Numicon Intervention Programme – Activity Group 19 – Adding and subtracting higher numbers1
Key mathematical ideas Adding, Subtracting, Place value, Pattern, Mathematical thinking and reasoning
19
Adding and subtracting higher numbers
Teaching notes
To find efficient solutions to problems children will need a
secure understanding of the column value and quantity
value of 2-digit numbers, and knowledge of number facts
within 10. Without this they will probably not be able to use
their knowledge of number relationships and may continue
to count in ones rather than calculate. They also need to be
able to use part–whole relationships and to find patterns
within calculations. However, once they understand Activity 3
– although they need further opportunities to experience
many different patterns within calculations – it is not
recommended that further Intervention time be used for this.
Activities 6 and 7 should only be used after Activities 4 and 5
have been understood. It may be advisable for many children
to return to Activities 6 and 7 after completing Activities 8 to 11.
Activities
Stage 4
Step 2
Talk about the relationships that can be seen from the
apparatus and from the number sentences. Explain that the
number facts within 10, that is, the 3 + 4, can help solve the
problem because only the units need to be added together
as there are no tens to add. Combine the 3- and 4-shape to
show the total of 7 units, then add the two 10-shapes giving
the total of 27 mini figures (see  Fig. 1 ).
Step 3
Show 23 + 4 using the tens and units frame and write the
adding sentence in columns. Look again at how the units
have been added together and are in the units column but
the tens in the tens column have stayed the same (see  Fig. 2 ).
Step 4
Make up further adding problems where a 1-digit number
has to be added to a 2-digit number, ensuring the total
stays within the same ‘ten’. Check children understand that
e.g. 4 + 23 = still equals 27 and the total can be found in the
same way.
Further practice activities
Activity 1: Adding a 1-digit number to
a 2-digit number
Have ready: Numicon Shapes, Numicon 10s Number Line,
Numicon 1–100 cm Number Rod Track, number rods, Adding
to 10 Cards (cut from photocopy masters 4a and 4b)
Learning aims
•• Child 1 takes an adding to 10 card and rewrites the adding
sentence, changing one of the numbers into a 2-digit
number by adding some tens, e.g. 4 + 5 =, could become
34 + 5 =, or 4 + 35 =. Child 2 finds the total. Both check
with Shapes or number rods. Practise writing as column
addition if appropriate.
•• To use adding facts within 10 to find efficient solutions when
adding 1-digit numbers to 2-digit numbers.
•• To realize that knowing adding facts for numbers to 10 helps
when adding numbers to find a total greater than 10 and know
when to use them to solve problems.
•• To use understanding of place value to add 1-digit numbers to
2-digit numbers.
•• To further develop understanding of adding in columns.
Words and terms for use in conversation
equal to, add, plus, how many more, adding, multiples of 10, tens,
units, tens number, 2-digit number, column
Record of Progress
+
•• Task 13
Have ready: Numicon Shapes, Tens and Units Frame
(photocopy master 23)
23
=
+
4
=
27
1
Step 1
Set the scene by explaining to children that they are going
to learn an easy way to answer calculations that use higher
numbers by using what they already know. Give them a
word problem, e.g. ‘Sanji had a collection of twenty-three
mini figures and was then given four more. How many did he
have altogether?’
Tens
Units
Children write the expression, 23 + 4 = and illustrate the
problem with Shapes.
2
3
2
3
+
4
7
2
Numicon Intervention Programme – Activity Group 19 – Adding and subtracting higher numbers2
Activity 2: Subtracting a 1-digit
number from a 2-digit number
Activity 3: Patterns of similar
calculations
Learning aims
Learning aims
•• To use subtracting facts within 10 to find efficient solutions when
subtracting 1-digit numbers from 2-digit numbers.
•• To realize that knowing subtracting facts for numbers to 10 helps
when subtracting with higher numbers and know when to use
them to solve problems.
•• To use understanding of place value to subtract 1-digit numbers
from 2-digit numbers.
•• To further develop understanding of subtracting in columns.
•• To use adding and subtracting facts within 10 to find efficient
solutions when adding and subtracting 1-digit numbers to and
from 2-digit numbers without crossing the tens boundary.
