Download Maths in Year 5 - Heddington Church Of England Primary School

Year 5
Heddington C.E Primary School
M. Dobbin 2013
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Introduction
This booklet is intended to clarify and explain some of the ways in
which your child is taught to write down calculations. You may be
surprised to find your child’s Mathematics book contains writing,
pictures, diagrams, jottings or blank number lines and not many
‘formal calculations’.
Certainly, many of the methods your child uses may be very different
from those that you learned at school and this can cause confusion
when you are trying to support your child at home.
From the very early years at school the emphasis on mathematics
learning is upon children understanding and applying the skills they
have learnt rather than just learning by wrote a formal written method
that they may not fully understand .
Here in this booklet we have tried as simply as possible to aid you in
understanding some of the strategies your children may use, in their
current year group, to help you, to help your children. You’ll be
amazed at how many different ways there are to attempt the same
idea!. The booklet contains the approaches your children may use to
support their thinking when solving addition, subtraction,
multiplication and division calculations. We have also included typical
mathematical vocabulary your child may be acquiring and using at
this stage.
This is a guide only; children will always progress at different speeds,
however support from you will undoubtedly be of great benefit to
them at all times.
We have tried to make the strategies as clear as possible however if
you are unsure of any ideas in the booklet please do not hesitate to
ask your child’s class teacher
Mrs. Dobbin
(Numeracy leader)
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Addition
Key Vocabulary: add, addition, more , less, sum, total ,
altogether, adjust, how many more, partition, hundreds,
tens, units, ones, decimal
In year 5 some children may continue to use a number line in
order to carry out addition, usually with larger numbers as
below, but will be encouraged to use the more formal standard
compact written method for addition.
 Informal jotting using a number line.
Some children will use an empty number line to support their
mental methods.
Eg: 236+ 353
+200
353
+ 30
553
+6
5 83
Answer= 589
5 89
 Standard compact written method
The expanded written method leads to a more compact method
involving carrying where necessary. However because the
children have gone through the process of the expanded
method, they have a greater understanding of what this new
method is all about.
e.g. 148 + 286
148
add the units eight plus six is fourteen
286
put one ten under the tens column and 4 in the
434
units column
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add the tens; forty plus eighty is one hundred and
Twenty add ten underneath, is one hundred and
thirty; put thirty in the tens column and one
hundred under the hundreds column.
add the hundreds; one hundred plus two hundred is
three hundred, plus one hundred underneath is four
hundred; put the four hundreds in the hundreds
column.
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Children will then use these same methods for the addition of
larger numbers, those with a different number of digits and
those with decimals.
For example 6.72+ 8.56+2.3
6.72
+ 8.56
2.30
17 . 58
1
4
Key Vocabulary: Subtract, minus, left, less, fewer,
decrease, leave, difference between, partition. recombine
Subtraction
Children will continue to be encouraged to think of subtraction
in two ways, finding the difference or taking away. Within
school children are taught both methods and will choose
whichever is most appropriate or easiest for them to use
according to the problem they are solving. In year 5 some
children may continue to use the number line to solve these
types of problems to support their mental thinking with
increasingly larger numbers but will be encouraged to use the
more formal compact method of subtraction
 .Informal jottings using an empty number line (by
counting forwards eg; finding the difference)
The mental method of counting up from the smaller to the
larger number can be recorded using a number line. Children
usually find it easiest to make the first jump to the next
multiple of ten.
Eg: 326 – 178=148
Most children will now be able to make larger jumps of
numbers, especially as they become more confident mentally.
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 Compact method of subtraction
441 – 122 =
3
4 4 11
-1 2 2
3 1 9
exchanging one ten
Children will again then apply these same methods to the
solving of problems with larger numbers and decimals, knowing
that the decimal points should line up with one another.
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Key Vocabulary: times, multiply, lots of, multiple,
product, repeated addition, array, grid method, double ,
grid method
Multiplication
Children in year 5 will continue to focus on learning
multiplication tables facts up to 10x10 and their associated
division facts. They will also be encouraged to related
these facts when solving problems using fractions and
percentages. They also need to use their knowledge of
place value to multiply and divide whole numbers and
decimals by 10 and 100.
Some children will continue to use the grid method of
multiplication to solve 2 and 3 digit multiplication problems and
will also learn an expanded written method before moving to a
more formal compact method
 Grid method of multiplication
Children will then progress to using a grid to multiply 2 digit by
1 digit numbers
Eg: 43 x 36
30
6
40
1200
240
3
90
18
Total
1290
258
1548
Total of 1548
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 Expanded Written Method
When multiplying by a single digit number an alternative
method for children in year 5 and 6
Is setting out multiplication is as a vertical calculation, e.g:
33 x 7:
3x7
30 x 7
total
33
x 7
21
2 1 0
2 3 1
multiply the units
multiply the tens saying thirty times 7
 Compact Written Method
Once children have a full understanding of the process some
will choose to and be ready to use a more concise method in
year 5 . The recording is reduced further, with carry digits
recorded below the line. If, after practice, children cannot use
the compact method without making errors, they should return
to the expanded format.
