Level 1 to 2
Can I round a
two-digit
number to the
nearest 10?
•
1 CUN
•
If I am on number 14 on a number line, what is the nearest multiple of
10?
Is 36 closer to 30 or 40? Can you explain why?
Which of these numbers round to 30? 32, 36, 22, 34, 27 How do you
know?
Can you tell me two different numbers that round to 20?
I have 22 rabbits. Do I have about 20 or about 30 rabbits? Why?
What numbers between 21 and 30 round to 30? Why?
Can you explain how you round these numbers to the nearest 10?
12, 16, 25, 31, 49
Which of these numbers round to the same multiple of 10? 29, 22, 18
•
•
Put these numbers in the right place on this number line; 50, 90, 20,
25, 75. How did you decide where to put them?
•
•
Show me where the number 17 goes on this number line. How do you
know?
•
•
•
•
•
•
Can I show
where a whole
number is on a
0 to 100
number line?
Opportunities to use and apply
Possible contexts include:
Review questions
Reading scales, e.g. approximating a measurement to the nearest 10
units.
• Approximating calculations, e.g. what is the approximate total of 32
and 21? How does rounding help you to work it out?
• Calculations involving bridging through the next multiple of 10, e.g.
what is 17 + 8? Show how you can work this out using two jumps on the
number line by partitioning the 8 into 3 and 5.
•
•
•
•
•
•
2 CUN
•
•
•
Which tens number is 57 closest to?
• On a 100-bead string, show me a quick way to find 19. Explain how you
did it.
Confirming learning
Ask probing questions such as:
•
•
Science, e.g. monitor the growth of sunflowers and then represent
their changing heights on a 0-100 number line.
PE, e.g. record standing long jump measurements on a metre stick
marked in centimetres.
Length, e.g. what length does this mark between 10cm and 20cm on
the ruler show?
Reading scales, e.g. use a metre stick to find an object that is longer
than 27cm.
Weight, e.g. this scale shows the weight of some parcels. How much
do they weigh?
Mark and write a number on the number line that is just after 70.
What number did you choose? What about just before 40?
• What number do you think the arrow is pointing to? How did you
decide?
Look at these numbers: 39 42 51 64 43 34. Which of the numbers lie
between 35 and 50 on the number line? How do you know?
• How does knowing where number 10 is on a number line help you to
know where number 15 goes?
• Explain to me how I could work out where to place 17 and 71 on this
number line.
•
•
What numbers do you think the arrows are pointing to? Explain your
thinking.
•
Think of three numbers that could be placed between the two arrows.
Are there any others?
•
Can I tell
someone how
to order twodigit numbers?
3 CUN
•
Put these numbers in order from largest to smallest. 35, 24, 47, 32,
28 Now explain how you did it.
These numbers are in order, smallest to largest, but one of them is in
the wrong place. Which one is it? Where should it go? 23, 36, 46, 39,
47, 55
Explain how you could find a two-digit number that is bigger than 27
but smaller than 45.
These numbers are in order, largest to smallest. 56
45
37
33 Think of a number that could go into each of the empty boxes.
How do you know whether 56 is larger or smaller than 65? What
number could you place between these numbers?
• Tell me how to put these in order from largest to smallest.
50p, 54p, 40p, 55p, 45p
•
Money, e.g. comparing costs by ordering items from the cheapest to
the most expensive.
• Measures, e.g. comparing lengths by ordering them from shortest to
tallest/longest.
• PE, e.g. ordering the lengths of standing long jumps (cm) or the time
taken (seconds) to run a short distance.
• Finding all possibilities, e.g. how many two-digit numbers can you make
using the digits 5, 6, 7 and 8? Put them in order from smallest to
largest to help you check whether you have found them all.
•
Dee was saving up for a computer game costing £40. She had saved
£36. She decided she had nearly enough money. Was she correct?
Why?
Nicky had collected 74 stickers. She said she had about 70
altogether. What did she mean?
What is the largest number that rounds to 60? Why?
What is the smallest number that rounds to 60? Why?
Ben says he can think of 9 different numbers that you can round to
20. Show me why you agree or disagree with him.
I think of a number and round it to the nearest 10. The answer is 50.
What could my first number be? What other numbers could it be?
When you order a set of two-digit numbers, do you look at the units
digit or the tens digit first? Why?
• Would you rather have £75, £76, £67 or £66? Why?
• I need to order these numbers from smallest to largest. Can you
explain to me how to do it? 36, 63, 66, 35, 69, 39
• These numbers are ordered, largest to smallest. Place numbers that
•
could go in the empty boxes. 87
85
78
76
44
41
Did you always have a choice of numbers for a box? Why?
• I am thinking of a two-digit number. It is larger than 60, smaller than
80 and has the digit 2 in it. What number could it be?
Level 1 to 2
Can I partition
a two-digit
number into
tens and ones
(units) and use
this to create
related
addition and
subtraction
sentences?
Opportunities to use and apply
Possible contexts include:
Review questions
Use some place-value cards to make 16. What is it made up of? How
would you make 61?
• If I partition these numbers into tens and ones, which has the most
tens and which has the most ones? 18, 27, 94, 56, 77
• What two-digit number would these place value cards make?
•
5 CUN
Can I count on
and back in
equal steps and
explain the
patterns?
Can you fill in the missing numbers? 90 +
= 94
70 =
−5
Reasoning about numbers, e.g. use a set of 0-9 number cards to make
some two-digit numbers. What are the five largest two-digit numbers
you can make?
• Working out related number sentences, e.g. if you partition 23 into
tens and ones what addition and subtraction number sentences can
you make with the numbers?
• Calculation, e.g. how can partitioning help you to add 37 and 23? What
about 48 + 25?
What can you tell me about the digits in this number (14)? What
about this number (41)? What is the same and what is different about
these two numbers?
• Complete these number sentences.
•
•
•
•
Which number goes into the empty box? Can you tell me without
counting?
4 CUN
Can I partition
one and twodigit numbers
in different
ways?
Word problems and puzzles, e.g. I had 45p and spent 40p on a pen.
How much did I have left?
• Dad baked some cakes and then our dog got into the kitchen and ate
10 of them! We've only got 7 left. How many cakes did Dad bake?
•
Confirming learning
Ask probing questions such as:
•
Can you complete these number sentences? What do you notice?
•
10 + 4 =
14 −
= 10
14 =
+4
− 10 = 4
What two-digit number is the same as six tens and four ones (units)?
Gina had 9p to spend on two items. What could they have cost each?
How many different pairs of numbers can you find that total 8?
• Alex made two jumps on a number line and landed on 7. What could his
two jumps have been?
•
•
•
18 + 6 =
•
Here is one way of making 41p. Can you think of other ways?
•
Fill in the empty boxes: 87 =
•
87 =
+ 37
This bead string shows one way of partitioning 54 into some tens and
ones. What other ways can you think of?