•• To realize that knowing adding and subtracting facts for numbers
to 10 helps when adding or subtracting numbers with higher
numbers and know when to use them to solve problems.
•• To use understanding of place value to add and subtract 1-digit
numbers to and from 2-digit numbers.
Words and terms for use in conversation
Words and terms for use in conversation
how many left, left over, equal to, subtract, minus, how many fewer,
how many less, subtracting, multiples of 10, tens, units, tens number,
2-digit number, difference, column
add, plus, how many more, how many left, left over, equal to, subtract,
minus, how many fewer, how many less, adding, subtracting,
multiples of 10, tens, units, tens number, 2-digit number, difference
Record of Progress
Record of Progress
•• Task 13
•• Task 13
Have ready: Numicon Shapes, Tens and Units Frame
(photocopy master 23), Subtracting Covers 1–10 (photocopy
master 20)
Have ready: Numicon Shapes, Numicon 10s Number
Line, Numicon 1–100 cm Number Rod Track, number rods,
Adding to 10 Cards (cut from photocopy masters 4a and 4b),
Subtracting from 10 Cards (cut from photocopy masters 21a
and 21b), Subtracting Covers 1–10 (photocopy master 20)
Step 1
Set the scene by explaining to children that they are going
to learn an easy way to answer calculations that use higher
numbers by using numbers they already know. Give them
a word problem, e.g. ‘The shopping bill was £57 last week.
This week it is £3 less. How much was the bill?’
Children write the expression, 57 − 3 = and build 57 with Shapes.
Step 2
Talk about the relationships that can be seen from the
apparatus and from the number sentences. Explain that
the number facts within 10, that is, the 7 − 3, can help solve
the problem because only the units need to have some
subtracted, as there are no tens to subtract. Using the
subtracting cover, subtract 3 from the 7-shape to show the
answer of 4 units, then include the five 10-shapes giving the
answer of £54 (see  Fig. 3 ).
Step 1
Set the scene by explaining to children that they are going
to look for patterns when using the Shapes (or number rods)
and when they write their calculations.
Choose an adding to 10 card and show the adding sentence
with Shapes or number rods on the appropriate number line,
e.g. 3 + 5 = 8. See  Fig. 5 .
57 – 3 = 54
3
Step 3
Show 57 − 3 using the tens and units frame and write the
subtracting sentence in columns. Look again at how the units
have been subtracted and are in the units column but the
tens in the tens column have stayed the same (see  Fig. 4 ).
Tens
Units
Step 4
Make up further subtracting problems where a 1-digit
number has to be subtracted from a 2-digit number,
ensuring the answer stays within the same ‘ten’.
Further practice activities
Have ready: Numicon Shapes, Numicon 10s Number
Line, Numicon 1–100 cm Number Rod Track, number rods,
Subtracting from 10 Cards (cut from photocopy masters 21a
and 21b), Subtracting Covers 1–10 (photocopy master 20)
•• Child 1 takes a subtracting from 10 card and rewrites the
subtracting sentence, changing the first number into a
2-digit number by adding some tens, e.g. 8 − 6 = could
become 48 − 6 =. Child 2 finds the answer. Both check with
Shapes or number rods. Practise writing the subtraction in
columns if appropriate.
5
3
5
0
zero
7
–
3
4
10
ten
4
5
Numicon Intervention Programme – Activity Group 19 – Adding and subtracting higher numbers3
Step 2
Have ready: Numicon Shapes, Numicon 10s Number Line
Add a 10-shape or 10-rod from zero (e.g.  Fig. 6 ) and write a
new corresponding adding sentence, such as 13 + 5 = 18.
Step 1
Step 3
Continue to add 10-shapes or 10-rods from zero to extend
the pattern of adding sentences and continue to write the
corresponding adding sentences (see  Fig. 7 ). Some children
may be able to continue the pattern beyond 100.
Step 4
Starting with a subtracting from 10 card, illustrate with Shapes
or number rods on a number line, e.g. 9 − 3 = 6 and write
the subtracting sentence. Add a 10-shape or 10-rod to show
19 − 3 = 16 and write the subtracting sentence. Continue to
increase the starting number by adding a 10-shape or 10-rod
each time. Write the number sentences to show the pattern
(see  Fig. 8 ).
