Download Year 6 - Tetsworth Primary School

Year 6
Mathematics in School
Numeracy is a key life skill. It requires an understanding of the
number system, and an ability to solve numerical problems in a variety of
situations. It also includes practical understanding of shapes and measures
together with an ability to gather information and interpret graphs, diagrams,
charts and tables.
This booklet has been produced to help parents understand the methods used to
teach the skills of addition, subtraction, division and multiplication. It
exemplifies how each area will be taught in Year 6.
We hope this booklet will be useful to you and will show you how to help your
child in Mathematics.
Targets- Year 6
By the end of this year, most children should be able to…

Know all tables to 12 x 12 by heart and relate these to division facts
eg 3 x 4 = 12 & 12 ÷ 4 = 3. They should also be able to work out
remainders, eg 52 ÷ 7 = 7 remainder 3.

Multiply and divide decimals by 10 or 100 in their heads, e.g. 2.61 x
10 = 26.1 and 53.2 ÷ 100 = 0.532.

Put numbers, including decimals, in order of size, e.g. 1.06, 0.099,
0.25, 1.67 = 0.099, 0.25, 1.06 , 1.67.

Use pencil and paper to multiply and divide, e.g. 387 x 46, 21.5 x 7,
539 ÷ 13, 307.6 ÷ 4.

Use pencil and paper to add or subtract decimals. e.g. 3.91 + 8.04 +
24.56, or 13.3 - 1.27

Cancel fractions e.g. reduce 4/20 to 1/5 and work out which two
fractions is bigger, e.g 7/12 or 2/3. And place them in order.

Work out simple percentages of whole nummbers, e.g. 25% of £90 is
£22.50.

Know equivalent fraction, percentages and decimals eg 1/2 = 50% =
0.5 and 1/5 = 20% = 0.2

Estimate angles and use a protractor to measure them.

Work out the perimeter and area of simple shapes that can be split
into rectangles.

Solve word problems and explain their methods.

Use co-ordinates to plot the position of points.

Understand and use information in graphs, charts and tables.
Addition
This booklet reminds you how addition is taught in Year 5 and is reinforced in
Year 6.
In year 6 children will continue to work with larger numbers adding HTU + HTU,
ThHTU + ThHTU , decimal numbers and solving word problems adding
numbers with different numbers of digits.
Written methods
With this method it is essential that the children place the digits in the correct
place value column.
H T U
3 5 7
2 4 6
6 0 3
1
1
*We start at the units 6 +7 = 13. The 3 units are placed and the
ten is carried to the tens.
* We then move to the tens column 5 + 4 = 9. But we must
include the ten carried over from the unit calculations so the
answer is 10. We place the 0 and carry the 1.
* Lastly we add the hundreds column, 3 + 2 ,but again we
must remember the 1 carried over so the answer is 6.
Recipes
Find a recipe for 4 people and rewrite it for 8 people, e.g
4 people
8 people
125g flour
250g flour
50g butter
100g butter
30ml teacle
60ml treacle
Can you rewrite it for 3 people? Or 5 people?
Fours




Use exactly four 4s each time
You can add, subtract, multiply or divide them.
Can you make each number from 1 to 100.
Here are some ways of making the first two numbers.
1= (4+4) ÷ (4+ 4)
2 = 4÷ 4 + 4 ÷ 4
Three in row
For this game you need a calculator and you need to draw a line like this.
0
Cross out the bottom
numbers when you
have added them on.
This can
also be applied to addition with decimals again children must be careful to place digits in the correct place value position. Eg. 24. 7
+ 9. 45
T U.t h
2 4.70
9.4 5
3 4.1 5
1
We still start from the lowest value, this time hundredths.
The process is the same but we must remember to bring
the decimal point down as we are moving along.
1
Mental methods
Many mental methods are explored such as:

Partition 342 + 156 = ( 2 + 6 ) + (40 + 50) + (300 + 100) = 8 + 90 + 400 =
498

Or counting on to the next multiple of ten then subtracting
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9 1

Take it in turns to choose a fraction, say 2/5. Use the calculator to convert it
to a decimal (i.e. 2 ÷ 5 = 0.4) and mark your initials at this point on the line

The aim of the game is to get 3 crosses in a row without any of the other
player’s marks inbetween.
Some fractions are harder to place then others, e.g ninths.
Four in a Line
Draw a 6 x 7 grid and fill it with numbers under 100.
Take it in turns to roll three dice, or throw one dice three times.
Use all three numbers to make a number on the grid.
You can add, subtract, multiply or divide the numbers
e.g. if you roll a 3, 4 and 5, you could make 3 x 4 - 5 = 7
54 — 3 = 18, (4+5) x 3 = 27, and so on.
Cover the number you make with a coin or counter.
The first to get four of their counters in a straight line wins!
Subtraction
Fun Activities to do at Home
Catalogue or advertisement

Ask your child the cost of a favourite item .
Ask them to work out what 7 of these would cost, or 8 or
How much change would there be from a given value?
Find the difference between price of one item and another.
The children will continue to develop understanding of subtraction, using counting up
and decomposition. Here is a reminder of how subtraction is taught in year 5 and
reinforced in year 6.
9.
Sale of the Century

When you go shopping, or see a shop with a sale on, ask your child to
work out what some items would cost with:
50% off
25% off
10% off
5% off
Ask your child to explain how s/he worked it out.
Card Game:Use a pack of playing cards and take out the jacks, queens and
kings.

