm cm² m m² kg
Size of a bottle cm cm² litres (l) millilitres (ml)
Size of lamp post kg cm cm² m m²
Size of a puddle cm m litres (l) millilitres (ml)
I SEE REASONING
Odd One Out
MEASUREMENT
Extend: Can you think of a reason why each one
could be the odd one out?
Centimetres (cm)
Explore
Agree or Disagree?
100 metres is approximately
the same length as 110 yards.
Ounces (oz) Kilograms (kg)
Which unit of measure is the odd one out?
This means a yard is longer than a metre
Metric measures Measures of length
Write these measures in the correct section of the
Venn diagram: litres, inches, kilometres, stones, yards
Extend: Add another unit of measure to each section.
I SEE REASONING
Explain the Mistakes
MEASUREMENT
800m = _____km8
25mm = _____cm2503.8m = _____cm308
Agree or Disagree?
𝟏
𝟐litre = ______ml5000
408cm = ______m4.8 4090g = ______kg4.09
True or False?
(a) 75cm is more than 0.6m and less than 800mm
(b) 0.7m is more than 55cm and less than 600mm
(c) 410mm is more than 40cm and less than 𝟏
𝟐metre
Compare
1 yard = 36 inches 1 metre (m) = 100centimetres (cm)
6m = cm
6 yards = inches
2.5m = cm
2.5 yards = inches
It is harder/easier converting between… because…
𝟑
𝟒metre = ______cm75
I SEE REASONING
Explain the Mistakes
MEASUREMENT
Which Answer?
Small Difference Questions
minutes = 1 hour and 40 minutes
minutes = 3 hours and 20 minutes
minutes = 5 hours
150 minutes = hours and minutes
250 minutes = hours and minutes
The time is 2:10pm. What was the time 𝟐𝟏
𝟐hours ago?
4:40pm 11:40pm11:20am
11
4hours ago the time was 4:50pm. What is the time now?
(a) 3:25pm (b) 3:35pm (c) 6:05pm (d) 6:15pm
The train left at 6:45 and arrived at 9:20.
How long was the journey?
(a) 3 hours 25 minutes (b) 2 hours 35 minutes
Extend: create two questions converting between minutes and hours and minutes
I SEE REASONING
Compare
MEASUREMENT
Use the symbols < = > to compare the lengths of time:
6 weeks 44 days
100 hours 4 days
120 hours 5 days
120 hours 5 days
3 months 2400 hours
3 months 12 weeks
3 months 63 days
3 months 63 days
Multi-Step
weeks is more than 2 months and less than 65 days.
days is less than than𝟏
𝟒year and more than 12 weeks.
Extend: Write your own example. Make the difference between the lengths of time small.
Multi-Step
Order the lengths of time from shortest to longest:
Question A:
180 days 27 weeks 7 months 1
2year
Question B:
140 days 18 weeks 3 months 1
3year
I SEE REASONING
Different Ways
PERIMETER, AREA, VOLUME
Which method(s) correctly
calculate the perimeter of
the rectangle?
3cm
5cm
5cm × 3cm Double 5cm + 3cm
5cm + 3cm5cm + 3cm + 5cm + 3cm
ExplainFor each shape, how many sides need to be measured to calculate the perimeter?
rectanglesquare
Estimate
isosceles
trianglecross
Explain why you don’t have to measure every edge.
7cm
Estimate the perimeter of the rectangle.
OrderOrder these shapes from smallest to largest perimeter without measuring them:
I SEE REASONING
Explain
PERIMETER, AREA, VOLUME
Here are two identical rectangles. They are put together to make one rectangle.
I know… so…Each shape is made using identical rectangles.
Calculate the perimeter of each shape.
How can this be done to make the perimeter of the new rectangle as small as possible?
Or as large as possible?
1.5cm
2.5cm
Perimeter = 8cm Perimeter = cm Perimeter = cm
Perimeter = cm Perimeter = cm
Perimeter = cm
I SEE REASONING
Small Difference Questions
PERIMETER, AREA, VOLUME
Explain
Each shape is made using squares.
Calculate the perimeter of each shape.
Perimeter = cm
12cm 12cm
Perimeter = cm
12cm
Perimeter = cm
Complete the sentences:
purple + orange =
black – blue =
Write your own.
Agree or Disagree? 6cm
To calculate the
perimeter, more
information is needed
9cm
8cm
I SEE REASONING
Which Answer?
PERIMETER, AREA, VOLUME
Which answer is correct?
Explain the mistakes.
Agree or Disagree?
Estimate
7cm
12cm
7cm
12cm
Calculate the area:
12 × 7 = 84cm²
12 × 7 × 12 × 7 = 7056cm²
12 + 7 + 12 + 7 = 38cm
If the lengths of the sides of a rectangle are doubled, the rectangle
becomes four times bigger.
Tip: Use an example to support your opinion.
Estimate the lengths shown by the arrows:
Area = 24cm² Area = 24cm²
not to scale
I SEE REASONING
Spot the Mistake
PERIMETER, AREA, VOLUME
Calculate the area of the shape:
3cm
6cm
10cm
9cm
7cm
3cm × 10cm = 30cm²
7cm × 9cm = 63cm²
30cm² + 63cm² = 93cm²
Different Ways
Calculate the area:
4cm
10cm
8cm
5cm
3cm 6cm
Method 1
Do 10cm × 5cm
Add cm × cm
Method 2
Do 8cm × 4cm
Add cm × cm
Method 3
Do 10cm × 8cm
Subtract cm × cmArea = cm²
I SEE REASONING
Spot the Pattern
PERIMETER, AREA, VOLUME
Calculate the area and perimeter of each shape:
What do you notice?
Shape A6cm
6cm
Shape B4cm
8cm
Shape C2cm
10cm
Same and Different
Part 1 Draw a rectangle with
the same perimeter and a larger area.2cm
8cm
Part 2
Draw a rectangle with
the same perimeter and a smaller area.5cm
6cm
ExplainA rectangle has a perimeter of 28cm.
What is the largest possible area for the shape?
Explain how you know.
I SEE REASONING
Small Difference Questions
PERIMETER, AREA, VOLUME
Part 1Draw a rectangle with
the same area and a larger perimeter.4cm
6cm
Part 2Draw a rectangle with
the same area and a smaller perimeter.4cm
10cm
Extend
Design a rectangle with a smaller perimeter and a larger area.
3cm
9cm
Part 3Draw a rectangle with
the same area and a larger perimeter.4cm
10cm
I SEE REASONING
True or False?
PERIMETER, AREA, VOLUME
True or False?
Explore
This cuboid is made
using 20 cubes
A cube can be made using 16 smaller cubes
Make a cuboid using
18 cubes.
Your cuboid must have two square faces.
How Many Ways?
Make a cuboid using 16 to 18 cubes.
There must be at least 4 squares on each face of the cuboid.
Level 1: I can find a way
Level 2: I can find different ways
Level 3: I know how many ways there are
6 squares on this face
square face
rectangular face
A cube can be made using 8 smaller cubes
I SEE REASONING
Order
ANGLE
Tip: Make each angle with a pair of scissors.
Order the angles from smallest to largest without using a protractor:
Explore
Find all the acute angles, right angles and obtuse angles:
ExplainIs each angle acute, a right angle or obtuse?
Explain how you know. Don’t use a protractor.
I SEE REASONING
Explain the Mistakes
ANGLE
84° 122°
40°
Which Answer?
47° 127°
133°
Explain the mistakes.
I SEE REASONING
Which Answer?
ANGLE
(a) 104˚
(b) 76˚
(c) 86˚
For each example, what is the missing angle?
(a) 245˚
(b) 255˚
(c) 65˚115˚61˚
43˚
Explain
Angle A is larger than angle D.
A
Angle B is larger/smaller than angle C.
C DB
Small Difference Questions
Calculate the missing angles:
G
68˚
F
E
64˚
64˚ 68˚
H
E =
F = G = H =
I SEE REASONING
Small Difference Questions
ANGLE
Calculate the missing angles:
J76˚ K41˚
35˚
L41˚
65˚
J = K = L =
M
41˚
65˚
M =
90˚
N
51˚
75˚
N =
90˚
True or False?
(a) A 360˚ turn can be made with four acute angles.
(b) A 360˚ turn can be made with a reflex angle and two acute angles.
(c) A 360˚ turn can be made with a reflex angle and two obtuse angles.
Extend: A 360˚ turn can be made with obtuse angles.
How many ways can this question be answered?
Always, Sometimes or Never?
Triangles have smaller angles than quadrilaterals
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Multi-Skill
ANGLE
12 12
3
4567
8
9
10
11
At each time, is the smaller angle between the minute hand and the hour hand acute, obtuse or a right-angle?
10:30am
obtuse
7:10am 4:00pm 9:00am
9:30pm 8:55pm
Which Answer?
12 12
3
4567
8
9
10
11
Draw the times on the clocks.
At each time, what is the smaller angle between the minute hand and the hour hand?
5:00pm
(a) 150˚
(b) 25˚
(c) 120˚
12 12
3
4567
8
9
10
11
6:30am
(a) 0˚
(b) 30˚
(c) 15˚
12 12
3
4567
8
9
10
11
4:30pm
Multi-Skill
12 12
3
4567
8
9
10
11
At each time, what is the smaller angle between the minute hand and the hour hand?