Step 5
Start with Shapes or number rods along a number line
showing 99 − 3 = 96. Children remove a 10-shape or 10-rod
each time, writing the pattern of number sentences.
Further practice activities
Have ready: Numicon Shapes, Numicon 10s Number
Line, Numicon 1–100 cm Number Rod Track, number rods,
Adding to 10 Cards (cut from photocopy masters 4a and 4b),
Subtracting from 10 Cards (cut from photocopy masters 21a
and 21b), Subtracting Covers 1–10 (photocopy master 20)
Set the scene by saying any decade of numbers and asking
children to say the next multiple of 10, e.g. if you say ‘fifties’
children say ‘sixty’. Write ‘60’ for children to see. Repeat with
other examples.
Now tell children a word problem: ‘Packs of pens come in
multiples of 10. Aisha had four boxes, but only 38 pens. How
many pens were missing?’
Step 2
Make 38 with Shapes. Children say the next multiple of 10
and which Shape is needed to reach it. They put a 2-shape
with the 8-shape (see  Fig. 9 ).
Step 3
Place the Shapes along the 10s Number Line (see  Fig. 10 ),
connecting the answer with the word problem – that the
boxes of pens should have contained 40 pens so 2 were
missing. (Rods and the 0–100 cm Number Line can be used
for this activity; see  Fig. 11 .)
Step 4
Choose other numbers between 30 and 40 for children
to use their knowledge of different adding facts of 10,
e.g. 31 + 9, 37 + 3.
•• Children repeat Activity 3 using different adding to 10 cards
and subtracting from 10 cards.
Activity 4: Using adding facts of 10 to
reach the next multiple of 10
Learning aims
•• To be fluent with the facts of 10 and to know when to use them to
solve problems with higher numbers.
•• To use understanding of the structure and quantity of 2-digit
numbers to solve problems.
•• To have confidence to use known facts to solve problems
mentally.
9−3=6
19 − 3 = 16
29 − 3 = 26
39 − 3 = 36
49 − 3 = 46
59 − 3 = 56
69 − 3 = 66
79 − 3 = 76
89 − 3 = 86
99 − 3 = 96 8
9
Words and terms for use in conversation
recall, facts, add, more, plus, how many more to make, tens
number, equals, pair, digit, doubles
Record of Progress
0
zero
•• Task 13
0
zero
10
ten
20
twenty
6
13 + 5 = 18
23 + 5 = 28
33 + 5 = 38
43 + 5 = 48
53 + 5 = 58
63 + 5 = 68
73 + 5 = 78
83 + 5 = 88
93 + 5 = 98
7
10
ten
20
twenty
30
thirty
40
forty
22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46
10
11
Numicon Intervention Programme – Activity Group 19 – Adding and subtracting higher numbers4
Step 5
Step 2
Repeat with examples in other intervals of 10.
Point to each multiple of 10 along the tens Number Line as
children count backwards in tens (or along the 0–100 cm
Number Line). Say any multiple of 10 for children to call out
which set of numbers comes before it, e.g. if you say ‘sixty’,
children answer ‘fifties’.
Step 6
For older children, write as a missing number problem,
e.g. 38 +  = , and talk children through the process of
writing the multiple of 10, i.e. 40, in the total box and then
filling in 2.
Further practice activities
Have ready: 2-digit numbers (do not include multiples of 10)
from Numicon 0–100 Numeral Cards
•• Turn a Card. Children read the number and say what the
next multiple of 10 will be.
•• Turn a Card. Children read the number and say how many
to reach the next multiple of 10.
Have ready: Numicon 10s Number Line, Numicon Shapes,
cards from the Numicon 0–100 Numeral Cards
•• Child 1 turns a Card, uses Shapes to make the number and
places them along the 10s Number Line. Child 2 finds the
Shape needed to reach the next multiple of 10. Both write
the adding sentence.
Have ready: Numicon Shapes, number rods
•• Children build an 11–20 number line using Shapes or
number rods. Starting at 11, children think what should
be added to 11 to equal 20 and place the appropriate
Shape to show the addition. They continue to find each
Shape along the number line. Children read each adding
sentence and write them, e.g. 11 + 9 = 20, 12 + 8 = 20.
