Transcript Progression In Calculations.

Progression In Calculations.
Division
Mathematical Calculations in East Worthing Schools.
This document has been discussed and agreed by all East Worthing Maths
Leaders and is designed to help you to understand the calculation
methods your child will be taught in school. When supporting your child
at home with Maths work it would be helpful if you could reinforce these
methods rather than teach them the way that you were taught. Your
child’s teacher will be able to direct you to the appropriate method
within this document to use at home.
Remember each child progresses at their own pace.
Understanding Division as sharing.
Share 10 sweets between 2 friends.
One for you, one for me, one for you….
Until all shared out equally. Count both
piles to ensure that they are equal.
Use Numicon to explore how many
shapes cover another larger one. Eg,
how many 2 shape cover an 8 plate?
So 10 shared by 2 is 5.
Key Questions/Vocabulary
Share, share equally, share between
Share fairly, halve
How many each?
How many in each group?
Explanation
Children need to experience
sharing a set of objects equally
between people or teddies,
initially between 2. It is
important that they realise that
things must be shared equally.
Success Criteria
• I can share a set of
objects equally between
people.
Understanding Division as Grouping.
How many lengths of 2 metres can be cut from a
10 metre length of ribbon? This links to the
understanding of division as repeated
subtraction.
10 – 2 – 2 – 2 – 2 – 2 = 0
Encourage children to read divisions as
‘How many in?’ (EG. 10 ÷ 2 is How many
2’s in 10?) In this way children are able
to begin to apply their times table
knowledge by seeing how many times
they count in 2’s to reach 10.
So 5 lots of 2 metres can be cut.
Key Questions/Vocabulary
Share, share equally, share between
Divide, repeated subtraction
How many each?
How many groups?
Explanation
Children need to experience
dividing a set of objects by
grouping them equally or
repeatedly taking away groups
of equal size.
Success Criteria
• I can understand division as
‘How many in?’ and use my
times table knowledge to help
me to solve them.
Division on a Number Line.
Division can be understood on a number line. It is important to remember that the
answer will be found by counting how many jumps were needed to reach the target
number.
It is easier to count on than count
15 ÷ 5 = 3 (read as How many 5’s are in 15?’)
3 groups of 5 were jumped from 0 to reach 15.
5
0
5
5
Key Questions/Vocabulary
Share, share equally,
share between
Divide, division, grouping
How many ...... in ...?
Inverse
5
10
back, so by getting children to read
division calculations as ‘How many...
in...?’ they can link their times tables
to division. In this way they are able
to apply their knowledge of inverse
operations. This enables them to solve
divisions by counting on instead of
having to repeatedly subtract and
count back.
15
Explanation
Blank number lines can be used to enable children
to count in jumps of repeated sizes. Children
are taught to draw their own blank number lines,
enabling them to do calculations within any range
of numbers. Initially they need to work with ÷ 2, 5
and 10 with no remainders.
Know doubles up to
double 10 and
corresponding halves.
Know ÷ facts for related
2, 5 and 10 times
tables.
Success Criteria
• I can understand
division and represent
it as jumps on a
number line.
Division with Remainders.
It is important to remember that the answer will be found by counting how many
times the dividing number will go into the first number until it is impossible to do
any more even jumps. The left over amount is the remainder and cannot be greater
than or equal to the dividing number.
21 ÷ 5 = 4 r 1
How many 5’s are in 21? There were 4 jumps of 5 with 1 left over.
5
0
5
5
Key Questions/Vocabulary
Share, share equally, share between
Divide, division, grouping
Remainder, left over
How many ... in...?
How many are left over?
5
10
5
15
Explanation
When children understand division and are
able to accurately solve TU ÷ U with no
remainders, then they are ready to solve
more complex problems that do involve
remainders. Initially this would be with
remainder 1, moving on to other remainders
when they understand the concept.
20
21
Know by heart the
2, 5 and 10 times
tables.
Success Criteria
• I can solve
division with
remainders on a
number line.
Division using Chunky Jumps with Remainders.
When children are ready to move on to this more efficient method, they need to be applying their
knowledge of times tables in chunks to reach the number they are dividing. It helps to write a ‘What I
Know!’ Box listing the key facts for x1, x2, x5 and x10.The answer is found by counting how many chunks
of the divisor were taken.
What I know!
3x1=3
3x2=6
3 x 5 = 15
3 x 10 = 30
73 ÷ 3 = ? How many 3’s are in 73?
So 3 x 10 =30
And another 3 x 10 = 30 takes you to 60
That leaves 13 left and I know that 3 x 4 = 12 so 73 ÷ 3 = 24 r 1
3 x 10
0
Key Questions/Vocabulary
Share, share equally, share between
Divide, division, grouping
Remainder, left over
How many ... in...?
How many are left over?
3 x 10
30
3x2
60
Explanation
When children understand division with
remainders and are able to solve them
effectively using a number line, then they
are encouraged to apply their knowledge of
times tables to become more efficient in
their calculation strategies. To begin with
this would still be with TU ÷U but moving on
to HTU ÷ U.
3x2
66
72 73
Know the 2, 3, 4, 5 and
10 times tables. Begin
to know the 8 times
tables.
Success Criteria
• I can solve
division with
remainders on a
number line.
Moving from Chunky Jumps to Short Division.
When children are ready to move on to this more efficient method, they need to be applying their
knowledge of times tables in chunks to reach the number they are dividing. It helps to write a ‘What I
Know!’ Box listing the key facts for x1, x2, x5 and x10.The answer is found by counting how many chunks
of the divisor were taken.
What I know!
Key Questions/Vocabulary
Share, share equally, share
between
Divide, division, grouping
Remainder, left over
How many ... in...?
How many are left over?
•
•
Explanation
When children understand division with
remainders and are able to solve them effectively
using a number line, then they are encouraged to
apply their knowledge of times tables to become
more efficient in their calculation strategies. To
begin with this would still be with TU ÷U but
moving on to HTU ÷ U. Those very confident with
these strategies should be able to move onto the
short division methodology.
Y4 – up to 3 digit ÷ 1 digit with whole number
answers
Y5 – up to 4 digit ÷ 1 digit with remainders
Know all your times
tables.
Success Criteria
• I can solve
calculations using
short division
Short Division / Long Division
Once children have conquered short division they will move on to this compact method of long division with
up to 4 digits ÷ 2 digits. They still need to be applying their knowledge of times tables in chunks to reach
the number they are dividing. It helps to write a ‘What I Know!’ Box listing the key facts for x1, x2, x5
and x10.
Key Questions/Vocabulary
Share, share equally, share between
Divide, division, grouping
Remainder, left over
How many ... in...?
How many are left over?
Explanation
When children understand division with
remainders then they are encouraged to
apply their knowledge of times tables to
become more efficient in their calculation
strategies. Examples above show how
chunking fits in too.
•
Y6 – up to 4 digit ÷ 2 digit with decimals
up to 2 decimal places in answers
Know all your times
tables.
Success Criteria
• I can solve
calculations using
short or long
division