1:00pm
12 12
3
4567
8
9
10
11
8:00pm
12 12
3
4567
8
9
10
11
5:30pm
12 12
3
4567
8
9
10
11
3:20pm
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Small Difference Questions
SHAPE
How many lines of symmetry does each shape have?
Explain
All four shapes… Three shapes have…
Two shapes have… One shape has…
Odd One OutThink of a reason why each shape could be the
odd one out:
Use different properties of shape in your answers.
Use different properties of shape in your answers.
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Explain
SHAPE
Draw shapes in different sections of the Venn diagram:
Two Acute Angles No Lines of Symmetry
At Least Two Pairs of Parallel Lines
Explore
Circle the regular shapes.
For each irregular shape, explain why they are not regular.
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SHAPE
cuboidsquare-based
pyramidtriangular prism
Think of a reason why each shape could be
the odd one out:
Odd One Out
A cuboid has more face(s),
more edge(s) and more vertices
than a triangular prism.
For each pair of shapes, calculate the difference
between the number of faces, edges and vertices:
Small Difference Questions
A square based pyramid has more face(s),
more edge(s) and more vertices than
a triangular pyramid.
Extend: Design your own question to compare the faces, edges and vertices of different prisms or pyramids.
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SHAPE
Correct or Incorrect?
One more square needs adding to this diagram to make the net of a cube.
Which diagrams have been completed correctly to make the net of a cube?
Correct or Incorrect?
Which nets can be folded into a cuboid?
Extend: Design your own net for a cuboid.
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Explain the Mistakes
POSITION, DIRECTION, COORDINATES
Which Answer?For each example, has the black shape
been reflected, translated or rotated?
Reflect the shape in the
mirror line.
mirror
Mistake 1
mirror
Mistake 3
mirror
Mistake 2
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POSITION, DIRECTION, COORDINATES
Explain the Mistakes
Translate 2 squares right and 3 squares up.
Mistake 1
Explain
The shape has been reflected
The shape has been translated
The shape may have been translated or reflected
The shape has been reflected
The shape has been translated
The shape may have been translated or reflected
Start position End position Start position End position
Tick the correct box for each example.
Explain your choice.
Mistake 2
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POSITION, DIRECTION, COORDINATES
Different Ways
Estimate
Could the coordinates of the blue dot be:
(5,3) (6,10)
(30,50) (4,5)
Estimate the coordinate points of the red and blue dots.
Think of possible coordinates for the blue dot:
(8,0)
Estimate
Estimate the coordinate points of the green and purple dots.
(18,24)
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POSITION, DIRECTION, COORDINATES
Agree or Disagree?
Explain the Mistake
Which Answer?
(9,6)The blue dot is (9,0)
The red dot is (6,0)
(0,4)Point B is (7,4)
Point B is half-way between point A and point C.
(14,8)
A
B
C
(3,2)
Inside, on the edge or outside the rectangle?
(10,7) Inside Edge Outside
(3,5)
(9,3)
(2,6)
(8,7)
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POSITION, DIRECTION, COORDINATES
Different Answers
(0,12)
Each square is the same size.
Find coordinates that
are on the edge, at
the corner and on
the inside of the red
square.
Different Answers
Both rectangles are the same size.
Find coordinates that are on the edge, at the
corner and on the inside of the blue rectangle.
(5,8)
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STATISTICS
What’s the Question?
Here is a train timetable:
1. The answer is 8:08. What’s the question?
2. The answer is 9:05. What’s the question?
3. The answer is 11 minutes. What’s the question?
Macclesfield 7:45 8:27 9:05 9:52
Poynton 7:57 8:38 9:17 10:04
Cheadle Hulme 8:03 8:45 9:24 10:10
Stockport 8:08 8:50 9:30 10:16
Manchester Piccadilly 8:19 9:01 9:41 10:27
Multi-StepHere are two train timetables:
Helen lives in Crewe.
She is travelling to
Cannock.
Helen needs to arrive
by 16:30 at the latest.
What time does Helen
need to arrive at
Crewe railway station?
Crewe 13:56 14:20 14:52
Stafford 14:15 14:39 15:11
Wolverhampton 14:38 15:05 15:37
Birmingham 14:55 15:23 15:54
Wolverhampton 14:12 14:56 15:45
Dudley 14:26 15:10 15:58
Walsall 14:58 15:41 16:30
Cannock 15:14 15:58 16:45
Why does this question use two train timetables?
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STATISTICS
Fill the GapsHere are the results from six football matches:
Won Drawn Lost Points Goals
For
Goals Against
Ashton 7 5
0 1 6 6
1 8
Duddon 0 5
Contexts
Fill the gaps in the league table:
Kelsall 2 – 3 Tarvin
Ashton 5 – 2 Duddon
Duddon 2 – 4 Kelsall
Tarvin 1 – 3 Ashton
Ashton 2 – 2 Kelsall
Tarvin 5 – 1 Duddon
3 points for a win, 1 point from a draw, 0 points for a loss.
For each example, should the data be presented as a bar graph or a line graph?
Temperature in Garden on 1st July
Number of Different Vegetables Grown in Garden
Rainfall per Month in Garden
Think of other contexts where we use bar graphs.
Think of other contexts where we use line graphs.
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STATISTICS
Which Graph?Draw lines to match the heading to the correct graph.
Favourite Fruit
for Children in Y5/6 Class
Number of Children in Each Class in School
Shoe Size for Children in Y5/6
Age of Children in Y5/6 Class
Which Graph?Draw lines to match the heading to the correct graph.
Speed of
Runner in Hill Run Race
Speed of Runner in Marathon Race
Speed of Runner in 100m Race
Explain the differences in the graphs.
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STATISTICS
Act the Graph
Speed of Running on the Spot
spe
ed
Time (seconds)
very
slow 15 30
Fear in Facial Expression:
Rollercoaster Ride
Act the Graph
exc
ite
me
nt
Time (seconds)
100%
0%
50%
10 20
very
fast
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STATISTICS
Which Answer?This graph shows the speed of a 400m runner.
What is happening at the point showed by the arrow?
(a) The runner’s fastest speed
(b) The runner finishes
(c) The runner slows down
Speed of Runner
Sp
ee
d (
mp
h)
Time (seconds)
20
50
10
00
Which Answer?This graph shows the distance travelled by a cyclist.
What is happening at the point showed by the arrow?
(a) The cyclist has stopped
(b) The cyclist is riding slower
(c) The cyclist is riding at the
same speed
Distance Travelled by Cyclist
Dis
tan
ce
(m
ph
)
Time (hours)
50
3
25
00
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ANSWERS
Place Value, page 7:
True or False? True examples: 3 hundreds, 9 tens, 2 ones1 hundred, 29 tens, 2 ones
Different Ways 3 tens 23 tens 12 tens Example answers: 53 tens & 4 ones 43 tens & 14 ones
Different Ways Fewest counters = 7 (2 thousands, 4 hundreds, 1 ten)
Most counters = 241 (241 tens)2410 with 16 counters: 2 thousands, 3 hundreds, 11 tens2410 with 16 counters: 1 thousand, 14 hundreds, 1 ten
Place Value, page 8:
Which Answer? 3004 fifty thousand and seventy 60002 twenty thousand and six
Small Difference Questions: Thirty-five thousandThirty thousand five hundred Thirty thousand and fiftyThree thousand and fifty Three hundred thousand and five
Order: 56020 (2 zeros) 300270 (3 zeros) 13031 (1 zero)
Place Value, page 9:
Spot the Pattern: Line 1 gaps: 754 794 804Line 2 gaps: 973 993 1003 Line 3 gaps: 1306 1006 906
Small Difference Questions: Left column: 1000 1099 1009Right column: 10000 10999 10099
Estimate: Estimates: blue = 800 red = 8400 purple = 3000 green = 78000
Place Value, page 10:
Estimate: Example reasoning, line 1: 500 is half-way, split 500→1000 into 5 steps of 100, position 836. Line 2: 836 slightly less than one-tenth along number line. Line 3: split 800 → 850 into 5 steps of 10, position 836. Line 4: 850 is half-way, position 836.
Estimate: Example reasoning, line 1: 5000 is half-way, split 0→5000 into 5 steps of 1000, position 3280. Line 2: Double the distance of line 1.Line 3: 3500 is half-way, split 3000→3500 into 5 steps of 100, position 3280.
Line 4: 3280 is 4
5along the number line.
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Answers
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Place Value, page 11:
Small Difference Questions: 100 10000 500
Different Ways: Example answers: 0 & 450 190 & 200 100 & 240
Different Ways: Example answers: 0 & 5000 2000 & 3600 3000 & 3100
Place Value, page 12:
Explain: Answer = 9. Less than 100 is added to a 3-digit number to make 1000 or more. Therefore, the 3-digit number must be more than 900.
Agree or Disagree? Agree: Jen’s number could be 70 and Molly’s number could be 69.
Different Ways: 691 or 709
How Many Ways? 6 ways: 5210, 5120, 5102, 5012, 4310, 4130
Decimals, page 13:
Small Difference Questions: 0.8: Small Difference Questions: 0.36
Agree or Disagree? Disagree, the arrow shows the position of 0.7
Decimals, page 14:
Different Ways: Example answers for 3.74:
Agree or Disagree? Blue is true, red is false. Look at the most significant column. 140 has more 100s than 80; 0.8 has more tenths than 0.14.
