Transcript Vocabulary/Language - Lyndhurst Infant School

Progression In Calculations at
Lyndhurst First School.
Multiplication and
Division
Mathematical Calculations in School Today.
The phases indicate progression in the development of children’s
jottings to support their calculations. The phases do not
represent any specific Year Group or National Curriculum level.
Remember each child progresses at their own pace.
Phase 1 - Understanding Multiplication as repeated addition.
Children could count out repeated groups of the same size using
sweets, pencils, counters etc.
2 add 2 add 2 makes 6
2+2+2=6
3 lots of 2 makes 6
Vocabulary/Language
Lots of, groups of
Double
Repeated addition
Once, twice, three times…..
Explanation.
Children need to experience physically
counting repeated groups of the same
size. This is best done in a ‘real-life’
context.
Phase 1 –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.
Vocabulary/Language
Share, share equally, share between
Halve
How many each?
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.
Phase 1 –Understanding Division as grouping.
Share 10 sweets between 2 friends by
repeatedly taking away groups of 2 and
counting how many piles there are.
Vocabulary/Language
Share, share equally, share between
Divide
Halve
How many each?
Explanation
Children need to experience dividing a set
of objects by grouping them equally or
repeatedly taking away groups of equal
size.
Phase 1 – Recognising Patterns in Numbers.
By counting on in twos and
colouring in the numbers it is
clear to see the pattern
created. This helps children
to understand odd and even
numbers and recognise what
multiples of 2 end with.
This activity can be done
with any times table and
allows children to see
patterns in the times tables
which may help them to
learn them.
Vocabulary/Language
Count on in twos, fives, tens…
Add, plus, more than, count on
Digits, pattern
Multiples of…
1
2
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100
Explanation
Working with a hundred square helps
develop a childs’ understanding of the
number system. Looking at the patterns in
numbers created by colouring in steps of
the same size can help a child to learn and
predict the times tables.
Phase 2 – Multiplication on a Number Line.
Multiplication can be understood as a series of additions on a number line. It is
important to start at 0 and ensure that each jump is the same size.
4 lots of 2 is 8
6 lots of 5 is 30
2+2+2+2=8
5 + 5 + 5 + 5 + 5 + 5 = 30
2x4=8
5 x 6 = 30
0
2
4
6
8
Vocabulary/Language
Lots of, groups of, times, multiplied by
Repeated addition
0
5
10
15
20
Explanation
25
30
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, although initially they learn the
2, 5 and 10 times tables.
Phase 2 – Division on a Number Line.
Division can be understood as repeated subtraction on a number line. It is
important to remember that the answer will be found by counting how many times
the number was repeatedly subtracted until 0 was reached.
15 ÷ 5 = 3
3 groups of 5 were subtracted from 15 to reach 0.
-5
0
-5
5
Vocabulary/Language
Share, share equally, share between
Divide, division, grouping
-5
10
15
Explanation
Blank number lines can be used to enable
children to count back 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.
Phase 2 – Multiplication as an Array.
2 lots of 3 = 6
3 lots of 2 = 6
3x2=6
2x3=6
Vocabulary/Language
Lots of, groups of, times, multiplied by,
multiplication, product
Equals
Array, grid, representation
Explanation
The arrangement of circles clearly represents
the number sentence and can aid visual
learners to understand multiplication.
This can be developed to grids used as a
visual model.
Phase 3 – Multiplication on a Grid.
30
30
5
20
210
7
35
3
7 x 35
7 x 30 = 210
1
600 20
90
3
23 x 31
245
7 x 5 = 35
Vocabulary/Language
Lots of, groups of, times, times by, multiplied
by, multiplication, multiply, product
Repeated addition
Equals
600 + 90 + 20 + 3 = 713
Explanation
The grid method of multiplication is a
development of the Array and allows more
complex problems to be broken down into
more manageable calculations. Children
would be working on problems with TU x
U, progressing to TU x TU.
Phase 3 – Division with Remainders.
It is important to remember that the answer will be found by counting how many
times the dividing number was repeatedly subtracted until it is impossible to
subtract the same number again without going past 0. The left over amount is the
remainder and cannot be greater than or equal to the dividing number.
21 ÷ 5 = 4 R1
4 groups of 5 were subtracted, with 1 left over.
-5
0 1
-5
6
Vocabulary/Language
Share, share equally, share between
Divide, division, grouping
Remainder, R, left over
-5
11
-5
16
21
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.