Activity 5: Subtracting a 1-digit
number from a multiple of 10
Learning aims
•• To be fluent with the facts of 10 and to know when to use them to
solve problems with higher numbers.
•• To use understanding of the structure and quantity of 2-digit
numbers to solve problems.
•• To have confidence to use known facts to solve problems mentally.
Words and terms for use in conversation
recall, facts, add, more, plus, how many more to make, teens
number, equals, pair, digit, doubles
Record of Progress
•• Task 13
Have ready: Numicon Shapes, Numicon 10s Number Line,
selection of cards from Numicon 0–100 Numeral Cards (or
number rods and the Numicon 0–100 cm Number Line).
Step 3
Remind children about the car park question and highlight 70
on the 10s Number Line. Agree that 5 should be subtracted
from 70 and place a 5-shape from 70 towards 60, saying
‘70 subtract 5 equals?’ (see  Fig. 12 ). Remind children about
the facts of 10 that they know and help them to make the
connection so they can work mentally. Agree there were 65
cars left in the car park.
Step 4
Repeat with other examples.
Further practice activities
Have ready: Numicon Shapes, Numicon Feely Bag, Numeral
Cards – Multiples of 10 (cut from photocopy master 13)
shuffled and face down in a pile, number rods
•• Child 1 turns a card from the pile. Child 2 takes a Shape
from the Feely Bag. Both subtract the amount of the Shape
from the multiple of 10 and write the subtracting sentence.
•• Children build an 11–20 number line using Shapes or
number rods. Beginning with 11 plus 9 they take away the
9-shape saying ‘twenty subtract nine equals eleven’ and
write the number sentence. They continue to take away
one Shape from each number, taking care to continue the
descending pattern, 20 − 8 = 12, 20 − 7 = 13 and so on.
Activity 6: How many more to 100?
Learning aims
•• To be fluent with the facts of 10 and to know when to use them to
solve problems with higher numbers.
•• To use understanding of the structure and quantity of 2-digit
numbers to solve problems.
•• To have confidence to use known facts to solve problems mentally.
Words and terms for use in conversation
recall, facts, add, more, plus, how many more to make, equals,
tens, units, pair, multiples of 10
Record of Progress
•• Task 13
Step 1
Set the scene by telling children a subtracting word problem
which will require them to use the facts they know about 10,
e.g. ‘There were seventy cars in the car park. Five people
came and drove one car each out of the car park. How many
were left?’
50
fifty
60
sixty
70
seventy
80
eighty
52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76
12
Numicon Intervention Programme – Activity Group 19 – Adding and subtracting higher numbers5
Activity 7: Finding change from £1
Have ready: Numicon Shapes, Numicon 10s Number Line (or
number rods and Numicon 1–100 cm Number Rod Track)
Learning aims
Step 1
•• To be fluent with the facts of 10 and to know when to use them to
solve problems with higher numbers.
•• To use understanding of the structure and quantity of 2-digit
numbers to solve problems.
•• To have confidence to use known facts to solve problems mentally.
Set the scene by telling children ‘One hundred people were
allowed in the swimming pool. There were only forty-seven
people swimming so far. How many more would be able to
swim?’
Place 47 with Shapes along the 10s Number Line (or 47 with
rods along the 1–100 cm Number Rod Track) and look at
the space left to 100. Agree with children that a 3-shape or
3-rod will fill the gap to 50 and then five 10-shapes or five
10-rods will fill the gap to 100, so there are spaces for 53
more people.
Words and terms for use in conversation
recall, facts, add, more, plus, how many more to make, equals,
tens, units, pair, multiples of 10
Record of Progress
•• Task 13
Step 2
Have ready: Numicon Shapes, Numicon 10s Number
Line, Numicon 1–100 cm Number Rod Track, number rods,
Subtracting Covers 1–10 (cut from photocopy master 20),
items costing less than £1 (cut from Shopping List, photocopy
master 17)
Talk with children about how their knowledge of number
facts to 10 helps them and about the steps needed to find
the answer: using facts of 10 to reach the next multiple of 10
(3 more because 7 + 3 = 10) and then the related whole ten
facts to reach 100 (5 tens because 5 tens and 5 tens equal
10 tens or because 50 and 50 equals 100). Then talk about
finding the total, 3 units add 5 tens equals 53 or 3 add 50
being 53.