Compare: 0.64 < 0.9 0.64 > 0.614 0.64 < 0.6440.7 = 0.70 0.55 > 0.505 0.08 < 0.088 0.915 < 0.92
ANSWERS
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Answers
3.7 3.8
0 10
3 4
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ANSWERS
Decimals, page 15:
Explain the Mistakes: Blue example: 0.3 should be added to the tenths, answer = 0.77. Red example: 0.8 + 0.2 = 1, 0.08 + 0.02 = 0.1, answer = 1.1
Compare: 0.33 < 0.3 + 0.3 0.33 = 0.3 + 0.030.41 > 0.4 + 0.004 0.67 = 0.60 + 0.07 0.87 > 0.7 + 0.08
How Many Ways? Q1: 5 ways: 4 × 0.1 & 2 × 0.01 3 × 0.1 & 12 × 0.01
2 × 0.1 & 22 × 0.01 1 × 0.1 & 32 × 0.01 42 × 0.01Q2: 3 ways: 2 × 0.1 & 4 × 0.01 1 × 0.1 & 14 × 0.01 24 × 0.01
Spot the Pattern: 0.4, 0.41 0.1, 0.11 0.4, 0.04 0.5, 0.25
Decimals, page 16:
Small Difference Questions: 20.5 2.05 805 0.805
Which Answer? Correct answer = 53. Mistakes: 54 is incorrect because the number should be rounded down; 53.5 is not a whole number.
Number Lines: 38.42 rounds to 38 39.08 rounds to 39 39.6 rounds to 4040.27 rounds to 40 40.82 rounds to 41
23.555 rounds to 23.6 23.64 rounds to 23.6 23.708 rounds to 23.723.78 rounds to 23.8
Decimals, page 17:
Different Ways: Example answers: 3.3 & 3.7 3.45 & 3.55 3.499 & 3.501
Small Difference Questions: 30 ÷ 30 = 1 30 ÷ 100 = 0.3 30 ÷ 300 = 0.1
40 ÷ 100 = 0.4 40 ÷ 40 = 1 40 ÷ 80 = 0.5
Different Ways: Example answers: 0.07 + 0.03 = 0.1 10 ÷ 100 = 0.10.01 × 10 = 0.1 2 ÷ 10 = 0.2 2 – 1.8 = 0.2 0.8 + 79.2 = 80 0.8 × 100 = 80
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Answers
38 39 40 41
38.42 39.08 39.6 40.27 40.82
23.5 23.6 23.7 23.8
23.555 23.64 23.708 23.78
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ANSWERS
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AnswersDecimals, page 18:
Spot the Pattern: 1.2, 1.5 0.08, 0.1 0.1, 0.2 0.3, 0.6
Different Ways: Example answers: 30×0.1 = 3 10×0.3 = 3 6×0.5 = 3Example answers: 6×0.4 = 2.4 0.4×6 = 2.4 24×0.1 = 2.4
Small Difference Questions: Left column: 3 1.5 0.5Middle column: 20 40 8 Right column: 10 8 4
Negative Numbers, page 19:
Contexts: Sweets example incorrect (negative numbers don’t describe quantities). Face paints is incorrect as the profit is £5. The other examples are correct.
Contexts: £4 - £6 = -£2 -2 + 5 = 3 Example question: The temperature was 5˚c. Then the temperature fell by 7˚c. What is the temperature now?
Negative Numbers, page 20:
Explain the Mistake: Counting all the numbers is incorrect because you don’t include the first number in a count to calculate the difference.
Different Ways: 30 and -70 8 and -42
Estimate:
Negative Numbers, page 21:
Estimate: Approximate values: -5 -7 and 13 -5 and 3
Estimate: First line 0 is 1
2along. Second line 0 is
1
3along.
Third line 0 is 1
3along. Fourth line 0 is
1
5along.
Negative Numbers, page 22:
Small Difference Questions: top left: 6 bottom left: 1 top right: -1 bottom right: 1
Small Difference Questions: 2 -2 -4 2 10
Small Difference Questions: 11 4 3 19
-20 0-8-14 -3 1710 20-10
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ANSWERS
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AnswersNegative Numbers, page 23:
Which Answer? Red answer is correct. Blue is incorrect as the pattern in the ones value when subtracting 5 changes when bordering 0.
Rank by Difficulty: Blue = -1 (highest start number, - 2 so odd number pattern); Red = -6 (120 is a multiple of 6 so zero will be in the sequence); Green = -4 (lowest start number but calculation bordering 0 is harder).
How Many Ways? 4 ways: 4 5 10 20
Different Ways: Example sequences: -5, -1, 3, 7, 11 31, 19, 7, -5, -17
Rounding, page 24:
Explain: Example answers: The population of Scotland is impossible to measure exactly so it is rounded. It may be rounded to the nearest thousand or the nearest million depending on the context. We typically give the time to the nearest 5 minutes.
Explain: Typically, a school would say the exact number of children in their school. Recipe quantities are rounded. A 400m race time would be
rounded to the nearest second for normal races, but given to 2 decimal places for professional races.
Which Answer? 198 – 57 can be calculated by rounding 198 to 200. 503 + 246 doesn’t require any carries so rounding may not make this easier. 249 + 148 can be rounded to 250 + 150 – 3. When multiplying, typically rounding is only used when one number is rounded. 60 × 4 can be used to derive 59 × 4.
Rounding, page 25:
Number Lines: Nearest 20: 607 closest to 600 632 closest to 640
668 closest to 660 685 closest to 680Nearest 50: 376 closest to 400 419 closest to 400 438 closest to 450 471 closest to 450
Number Lines: 437: closest 10 is 440, closest 100 is 400. 446: closest 10 is 450, closest 100 is 400.453: closest 10 is 450, closest 100 is 500.
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ANSWERS
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AnswersRounding, page 26:
Small Difference Questions: 250, 200, 300, 500, 500
Small Difference Questions: 570 100 550 20
Agree or Disagree: This is true if the number is rounded to 10, 100 or 1000. However, if the number is rounded to the nearest 20 or the nearest 50 then it would round to a smaller number.
Rounding, page 27:
Explain the Mistakes: Blue answer: When rounding to the nearest 1000, the hundreds value determines how the number is rounded.Red answer: The hundreds value has been rounded correctly, but the nearest 100 is 4300 (the 4000 has not been included in the answer).
Which Answer? The purple answer is correct as 400 is a multiple of 10.
Which Answer? 1549
Explain: Example answer: 349 and 350 are consecutive but rounded to the nearest 100 349 is 300 and 350 is 400.
Rounding, page 28:
Different Ways: Left: 245→249 Centre: 250→254 Right: 255→349
Multi-Step: The least Tim could have is £1.45, the most Kam could have is £2.74, therefore the maximum possible difference is £1.29
Multi-Skill: Question 1: 246, 249, 252 Question 2: 301Example question: To the nearest 10, my number is 200. My number is a multiple of 6. What could my number be? (198 and 204).
Roman Numerals, page 29:
Compare Questions: LXVI = 66 LXIV = 64 XLVI = 46 XLIV = 44
Rank by Difficulty: 33 = XXXIII 49 = XLIX (note that for 40 and 9 symbols are used for less than 10 & 50) 65 = LXV
Compare Questions: XL = 40, IX = 9 (similar structures, both use a symbol for 1/10 less than 10/50). XIII = 13, LXXX = 80 (similar adding structures).
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ANSWERS
Roman Numerals, page 30:
Rank by Difficulty: 230 = CCXXX 490 = CDXC (symbols needed for 100 less than 500 and 10 less than 100) 780 = DCCLXXX (7 symbols needed).
Order: DIII = 503 DXX = 520 CM = 900 M = 1000 (note that with these examples, the numbers with more symbols are larger).
Explain: Red: symbols can be used for less than. Example: in XL, the X
represents 10 less than 50, making the number smaller.Blue: Some numbers above 200 have fewer symbols than numbers below 20. Examples: 18 = XVIII (5 symbols), 201 = CCI (3 symbols).
Roman Numerals, page 31:
Spot the Pattern: LXXX, XC, C, CX, CXX
CCX, CCXX, CCXXX, CCXL, CCL DLX, DLXX, DLXXX, DXC, DC
Small Difference Questions: XLII XLIV LIII XXXIII XXIX XL LXXX
Roman Numerals, page 32:
Extend: XLIV (44)
How Many Ways? 7 answers: XIV XVI XLI XLV LIV LVI LIX
How Many Ways? 15 answers: CDI CDV CDX CDL DIV DVI DIX DXI DLI DLV DLX DCI DCV DCX DCL
Addition, page 33:
Simplify: Top row: 232 15 Bottom row: 130 2
Simplify: Top row: 2623 200 Bottom row: 35 110
Small Difference Questions: Left column: 520, 520, 502, 502Right column: 1031, 1031, 1028, 1018
Mental or Written Method? 4731 + 5268 = 9999 (can add each column)463 + 278 = 741 (may suit column method)895 + 385 = 1280 (can change to 900 + 380)2480 + 2520 = 5000 (equal to 2500 + 2500)
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Answers
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ANSWERS
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AnswersAddition, page 34:
Explain the Mistakes: Left example: the numbers are not lined up correctly. Middle example: error in addition of hundreds column. Right example: the digits that have been carried haven’t been added.
