Transcript count on in multiples

Wallands Community Primary School
Mathematical Methods
Information for parents
Key Stage 2
Mathematical Methods
This booklet is designed to give you information about the main
methods for calculating in mathematics that your children are
learning in school. The children start by learning mental methods
and informal jottings and progress to formal written calculations.
•
•
•
•
Addition
Subtraction
Multiplication
Division
Addition
+
Key Words
add, addition, plus, total, sum
of, more, increase, altogether
Mentally children should add using a count on method.
They may imagine an empty number line in their heads, e.g.
85 + 47 =
+40
85
125
+7
count on…
Or they may partition into tens and units adding each
separately, e.g.
85 + 47 = 132
80 + 40 = 120
5 + 7 = 12
120 + 12 = 132
132
For trickier additions they are more likely to use a column
method as shown below:
85
+47
132
1
To help with addition,
practise quick recall of
number bonds to 10
and adding through
multiples of 10, e.g.
18 + 7, 43 + 9 etc
Subtraction
-
Key Words
take away, subtraction,
subtract, minus, decrease,
difference, less than,
leave, left over
For subtraction we use an empty number line method as this encourages the
children to understand what is happening in the calculation.
85 - 47 =
Here is the answer, 3+30+5 = 38
Remember you can re-order the numbers
in an addition. Put the biggest number first
so 30+5+3 = 38
+30
+3
+5
47 50
80 85
count on…
Most children find it
easier to count on.
When we count on, we are actually finding the difference.
• Place the lowest number on the left of the number line.
• How much do you need to count on to get to the larger number?
Or, you could do it like this…
Here is the answer
-7
38
45
-40
85
…count back
Some children prefer to count back.
• Place the highest number on the right of the number line.
• Count back splitting the number into tens and units.
For trickier subtraction the children will learn a column
method. First they will learn an expanded method where
the numbers are split into hundreds, tens and units.
56 – 32 =
T
U
TU
50 +
6
56
- 30 +
2
- 32
20 +
4
24
By teaching the children this expanded
method, they are able to understand
decomposition of numbers (borrowing)
when it comes to more complex
subtractions.
Decomposition:
754 = 700 + 50 + 4
- 286
200 + 80 + 6
-------------------------
700 + 40 + 14
- 200 + 80 + 6
600 + 140 + 14
- 200 + 80 + 6
---------------------400 + 60 + 8 = 468
Start with the units.
4 – 6 can’t be done!
So 700 + 50 + 4 becomes
700 + 40 + 14
Now the units column can be
subtracted, work it out and move on to
the tens and the hundreds etc.
The final stage in subtraction is to use a more compact and
efficient method like this:
6 14
7 5 14
-286
468
Don’t forget to line up the hundreds, ten
and units carefully!
When children are confident with this
type of subtraction, they will work with
bigger numbers and decimals in
exactly the same way.
Multiplication
x
Key Word
multiplication, multiply by,
times, product, multiple, lots
of, groups of, product, array
When multiplying quick recall of tables is the most
important thing. So knowing multiplication and
division facts up to 10x10 is vital.
When using repeated addition a number line or informal
jottings can be used, e.g.
…or children may count up in multiples, e.g. 3 x 5
“3… 6… 9… 12… 15!”
…or children may draw an array, e.g. 4 x 2
Grid method multiplication involves partitioning each
number into tens and units before multiplying and then
adding back together.
12 x 4 =
10
X
4
10x4
= 40
2
2x4
=8
40 + 8 = 48
It is very important for children to estimate their answers before
starting a calculation!
By setting the final
adding part out vertically as in this
example, children are able to see
how this links to short multiplication.
68 x 7 =
X
7
60
60x7
=420
8
7x8
=56
420
+56
476
52 x 49 =
X
40
9
50
2
40x50
=2000
40x2
=80
50x9
=450
9x2
=18
2000
+450
80
18
2548
1
Short multiplication is taught in Year 6.
It is a quick method which is particularly useful when multiplying
using decimals.
Estimate your answer first:
7.92 x 6 =
7.92 is between 7 and 8,
but closer to 8.
7 X 6 = 42
8 x 6 = 48
So the answer must be between
42 and 48 but closer to 48.
7. 9 2
x
6
4 7. 5 2
5 1
1 2 5 8
x
3
3 7 7 4
1 2
Division
÷
Key Words
divide, division, divided by,
divided into, share, group, split
into equal groups, count in
multiples, repeated subtraction
remainder, factor, quotient,
divisible by, inverse
Children learn about division through practical activity.
They need lots of practice sharing out to make groups
and counting in multiples.
When dividing it is vital that children know their division facts,
e.g. 15 ÷ 3 = 5
Children are encouraged to ask a division as…
… How many 3’s are there in 15?
When using repeated subtraction children use informal
jottings to group, e.g. How many 3’s in 15?
…or children may count on in
multiples like this:
…or children may
share out into
groups like this:
Chunking
(division as the inverse of multiplication)
After lots of practical work and using known division facts
children will move onto the first written method of division –
chunking. This method makes use of their multiplication
facts, which they should feel fairly secure in by the time
they attempt chunking (usually around Year 4). Chunking
helps them to see how division is the inverse of
multiplication.
91 ÷ 7 =
The inverse of this is 7 x ? = 91
Work out how many 7s are in 91
Use multiplication facts that you feel confident with and build
up towards your target number.
This is the
number you
multiply by
Your target number is 91. This is the number you
want to reach by counting up in 7s as you want to
find out how many 7s are in 91, which is the same
as 91 ÷ 7. It will take too long to count
up 7,14,21 etc so take a short cut by
using your multiplication facts.
7 x ? = 91
7 x 10 = 70
7 x 3 = 21
This is close to 91, but not close enough.
Can you fit anymore 7s into 91?
Add this column to get your answer. This is how many times you multiplied
7 to get 91, which is the same as saying 91 ÷ 7.
7 x 13 = 91
So, 91 ÷ 7 = 13
Bus stop method
Chunking is a great method to help children
really understand what is happening in division.
The bus stop method is a more efficient
method once the understanding is there. We
always teach chunking first.
How many 4s in 7?
1 and 3 left over.
2 1r3
How many 4s
in 8? 2
4
)8
7
1 3r5
2
)
7 9 6
How many 7’s are there
in 9?
How many 7’s are there
in 26?