Step 1
Set the scene by explaining to children that they are going
shopping with a £1 coin. The items in the shop all cost less
than £1. Look at the items on the shopping list and ask the
children what they might buy.
Step 3
Show the steps on an empty number line (see  Fig. 13 ).
If they had to buy an item for 94p what change would
they get? Children write the number sentence for the
problem. Some might use take away, others may find the
difference, others may add on. Illustrate the problem using
structured apparatus.
Step 4
Write the calculation using an empty box, 47 + o = 100 and
as a subtraction, 100 − 47 = o. Talk with children about
how these could both represent the problem and about
the different ways they might find the answer. Agree on an
efficient method.
Step 2
Discuss with children which number facts they know that help
to find out how many more, e.g. from 94 to 100, and agree
the change would be 6p.
Further practice activities
Have ready: Numicon Shapes, Numicon 10s Number Line, a
selection of 2-digit Numicon 0–100 Numeral Cards
Step 3
Explain that another item costs 65p. What change would
they get from their £1? Illustrate with structured apparatus
along the appropriate number line, e.g.  Fig. 14 , and talk with
children about the 35 shown representing 35p.
•• Child 1 takes a Card, builds the number with Shapes along
the 10s Number Line and writes the empty box calculation.
Child 2 finds how many more to 100 using Shapes and fills
in the missing number.
Step 4
Show on an empty number line (see  Fig. 15 ).
Further practice activities
Have ready: Numicon Shapes, Numicon 10s Number Line,
Numicon 1–100 cm Number Rod Track, number rods, coins
•• Give children shopping stories or shopkeeper games
where one item costs less than £1 and they need to find
change from £1.
50
fifty
60
sixty
70
seventy
+50
90
100
ninety one hundred
30
+3
47
80
eighty
5
50
100
13
65
70
100
15
14
Numicon Intervention Programme – Activity Group 19 – Adding and subtracting higher numbers6
Activity 8: Adding two 1-digit
numbers and bridging 10; Adding a
1-digit number to a 2-digit number
and bridging a multiple of 10
Learning aims
•• To use adding facts within 10 to find efficient solutions when
adding two 1-digit numbers.
•• To recognize that multiples of 10 are useful landmarks on the
number line when calculating.
•• To realize that knowing adding facts for numbers to 10 helps
when adding numbers with a total greater than 10 and know
when to use them to solve problems.
•• To use understanding of place value to add two 1-digit numbers.
•• To learn how to bridge through a multiple of 10 when adding.
Words and terms for use in conversation
add, plus, how many more, how many left, left over, equal to, how
many fewer, how many less, adding, subtracting, multiples of 10,
tens, units, tens number, 2‑digit number, partition
Record of Progress
•• Task 13
Have ready: Numicon Shapes, Numicon 10s Number Line
Step 1
Set the scene by explaining to children that they are going to
learn how to add two numbers that total more than 10, e.g. ‘If
you score eight points in one round of a game and then five
points in your second round, how many points would you
have scored altogether?’
Children find Shapes for both numbers and lay them along
the 10s Number Line. They can see the mark on the 10s
Number Line for ‘10’ and see how many past 10 the two
Shapes reach, showing the total of 13 points. Make the
connection with the word problem, that the total points
scored was 13.
Step 2
Ask children how many holes of the 5-shape are needed
to reach the ‘10 mark’ (point to the two holes) and then how
many left (pointing to the three holes) which have to be
added to the 10 to give the total.
Step 3
Illustrate by placing a 10-shape on top of the 8- and
5-shapes, a 2-shape above and then a 3-shape above
(see  Fig. 16 ). It can help children see the partitioning of 5 and
make connections by providing imagery for the mental steps
that need to be taken.
Step 4
Repeat with 8 + 6, 8 + 7 and 8 + 9 (children may suggest
using near doubles).
Step 5
Give children another problem: ‘There were seventeen
people in a queue for football, then four more came. How
many were in the queue?’ Children repeat Steps 1–4,
partitioning the 4 into a 3 and 1 using 3 to reach 20, then
adding 1 more to give the total 21 (see  Fig. 17 ). Try examples
using higher numbers that bridge any multiple of 10.