Correct or Incorrect? Left example is incorrect: the numbers are not lined up correctly (see the decimal point). Middle example is correct.
Right example is incorrect: error in tens value addition.
Rank by Difficulty: 4065 + 3205 = 7270 (the same as 4070 + 3200).744 + 579 = 1323 (may suit column method). 473.6 + 516.2 = 989.8 (can add each column).2996 + 2995 = 5991 (can do 3000 × 2 – 9).3509 + 3444 = 7003 (the same as 3503 + 3500).
Different Ways: 1442 and 1532. 1523 has an incorrect ones value. The hundreds value can’t be 6 so the answer can’t be 1652.
Addition, page 35:
Which Answer? The red answer is correct. In this case, the blue statement is incorrect as one more hundred needs to be added, so the missing tens value in the addend must be 9.
How Many Ways? 4 ways: 28 + 76 = 104 26 + 78 = 104
68 + 72 = 140 62 + 78 = 140
Different Ways: First question has 3 answers: 1025 + 739 = 17641125 + 739 = 1864 1225 + 739 = 1964Second question has 2 answers: 1243 + 836 = 2079 1243 + 936 = 2179Third question has 1 answer: 1928 + 158 = 2086
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ANSWERS
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AnswersSubtraction, page 36:
Simplify: Top row: 541 552 Bottom row: 699 500
Rank by Difficulty: 43.2 – 16.8 = 26.4 (using the column method, two regroups are needed so relatively challenging)845 – 297 = 548 (equivalent to 848 – 300)601 – 337 = 264 (equivalent to 599 – 335 which can be done using the
column method without regrouping)869 – 321 = 548 (can use the column method without regrouping)
Simplify: Top row: 7277 3122 Bottom row: 3799 2000
Rank by Difficulty: 8765 – 2543 = 3222 (can use the column method without regrouping)7002 – 3497 = 3505 (5 more than 7000 – 3500)5432 – 2543 = 2889 (using the column method, two regroups are needed so relatively challenging)6672 – 3994 = 2678 (equal to 6678 – 4000)
Subtraction, page 37:
Different Methods: 3728 – 1465 = 2263 (strategy: column method)3012 – 2994 = 18 (strategy: calculate the difference)3000 – 30 = 2970 (strategy: count back)900 – 452 = 448 (strategy: near doubles)764 – 296 = 468 (strategy: equivalent to 768 – 300)
Small Difference Questions: Left column: 15, 465, 4965, 49965Right column: 725, 7925, 7250, 79250
Small Difference Questions: Left column: 325, 325, 365, 365, 5765Right column: 4010, 3983, 3663, 3653, 3687
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ANSWERS
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AnswersSubtraction, page 38:
Explain the Mistakes: Left example: 5 – 8 ≠ 3 and 0 – 2 ≠ 2Middle example: the numbers are not lined up correctly.Right example: Should be regrouped into 5000, 900 & 100 (so the 0 in the hundreds column should be crossed out and a 9 positioned above)Correct or Incorrect: Left and right examples are correct. The middle example is incorrect because to get the extra 10 for the ones column the 8 tens must become 7 tens.
Rank by Difficulty: 4600 – 1280 = 3320 4006 – 1280 = 2726 Note that the second questions requires more regrouping. This is more challenging with zeros: three columns are adjusted on the first regroup.23.64 – 12.8 = 10.84 23.8 – 12.64 = 11.16 Note that the second calculation in particular is made simpler when 23.8 is written as 23.80
Explain: If the tens value of the minuend is smaller than the tens value of the subtrahend, then the digit in the red box will be 3. This can be shown using the column method, because in this case a regroup would be
required. Example: 615 – 234 = 381
Subtraction, page 39:
Explain: Example answers: 47 – 15 = 32 55 – 17 = 32Difference between digits in blue box = 3, difference between digits in red box = 4 Explanation: in the second example, the ones value of the subtrahend is smaller than the ones value of the minuend. Therefore, for the difference to be 30+, the difference between the tens values must be more than 30.Different Ways: First question has one answer: 839 – 285 = 554Second question has one answer: 916 – 160 = 756Third question has two answers: 479 – 186 = 293 479 – 196 = 283
How Many Ways? Four possible answers: 602 – 237 = 365 612 – 237 = 375 622 – 237 = 385 632 – 237 = 395
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ANSWERS
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AnswersAddition and Subtraction, page 40:
Broken Calculator: Example methods: 750 + 850 = 800 × 2 505 – 367 = 499 – 361 866 – 597 = 869 – 600 7.5 – 5.5 = 8 – 6 63.5 + 79.5 = 63 + 80 1.4 – 0.7 = 1.4 ÷ 2
Contexts: (b) 30 + 12 (a) 15 + 7 (b) £15 + £25 (a) 200 – (55 + 85)
Addition and Subtraction, page 41:
Building Questions: Raja buys three apples and three bananas. How much does it cost him?
Mo has £2. How many oranges can he afford?
Ben has £2. He wants four oranges and three apples. How much more money does he need?
Matt has £2. He wants four oranges and three bananas. How much change does he get?
Which Bar Model: The right-side bar model is correct: £2 is more than the cost of the fruit so change is given.
Explain: Largest number = 3 oranges. 3 apples cost 75p. £2 – 75p = £1.25. With £1.25, 3 is the maximum number of oranges that can be bought (3 × 35p = £1.05).
Addition and Subtraction, page 42:
Small Difference Questions: 1. £2.55 2. 55p 3. 45p 4. 8 apples5. 5 oranges 6. A drink and 2 oranges
Building Questions: Example line 1: Lucy buys 3 pineapples. She pays £3. Example line 1: Kelly buys 3 melons and a mango. She pays £4Example line 2: Tom want to buy 3 mangos. He has £1.50Example line 2: Jim has £3. He wants to buy 3 pineapples and a melon.Example line 3: Zara has £4.50 (any value in the range £4.50→£5.39)
Addition and Subtraction, page 43:
Multi-Step: John bought 4 oranges.Kelly bought 2 apples, 2 oranges and 1 banana.Ben bought 4 apples and 2 bananas.
Which Bar Model? The bottom left bar model is correct.
Agree or Disagree? The one correct answer is 17 boys.
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ANSWERS
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AnswersAddition and Subtraction, page 44:
Small Difference Questions: 1. 5 girls 2. 15 boys 3. £16 4. £15.50
Small Difference Questions: 1. 30p 2. 50 women 3. £25 4. 75g 5. 85 and 155
Rank by Difficulty: Orange = 180g 12 boys circle = 17.5 square = 12.5Note that the oranges/pears calculation is the same as the boys/girls
except it’s 10 times bigger and the answer asks for a different part. The shape puzzle is different in that the answer is a decimal. This happens when the sum is even and the difference is odd and vice versa.
Addition and Subtraction, page 45:
How Many Ways? 4 ways: 22 & 30 23 & 31 24 & 32 25 & 33Which Answer? 485 is correct. The mistake for 395 is to subtract the 45, ignoring that the subtraction is on the other side of the = sign. The mistake for 440 is to ignore the – 45.
Small Difference Questions: 75 + 45 > 120 – 10 75 + 65 = 150 – 10
85 + 75 > 160 – 20 85 + 75 < 160 + 20 95 + 85 = 155 + 25230 – 165 = 83 – 18 230 – 165 = 93 – 28 230 – 185 = 93 – 48230 – 85 > 93 + 48 230 – 85 < 103 + 48
Addition and Subtraction, page 46:
Agree or Disagree: The red statement is false. Example: 50 + 5 = 70 – 15The green statement is true.
Multi Step: Example answer: 8 > 6 4 + 2 = 7 – 1 5 + 3 < 9Note that the only digit that can go in the bottom box is 9. The middle line can only be completed using the 7 as shown in the example above.
Multi Skill: Left box: 36 36 48 Right box: 42 48 72
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AnswersAddition and Subtraction, page 47:
Agree or Disagree: The blue statement is true: the circle = 13, one additional circle increases the sum by 13. Therefore the star = 19The red statement is true: the pentagon is 5 more than the diamond but the value of those shapes will differ depending on the value of the oval.
Explore: = 15 as three hexagons = 45. Therefore = 8 (middle row)
and = 12 (middle column).
= 7 (compare top row to middle column). Therefore = 9 = 5
Extend: = 10 (compare the top row to the 4th column).
Therefore = 11 (use 4th column) and = 6
Multiplication Calculation, page 48:
Different Ways: Examples: partition into two sections of 15×4; partition into three sections of 5×8; partition into 11×8 and 4×8
Small Difference Questions: Left column: 84, 108, 216, 324, 315, 630Middle column: 96, 128, 112, 126, 108, 108Right column: 120, 120, 136, 476, 462, 231
Multiplication Calculation, page 49:
Matching Number Sentences: 6×9 (also could be 3×19 or 2×27). 8×7 (also could be 4×14 or 2×28). 6×10 (also could be 3×20 or 2×30). 3×19
Matching Number Sentences: 3×14 9×9 8×15 (also could be 4×30 or 2×60) 7×12
I know… so… 24×19 = 456 (24 more) 40×15 = 600 (150 more)38×12 = 456 (36 more)
Multiplication Calculation, page 50:
Small Difference Questions: Left column: 150, 138, 108, 216, 864, 984Right column: 630, 315, 336, 416, 624, 936
Rank by Difficulty: 37×6 partitioned and multiplied gives 180 and 42. 804×6 partitioned and multiplied gives 4800 and 24. Easier addition.98×6 can be calculated using rounding. 45×6 = 90×3
Rank by Difficulty: 32×50 = 16×100. Use rounding for 99×4. Partitioning and multiplying 46×7 gives 280 and 42. Partitioning and multiplying 409×6 gives 2400 and 54. Easier addition.