6 CUN


How could you partition 6 to help answer this question?
+ 7; 87 =
+ 17; 87 =
Solving problems or puzzles, e.g. how many different dominoes are
there with a total of 9 spots? Do you think there are more or less
dominoes with a total of 7 spots?
• Write as many ways as you can of adding two numbers to make the
number 30.
• Calculations involving partitioning single-digit numbers to cross a tens
boundary, e.g. 27 + 7 = 27 + 3 + 4 = 34 and 32 − 6 = 32 − 2 − 4 = 26
•
What numbers are missing? 60, 50,
check?
, 30, 20,
•
•


. How can you
The yellow numbers show the beginning of a number sequence.
What are the next three numbers? Explain your thinking.
•
•
Partition 9 in as many ways as you can. How do you know you have
found them all?
• How many different ways can you partition 46 into tens and ones?
Write the number sentences to match the different ways.
• How can partitioning the one-digit number help you calculate 26 + 7 or
45 + 6?
•
•
•
What number comes next? 20, 18, 16, 14...? How do you know?
How would you describe this sequence to someone else? 7, 17, 27,
37, 47...
•
Fill in the missing numbers in these addition calculations: 67 =
30 + 19 =
+ 27;
What number comes next in this sequence? 2, 4, 6, 8... What about
this sequence? 1, 3, 5, 7... What is the same about and what is
different about these sequences?
•
10 = 16 −
; 16 −
= 6; 16 = 10 +
; 10 +
= 16. Now make up some
similar sentences that use the number 41.
Tara wrote the number twenty-two like this; 202. How would you
write this number? Why?
Jenny wrote 30 + 9 = 309. What could you do to help Jenny?
In one step (operation) change 49 to 9. What did you do?
What makes 60 and 67 different?

Finding missing numbers in calculations, e.g. 67 = 30 + 30 +
+ 2.
Money, e.g. how many different ways can you find to make 32p?
Identifying patterns in number sequences, e.g. choose your own
starting number and make up your own sequence that counts on or
back in fives. What do you notice abut the numbers in your
sequence? Start the sequence from the number that is one more
than you started with last time. What do you notice now?
Counting in equal steps to solve mathematical problems, e.g. Emma
had some fireworks. Some made 3 stars and some made 4 stars.
Altogether the fireworks made 19 stars. How many of them made
3 stars?
Investigating a general statement to decide whether it is always,
sometimes or never true, e.g. when I count from zero in twos all of
the numbers I say are even. When I count from zero in fives all of
the numbers I say are odd.
+ 28; 50 +
= 10; 25 − 15 =
; 31 = 51 −
+ 7;
= 76.
What numbers are missing from these subtractions? 15 −
23 −
•
; 48 =
= 10;
.
Explain how you would partition 6 to answer 44 − 6 =



Count on in tens from 5. Will you ever say number 72? Why not?

5, 10, 15, 20,
, 30,
, 40,
, 50. What do you notice about all
the missing numbers in this sequence? Why is this?

Describe this sequence to your maths partner and see if they can
write it down: 45, 35, 25, 15, 5. You can only say the first number
in the sequence and then describe the pattern.