33 x 7
33
x7
1
seven times 3 is twenty one
put the twenty under the tens column
and the one in the units column
2
3 3
x 7
2 31
2
seven times thirty is two hundred
and ten plus the twenty underneath
makes two hundred and thirty
put the thirty in the tens column and the
two hundred in the hundreds column
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Again a method that can be applied to 2 and 3 digit
multiplication and multiplication of decimals
 Expanded written method -2 and 3 digits
Eg:
THTU
56
X 27
42
6x7=42
120
6x 20=120
350
50x7=350
1000
50x20=1000
1512
 Compact written method -2 and 3 digits
THTU
56
X 27
392
4
1120
1512
1
6x7=42 place 2 in units, put 4 tens under tens column
50x7= 350 + 40 = 390 giving a total of 392
6x20=120 + 50x20=1000 giving a total of 1120
add them together to give a final total of 1512
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Division
Key Vocabulary: share. group, divide, remainder, half,
array, repeated subtraction, divisor , factor, quotient,
divisor. chunking
In year 5 the numbers to be divided will become larger and
the children begin to use a method referred to as ‘chunking’
(Chunking refers to the ability to ‘group’ together or chunk’
large amounts when dividing)
 Simple chunking
40 10 lots of 4
16 4 lots of 4
56
Count up the lots of 4: 10 + 4 = 14
The answer can be similarly obtained by counting backwards
56
-40
16
-16
0
10 lots of 4
= 14 lots of 4
4 lots of 4
and again be used where there are remainders
eg: 96+ 7 =
96
-70
26
-21
5
10 lots of 7
= 13 r 5
3 lots of 7
10
 Expanded Written Method - ‘Efficient chunking’
As the number to be divided gets even larger, the method
needs to be made more efficient by working with larger
‘chunks’, e.g. 270 ÷ 7
If 10 lots of 7 are 70, what’s the biggest chunk (lot) of 7 I can
get from 270?
3x70= 210 so
2 7 0
-2 1 0
6 0
30 x 7
How many 7 are there in 60 8x7=56
2 70
- 2 1 0
6 0,
56
4
30 x 7
Count up the chunks
30 +8 = 38 with 4 left
answer = 38 r 4
8 x7
And again using larger numbers and decimals
972 ÷ 36
How many thirty sixes are there in 972?
What is the biggest ‘chunk’ (lot) of 36 I can get from 972?
36) 972
720 20 x 36
252
How many thirty sixes in 252?
36) 972
- 720
252
20 x 36
(10 x 36 = 360, double 360=720)
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-180 5 x 36 (10 x 36 = 360, halve 360=180)
72
- 72 2 x 36
0
Count up chunks or multiples of 36 = 20+5+2
so 972 ÷ 36= 27
.
If ready some children will also be introduced to the short ‘bus
stop’ method of division once they have a thorough
understanding of the division process
32r4
6) 11916
Web sites
Many parents have asked about web sites they could use with
their children to help them with their maths.
Here are a few suggestions but this list is not exhaustive and
remember all children in year 3 have a Mathletics
(mathletics.co.uk) account and this is probably the best
website to use as it is particularly geared to your year group.
If you cannot remember your sign in and password, ask your
class teacher.
www.mathszone.co.uk
www.mathsisfun.com
www.funschool.com
www.ictgames.com
www.woodlands-junior.kent.sch.uk/maths
wwwmaths-games.org
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Top tips
Here are some other top tips that may help
 Talk to your child about maths
 Be positive about Maths!! Let your child know that
everyone can learn math. Be positive about your own math
abilities. Try to avoid saying "I was never good at maths"
or "I never liked maths".
 Let your child know that you think math is important and
fun.
 Praise your child when he or she makes an effort, and
share in the excitement when he or she solves a problem
or understands something for the first time.
 When your child is trying to solve a problem, ask what he
or she is thinking. If your child seems puzzled, ask him or
her to tell you what doesn't make sense. (Talking about
their ideas and how they reach solutions helps children
learn to reason mathematically.)
 Treat errors as opportunities to help your child learn
something new. We all learn from mistakes.
 Make maths part of your child’s day: Include your child in
everyday activities that involve math – making purchases,
measuring ingredients, counting out plates and utensils
for dinner.
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