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Multiplication, page 51:
Different Methods: Examples: 14×25 becomes 7×501.5×6 becomes 3×3 5×18 becomes 10×9
Different Ways: Blue: 8 Red: 48 Green: 12×8 or 24×4
Broken Calculator: 26×8 example ways: 52×4 or 26×10 – 5280×15 example ways: 40×30 or 79×15 + 15
Multiplication, page 52:
Estimation: Odd. Estimate slightly closer to 2800 than 2100.
Estimation: Even. Estimate significantly closer to 5400 than 4500.
Estimation: Even. 4-digit number. Closest to 1100: 300×4 = 1200,the answer is less than this so is closer to 1100 than 1300.
Checking Possible Answers: Not 3028: 500×6 = 3000, answer must be less than 3000. Not 2941, answer must be even.
Multiplication, page 53:
Explain the Mistakes: The 2 hundreds from 60×4 = 240 should be positioned below the line and added to 200×4 = 800. The 3 tens from 7×5 = 35 have not been added to the 10×5 = 50. Error in the calculation of 800×6.
Part-Complete Examples: 2445 2892 3704
Different Methods: The same calculations. For the grid method, the multiplication and addition are done separately. For the short method, the multiplication and addition calculation are done simultaneously.
Multiplication, page 54:
Estimation: Even. Estimate nearer to 900 than 400.
Estimation: Odd. Estimate slightly more than 3600.
Estimation: Odd. 4-digit number. Closest to 1000: close to 50×20 = 1000.
Checking Possible Answers: Not 1602: 40×40 = 1600, answer must be less than 1600. Not 1543 as the answer must be even.
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Multiplication, page 55:
Different Methods: For the grid method, the multiplication and addition are done separately. This is the same for the expanded method but the numbers are aligned in columns. In the long multiplication method, the multiplication and addition calculation are done simultaneously so only two numbers need to be added as the final step.
Explain the Mistakes: 72×43: no zero in the ones column in the second line of the calculation. 41×23: the calculation done is 41×32. 84×52: The second line of the calculation should be 4200, not 40200.
Part-Complete Examples: 63×53: line 1 is 189, line 2 is 3150, line 3 is 3339.24×16: line 1 is 144, line 2 is 240, line 3 is 384. 81×46: line 1 is 486, line 2 is 3240, line 3 is 3726.
Multiplication, page 56:
Missing Digits: 428×6 = 2568 524×8 = 4192 695×5 = 3475
Different Answers: 931×4 = 3724 or 532×7 = 3724
How Many Ways? 3 ways: 27×3 = 81 19×3 = 57 29×3 = 87
Division, page 57:
Different Methods: Possible methods: 480 ÷ 4 = 120 (halve twice)480 ÷ 6 = 80 (6 × 8 × 10) 480 ÷ 10 = 48 (move digits one column)480 ÷ 20 = 24 (480 ÷ 2 ÷ 10) 480 ÷ 240 = 2 (counting the 240s in 480)
I know… so… 78 ÷ 3 = 26 (2 more 3s) 168 ÷ 6 = 28 (double)108 ÷ 6 = 18 (10 more 6s) 91 ÷ 7 = 13 (1 less 7) 144 ÷ 8 = 18 (doubling the dividend and the divisor = same quotient) 192 ÷ 4 = 48 (20 more 4s)
Small Difference Questions: First column: 18, 36, 18, 18
Second column: 16, 26, 36, 18
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Answers
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Division, page 58:
Small Difference Questions: First column: 28, 28, 38, 43Second column: 36, 72, 82, 87
Which Operation? 100 ÷ 5 = 20 (division) 2000 ÷ 100 = 20 (multiplication) 40 × 5 = 200 (division) 5 = 20 ÷ 4 = 120 (division) 4 = 80 ÷ 20 (multiplication)
Contexts: 64 ÷ 16 = 4 Number sentence: 90 ÷ = 15
Example question: Some people are going to the match. 5 people travel in each car and there are 60 cars. How many people are going to the match?Example question: The bill for a group of friends at the café is £60. Each person pays £5. How many friends at the café?
Division, page 59:
Estimate: 165 ÷ 6 can’t give a whole number answer. A reasonable estimate will be significantly nearer to 30 than to 20.344 ÷ 8 could give a whole-number answer but it isn’t immediately obvious if it does. A reasonable estimate will be nearer to 40 than to 50.
Estimate: 705 ÷ 3 could give a whole-number answer although it isn’t immediately obvious that it does. A reasonable estimate will be nearer to 200 than to 300.719 ÷ 4 can’t give a whole number answer. A reasonable estimate will be significantly nearer to 200 than to 100.
Explain: 70 ÷ 5: 2-digits (more than 10 × 5). 435 ÷ 5: 2-digits (less than 100 × 5). 3000 ÷ 4: 3-digits (less than 1000 × 4). 3075 ÷ 3: 4-digits (more than 1000 × 4). 615 ÷ 5: 3-digits (more than 100 × 5).
Division, page 60:
Which Answer? The green answer is incorrect because 90 and 2 are not multiples of 4. The blue and red responses are correct. When using written calculation we partition as shown by the blue response.
Next Step: Top row: 1 2 0 1 Bottom row: 3 0 1 1
Next Step: Top row: 2 0 2 Bottom row: 2 1 2
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Division, page 61:
Part-Complete Examples: Top row: 13 23 223 Bottom row: 111 r 4 61 r 4 198
Part-Complete Examples: Top row: 284 287 r 1 254Bottom row: 74 r 4 141 r 2 139 r 4
Which Answer? The middle answer is correct. Left-hand calculation
incorrect because the remainder is larger than the divisor. Right-hand calculation incorrect because there are not 9 lots of 4 in 34.
Division, page 62:
Explain the Mistakes: Left example: there are 7 lots of 6 in 45, not 8 lots. Middle example: the answer has a remainder of 2Right example: the final remainder carried should be 3 rather than 1 (the difference between 7 × 6 and 45 is 3).
Form of Answer: Sunflower = 8.5cm 8 teams (3 teams have a substitute)8 hours 30 minutes
Form of Answer: The red answer is correct. 29 ÷ 4 = 7 r 1 and that represents quarter of an hour.
Division, page 63:
Mental or Written? 320 ÷ 3 = 106 r 2, partitioning 320 into 300 and 20 so may not require written method. 320 ÷ 5 = 64, can be done as 320 ÷ 10 × 2. 320 ÷ 6 = 53 r 2, partitioning 320 into 300 and 20 so may not require written method. 320 ÷ 8 = 40, can be done mentally. 320 ÷ 9 = 35 r 5, likely to require written method. 320 ÷ 10 = 32, can be done mentally.
Mental or Written? 540 ÷ 4 = 135, can calculate by halving twice.
540 ÷ 6 = 90, can be done mentally. 540 ÷ 7 = 77 r 1, likely to require written method. 550 ÷ 55 = 10, can be done mentally using place value knowledge. 550 ÷ 25 = 22, can be done mentally if we know 100 ÷ 25 = 4. 550 ÷ 15 = 36 r 10, likely to require a written method.
Small Difference Questions: Left column: 140 70 80 62 r 2 63 126Right column: 147 147 73.5 83.5 167 167
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Division, page 64:
Rank by Difficulty: Example methods: 340 ÷ 20 = 17, same as 34 ÷ 2546 ÷ 6 = 91, partitioning 546 into 540 and 6 which may be done mentally.500 ÷ 3 = 166 r 2, likely to require a written method.425 ÷ 5 = 85, can be done by 425 ÷ 10 × 2550 ÷ 30 = 18 r 10, can use 55 ÷ 3 = 18 r 1Broken Calculator: Example methods: 522 ÷ 2 ÷ 3 = 87624 ÷ 8 = 312 ÷ 4 = 78
How Many Ways? 6 ways: 36 ÷ 2 = 18 76 ÷ 2 = 38 86 ÷ 2 = 43 96 ÷ 2 = 48 76 ÷ 4 = 19 96 ÷ 4 = 12
Multiplication and Division, page 65:
Contexts: (a) subtraction to calculate the difference between their ages and addition to calculate Jack’s future age. (b) multiplication (c) subtraction to calculate the amount that needs saving and division to work out how many weeks she needs to save for.
Agree or Disagree? Disagree: Kam has 3 × 6 × 2 = 36 outfits, Pete has 3 × 5 × 3 = 45 outfits.
Extend: Mr James has 4 × 5 × 8 = 160 outfits including a tie and 4 × 5 = 20 outfits without a tie, a total of 180 outfits.
Multiplication and Division, page 66:
Spot the Difference: (a) £105 (b) 1 hour 45 minutes
Explore: Example questions: (a) How much does it cost for 5 apples at the market? (b) Tim buys ten apples at the market. Mo buys 6 apples at the shop. How much do they spend in total? (c) Kerry bought 12 apples at the market. She paid with a £5 note. How much change did she get? (d) Tom has £2. How many apples can he afford from the market?