Here are some numbers in my sequence 13, 15, 17, 19. What
numbers come next in my sequence? What numbers come before?
Give me a number greater than 30 that is in my sequence. How do
you know this number is in my sequence? How could you check?
Count back in tens from 92. Will you say 32? How do you know?
,
,
, 14, 12, 10, 8,
. What numbers are missing? How can
you work it out? How can you check your answers?
Level 1 to 2
Can I recall all
addition and
subtraction
facts for each
number to 10?
7 KNF
Opportunities to use and apply
Possible contexts include:
Review questions
•
What addition sentences could you write to match the pegs on this
coat hanger?
•
What is 8 subtract 3?
Patterns in calculation, e.g. What is 5 + 4? How can it help with 15 + 4,
25 + 4, 35 + 4? What do you add to 6 to make 10, to 16 to make 20, to
26 to make 30? What is 6 − 2? Can you use this to work out 16 − 2 and
26 − 2?
• Using inverse operations, e.g. I thought of a number and subtracted 3.
The answer was 6. What was my number? How do you know?
• Word problems, e.g. write numbers in the boxes to make these
•
number stories true: Sam has
stickers and Kate has
Altogether they have 7 stickers.
+
= 9. What could the missing numbers be?
How many different pairs of numbers can you remember that have a
total of 7?
• If there are 10 counters altogether, how many are hidden in the pot?
What subtraction sentence could you write to show this?
•
•
Can I recall all
pairs of
numbers that
total 20?
8 KNF
Can I count on
in twos, fives
and tens and
use this to
begin to say
multiplication
facts?
9 KNF
•
If you know 7 + 3 = 10, what is 10 − 7 and 10 − 3?
•
10 =
•
What addition sentences could you write to match the beads on this
bead string?
•
What is 20 subtract 15?
There are 9 people on the minibus.
+
= 20 What could the missing numbers be?
• If you know 17 + 3 = 20, what is 20 − 17 and 20 − 3?
• If there are 20 counters altogether, how many are hidden in the pot?
What subtraction sentence could you write to show this?
•
How many different pairs of numbers can you remember that have a
total of 20?
•
20 =
•
Count in tens along the counting stick until you reach the arrow. What
are five tens?
stickers.
•
are left?
sentence with a total of no more than 9. 7, 3, 2, 6, 5.
+
=
How many different pairs of numbers can you remember that have 6?
How can you be sure you have got them all?
Using inverse operations, e.g. I thought of a number and subtracted 6.
The answer was 14. What was my number? How do you know?
• Word problems, e.g. write numbers in the boxes to make these
number stories true:
•
Petra has
20 beetles.
•
beetles and Kate has
beetles. Altogether they have
There are 20 people in the lift.
get out,
are left.
Finding all possibilities, e.g. using a set of 0–20 number cards, how
many different pairs can you find that total 20?
Anna says she can think of ten different pairs of numbers that have a
total of 20. How can you find out whether she is right?
• Write one of these numbers into each box to make an addition
•
sentence totalling 20. 5, 9, 14, 3, 15, 17
+
= 20
Are there different ways to do it?
• How does 6 + 4 = 10 help you to find a related pair of numbers that
total 20?
• Fill in the missing numbers for these pairs that total 20:
14 +
= 20,
4+
= 20,
6+
= 20, 6 +
= 20
What do you notice?
• What number sentences can you say and write using 5, 20 and 15?
+ 13
Count on in twos from 0 to 12. How many twos did you count? How can
you say this as a multiplication fact?
• What are four fives? Count up in fives to find out. How many fives
are in 20?
• What are three twos? How many twos are there in 6? What number
sentences can we write for this?
•
•
get off,
Anna says she can think of four different pairs of numbers that have
a total of 8. How can you find out whether she is right?
• 3 + 4 = 7. Can you make two subtraction sentences using these
numbers?
• Using numbers up to 10 find as many subtraction facts as you can with
an answer of 5.
• Write one of these numbers into each box to make an addition
•
+4
•
•
Confirming learning
Ask probing questions such as:
2×7=
6 × 10 =
5×5=
How did you work out your answers?
What is 5 multiplied by 2? Show me how you can quickly find the
answer to this question.
Practical activities, e.g. counting sets of interesting objects
(vouchers, marbles, etc.) by putting them into groups of ten and then
counting them in tens to find how many there are. Adding small values
of coins by putting them into groups of 10p.
• Word problems, e.g. balloons come in packs of 10. I've bought 6 packs.
If 65 children are coming to my party will that be enough for
everyone to have a balloon?
We are planting bulbs, 5 to a pot. How many bulbs do I need to fill 5
pots?
• Puzzles, e.g. I've got 5 coins in my pocket. They are 5p and 10p coins.
How much money could I have? What if I had 6 coins?
• Patterns in numbers, e.g. On a 100-square count up to 50 in fives.
What patterns do you notice? Which of the numbers that you counted
are in the ten times-table as well?
•
•
•
•
•
•
•
•
Think of a number bigger than 50 that would be in the 5 times-table.
Why do you think that number would be in the table?
What tips would you give someone to help them remember the 10
times-table?
If I count from zero in fives which of these numbers will I say: 20,
33, 40, 45? Explain your thinking.
How do you know if 16 is in the 2 times-table? What other numbers
between 10 and 20 are in the two times-table? How do you know?
If there are 30 children in a class, could they get themselves into
pairs? What about teams of 10? How many teams would there be?
What about teams of 5?
6 × 2. Sam can't think of a quick way to answer this question. How
could you help him?
What multiplication sentences can you say and write using 4, 5 and
20?
Level 1 to 2
Can I say what
needs to be
added to a
two-digit
number to
make the next
multiple of
ten?
10 C
•
Show me 36 on a bead string. What do you need to add to 36 to make
the next multiple of 10? How do you know? What number fact to 10 is
helpful?
32 +
= 40
What must I add to 14 to make 20? What addition bond to 10 could
help?
• What is 30 subtract 27? How did you work that out?
• What could the missing sign and number be on this number line?
•
•
•
Can I add and
subtract a
multiple of
ten?
What is the difference between 6 and 10? What about 16 and 20, and
