Division activities
• The remainders game
• Using a 1-6 die, play like connect four – or if you
only want to divide by 2, 5 and 10, adapt the die
to have these numbers
• Children choose a number between 20 and 50
• Roll the die. Divide the chosen number by the
number shown on the die and cover up the
remainder with a counter on the board.
• First to get 4 counters in a row wins.
• Board for 1-6 die:
A gang of 6 pirates shared out
the pile of gold bars they had
stolen. They had one bar left
over. They argued about who
should have it. A fight began.
One of the pirates was killed.
The remaining pirates shared
out the gold again hoping it
would work out exactly. It
didn’t. This time there were
four bars left over.
How many gold bars had they
stolen?
Can you find more than one
right answer?
• Can you order the digits 1 2 3 4 5 and 6 to
make a number which is divisible by 6 ...
• ... so that when the final or last digit is removed it
becomes a 5-figure number divisible by 5?
• And when the final digit is removed again it
becomes a 4-figure number divisible by 4?
• And when the final digit is removed again it
becomes a 3-figure number divisible by 3?
• And when the final digit is removed again it
becomes a 2-figure number divisible by 2,
• then finally a 1-figure number divisible by 1?
Division party scenarios
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How many apricots will we each have if 1kg is shared between 12 of us? There are roughly 30
apricots in one kilogram.
There are 40 sandwiches and 12 people at the party. How many will each guest be able to
have? What shall we do with the spares?
Here is a cake, we need to share it between the 12 people at the party. How do we do it?
There are 5 pizzas. How can we share them between the 12 people?
We have 3 litres of juice for a party of 12 people. How many 120ml glasses will it fill? How
many glasses each will that give everyone?
I am making invitations for a party and want them to be 10cm by 12cm. How many will I be
able to cut out of each A4 sheet of card that I have? How many sheets of card will I need to
make 12 invitations.
I am making bunting to hang across the room. How many flags will I need to make to reach
across the diagonal of the hall measuring 6m by 7m? You will need to think about the size of
the flags, their shape, the tape or string they are fixed to and the gaps between them. To put
them across both diagonals and along all four of the sides, how many more will I need?
I have a bag of 30 balloons to decorate the hall. How many groups of 4 can I make?
If 12 people come to the party, how can I divide them into teams? What would be the best way
to do this?
If 12 people come to the party and they all go bowling by car from the hall, how many cars will
be needed if each car can take 5 people? How many cars will be needed if each car has to
have an adult to drive it in addition to the party guests?
• The remainders game
• Using a 1-6 die, play like
connect four – or if you
only want to divide by 2, 5
and 10, adapt the die to
have these numbers
• Children choose a
number between 20 and
50
• Roll the die. Divide the
chosen number by the
number shown on the die
and cover up the
remainder with a counter
on the board.
• First to get 4 counters in
a row wins.
• Board for 1-6 die:
1
2
3
5
0
3
0
1
1
0
2
3
2
1
4
4
3
4
5
0
5
3
0
5
4
• 1. Introducing division ‘How many in ….?’
• (Key ideas: Division – quotient structure, inverse)
• To begin to understand quotient division as the inverse of
multiplication.
• Activity 1 (introduce on the table top or using Numicon software)
• 1. Teacher places a marker on the number track on any number that
appears as a product in one of the multiplication tables 2,3,5,or 10
eg 50.
• 2. Ask ‘How many 10s are contained in the 40?’ The children can
insert the 10-rods into the Track to show that 4 are needed.
• 3 Teacher continues to move the marker from place to place (onto
any product of the 10x table) each time asking the question, ‘How
many 10’s in the number?’.
• 4. Once children are used to the activity, discuss how this may be
written. The a division number sentence as ‘How many 10’s in 40?’.
• 1. Reverse the game so that the children read the written
question, place the marker and find the answer.
• 2. Ask children how the answers may be found and
relate these to multiplication. Using the rods, make the
connections between multiplication and division.
Reinforce by putting together and taking apart the
multiplication and division facts.
• Activity 3 Find The Partner (Games for 2 players)
• 1. One player takes rods and says how many ? are in ?
Second player has to use the rods and say the
multiplication fact. Record both the division and inverse
multiplication fact.
• 2. Reverse the above game so first player says the
multiplication fact and the second says how many ? are
in the number.
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. Divison beginning to understand remainders.
(Key mathematical ideas – quotation division, using inverses)
To experience remainders in quotation remainders.
1. Teacher places a marker on any number, eg 32. Write the fact to
be solve as it is being asked ‘How many 5’s are in 32?’
• 2. Children place the 5 rods in the Number Track obviously up to 30.