Explore: Example questions: (a) 60 cars are being driven to the match. How many coaches are needed? (b) 4 coaches are going to the match. How many cars are needed?
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Multiplication and Division, page 67:
Small Difference Questions: (a) 6 tents (b) 6 tents (c) 6 tents(d) 4 person tents (e) 29→32 people (f) 25→32 people
Explore: Example questions: (a) There are 32 children in the class. The teacher has 4 2-litre bottles of orange juice. How much juice can each child have?
(b) There are 20 children in the class. The teacher has 3 2-litre bottles of orange juice. Each child has 250ml juice. How much juice is left?(c) The teacher has three 2-litre bottles of orange juice. Each child drinks 500ml of juice. How many children are there in the class?
Extend: Adam is 35, Lara is 5 (next year Adam = 36, Lara = 6).
Multiplication and Division, page 68:
Explain the Mistakes: 480÷100 = 4.8, digits need to move two columns.3600÷36 = 100, 36 is 100 times smaller than 3600.7.6×10 = 76, the digits need to move one column.3.05×1000 = 3050, each digit must move 3 places.
Correct or Incorrect? Correct responses to incorrect examples:360÷100 = 3.6 0.34÷10 = 0.034
I know… so… 17×60 = 1020 170×60 = 10200160÷16 = 10 1600÷16 = 100 420÷60 = 7 420÷6 = 70
Correct or Incorrect? Correct responses to incorrect examples:60×70 = 4200 403÷100 = 4.03 400÷50 = 8
Multiplication and Division, page 69:
Which Answers? Factors of 12: 4 and 6 Multiples of 30: 90 and 120
Which Answers? Prime numbers: 31 41 61 71
Which Answers? The only prime number is 137. Factors of 87 include 3, factors of 121 include 11, factors of 375 include 5
Spot the Mistakes: 9cm×9cm = 81cm² (not cubed).5cm×5cm×5cm = 125cm³ (not squared).
Which Answers? Square numbers: 36, 64, 121 Cube numbers: 27, 64
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Multiplication and Division, page 70:
Mental or Written Calculation? Factors of 128: 1 2 4 8
Mental or Written Calculation? Factors of 624: 1 2 3 4 6 8
Spot the Pattern: Example answers: 70×6 = 420 35×2×6 = 420 7×5×2×6 = 420 7×5×2×3×2 = 420
Multiplication and Division, page 71:
I know… so… Note that factors of 24 and 15 must also be factors of 360. Factors of 360: 1 2 3 4 5 6 8 9 10 12 15 18 20 24 30 36 40 45 60 72 90 120 180 360
Order 35 has 4 factors: 1 5 7 35 45 has 6 factors: 1 3 5 9 15 4536 has 7 factors: 1 2 3 6 12 18 36
Explain the Mistake Some multiples of 5 are not multiples of 10, for example 25. However, every multiple of 10 is also a multiple of 5.
Small Difference Questions: Example answers: Every multiple of 8 is also a multiple of 4. Every multiple of 12 is also a multiple of 6. Every multiple of 15 is also a multiple of 5.
Multiplication and Division, page 72:
Which Answers? Left question: 2, 3, 6 Right question: 3, 9
Different Answers: Example answers: Left oval: 16, 32. Right oval: 18, 30. Middle section: 12, 24. Outside: 7, 10.
Different Answers: Example answers: Left oval: 16, 20. Right oval: 3, 6. Middle section: 8, 12. Outside: 5, 14.
Multiplication and Division, page 73:
Correct or Incorrect? The blue and green statements are correct.
Different Ways: Example answers: 20×2 = 10×4 20×3 = 15×420×5 = 25×4 20×10 = 50×4 The number in the red box is five times as large as the number in the blue box.
Small Difference Questions: 6×32 > 200–20 6×36 < 200+20 6×40 > 240÷4 6×20 = 240÷2 12×20 = 120×2
How Many Ways? Six possible answers: 60÷1 = 3×20 60÷2 = 3×1060÷4 = 3×5 60÷5 = 3×4 60÷10 = 3×2 60÷20 = 3×1
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Fractions, page 74:
Read the Picture: Red = 𝟏
𝟒Green =
𝟏
𝟒Yellow =
𝟏
𝟖(half the size of red)
Blue = 𝟑
𝟖(the rest of the shape and same size as red + yellow)
Read the Picture: Blue = 𝟏
𝟓Red =
𝟏
𝟒Green =
𝟏
𝟑
Explain: The red fraction is smaller, despite the red piece being a smaller
area than the blue piece. The red part is 𝟏
𝟒of its rectangle whilst the blue
part is 𝟏
𝟔of its rectangle.
Fractions, page 75:
Explain: Example 1: fingers as a fraction of a hand. Example 2: fingers as a fraction of a hand. Example 3: the brain as a fraction of the head. For each example, compare relative sizes of parts and wholes.
True or False? 𝟏
𝟓and
𝟓
𝟖are false,
𝟑
𝟖is true
Estimate: Top left: 𝟏
𝟑Top right:
𝟏
𝟓Bottom left:
𝟑
𝟒Bottom right:
𝟒
𝟓
Fractions, page 76:
Context Question: 𝟓
𝟖pizza each. Could show by dividing each pizza into
eighths; could divide four pizzas into halves and one pizza into eighths.
Context Question: 2𝟑
𝟒pieces of toast each. Could show by dividing each
piece of toast into quarters giving 𝟏𝟏
𝟒or could share 8 pieces of toast and
share the remaining 3 pieces of toast, e.g. 2 whole pieces, one half and one quarter per person.
Estimate: Correct answer is 2 eggs each if you don’t think you can share
a boiled egg or 2𝟏
𝟒eggs each if you think you can share a boiled egg.
Fractions, page 77:
What Fraction? 𝟏
𝟑
𝟏
𝟒
𝟏
𝟐
𝟏
𝟖
Different Number Lines:
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Fractions, page 78:
Explain: Example pairs of equivalent fractions: 4
10&
2
5
5
10&
2
4
Agree or Disagree? All thirds have an equivalent in sixths, for example2
3&
4
6. Some fractions in sixths don’t have an equivalent in thirds, e.g.
5
6
Read the Picture: Smallest to largest: 𝟔
𝟖
𝟒
𝟓
𝟓
𝟔
Fractions, page 79:
Which Answer? 1
12which is half of
1
6
Odd One Out: All are 𝟑
𝟒apart from the top-right square which is
𝟑
𝟖
Odd One Out: All are 𝟐
𝟑apart from the top-left number line which is
𝟑
𝟒
Fractions, page 80:
Agree or Disagree? Agree,1
6is equivalent to
2
12
Explain the Mistake: To find an equivalent fraction you must multiply or divide the numerator and denominator by the same number.
Small Difference Questions: 2
8=
1
4
4
8=
1
2
1
8<
2
4
Fractions, page 81:
How Many Ways? 9 ways: 1
2=
3
6
1
2=
6
12
2
4=
6
12
1
3=
2
6
1
3=
4
122
6=
4
12
1
4=
3
12
1
6=
2
12
2
3=
4
6
Explain the Mistake: 3
4is
1
4less than 1, whereas
5
6is
1
6less than 1. Therefore
5
6
is larger as it is a smaller amount less than 1.
Rank by Difficulty: Larger fractions (left to right): 1
4
4
6
9
10
3
4
Note the processes for comparing fractions. When the numerator is the same, fractions with a larger denominator are smaller. When the denominator is the same, fractions with a larger numerator are larger. For example 3, consider how much less than 1 each fraction is. For the
last example, compare the fractions by converting 3
4into eighths.
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Fractions, page 82:
Read the Pictures: Blue is 21
2circles. Yellow is 2
1
4circles. More blue.
Finish the Pictures: 31
2=
7
2which is shown by splitting circles into halves.
31
2=
14
4which is shown by splitting circles into quarters.
Explain: Order (smallest to largest): 11
5
10
4
18
6
10
3Note that the largest
fraction has the smallest denominator.
Fractions, page 83:
Small Difference Questions: 4 = 20
543
5=
23
553
5=
28
512
4= 3
15
4= 3
3
4
19
4= 4
3
4
Agree or Disagree? Agree. Note the same method for calculating
equivalent fractions applies to mixed numbers. Both fractions = 2𝟐
𝟑
Different Ways:11
4= 2
3
4and
11
5= 2
1
5Extend example:
15= 2
Fractions, page 84:
Explain the Mistakes: Mistake A: the quarters are not equal. Mistake B: 24 ÷ 3 = 8 Mistake C: the answer given is four-fifths
Finish the Pictures: Each question has multiple possible answers. Check
answers match bar models. Example answers: 2
3of 12 = 8
3
4of 40 = 30
3
5of 20 = 12
Fractions, page 85:
Two Ways: Example answers line 1: 1
3of 45 = 15
1
9of 45 = 5
Example answers line 2: 2
3of 24 = 16
2
4of 24 = 12
Example answers line 3: 3
4of 60 = 45
3
10of 60 = 18
I Know… so… Left to right: 60 186 90 180
I Know… so… Left to right: 48 192 32 96
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Fractions, page 86:
Small Difference Questions: Left column: 8, 16, 64, 68
Right column: 15, 30, 32, 64
Small Difference Questions: Left column: 6, 4, 8, 8, 16Right column: 16, 8, 24, 48, 24
Small Difference Questions: Left column: 120, 120, 120, 300Right column: 45, 180, 150, 175
Fractions + – ×, page 87:
Explain the Mistakes: Mistake A: the denominators have been added and a common denominator has not been found.
