Cambridge University Press
1845659570 - KS2 Addition and Subtraction Teacher’s Notes
Anthony David and John Spooner
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Year 3 Addition and subtraction
Multiples of 5 and ‘a bit’
Expressing 2-digit numbers as multiples of 5 and ‘a bit’
Objective
•
AS3S1
Move through the other questions, each time asking children
to express the number given as a multiple of 5 and ‘a bit’.
They show their answers on their small whiteboards.
(Page 2 on whiteboard)
Partition numbers into multiples of 5 and ‘a bit’.
(This can be applied to addition of 6, 7, 8 or 9, e.g.
47 + 8 = 45 + 2 + 5 + 3)
Prior knowledge and skills
•
Recognising 2-digit multiples of 5
•
Counting on to find a small difference
Vocabulary
multiple of 5, greatest, less than, count on
Resources
•
small whiteboards and pens
Main teaching activity
You could highlight numbers on the 100 square on this page
for children to express as a multiple of 5 and ‘a bit’. To
highlight a number, click on one of the ‘Fill colour’ buttons on
the toolbar and then on the appropriate grid square. Clicking
on the ‘Remove colour’ button and then on a highlighted
square will remove its highlighting.
Personal notes
Whole class
(Page 1 on whiteboard)
Q What is a ‘multiple of 5’?
Invite children to demonstrate their understanding by giving
a variety of multiples of 5.
Establish that the number highlighted in red on the 100
square on the board (19) is not a multiple of 5.
Q What is the greatest multiple of 5 that is less than
19? (15)
Click on 15 to colour it blue and to enter 15 into the addition
beside the grid.
Explain that 19 can be described as 15 and ‘a bit’.
Q How much bigger than 15 is 19?
Demonstrate by counting on from 15 to 19 on the 100
square that the extra bit is 4. Click on the yellow box in the
addition, and explain that 19 can be expressed as 15 + 4.
Mult-e-Maths © Cambridge University 2004
© Cambridge University Press
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Cambridge University Press
1845659570 - KS2 Addition and Subtraction Teacher’s Notes
Anthony David and John Spooner
Excerpt
More information
Year 3 Addition and subtraction
Missing numbers
AS3S2
Using addition and subtraction facts for numbers to 20 to
complete missing number calculations
Refer to the missing number subtraction sentence on the
board. Explain that you want to find pairs of numbers, from 0
to 20, to make the subtraction correct.
Objective
Q What could the missing numbers be?
•
Know addition and subtraction facts for numbers to 20.
Prior knowledge and skills
•
Using mental addition and subtraction strategies to
deduce addition and subtraction facts to 20
Vocabulary
add, subtract, addition, subtraction, number sentence
Resources
•
small whiteboards and pens
Main teaching activity
Ask each child to write a suggestion on their small
whiteboard. Invite children to show their suggested numbers
and to try them on the board by dragging the numbers into
the boxes. A correct solution will automatically be recorded
beneath the subtraction. If incorrect numbers are dragged
into the subtraction, or a pair of numbers is repeated, the
numbers will jump back to the top of the screen. When all
different suggestions have been exhausted, ask:
Q Are there any other solutions that we haven’t
recorded yet?
Find as many different solutions as possible (there are 14
possibilities in all).
Q How can we be sure we have found all the possible
subtractions? (e.g. By checking that you have a
subtraction beginning with 20, one beginning with 19,
one beginning with 18 … one beginning with 7.)
Whole class
(Page 1 on whiteboard)
Personal notes
Point to each missing number addition sentence on the
screen in turn. Each time ask children to show on their small
whiteboards the correct number to complete the number
sentence.
Q How did you work out your answer?
How can you check your answer?
Invite children to drag numbers from the top of the screen to
show their answers. The rest of the class should check the
completed additions. Discuss any incorrect answers.
(Page 2 on whiteboard)
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Cambridge University Press
1845659570 - KS2 Addition and Subtraction Teacher’s Notes
Anthony David and John Spooner
Excerpt
More information
Year 3 Addition and subtraction
Matching additions and subtractions
AS3S3
Using knowledge of number facts to 20 to make additions
and matching subtractions
Invite a child to create the matching subtraction sentence,
e.g. 19 4 = 15, by dragging numbers into the first
subtraction sentence.
Objectives
Point to the second addition and ask:
•
Know addition and subtraction facts for numbers to 20.