26 and 30? Which number fact are you using each time?
Start at 34 and count on three lots of ten. Show that on a number
line. Where do you land? Now write that as a number sentence.
• What is 23 + 10? 23 + 20? 23 + 50?
• Complete the empty boxes.
•
11 C
•
= 26 + 20
Altogether Sam and Annie have 96p. If Sam has 66p how much money
must Annie have?
What is 56 − 10? 56 − 30? 56 − 50?
Subtract 30 from 56. What did you write, draw or imagine to help
you?
Fill in the empty boxes.
•
What is 17 + 3? 17 + 4? 17 + 5? How did you work these out?
•
•
•
12 C
Calculations that involve counting on to find the difference, e.g. 32 −
28, 41 − 27 How could knowing what to add to make the next multiple
of 10 help you to find the difference between these pairs of
numbers?
• Calculations that involve crossing a multiple of 10, e.g. solving 24 + 8
by partitioning the 8 into 6 and 2 (and so working out that 24 + 6 = 30
and 30 + 2 = 32).
• Word problems, e.g.
It is 50 miles to London from our house. We have travelled 46 miles.
How much further is there to go?
My brother weighed 43kg a few months ago and now he is 50kg. How
much weight has he put on? How did you work it out?
• Measures, e.g. how much further does the plant need to grow to reach
50cm? How much longer does your standing long jump need to be to
reach 50cm?
•
Word problems involving money and measures, e.g. the bike I want to
buy costs £85. I have saved £55. How much more do I need to save?
A plant is 48cm tall. It grows another 30cm. How tall is it now?
• Sequences, e.g. Complete these sequences:
•
, 23, 33, 43,
,
,
, 55, 75, 95
Find examples that satisfy a statement, e.g. When I subtract 20 from
a number the units number stays the same.
• Explaining reasoning, e.g. Count on in tens from the number 27. Will
the number 85 be in the count? How do you know? Use some
equipment or an image to help you explain.
• Add or subtract a near multiple of ten, e.g. work out that 35 + 19 = 54
because it is the same as 35 + 20 − 1.
Confirming learning
Ask probing questions such as:
•
What is the total of 28 and 5? Do you need to count on in ones? How
can you partition 5 to help?
• How can you work out 27 + 6? Can you work it out using two steps?
Show me your steps on a number line.
• What is 23 − 3? 23 − 4? 23 − 5? How did you work each of these out?
•
What is 42 subtract 5? Do you need to count back in ones? How can
you partition 5 to help?
• How can you work out 24 − 6 using two steps? Show me your steps on
a number line.
•
Problems involving money and measures, e.g.
5cm is cut off the following lengths of ribbon: 37cm, 34cm, 31cm,
39cm, 36cm, 32cm, 38cm. Which will be shorter then 30cm?
Sam's best long jump so far was 75cm. Today he jumped 8cm further.
How far did he jump? His friend has really long legs and jumped 8cm
further than Sam jumped today. How far was that?
• Problems involving time, e.g. It is 15 March today. What will the date
be in one week's time?
• Number sequences, e.g.
•
How would you work out the missing number in 23 +
= 40? What
about 60 −
= 55? What about 60 –
= 45?
• Look at this number sentence, 54 + 6 = 60. Ben said that he worked it
out by putting the biggest number in his head and then counting on
using his fingers. Ali said that she found it really easy to work out
because she knew that 4 + 6 =10. What did she mean?
• 50 − 7. Saida said that she used her fingers to count back 7 from 50.
Her answer was 44. Was she right? How would you work out the
answer?
• What calculation might this be? Explain why? Could it be a different
calculation?
•
•
•
Can I add or
subtract a
one-digit
number to or
from a twodigit number
(bridging
through a
multiple of
ten)?
Opportunities to use and apply
Possible contexts include:
Review questions
What could the missing sign and number be on the jump on this
number line?
•
Is there more than one possibility?
David said that 17 + 20 = 19. Can you think of what he might have done
to get this answer? How would you show him how to find the answer?
•
What could the missing numbers be?
is 10 less than
,
is 20
more than
What other numbers could you choose?
• When I subtract a multiple of 10 from a two-digit number the units
number always stays the same? Is this true?
Sanjay drew two jumps on a number line to help him work out 48 + 7.
What size jumps do you think he used? Why?
• Rosie worked out 45 − 7 and got an answer of 42. Is she right? What
do you think she did? Can the answer be more than 40? Why?
• Jamie added a number to 37 and got the answer 44. How much did he
add on? How might he have done it?
• Explain how you would partition 5 when adding it to these numbers:
26, 27, 28 and 29. Explain how you would partition 6 when subtracting
it from these numbers: 21, 22, 23 and 24.
•
•
Sam was trying to solve 47 +
= 52. He drew these jumps on a
number line. What do you think the two jumps were and why?
Level 1 to 2
Can I find the
difference
between a pair
of numbers?
13 C
What is the difference between 20 and 17? What number fact could
you use to help?
• How many more is 11 than 3?
• How many less than 18 is 7?
• How could you work out 25 subtract 16?
•
•
•
•
•
•
•
•
•
Can I write
addition and
subtraction
sentences that
use the same
three numbers
and explain
how they are
linked?
14 C
Can I record
number
sentences and
explain what
the signs and
numbers mean?
15 C
Opportunities to use and apply
Possible contexts include:
Review questions
11 +
= 14
How many more do you need to add to 27 to make 35?
56 − 48 = 8. Can you read this number sentence and use the word
difference?
Make two rows of cubes with a difference of 5.
Find three pairs of numbers with a difference of 10.
If you are 6 and your brother is 13, how much older is your brother?
I have read 7 of the 20 pages in my book. How many more pages must
I read to finish the book?
You buy a banana for 26p and give the shopkeeper 30p. How much
change will you get?
•
Say two addition and two subtraction sentences to link the numbers 3,
5 and 8.
•
Complete these number sentences;
5+
= 9;
+ 4 = 9; 9 –
= 5; 9 –
=4
What do you notice?
• Draw jumps on a number line to show 9 − 3, 6 + 3, 3 + 6 and 9 − 6.
• Write two addition and two subtraction number sentences to link 10,
4 and 14.
•
What addition and subtraction sentences can you write for this
number line?
•
Use 1, 4, 5 and + , − , = . How many different calculations can you
write?