Mistake B: 1
4becomes
2
8so the numerator of the answer is 5
Small Steps: Common denominators: 5 12 20 or 2 50 24
Explain:3
4+
2
8= 1 as
2
8is equivalent to
1
4(not a mixed number)
5
10+
3
4is a mixed number as
5
10is equivalent to
1
21
2+
3
8is not a mixed number as
3
8is less than half
7
10+
2
5is a mixed number as
2
5is equivalent to
4
10and
7
10+
4
10= 1
1
107
20+
3
5is not a mixed number as
3
5is equivalent to
12
20and
7
20+
12
20=
19
20
Fractions + – ×, page 88:
Small Difference Questions: Left column: 3
6
5
61
Middle column: 7
8
13
16
13
16Right column: 1
1
20
29
40
36
40
Small Difference Questions: Left column: 5
9
6
9
8
91
Middle column: 9
20
15
20
7
10
19
40Right column: 1
8
12
9
16
15
16
Rank by Difficulty: Answers (left to right): 5
1212
51
5
18
9
12
16
20
Areas to discuss: the relative difficulty of finding a common denominator; questions which produce an answer of more than 1; note
that 2
4+
10
20is equivalent to
1
2+
1
2
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Fractions + – ×, page 89:
Different Ways: Convert 3
4into
6
8
1
2+
1
2+
1
4+
1
8Split
5
8into
2
8and
3
8
Different Ways: Example answers: 2
8+
1
2=
3
4
4
8+
1
4=
3
4
5
8+
1
8=
3
4
How Many Ways? 4 ways: 1
3+
1
6=
3
6
1
3+
1
3=
4
6
1
3+
1
2=
5
6
2
3+
1
6=
5
6
Fractions + – ×, page 90:
Explain the Mistakes: Mistake A: the denominators have been subtracted. Also, a common denominator has not been found.Mistake B: a common denominator needs to be found before subtracting the numerators.
Small Difference Questions: Left column: 4
6
2
6
9
12
Right column: 5
8
1
8
1
8or
2
16
Small Difference Questions: Left column: 7
811
8
7
8
Right column: 11
8
7
8
7
8
Fractions + – ×, page 91:
Explain: 13
10−
1
5is a mixed number as
1
5is less than
3
10
11
8−
1
4is not a mixed number as
1
4is more than
1
8
33
8− 1
3
4is a mixed number as less than 2 is being subtracted from more
than 3 so the answer will be more than 1
22
6− 1
1
3= 1 (not a mixed number)
Different Methods: 13
5−
7
10=
9
10can be done by subtracting
6
10then
1
10
11
2−
3
4=
3
4and can be done by halving
11
3−
5
6=
3
6and can be done by finding the difference
How Many Ways? 3 ways: 6
8−
1
2=
1
4
4
8−
1
4=
1
4
3
8−
1
8=
1
4
Extend: 1
2+
1
8=
3
4−
1
8
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Fractions + – ×, page 92:
Which Answer? Answer B is correct, the answer can be simplified to 4. The mistake in answer A is multiplying the denominator as well as the numerator. The mistake in answer C is only multiplying the denominator.
Different Methods: 21
10as an improper fraction. 2
1
10as a mixed number.
9
10less than 3.
Spot the Pattern:2
5× 5 = 2
3
8× 8 = 3 Multiplying by the denominator
makes the product the same as the numerator of the fraction.
Fractions + – ×, page 93:
I know… so… 3
4× 6 = 4
1
2(1
1
2more)
4
5× 7 = 5
3
5(4
5more)
2
7× 14 = 4 (
4
7more)
Rank by Difficulty: Answers (left to right): 5 83
481
426
7
Areas to discuss: the relative difficulty of multiplying mixed numbers and converting improper fractions into mixed numbers.
Different Ways: Example answers: 1
2× 3 = 1
1
2
1
4× 6 = 1
1
2
3
4× 2 = 1
1
2
Example answers: 1
3× 10 = 3
1
3
1
6× 20 = 3
1
3
2
3× 5 = 3
1
3
Fractions, decimals, percentages, page 94:
True or False? Correct answers: 1
5and
65
100
Which Answers: 0.05 = five hundredths and 5
100
0.006 = six thousandths and 6
1000
Odd One Out: 1
70.4
Fractions, decimals, percentages, page 95:
Two Ways: 1st number line: 0.05 or 5
1002nd number line: 0.03 or
3
100and
0.065 or 65
10003rd number line: 0.001 or
1
1000and 0.007 or
7
1000
How Many Ways? 4 ways: 1
3
2
5
3
10
4
10
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ANSWERS
Fractions, decimals, percentages, page 96:
Explain: Incorrect because the three sections must add up to 100% (ensure that children’s estimates total 100%).
I know… so… 1
2= 50%
1
25= 4%
1
10= 10%
1
50= 2%
1
20= 5%
1
5= 20%
1
4= 25%
Agree or Disagree? Only true statement is 1
10= 10%, because 100 ÷ 10 = 10
Percentages, page 97:
Odd One Out: 1
3
1
5
Rank by Difficulty: 1
5= 20% (calculate by doing 100 ÷ 5) 0.6 = 60% (note
misconception 0.6 = 6%) 0.52 = 52% 39
50= 78% (discuss strategies for
doubling 39)
Rank by Difficulty: 36
50= 72% (discuss strategies for doubling 36)
4
8= 50%
(4 is half of 8, therefore 50%) 6
10= 60%
7
25= 28%
Different Ways: 2 ways: 2
3
3
5
Measurement, page 98:
Contexts: Adult footprint, area, cm² Water in cup, volume, mlSkipping rope, length, cm Football pitch, area, m²
Which Answer? Suggested answers: size of carpet m², size of lamp post m, size of a bottle millilitres or litres, size of puddle litres.
Which Answer? Light years measure length (the distance light travels in one year).
Measurement, page 99:
Odd One Out: Centimetres are a measure of length. Ounces are an imperial measure. Kilograms measure relatively larger objects.
Agree or Disagree? Disagree: there are more yards than metres in the same length, so one yard must be smaller than one metre.
Explore: Left oval: litres. Centre: kilometres. Right oval: yards, inches. Outside: stones.
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Measurement, page 100:
Explain the Mistakes: To convert 25mm into cm, divide by 10. 3.8m = 380cm, the 8 needs to be in the tens column. To convert metres into km, divide by 1000. In this example, 800 is divided by 100.
Agree or Disagree? Correct answers for mistakes: 408cm = 4.08m1
2litre = 500ml
True or False? (a) True (b) False (0.7m is more than 600mm) (c) True
Compare: 6m = 600cm 6 yards = 216 inches 2.5m = 250cm2.5 yards = 90 inches Note: conversion between units is easier using metric measures.
Measurement, page 101:
Explain the Mistakes: Blue answer: it was before 2:10pm, not after. Red answer: error in calculation, possibly thinking half an hour = 50 minutes. Green answer: the time will be am, not pm.
Which Answer: (c) 6:05pm (b) 2 hours 35 minutes
Small Difference Questions: 100 minutes 200 minutes 300 minutes2 hours 30 minutes 4 hours 10 minutes
Measurement, page 102:
Compare: 6 weeks < 44 days 100 hours > 4 days 120 hours = 5 days3 months < 2400 hours 3 months > 12 weeks 3 months < 63 days
Multi-Step: 9 weeks Answers in the range 85→91 days
Multi-Step: QA (shortest to longest): 180 days, 1
2year, 27 weeks, 7 months
QB (shortest to longest): 3 months, 1
3year, 18 weeks, 140 days
Perimeter, Area, Volume, page 103:
Different Ways: 5cm + 3cm + 5cm + 3cm Double 5cm + 3cm
Order: Smallest to largest perimeter: square, rectangle, star.
Explain: Rectangle: 2 sides Square: 1 side Cross: 1 sideIsosceles triangle = 2 sides
Estimate: Actual perimeter = 20cm
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Perimeter, Area, Volume, page 104:
Explain: Small as possible: Large as possible:
Long sides matching short sides matching
I know… so… Top line (left to right): 11cm 13cmMiddle line (left to right): 16cm 18cm Bottom line: 18cm
Perimeter, Area, Volume, page 105:
Small Difference Questions: Left to right: 40cm 48cm 60cm
Explain: purple + orange = red black – blue = green Note that black + red = purple + blue + orange + green
Agree or Disagree? Perimeter = 46cm The bottom length = 9cm + 6cm and the two missing vertical lengths add up to 8cm.
Perimeter, Area, Volume, page 106:
Which Answer? 12 × 7 = 84cm² is correct. Blue answer is the perimeter. Green answer multiplies all the side lengths rather than length × width.
Agree or Disagree? True. Examples: a rectangle with dimensions 4cm ×3cm has an area of 12cm². 48cm² is four times bigger than 12cm².