•
Say or write a subtraction statement corresponding to a
given addition statement.
Prior knowledge and skills
•
Knowing some addition and subtraction facts for
numbers to 20
•
Understanding that subtraction is the inverse of addition
Vocabulary
add, plus, subtract, minus, digit, number sentence
Q
What is the subtraction sentence that matches this
addition sentence?
Invite a child to drag appropriate numbers into the second
subtraction sentence.
Click on ‘Clear’ on the toolbar and invite a child to create a
different addition sentence. Invite other children to write a
matching addition sentence and two matching subtraction
sentences on their small whiteboards.
Repeat several times.
Personal notes
Resources
•
small whiteboards and pens
Main teaching activity
Whole class
(Page 1 on whiteboard)
Q Can you make an addition sentence using the
numbers 0 to 20?
Invite a child to drag numbers into the first missing number
addition on the whiteboard to create an addition sentence.
Check with the class that it is correct.
Q How can we use the same numbers to create another
addition sentence?
Invite a child to drag numbers into the second addition to
produce the same addition, but with the numbers before the
equals sign swapped around.
Point to the first addition and ask, e.g.
Q If 15 + 4 = 19, what is 19 4? (15)
Ensure children understand that if, e.g. adding 4 to 15 gives
19, then taking the 4 away takes you back to 15.
Mult-e-Maths © Cambridge University Press 2004
© Cambridge University Press
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Cambridge University Press
1845659570 - KS2 Addition and Subtraction Teacher’s Notes
Anthony David and John Spooner
Excerpt
More information
Year 3 Addition and subtraction
Total 100
Using a 100 square to identify pairs of multiples of 5 that
total 100
Objective
•
Derive pairs of multiples of 5 with a total of 100.
Prior knowledge and skills
•
Counting on in 5s and 10s to 100
AS3S4
Choose several multiples of 5 in turn (including some even
multiples of 5), and ask children to show the number that
needs to be added to make 100. Demonstrate counting up
in 5s and 10s using the 100 square as appropriate.
Q How did you know what units digit the answer would
have?
Personal notes
Vocabulary
multiple of, count on, total , add, make, units digit
Resources
•
number fans (or digit cards)
Main teaching activity
Whole class
(Page 1 on whiteboard)
Click on a ‘Fill’ button on the toolbar and then on 75 on the
100 square to highlight it. Click on the ‘Select’ button and
drag 75, from the 100 square, into the left-hand side of the
addition sentence. Ask:
Q What must be added to 75 to make 100?
Children show their answers using their number fans (or digit
cards).
Q How did you work it out?
Establish that one method is to count on from 75 to 100.
Demonstrate this on the 100 square.
Q What is the next multiple of 10 after 75? (80)
How many do we need to add to 75 to make 80? (5)
What do we need to add to 80 to make 100? (20)
So how much have we added altogether to 75 to
make 100? (25)
Confirm that we need to add 25 to 75 to get to 100.
Clicking on ‘Clear’ will allow you to highlight a different
square and drag its number into the first box of the addition.
Mult-e-Maths © Cambridge University Press 2004
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Cambridge University Press
1845659570 - KS2 Addition and Subtraction Teacher’s Notes
Anthony David and John Spooner
Excerpt
More information
Year 3 Addition and subtraction
Making 19
Identifying pairs of numbers with a total of 19 and
subtracting numbers to 10 from 19
Objective
•
Know addition and subtraction facts for numbers to 20.
Prior knowledge and skills
•
Knowing addition and subtraction facts for 19
Vocabulary
AS3S5
Q How did you work out your answer?
Ensure children understand that they can use their
knowledge of addition facts for 19 to help them with
subtraction facts for 19.
Repeat the activity as many times as you feel is useful.
You could repeat both questions using a different number
from 10 to 20.
Personal notes
sum, total, add, subtract
Resources
•
a number fan for each child (or digit cards)
Main teaching activity
Whole class
(Page 1 on whiteboard)
Refer to the numbers on the board.
Q Can you find a pair of numbers that total 19?
Invite a child to click on the ‘Fill colour’ button on the toolbar
and then on a suggested pair of numbers on the number grid
to highlight them. Invite children to highlight other pairs,
using a different colour for each pair. (To select a new
colour, click on the arrow next to the ‘Fill colour’ button.)
You could ask more able children:
Q Can you find three numbers that together total 19?