Further practice activities
Have ready: Numicon 5-, 6-, 7-, 8- and 9-shapes, Numicon
0–100 Numeral Cards, Numeral Cards 1–10 (cut from
photocopy master 11) shuffled and face down
•• Children take a card and a Shape and add the value of the
Shape to the number shown on the card. Use the Shape
to help with partitioning into the number needed to reach
10 and then the number left to be added to the 10 to give
the total.
Repeat with Numeral Cards ending in 5–9 from the
21–89 range.
•• Adult-led: practise recall for 5, 6, 7, 8 or 9 by holding up
any two cards which show one of these totals for children
to say the answer.
Activity 9: Subtracting a 1-digit
number from 2-digit number and
bridging multiples of 10
Learning aims
•• To use subtracting facts within 10 to find efficient solutions when
subtracting 1-digit numbers from 2-digit numbers.
•• To recognize that multiples of 10 are useful landmarks on the
number line when calculating.
•• To realize that knowing subtracting facts for numbers to 10 helps
when subtracting with higher numbers and know when to use
them to solve problems.
•• To use understanding of place value to subtract 1-digit numbers
from 2-digit numbers.
•• To learn how to bridge through a multiple of 10 when subtracting.
Words and terms for use in conversation
how many more, how many left, left over, equal to, subtract, minus,
how many fewer, how many less, subtracting, multiples of 10, tens,
units, tens number, 2‑digit number, difference, partition. partitioning
Record of Progress
•• Task 13
0
zero
10
ten
20
twenty
30
thirty
16
+
+
=
17
Numicon Intervention Programme – Activity Group 19 – Adding and subtracting higher numbers7
Have ready: Numicon Shapes, Numicon 10s Number Line,
Subtracting Covers 1–10 (photocopy master 20)
Step 1
Set the scene by explaining to children that they are going
to cross a multiple of 10 when subtracting. Say: ‘The minibus
had just taken thirteen children to the swimming pool. On the
way home five children got off at the first stop. How many
children were still on the bus?’
Further practice activities
Have ready: Numeral Cards 11–15 from Numicon 0–100
Numeral Cards shuffled and face down in a pile, Numicon 6-,
7-, 8- and 9-shapes
•• Children take a Card and a Shape and subtract the value
of the Shape from the number shown on the card.
Repeat with Numeral Cards ending in 1–5 from the
21–95 range.
Children make 13 with Shapes and place them on the 10s
Number Line.
Have ready: Numeral Cards 1–9 (cut from photocopy
master 11)
Step 2
•• Adult-led: practise recall (to support partitioning) by holding
up any two cards from 1 to 9 for children to subtract one
from the other and say the answer.
They partition the 5-shape, agreeing that 3 needs to be
subtracted to reach 10, which leaves a further 2 to be
subtracted. They place the subtracting cover for 5 from 13
on top of the 3- and 10-shapes so that they can see the
8-pattern left (check with an 8-shape if necessary). Make
the connection with the word problem so children see the
answer is 8 children left on the bus.
Activity 10: 2-digit numbers added to
2-digit numbers without bridging a
multiple of 10
Step 3
Learning aims
By placing the 3- and 2-shapes above the 13 shown by the
10- and 3-shapes it can help children see the partitioning of
the 5-shape, e.g.  Fig. 18  and make connections by providing
imagery for the mental steps that need to be taken.
•• To use the facts to 10 to add 2-digit numbers to 2-digit numbers
without bridging a multiple of 10 and know when to use them to
solve problems.
•• To use understanding of place value to add 2-digit numbers to
2-digit numbers.
•• To further develop understanding of adding in columns.
Step 4
Repeat with other examples that begin with a teen number
and subtract 5, 6, 7, 8 or 9 to cross the tens boundary.
Step 5
Give children another problem: ‘There were twenty-five
children in the playground and eight went in to finish some
work. How many children were left in the playground?’
Children repeat the above steps, partitioning the 8-shape into
5 and 3 and subtracting each part to reach the answer 17
(see  Fig. 19 ). Try examples using higher numbers that bridge
any multiple of 10.