20 =
+ 7 What number is missing? How do you know?
10 −
= 6 What number is missing? How do you know?
Questions involving reasoning, e.g. the difference between two
numbers is 5. What might the two numbers be? Can you think of at
least three other pairs of numbers where the difference is 5? How
did you find these pairs of numbers?
Measures, e.g. Measure the length of your shoe and your friend's
shoe to the nearest centimetre. Which shoe is longer? How much
longer?
Data, e.g. ask questions that involve finding the difference between
data represented on a pictogram or block graph.
Problem solving, e.g. what do you notice about pairs of numbers that
have a difference of 10? Why is this?
Word problems, e.g. A coach has fifty seats. If a class of thirty-four
children go to the zoo, how many adults could go with them?
Calendars, e.g. it is 17 May. How many more days is it until 25 May?
•
Solving problems involving inverses, e.g. I think of a number, I
subtract 9 and the answer is 20. What is my number? How did you
work it out?
• Using inverses when calculating, e.g. what addition facts could you use
to help you calculate these? 10 − 6, 20 − 8
•
•
•
•
•
•
•
•
Checking, e.g. 14 +
= 25. What is the missing number? How do you
know? What subtraction could you do to find the missing number?
• Reasoning, e.g. if you give me any addition number sentence I can
write one more addition sentence and two subtraction sentences using
the same numbers. Is it sometimes, always or never true?
• Word problems, e.g. eighteen children are on a bus. At the bus stop,
five children get off and five children get on. How many children are
on the bus now? How do you know?
•