How did you decide? (e.g. Knowing that 10 + 9 = 19
and 7 + 3 = 10, tells us that 7 + 3 + 9 = 19)
Clicking on ‘Clear’ will reset the screen to allow answers to
be highlighted.
Move to question 2.
Click on the spinner and then on the ‘Spin’ button on the
toolbar to select a number. Ask children to subtract the
number from 19 and show their answers using their number
fans.
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© Cambridge University Press
www.cambridge.org
Cambridge University Press
1845659570 - KS2 Addition and Subtraction Teacher’s Notes
Anthony David and John Spooner
Excerpt
More information
Year 3 Addition and subtraction
Adding multiples of 5 and ‘a bit’
Splitting numbers into a multiple of 5 and ‘a bit’ to make
addition easier
Objectives
AS3L1
Establish that they have both been split into two parts and
that the larger part of each number is a multiple of 5.
Q Does the order in which we add these numbers make
any difference to the total? (no)
Which order might be sensible to use, now that the
numbers are split?
•
Use knowledge that addition can be done in any order to
do mental calculations more efficiently.
•
Partition into 5 and ‘a bit’ when adding 6, 7, 8 or 9
(e.g. 47 + 8 = 45 + 2 + 5 + 3 = 50 + 5 = 55).
Establish that adding the multiples of 5 and then adding the
‘bits’ will be one sensible way. Click on ‘Play’ to see this
happen.
•
Use informal pencil and paper methods to support,
record or explain calculations.
Q So, what is the total?
Prior knowledge and skills
•
Recognising that addition can be done in any order
•
Understanding that more than 2 numbers can be added
Vocabulary
Elicit the answer (43). Click on ‘Play’ to reveal it on screen.
Repeat the activity with questions 2, 3 and 4. When you get
to question 4 (67 + 16), discuss how you will split the 16.
Establish that the same ‘5 and a bit’ method will split 16 into
15 + 1.
(Page 2 on whiteboard)
add, sum, total, more than, multiple of
Resources
•
interlocking cubes arranged in lengths of 1, 5 and 10
(optional)
Possible starter
AS3S1 Multiples of 5 and ‘a bit’
Main teaching activity
Whole class
(Page 1 on whiteboard)
This page allows you to demonstrate adding other pairs of
numbers using the 5 and ‘a bit’ method. Use it to try more
TU + TU additions, perhaps using numbers that children
suggest.
Clicking on the number boxes will reveal a number pad that
can be used to enter your own choice of numbers. Clicking
on ‘Play’ will then take the animation through the same
stages as on whiteboard page 1. Clicking on ‘Clear’ will reset
the screen and allow for another calculation.
(Page 3 on whiteboard)
Refer to the addition 37 + 6 at the top of the screen. Ask:
Q How would you work out the total?
Discuss suggestions. Tell children that you are going to look
at using 5 as a helpful number.
Click on ‘Play’ to rewrite the addition as (35 + 2) + (5 + 1).
Q What has happened to 37 and 6 from the starting
addition?
Ask children to highlight a set of numbers on the number
grid where the units digit is greater than 5, e.g. 16, 37, 49, 8,
77, 6 … Make sure that several single-digit numbers are
included. Select a ‘fill colour’ button and then click on a
square to colour it. To remove the colour, select the
Mult-e-Maths © Cambridge University Press 2004
© Cambridge University Press
www.cambridge.org
Cambridge University Press
1845659570 - KS2 Addition and Subtraction Teacher’s Notes
Anthony David and John Spooner
Excerpt
More information
Adding multiples of 5 and ‘a bit’
AS3L1
‘Remove colour’ button and click on the square again. Click
‘Clear’ to remove all shading.
Individuals
Ask children to choose pairs of highlighted numbers from the
grid. They then add their pairs of numbers using the 5 and ‘a
bit’ method, recording the splits that they make.
Support: Children make pairs by picking one 2-digit number
and one 1-digit number. They could use interlocking cubes
to model the pairs of numbers, splitting each number into a
multiple of 5 and ‘a bit’.
Extension: Ask children to add some of the highlighted
2-digit numbers to a 3-digit number such as 109 or 117.
Q Can you still use the 5 and ‘a bit’ method with larger
numbers such as these?
Plenary
Discuss some of the additions children created during the
independent activity. Ask questions such as:
Q How would you split the numbers?
Which parts of the numbers would you add first?