Estimate: Blue arrow = 6cm Red arrow = 3cm
Perimeter, Area, Volume, page 107:
Spot the Mistake: The right-hand section of the shape is an area of6cm × 7cm = 42cm², not an area of 9cm × 7cm. Area of shape = 72cm²
Different Ways: Method 1: Add 4cm × 3cm Method 2: add 6cm × 5cm
Method 3: Subtract 6cm × 3cm Area = 62cm²
Perimeter, Area, Volume, page 108:
Spot the Pattern: All three shapes have a perimeter of 24cm. The narrower the rectangle, the smaller the area.
Shape A area = 36cm² Shape B area = 32cm² Shape C area = 20cm²
Same and Different: Part 1: Example rectangle 5cm × 5cmPart 2: Example rectangle 9cm × 2cm
Explain: Largest possible area = 49cm² from a 7cm × 7cm square (which
is a type of rectangle).
ANSWERS
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Perimeter, Area, Volume, page 109:
Same and Different: Part 1: Example rectangle 8cm × 3cmPart 2: Example rectangle 8cm × 5cmPart 3: Example rectangle 20cm × 2cm
Extend: A 6cm × 5cm rectangle has an area of 30cm² (larger than
27cm²) and a perimeter of 22cm (smaller than 24cm).
Perimeter, Area, Volume, page 110:
True or False? False: there are 16 cubes (4 × 2 × 3). Note that 20 is the
number of squares that can be counted on the faces that are visible.
True or False? The blue statement is true. The red statement is false.
Explore: Dimensions of completed cuboid: 3 × 3 × 2
How Many Ways? 3 ways: cube dimensions 4 × 4 × 1 4 × 2 × 2 3 × 3 × 2
Angle, page 111:
Order: Smallest to largest: green, blue, red. Note: the green angle is the smallest even though the lines are longer and the angle marking is wide.
Explore: Acute angles = red, right-angles = blue, obtuse angles = green
Explain: Acute angles = red, right-angles = blue, obtuse angles = green
Angle, page 112:
Explain the Mistakes: 84˚: read the wrong scale.122˚: the angle is 2˚ less than 120˚, not 2˚ more. 40˚: protractor not lined up with the bottom line.
Which Answer? 133˚ is correct. The mistake with 47˚ is reading the wrong side of the protractor. The mistake with 127˚ is thinking the angle is 3˚ less than 130˚.
ANSWERS
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Answers
From vertex, lines 3← 3↑ and 3→ 3↑, creates right-angle
From vertex, lines 1← 4↑ and 5→ 1↑, creates obtuse angle
From vertex, lines 4← 1↑ and 2 ← 4↓, creates acute angle
From vertex, lines 4← 1↑ and 4→ 1↑, creates right-angle
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Angle, page 113:
Which Answer? (a) 245˚ (b) 76˚
Explain: Angle B is smaller than angle C. There is more to add to angle D to make 180˚ so angle C must be larger.
Small Difference Questions: E = 26˚ F = 116˚ G = 112˚ H = 292˚
Angle, page 114:
Small Difference Questions: J = 104˚ K = 104˚ L = 74˚ M = 164˚ N = 144˚
True or False? (a) False, 90˚ × 4 = 360˚, acute angles are less than 90˚
(b) True, sum of two acute angles is less than 180˚, 3rd angle is reflex. (c) False, sum of two obtuse angles is more than 180˚, 3rd angle is obtuse. Extend: 3 obtuse angles.
Always, Sometimes or Never? Individual angles of a triangle could be larger than individual angles of quadrilaterals (triangles can have obtuse angles). However, the sum of the angles in a triangle is always 180˚ and the sum of the angles in a quadrilateral is always 360˚.
Angle, page 115:
Multi-Skill: 7:10am = obtuse 4pm = obtuse 9am = right-angle9:30pm = obtuse 8:55pm = acute
Which Answer? (a) 150˚ (5 × 30˚)
(c) 15˚ (the hour hand is half-way between 6 and 7 which is 15˚)45˚, the hour hand is half-way between 4 and 5 which is 15˚, plus the 30˚ between 5 and 6
Multi-Skill: Left to right: 30˚ 120˚ 15˚ 20˚ (the hour hand is 1
3the
turn between 3 and 4, which is 10˚, so 20˚ between the hands)
Shape, page 116:
Small Difference Questions: Top line (left to right): 4 2 1Bottom line (left to right): 1 (diagonal bottom-left to top-right) 0 0
Explain: Example answers: All four shapes are hexagons. Three shapes have at least one line of symmetry (not 4th shape). Two shapes have at least one reflex angle (1st and 3rd). One shape is a regular hexagon (2nd).
Odd One Out: Example answers (left to right): Has acute angles. Is a hexagon. No lines of symmetry. No reflex angles.
ANSWERS
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Shape, page 117:
Explain: Left to right: the triangle isn’t: it has unequal angles and one unequal side length. The diamond isn’t: it has unequal angles. The next 3 shapes are regular. The pentagon isn’t: is has unequal angles and side lengths.
Explore: Examples:
Shape, page 118:
Odd One Out: Example answers: A cuboid doesn’t have 5 faces. A triangular prism doesn’t have a square face. The triangular pyramid is not a prism.
Small Difference Questions: A cuboid has 1 more face, 3 more edges and 2 more vertices than a triangular prism. A square-based pyramid has 1 more face, 2 more edges and 1 more vertex than a triangular pyramid.
ANSWERS
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Answers
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Shape, page 119:
Correct or Incorrect? Correct correct correct incorrect
Correct or Incorrect?
Position, Direction, Coordinates, page 120:
Explain the Mistakes: Mistake 1: translated, not reflected. Mistake 2: incorrect distance from the mirror line. Mistake 3: middle vertex different
Which Answer? Top left: rotated Top right: translatedBottom left: reflected Bottom right: either reflected or translated
Position, Direction, Coordinates, page 121:
Explain: Left example: may have been translated or reflectedRight example: reflected
Explain the Mistakes: Mistake 1: translation is 3 squares right, not 2Mistake 2: left vertex not positioned correctly
Position, Direction, Coordinates, page 122:
Different Ways: The blue dot is positioned in a ratio 3 along, 5 up. Possible coordinates include (6,10) and (30,50) and realistic estimates. Not correct examples are (5,3) as y coordinate is more than x coordinate and (4,5) as the ratio of the lengths is not correct.
Estimate: Blue = (8,5), red = (4,2), accept realistic estimates.
Estimate: Purple = (18,8), green = (36,18), accept realistic estimates.
ANSWERS
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Answers
faces overlap
3 square faces
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Position, Direction, Coordinates, page 123:
Agree or Disagree? Blue coordinate correct. Red coordinate incorrect, the correct coordinate is (0,6).
Explain the Mistake: The x coordinate is correct (7 is half-way between 0 and 14). The y coordinate is incorrect. The mistake comes from halving the second y coordinate of 8. To calculate the correct y coordinate,
find half-way between 4 and 8 which is 6. Correct coordinate = (14,6).
Which Answer? (9,3) inside (2,6) outside (8,7) edge
Position, Direction, Coordinates, page 124:
Different Answers: Corners: (4,4) (8,4) (8,8) (4,8) Examples for edges: (6,4) (8,6) Examples for inside: (6,6) (7,6)
Different Answers: Corners: (13,8) (13,3) (5,3) Examples for edges: (10,8) (13,5) Examples for inside: (9,5) (6,7)
Statistics, page 125:
What’s the Question? 1. What time does the first train arrive at Stockport? 2. At what time does the third train leave Macclesfield? 3. How long does the journey take from Stockport to Manchester Piccadilly?
Multi-Step Question: Helen needs to travel to Cannock on the second train, arriving 15:58. This train leaves Wolverhampton at 14:56. She therefore needs to get on the first train from Crewe, leaving at 13:56. There are two train timetables because there isn’t a direct train from Crewe to Cannock.
Statistics, page 126:
Fill the Gaps:
Explain: Temperature in garden: line graph. Number of different vegetables: bar graph. Rainfall per month: line graph.
ANSWERS
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Answers
6
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Statistics, page 127:
Which Graph? Children in each class: bottom right (bars are similar sizes). Shoe size: top left (some children have large/small feet; most have shoe sizes nearer the average). Age of children in Y5/6 class: top right graph (all children either 9, 10 or 11). Favourite fruit: bottom left (no pattern in size of bars).
Which Graph? Speed of 100m runner: top graph (fastest speed, acceleration from standing start). Speed of runner in hill race: left graph (variation in speed). Speed of marathon runner: right graph (relatively constant speed).
Statistics, page 128:
Act the Graph: Increase in speed at approximately 10 seconds and 30 seconds to reflect rise in graph.
Act the Graph: Facial expression to show increased fear at approximately 7 seconds and 14 seconds to reflect rise in graph. The last 5 seconds are more relaxed.
Statistics, page 129:
Which Answer? (c) this is not the top speed but the athlete continues running afterwards so it’s part-way through the race.
Which Answer? (a) the distance travelled stays the same so the cyclist has stopped.
ANSWERS
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A range of resources for developing deep, visual
mathematics can be found at www.iseemaths.com
The full range of I See Reasoning eBooks can be
found at www.iseemaths.com on the Products tab.
The I See Problem-Solving eBooks are also
available.
For more information, click on these link:
I See Problem-Solving – UKS2
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iPad app Logic Squares gets children applying
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children complete crossword-style number
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