Words and terms for use in conversation
add, plus, how many more, equal to, multiples of 10, tens, units,
2‑digit number
Record of Progress
•• Task 13
Have ready: Numicon Shapes, number rods, Tens and Units
Frame (photocopy master 23)
Step 1
Set the scene by saying, ‘Sabine and Leah were given a
game each by their grandparents. One cost £24 and the
other £32. How much did their grandparents spend?’
Write the adding expression 24 + 32 = and illustrate
with Shapes.
0
zero
10
ten
20
twenty 18
0
zero
10
ten
20
twenty
30
thirty
0
zero
10
ten
20
twenty
30
thirty
0
zero
10
ten
20
twenty
30
thirty
19
Numicon Intervention Programme – Activity Group 19 – Adding and subtracting higher numbers8
Step 2
Partition 24 into 2 tens and 4 units, and 32 into 3 tens and 2
units (also using the language ‘twenty’ and ‘four’ and ‘thirty’
and ‘two’) (see  Fig. 20 ).
Activity 11: 2-digit numbers
subtracted from 2-digit numbers
without bridging a multiple of 10
Step 3
Learning aims
Combine the units, so 4 + 2 = 6, then combine the tens so 2
tens add 3 tens equals 5 tens (or fifty).
•• To use the facts to 10 to subtract 2-digit numbers from 2-digit
numbers without bridging a multiple of 10 and know when to use
them to solve problems.
•• To use understanding of place value to subtract 2-digit numbers
from 2-digit numbers.
•• To further develop understanding of subtracting in columns.
Step 4
Recombine the tens and units so the total 56 can be seen
with the Shapes (see  Fig. 21 ) and agree that the total spent
was £56.
Step 5
Discuss with children which number facts to 10 have helped
(2 + 3 = 5 and 4 + 2 = 6). See  Fig. 22 .
Words and terms for use in conversation
equal to, how many left, left over equal to, subtract, minus, how
many fewer, how many less, subtracting, multiples of 10, tens, units,
tens number, 2‑digit number, difference
Step 6
Record of Progress
When children are secure with the above steps, write as
column addition. Some children may still need the support of
the tens and units frame or the ‘T’ and ‘U’ above the columns.
•• Task 13
Further practice activities
Have ready: Numicon Shapes, number rods, prepared
2-digit numbers to be added to 2-digit numbers where
neither the tens total nor the units total exceeds 9
•• Children find the answers to the problems.
Have ready: Numicon Shapes, Subtracting Covers 1–10
(cut from photocopy master 20), Tens and Units Frame
(photocopy master 23)
Step 1
Set the scene by saying: ‘Amos saved £78 and decided to
spend £26 on a new game. How much did he have left?’
Write the calculation 78 − 26 = and illustrate the 78 with Shapes.
Step 2
Partition the Shapes into the 7 tens and 8 units (or 70 and 8),
and then subtract 2 tens and 6 units (or 20 and 6).
Step 3
Recombine the tens and units left, 5 tens and 2 units (or 50
and 2). Complete the calculation, 78 − 26 = 52, agreeing that
Amos had £52 left.
Step 4
Discuss with children which number facts within 10 have
helped (7–2 = 5 and 8–6 = 2). See  Fig. 23 .
24
2 tens
‘twenty’
4 units
‘four’
Step 5
When children are secure with Steps 1–4, write as column
subtraction. Some children may still need the support of the
tens and units frame or the ‘T’ and ‘U’ above the columns.
Further practice activities
Have ready: Numicon Shapes, number rods
32
2 units
‘two’ 20
3 tens
‘thirty’
21
2 tens + 3 tens = 5 tens
•• Give children money problems, e.g. ‘Alma went to the
shops on Monday and spent 45p. On Tuesday she spent
52p. How much did she spend altogether?’, ‘Viraj had
saved 98p. He went to the shops and spent 57p. How
much did he have left?’
7 tens – 2 tens = 5 tens
24 + 32 = 56
4+2=6
•• Give children problems to solve where 2-digit numbers
have to be subtracted from other, larger, 2-digit numbers,
without crossing multiples of 10.
78 – 26 = 52
22
8–6=2
23