The total of 5 and 6 is 11. How can you write this as a number
sentence?
+
+
+×−=
Choose a sign to put in each box to make this correct.
16
4

Are there other pairs of numbers you could have used?
What numbers could go in the empty boxes? 17 +
12
=
+
=
O
Look at this number sentence, 23 =
− 7. What number is missing?
How did you work it out?
• Use a number line to help explain how you would find the difference
between 15 and 33.
•
Catherine said that 32 − 27 = 6. Is she correct? Which addition
calculation could she use to check her answer?
• Annie's teacher asked her to write two addition and two subtraction
number sentences to link the numbers 3, 5 and 8. She wrote these:
3 + 5 = 8, 5 + 3 = 8, 5 − 3 = 8, 3 − 5 = 8
Are they correct? Explain your thinking.
• Only one of these subtractions is correct. Which one is it? Explain
how you know using the link between addition and subtraction.
30 − 7 = 25, 28 − 5 = 18, 25 − 6 = 19, 14 − 4 = 12
• Ling wants to check her answer to this subtraction: 73 − 45 = 28
Which of these tells Ling that her answer is correct?
A. 73 + 45 = 118, B. 45 + 28 = 73, C. 28 + 73 = 91

20 = 15 +
Sally thinks the answer might be 35. Is she correct? Could the
answer be bigger than 20? Why not? What mistake might she have
made? What is the answer? How did you work it out?

Think of your own numbers to make a number sentence like this:
=
+
Choose three numbers for the square boxes and use + or − in the
circles to make this number sentence correct.
O
The difference between 25 and 33 is 8. How could you write this as a
number sentence? What other words could you use to read this
number sentence?
• How could you find the difference between 17 and 24? What number
facts might you use to help? What is the difference between 27 and
34? What do you notice? Work with a partner to find other pairs of
numbers with the same difference. Do you notice a pattern?
• Look at these numbers 25, 32, 34, 31, 27.
Find the pair of numbers with a difference of 5. Make up a similar
problem for someone else to answer.
+
=
–
Use the numbers 3, 4, 6 and 7 to complete the following number
sentence:
= 14 + 10 What number is missing? How do you know?
9=
Balancing equations, e.g. use the numbers 3, 5 and 8 to complete
the following number sentences:
Write numbers in these boxes to complete this number sentence:
Confirming learning
Ask probing questions such as:
= 11
Problem solving, e.g. these two dominoes have the same total
number of spots. How many spots are hidden?What
numbersentences could you write?
How did you choose your numbers?

19 = 15 + 4. Marc says this number sentence is wrong because it
has been written the wrong way round. Do you agree with him?
Why?

Use numbers and symbols to write 'seventeen add nine equals
twenty-six.' Can you think of another way to write it?

How many ways can you think of to say this number sentence? 23 −
5 = 18
= 27

−
Level 1 to 2
Opportunities to use and apply
Possible contexts include:
Review questions
Can I work out
and record the
information I
need to use to
solve a puzzle
or problem?
What calculation would you do to answer each of these problems?
16 C








A cheese string is 12cm long. I bite off and eat 4cm. How long is
the cheese string now?
My brother has five bags of 10 conkers. How many conkers does he
have altogether?
Five children can sit at one table. There are 25 children. How many
tables are needed?
Draw a picture or diagram to explain how you would solve one of
the above calculations.


Solving real-life problems, e.g. organising teams for PE, sharing out
items between tables, working out what you can buy with your
pocket money.
Making up number stories using given information or contexts, e.g.
write a number story about pets using addition and the numbers 6,
4 and 10. Now write a story using the same numbers and
subtraction. Can you use the numbers 5, 10 and 50 to write a story
involving division or multiplication?
Solving two-step problems, e.g. there are 60 sweets in a bag; 20
sweets are red, 16 sweets are yellow and the rest are green. How
many sweets are green?
Selecting numbers to make number stories true, e.g.
Sam has
stickers and Kate has
7 stickers.
Explore different ways of making 20p using 2p, 5p and 10p coins.
Record your working so that a friend can follow it. How could you
check that you have found all the possibilities?
Class 3 has


Think of your own word problem to match the calculation 23 − 14.