The remaining 2 spacs can be filled by the 2 rod to reach 32. Write
out the number sentence.
• 3. Practice other examples. Ask how the facts can be checked (by
relating to the multiplication facts – knowing the inverse – and then
finding the distance (or difference) between the multiple and the
given total to find the remainder.
• 4. Paired learning. The first player marks a number on the Rod
Number Track. The second player chooses which rods will be used
(2,3,4,5,10’s) to find out how many of them are in that number. Both
players write the fact and try to use their knowledge of multiplication
facts to answer. Check using the track. (Assessment question –
‘Can you find a fact that will give this answer.)
3. Finding half of small numbers
• (Division – scaling structure)
• 1. Put out the Numicon 8-shape and ask the children to find half.
• 2. Discuss which way they would split the amount and that half is
always 4.
• 3. Find half of 6. Place the two 3-shapes over the 6 and then give
half each to two children. Repeat with 10, 4 and 2. (Make between
halves and doubles).
• 4. Take a basket of objects. Stress that we must see the total before
we can find half. Arrange the objects into Numicon patterns. Now
children can see half the total
• (Discuss with children what would happen if you had an odd number
of objects. If the object were apples or fish fingers, how would you
share out the one left over? But if the objects were pencils or books
they could not be shared. Look at how to record ½. Ask the children
where they would place ½ on the number line.
• 5. Independently the children could count arrangements of pictures
on paper. Encourage them to find the total by counting then remind
them to recall the Numicon pattern using their mental imagery to see
half. (Assessment question – ‘How do you know you have half?’
4. Half of multiples of ten and other numbers
• (Division – scaling structure)
• To find half of multiples of ten and other numbers.
• 1. Say ‘If half of 4 is 2, what is half of 4 tens?’
• 2. Mak 40 with four Numicon 10-shapes. Share between two
children, so that they can easily see they each have 20.
• 3. Repeat with 60, 80 and 100.
• 4. Make 30 with three Numicon 10-shapes. Give one ten shape to
one child and one 10-shape to another. Discuss what is to be done
with the last 10-shape.
• 5. Replace the 10-shape with two 5-shapes, give each child their 5
and check by looking at each child’s shapes that half of 30 is 15.
• 6. Repeat for 50, 70 and 90.
• 7 Now extend to finding half of 22, 24, 26 and 28. Make the numbers
with Numicon and find half of the tens and half of the units.
• 8. Generate numbers using card and half them.
• (Assessment question – If 8 is half, what was the number I started
with?’)
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5. Beginning to understand fractions
(Division and fractions as operators)
To introduce fractions as operators and division as scaling.
Activity 1
1. Divide 12 cubes equally between 3 small baskets so that there are 4 in each
basket.
2. Record as 1/3 of 12 = 4. Explain that the line of 1/3 is a division line indicating that
the total has been dividd by 3.
3. Divide 12 by 6, 2 or 4 using 6,2 or 4 small baskets. Record results
12 divided by 6 = 2 1/6 of 12 = 2
12 divided by 2 = 6 ½ of 12 = 6
12 dividd by 4 = 3 ¼ of 12 = 3
4. Check results using the inverse multiplication fact. Lay the six 2 rods (or Numicon)
along the Number Track (or Numicon along the Tens Number Line) to see that 6 x 2
= 12 and that 12 divided into 6 parts equals 2 (for each part). Emphasise that when
the same number is divided into a varying number of parts, the size of the parts
becomes smaller as the number of parts increases.
5. Independent activity for pairs. Make a set of cards with the numerals divisible by
2,3,4,5,6,and 10. (6,8,10,12,15,16,18,20,24,25,28,30). On the reverse of the cards
write the fraction that the number may be divided into eg 18 with ½, 1/3 and 1/6
written on the back, 25 with just 1/5 written on the back. Use the Numicon fraction
spinner overlay, spin the spinner and then pick up a card with that fraction on it. Find
the fraction of the number. Challenge the children to make arrays of a particular
number by arranging counters eg Using 12 counters can they make a rectangle
where one side is 6?
Stories
• To help children to connect the symbols for
multiplication and division with a wide range of
situations and language.
• Give children some multiplication and division
statements (such as 8x3=, 15 divided by 3 =)
and ask them to write stories to go with them.
Encourage the children to use different models
and contexts for multiplication and division, by
giving the beginnings of some stories. For
example, children could be asked to writ a story
for 15 divided by 5, beginning @Meg had £15 to
spend on cds…..’ Another approach is to specify
contexts, for example by saying the 15 divided
by 5 story is about a person who walks for 15
miles.