Why?
How does the 5 and ‘a bit’ method help us?
You could use whiteboard page 2 to demonstrate some
examples.
Ask a series of mental questions encouraging children to
add doubles of numbers by partitioning numbers into
multiples of 5 and ‘a bit’, e.g.
16 + 16 = 15 + 1 + 15 + 1 = 30 + 2 = 32
Key idea and assessment
Mental addition can sometimes be made easier by splitting
numbers into useful parts.
Can children …
•
partition numbers into multiples of 5 and ‘a bit’?
•
use informal written methods to support addition?
Personal notes
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© Cambridge University Press
www.cambridge.org
Cambridge University Press
1845659570 - KS2 Addition and Subtraction Teacher’s Notes
Anthony David and John Spooner
Excerpt
More information
Year 3 Addition and subtraction
Using inverse operations
AS3L2
Using subtraction to find the missing numbers in addition
problems
Click the ‘Play’ button to complete the number statement
and label the line at 33. An arrow showing ‘ 4’ will also
appear. Ensure that children understand the labelling.
Objectives
Click the ‘Play’ button again and a second arrow will appear
below the line, this time pointing in the opposite direction
and labelled ‘+ 4’.
•
Extend understanding that subtraction is the inverse of
addition.
•
Use inverse operations to solve missing number addition
problems.
Prior knowledge and skills
•
Understanding the operations of addition and subtraction
Vocabulary
add, addition, altogether, count on, plus, take away,
subtract, subtraction, count back, minus
Resources
•
Establish that subtraction can be used to find the missing
number in the addition problem because subtraction undoes
addition.
Click on ‘Clear’ to repeat with other numbers. You must
always drag a green number into the green box and a yellow
number into the yellow box. Before clicking ‘Play’, ask
questions such as:
Q What will the missing number be?
What will the arrows show on the number line?
How do you know?
(Page 2 on whiteboard)
Resource sheet
Possible starter
AS3S3 Matching additions and subtractions
Main teaching activity
Whole class
(Page 1 on whiteboard)
This page allows you to use larger numbers than on the
previous screen and also lets you decide which of the boxes
to the left of the equals sign will contain the number, so you
can create missing number additions of the forms ? + 14 =
50 and 14 + ? = 50
Drag a number into one of the boxes on the left-hand side of
the equals sign and drag a larger number into the box on
the right-hand side. A question mark will automatically
appear in the third box.
There is no number line, so ask:
Drag 4 from the number grid into the green box in the
addition statement and 37 into the yellow box to make the
missing number problem ? + 4 = 37
Look at the number line, which will now be labelled 37 at its
right-hand end. Point to this number and ask:
Q I added 4 to a number and the total was 37.
Q There is no number line this time, so how will you
work out the missing number?
Establish that you can use subtraction to find the missing
number. (If appropriate, you could use the number line tool
from the Mult-e-Maths Toolbox set with suitable values to
illustrate this.) Click on the box with the question mark to
reveal the answer.
What number did I start at?
Repeat with different numbers as necessary.
How could you work it out?
Individuals
Elicit that you could count back 4 along the number line.
Count back together along the number line to identify that
the number would be 33.
Use the Resource sheet. Children make their own missing
number problems from the given numbers and solve them.
Once they have completed the first 6, they can make up
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1845659570 - KS2 Addition and Subtraction Teacher’s Notes
Anthony David and John Spooner
Excerpt
More information
Using inverse operations
AS3L2
further problems using any two numbers between 1 and 50.
They should record these on the back of their Resource
sheets.
Support: Keep the same total for the first 6 problems, e.g.:
? + 5 = 20
? + 9 = 20
Once children have completed these, use a second copy of
the Resource sheet and allow them free choice from the
given numbers.
Extension: Show whiteboard page 2 rather than using the
Resource sheet. Children make their own missing number
problems, some where the second number in the sentence
is missing (e.g. 6 + ? = 45) and some where the first
number is missing (e.g. ? + 6 = 45). They can choose freely
from the numbers on the grid, but must make sure that the
total is the largest number.
Plenary
Display whiteboard page 2 again. Invite children to show
some of their problems completed as part of the individual
work. They can drag the relevant numbers into the
statement.
For each problem, ask:
Q What will the missing number be?
How can you work it out?
Hear suggestions. If children suggest counting back along a
number line, you could use the number line tool from the
Mult-e-Maths Toolbox to show this, but encourage them to
work out the answer by performing a subtraction.