What important things do you need to think about when solving
word problems? What clues help you to work out which number
sentence to use?


stickers. Altogether they have
boxes of 10 pencils. Altogether they have
A pencil costs 20p and a ruler costs 35p. What word problems
could I ask based on this information? Can you write down the
number sentence to match each of your word problems?
Explore different ways of making 12p using 2p, 5p and 10p coins.
Record your working so that a friend can follow it. How could you
check that you have found all the possibilities?
Investigate different ways of making 50p using only 5p, 10p and
20p coins. How many different ways can you find? Record each
different way of doing it.
pencils.
I think of a number and add 8. My answer is 24. What was my
number? What could I record to help me solve this problem?
Three birds laid some eggs. Each bird laid an odd number of eggs.
Altogether they laid 19 eggs. How many eggs did each bird lay?
What practical equipment or drawings could you use to help you
solve this puzzle?

Count from zero in tens to 50. How many tens did you count? How
many tens are there in 50?
17 C

How many 5s are in 20? How do you know? How could you write this
as a number sentence?

Counting a set of objects reliably, e.g. count a handful of beads by
grouping them in 5s. How many 5s are there? How many left over?
How many beads altogether? What division sentence could you
write?

Reasoning, e.g. Davinder is counting in 2s to find numbers that
divide into groups of 2. Yasmin is counting in 5s. Will any of their
numbers be the same? Why?
How could you work out 15 ÷ 5?
How many 2s make 14?
Read these number sentences using the words 'How many...': 40 ÷
10, 25 ÷ 5, 12 ÷ 2




How many lengths of 10cm can you cut from 80cm of tape?

If you put 60 eggs in boxes of 10, how many boxes would you fill?
u

Amit spent 24p. He spent 8p more than Amy. How much did Amy
spend?
Can I use
grouping to
solve division
problems?




Confirming learning
Ask probing questions such as:
There are 12 identical socks. How many pairs can you make?
How many £2 coins do you get for £20?
How many sticks of 4 cubes can you make from a stick of 20
cubes?


PE, e.g. there are 28 children here today. How many groups of four
can we make for our PE lesson? What could we do if there were 30
children?
Word problems, e.g. Ben has 35p in 5p coins. How many coins does
he have? Pencils come in packs of 10. There are 56 pencils. How
many complete packs can be made?





A baker bakes 25 buns. She puts 5 buns in every packet. How many
packets can she fill? What if she had 30 buns? What if she had 31
buns?
What is 40 ÷ 10? How can you work it out? Can you work out 20 ÷
5? Can you think of another example that has the same answer?
Which of these numbers can you divide into equal groups of 5? 20,
50, 32, 40, 23, 10. Explain how you know.
Can you find four different numbers that you can divide into
groups of 3?
Can you think of a number that you cannot divide into equal groups
of 5? How do you know?
Level 1 to 2
Can I solve
problems that
involve
multiplication
as repeated
addition?
18 C
Opportunities to use and apply
Possible contexts include:
Review questions



You have got five 10p coins. How much money is this altogether?
What calculation could you do?
Four children have each been given £5 to spend while they are on
holiday. How much money do they have altogether? How could you
work this out?

Representing thinking using symbols and diagrams, e.g. there are 8
pairs of socks. How many socks are there altogether? Draw a
picture and write a multiplication number sentence to match this
problem.

Reasoning, e.g. would you rather be given 2p a day for 10 days or
10p a day for three days? Explain why.

Money, e.g. working out how much money you've got in a pile of
coins by first of all working out how much money you've got in the
sets of 1p, 2p, 5p, 10p coins, etc.
How can you make 20p using 10p coins?
Write this as a number sentence. Can you do the same using 2p and
5p coins?
I have got five coins. They are all the same.
How much money could I have altogether?
How many socks are there altogether? How could you record this
as a number sentence? Can you think of another number sentence
you could write for this?


Can I describe
an array and
write number
sentences
about it?
19 C
Describe this array:




Class 3 has six new packs of pencils. Each pack has ten pencils.
What are the different ways that we could work how many pencils
there are altogether? Which way would be quicker?
Write a number story where the same amount is added five times.
What multiplication could you write to go with the story?

Harry has six packs of five stickers. He works out how many he has
altogether like this: 5 add 5 makes 10, and then another 5 makes
15, and another 5 makes 20, another 5 makes 25, and then another
5 will make 30. How else could he have worked this out? Would
another way be quicker? What would he need to know to work it
out more quickly? (multiplication facts for 5)

Draw a picture to show me why 2 + 2 + 2 + 2 and 2 × 4 both equal 8.

There are 12 chairs arranged in three rows. How long is each row?
What multiplication and division sentences could you write about
the chairs?
Word problems, e.g. Jo's box is 5cm wide. Mary's box is twice as
wide as Jo's box. How wide is Mary's box?
There are 10 packs of stickers. Each pack has 10 stickers. What
calculation can you do to work out how many stickers there are
altogether?


Confirming learning
Ask probing questions such as:
How many 5s can you see? How many 3s can you see? How many
spots altogether? What addition sentences could you write? What
multiplication sentences could you write?
How many 5s are in 15? What division sentence could you write?
How many 3s are in 15? What division sentence could you write?

How many stars are there? Explain how you know without counting
them all. What number sentences could you write to describe the
stars?

Take 20 counters and arrange them in equal rows? How many rows
are there? How many columns are there? Can you arrange the
counters in a different way



Ask children to find examples of arrays in everyday life, e.g. eggs
in an egg box, sections of chocolate in a bar, stamps on a sheet,
panes of glass in a window, classroom drawer sets.
Word problems, e.g. eggs can come in boxes of 6. Draw how the
eggs are arranged in the box? What multiplication and division
sentences could you write to describe them?
Buns can come in packs of 12.
How might they be arranged in the pack?
What multiplication and division sentences could you write?
Problem solving, e.g. twelve counters can be arranged like this to
form a rectangle. What other numbers between 10 and 20 could
you use to make a rectangle? Write as many multiplication and
division sentences as you can for each number you have chosen.


Make up a story about this number sentence 5 × 3. What array
could you draw?
Create different arrays using 30 counters? Write the number
sentences to match your arrays.


Draw me a picture to show me why 2 × 5 and 5 × 2 both make 10.

Oliver said he could draw an array of 11 objects.
This is what he drew. Do you agree with him?
Can you draw an array of 11 objects?
Would you rather have a bar of chocolate in an array of 5 × 3
pieces or a bar of chocolate in an array of 2 × 6 pieces? Why?
Level 1 to 2
Can I name and
describe 2-D
and 3-D
shapes?
20 US
Opportunities to use and apply
Possible contexts include:
Review questions
How many hexagons can you see?
Can you see a square? How do you know? What is special about it?
• Find and name a shape this is not rectangular.
• Pick a shape and describe it. Can your friend guess which shape it is?
• Look at these 3-D shapes. Which ones will roll? What is special about
shapes that roll?
•
•
•
•
•
•
Find and name the shape with eight corners and six square faces.
Which of these shapes has no edges?
• Two of the shapes have one curved face and two flat circular faces.
Can you find them and name them?
•
•
Can I use
similarities and
differences
between
shapes to sort
them into sets
that I can
label?
21 US
•
Which of these shapes could not go into this set? Why?
Think of another label for the set. Which shapes belong in the set
now?
• Choose two shapes from this set. How are they the same? In what
ways are they different?
•
•
Art/design technology, e.g. build models and make pictures and
designs with 3-D and 2-D shapes. Describe them using shape
vocabulary.
Puzzles and riddles, e.g. I have rectangular faces. They are not all the
same size. What am I?
Games, e.g. look at a set of shapes then close your eyes while one is
removed. Open your eyes and describe to a partner the shape that
you think has been removed.
Maths trail, e.g. use a digital camera to make a shape trail around the
school and grounds, looking for shapes in different positions and
orientations. Make some questions for others to follow the trail.
Problems and puzzles, e.g. how many triangles can you count?
Confirming learning
Ask probing questions such as:
•
•
•
•
•
Here is a pink shape hiding behind a wall.
What shape could it be? How do you know? What shape couldn't it
be? Why?
Imagine a cube. Five faces are blue, the rest are yellow. How many
are yellow?
Imagine a hexagon in your head. Can you tell me about it so that I can
picture it?
If someone told you that all four-sided shapes are squares, what
would you say to them?
What is the same and what is different about these two shapes?
•
Describe a shape in a feely bag. What might it be? Why? What would
you expect to feel if I told you the shape in the bag is a cuboid?
Finding different ways to label the same set of shapes, e.g. think of a
label for this set of shapes that includes the word 'sides'. Now think
of a label that uses the words 'right angle'.
• Finding more examples that belong to a set, e.g. find other shapes
that could belong in this set. Now suggest some that could not belong.
• Handling data, e.g. sorting shapes using Carroll and Venn diagrams,
starting with one criterion and then if appropriate extending this to
two criteria.
•
Which shape is the odd one out? Why?
Estimating measures, e.g. give children a 1kg weight to hold. Then give
them a range of everyday items and ask them to say whether they
weigh more, less or about the same as 1kg.
• Estimate and then check how far you can jump from this line.
• Units used to measure everyday objects, e.g. look at food labels and
find a big packet of food that weighs less than a small packet of food.
• Comparing objects using appropriate measurements, e.g. working with
two or more objects to find the shortest, longest, heaviest, smallest
capacity, etc. and explain how this was done and what units of
measurement were used.
•
•
Choose some shapes that could go together in a set. What label would
you give the set? What label could you give to all the shapes that
don't belong in your set? Is there any other way you could label your
set?
• Kara has made a mistake sorting these shapes. Can you spot her
mistake?
•
Choose two of these shapes that are the same in some way; explain
why you have chosen them.
• How is the cone different from the sphere? Different from the
pyramid?
Which of the shapes could go into this set?
•
Can I choose
sensible units
to measure?
•
22 M
•
•
•
•
•
Sally and Josh measured the hall using their feet but they couldn't
agree how many feet long the hall was. Why do you think that
happened? What else could they use to measure the hall? Will that be
better? Why?
What could you use to find out how much water this container holds?
Would it be better to use multilink cubes or peas to balance the
weight of this shoe? Why?
Would you measure the length of a book in centimetres or metres?
Why?
What units would you use to measure the width of the classroom?
How about the weight of your teacher?
Look at a mug. Which of these amounts would you choose to say how
much water the mug holds?
1 metre, 1 litre, 1 centimetre, ¼ kilogram, ¼ litre
•
•
•
•
•
Think of something that would be better measured in metres rather
than centimetres. Explain why it is better.
Why wouldn't you measure the length of the playground using a ruler?
Alfie measured the length of his reading book and recorded the
length as 20kg. Could he be right?
Why do we need standard units like metres and centimetres to
measure accurately? What would happen if we didn't have standard
units?
Nisha says the table is 10 handspans long. Emily disagrees. She thinks
it is 11 handspans long. Why do you think they disagree? Can you think
of something else they could use to measure the length of the table
so that they will agree?
Level 1 to 2
Can I use the
position of
both hands to
tell the time to
the quarter
hour on a clock
face?
•
•
•
•
•
•
23 M
Can I read a
scale to find
how long or
heavy
something is?
24 M
Opportunities to use and apply
Possible contexts include:
Review questions
Why is one hand longer than the other on a clock face? What does
the long hand tell us? What does the short hand tell us?
Starting at 12, which number is halfway round the clock?
Can you move the hands on your clock to show 4 o'clock?
Explain to someone how you would move the hands on your clock to
show half past 4?
Which hand would you look at first in order to tell the time? Why?
Which of these clocks shows quarter past 3? How do you know?
What does each division on this scale stand for?
How heavy is Peter?
• Explain to me how I could find out how long the blue line is.
•
Matching times to everyday events, e.g. match some pictures of daily
events to some given clock faces showing their typical times.
• Comparing times, e.g. sort some given times into a sequence from
earliest to latest and draw hands onto corresponding clock faces.
• Problems involving the duration of time, e.g. School starts at 9
o'clock; show this time on your clock. Now show what time it would be
if you were half an hour late.
• I went out for a walk at half past 3 and walked for quarter of an hour.
Show me on these two clock faces what time I started and what time
I would then have finished.
•
Word problems, e.g. four weeks ago, the baby weighed 4kg; she is now
½kg heavier. Show me where the pointer would be on this scale.
Estimation, e.g. draw a straight line that you think is 10cm long. Now
measure it. How accurate were you? Can you now draw a line that you
think is 12cm long?
Capacity, e.g. extend reading scales in weight and length to capacity.
Problem solving, e.g. how could you mark out 2 metres if you only have
a one metre stick? Here is a strip of card that is 10cm long. How
could you use this to help you find a book that is about 20cm long?
How long do you think this line is?
•
•
•
•
Find something in the classroom that you think weighs more than 1kg.
Now use some weighing scales to see if you are right.
• How long is this red line that I've drawn for you, e.g. 2cm?
•
•
•
•
•
Use a ruler to find something in the classroom that is longer than
15cm.
• The parcels on these scales weigh 7kg. The pointer is missing. Show
me where it should be.
•
Can I use a
table,
pictogram or
block graph to
answer
questions?
25 HD
•
Who picked up the most cubes in one hand? How do you know?
Who do you think has the smallest hand? Why?
What else does this table tell you?
• Tell me one thing that this chart shows.
•
What can you say about lime flavour ice cream from this chart?
What does the tallest column mean?
How many people were asked? How do you know?
Confirming learning
Ask probing questions such as:
How could you measure it?
Cross–curricular links, e.g, in science discover how many different
kinds of minibeasts live in different parts of the school grounds.
• Testing a hypothesis, e.g. I think that most first names in our class
have more than five letters? What do we need to do to test if this is
true?
• Solving a problem, e.g. Is it quicker to write or type sentences?
Discuss how this could be answered, what data needs to be collected
and how it could be recorded to help answer this question.
•
•
•
•
•
The long hand on a clock is pointing to the 3, what number will it point
to when it has made half a turn?
What time could it be if the long hand is pointing to 12?
Close your eyes and imagine a clock face; the long hand is pointing at
12 and the short hand at 3; what time is it?
Imagine a clock that shows it is half past 3. Where is the long hand
pointing? Where is the short hand pointing?
This clock should be showing half past 7 but one hand is missing.
Which one? How do you know? Show me where it should be.
Show me where the pointer would be if the weight of the parcels is a
bit more than 4kg. Now show me nearly 1kg.
On a metre stick, what length is shown by the mark halfway between
20cm and 30cm?
• Ashley is measuring the length of this yellow rectangle. Can you
explain why he will not measure it accurately?
•
•
This scale shows the weight of a letter. How much does the letter
weigh? How do you know?
•
Look at this block graph.
Which way of travelling to school is used by most children? Explain
how you know
Can you think of another question you could ask and answer using the
data?
• Do you think it's true that most children in our class have packed
lunches? How could we find out? Make a list or table and explain what
you have found out.
Level 1 to 2
Can I organise
a set of
objects or
information,
using
properties
that they do
and do not
have in
common?
26 HD
Opportunities to use and apply
Possible contexts include:
Review questions
Make a list of all the multiples of 5 between 14 and 30. Is there
anything else you can say about the numbers in your list?
Tell me something about the numbers that are not in your list.
• Tell me one way we could sort this set of animals, vehicles etc. Can
you find a different way of sorting them?
• Choose from these shapes and make a set that all have something in
common. How would you label your set?
•
•
•
•
Could you choose a different set of shapes that do not have
something in common and label it
Confirming learning
Ask probing questions such as:
Sorting children in the class, e.g. sort everyone in the class using this
table.
•
Can you think of a way this set of dominoes has been sorted? What
label would you give each column in this table? Now sort them in a
different way, label your columns and explain your thinking.
Now find a different way to sort everyone into two groups.
Solving puzzles and problems, e.g. the digits in number 23 make a
total of 5; how many other two-digit numbers can you find like this?
Make a list. Explain how you know you have found them all.
•
Look at the diagram below. How many more children go to recorder
club than go to computer club? Do more children go to recorder club
than go to chess and computer club? How do you know?