Key idea and assessment
Subtraction undoes addition.
Can children …
•
find the missing number in an addition problem involving
1- and 2-digit numbers;
•
recognise that subtraction undoes addition?
Personal notes
Mult-e-Maths © Cambridge University Press 2004
© Cambridge University Press
www.cambridge.org
Cambridge University Press
1845659570 - KS2 Addition and Subtraction Teacher’s Notes
Anthony David and John Spooner
Excerpt
More information
Year 3 Addition and subtraction
Partitioning and addition
AS3L3
Partitioning numbers into tens and units to help with addition
the 50 card from 52 into the yellow box of the first addition
and the 2 card into the yellow box of the second addition.
Objectives
Make sure children understand both the partitioning and that
adding the four numbers produced will give the total for
24 + 52. Emphasise that it is sometimes helpful when adding
2-digit numbers to split them into their tens and units parts,
and to add the tens parts and then the units parts.
•
Use knowledge that addition can be done in any order.
•
Understand how to partition into tens and units, then
recombine (e.g. 34 + 53 = 30 + 50 + 4 + 3).
Q What total will we get if we add the tens parts?
Prior knowledge and skills
•
Understanding place value for units and tens
Click on the appropriate orange answer box to confirm that
the answer is 70.
•
Knowing that you can add more than two numbers
Q What total will we get if we add the units parts?
Vocabulary
Click on the appropriate orange answer box to confirm that
the answer is 6.
Resources
Establish that to find the answer to 24 + 52, you now need to
add 70 and 6. Click on the remaining orange boxes to
display this addition.
•
Resource sheet
Q What will we get if we add 70 and 6?
•
place value cards
Click on the blue answer box to confirm the answer as 76.
•
base 10 apparatus or spike abacus
Repeat the activity for the other three examples, clicking on
‘>>’ to move to the next example each time.
digit, units, tens, add, total, altogether
Possible starter
(Page 2 on whiteboard)
AS3S5 Making 19
Main teaching activity
Whole class
(Page 1 on whiteboard)
You could use this page to create, and work through,
examples of your own where the units digits have a total
greater than 10.
Refer to the addition on the board: 24 + 52
Draggable place value cards for units, multiples of 10 and
multiples of 100 can be created by clicking on the
appropriate number on the place value chart. Place value
cards can be combined by dragging them on top of one
another, e.g.
Q Which place value cards make 24?
Children hold up place value cards to show their answers.
Establish that you need a 20 card and a 4 card.
Q Which cards do I need to make 52?
Children use place value cards to show their answers.
Establish that you need a 50 card and a 2 card.
Explain that you are going to use the tens and units parts of
the numbers to help with the addition. Drag the 20 card from
24 on the board into the green box of the first addition, and
the 4 card into the green box of the second addition. Drag
Pairs
Children use the Resource sheet. They complete the tens
and units partitions and find the totals. They then write 4
additions for their partner to try. When they are completed,
Mult-e-Maths © Cambridge University Press 2004
© Cambridge University Press
www.cambridge.org
Cambridge University Press
1845659570 - KS2 Addition and Subtraction Teacher’s Notes
Anthony David and John Spooner
Excerpt
More information
Partitioning and addition
AS3L3
they swap and check each other's work.
Support: Children work on the Resource sheet as a group
with an adult. Use place value cards to perform the
partitioning. You could also model the addition and check
answers using base 10 apparatus or a spike abacus.
Extension: Challenge children to write their own problems
where the units digits make a total greater than 10, e.g.
29 + 47
Plenary
Use whiteboard page 2 to perform some of the additions
from the Resource sheet. As you do, ask questions such as:
Q How will you split the numbers?
What will the tens parts total? What will the units
parts total?
Would it make any difference if we added the units
parts first and the tens parts second?
Invite children to show some of the questions that they have
written. Work through them as a class to check children’s
answers.
Key idea and assessment
Splitting numbers into their tens and units parts can help us
to add the numbers.
Can children …
•
partition 2-digit numbers into their tens and units
components?
•
add two 2-digit numbers mentally?
Solutions
Resource sheet part A
1
38
2
37
3
57
4
79
5
69
6
85
7
88
8
77
Personal notes
Mult-e-Maths © Cambridge University Press 2004
© Cambridge University Press
www.cambridge.org