Take turns

Take a card and roll a dice.

Multiply the two numbers.

Write down the answer. Keep a running total.

The first to go over 301 wins!
Remainders : Draw a 6 x 6 grid and fill it with numbers
less than 100.

Choose the 7, 8 or 9 times table.

Take turns to roll a dice

Choose a number on the board, e.g. 59. Divide it by the tables number,
e.g. 7. If the remainder for 59 ÷7 is the same as the dice number, you
can cover the board number with a counter or coin.

The first to get four of their counters in a straight line wins.
Tables Facts
Focus on 2 or 3 table facts and work with them until they are learnt. Keeping
firing questions through the week every day eg 8 x 4, 7 x 6 and 6 x 8. But
vary the question form eg ask how many 6s in 48?
Once they are mastered select another three facts.
First begin by subtracting the bottom unit from the top unit, starting at the lowest
value—the units.
If the top unit is smaller than the bottom unit you will need to borrow from the tens
unit and add it to the digit being calculated.
6
74
7
47
-2
So begin by subtracting 7 from 4. You can’t do this so you need to
borrow a 10 from the 70. This will change the tens to 60 and the 4 changes to
14. Now you can subtract 7 from 14 which equals 7. Then subtract 2
from 6 which is 4. This gives you the answer 47.
Next try it with a HTU
2 3
342
-1 5 4
188
Begin by subtracting 4 from 2. You can’t do this so borrow a ten from the tens digit.
the tens digit changes from a 4 to a 3. The ones digit becomes a 12. Subtract the 4 from
1 2 ito get 8. Next subtract the 5 from 3. Again this can’t be done, so you will need to borrow
from the hundred digit. This becomes 2 and the 3 becomes 13. Subtract 5 from 13 which
is 8. Finally subtract the hundreds. 2 take away 1 is 1. The answer is 188.
They will work on ‘real life’ word problems involving money, decimals, measures and
time explain strategies they have used to produce the answer.
Children will continue to be encouraged to estimate answers and always check their
calculations and answers for sense.
If 342 -154 is 188
then 188 + 154
must be 342.
Multiplication
Division
Children will continue to build on and practise previous skills. They MUST learn
times tables they do not know off by heart.
Year 6 children should confidently be multiplying:
HTU x U and TU x TU, ThHTU x U, H T U . t h X U
The grid method may be used:
Multiplication Grid Method
38 x 72=
x
70
2
As in Year 5, the children will continue to develop their:

Knowledge of multiplication facts to derive quickly division facts.

Mental agility using division,

Division skills using a calculator,

Ability to round remainders up and down, ability to give an answer as a
decimal fraction. (43 ÷ 9 = 4 . 77̇ ̇)

Efficient standard method of recording.
partition the 2-digit numbers to ….
30
2100
60
8
560
16
= 2100 + 560 = 2660
= 60 + 16 =
76
2 7 36
Children should be approximating first, i.e. 72 x 38 is approximately 70 x 40 =
2800.
Children will now be encouraged to use the standard written method.
They will move away from the chunking method and go onto the ‘bus stop ‘
method
Knowledge of place value will be developed to extend their ability. For example
from knowing that 56 ÷ 7 = 8 we can understand that 560 ÷ 7= 80 as we know
that 560 is 10 times larger than 56 - the answer is ten times larger.
Bus stop method. Initially we teach children by using calculations that do not
have a remainder for example.
H T U Start at the units 4 x 3 = 12 ~ place the 2 and carry the ten (1)
5 4 3 Next the tens 4 x 4 = 16 ~ but we must add the 1 carried from
X
4 the units making 17. The 7 is placed and the 1 carried to the .
2 1 7 2 hundreds.
1 1
Lastly move to the hundreds 4 x 5 = 20 but again we must add
the 1 carried over from the tens making 21
Unlike the other three operations we start at the digit
that represents the highest value.
We ask how many 3s there are in 9 the answer, 3,
Is placed above. Next we move onto the 3. How many 3s are there in 3 the
answer, 1 is placed above the 3 . Lastly, how many 3s are there in 6, the answer
2 is placed finally above the 6. 936 ÷ 3 = 312.
The process is the same when multiplying by a two digit number but we must
place a 0 in the units column when we are multiplying by the ten value
As they become confident with this technique we move to more challenging calculations, first those with carrying and remainders and then those with decimal
answers.
7 ÷ 5 = 1 remainder 2 (so carry the 2)
1 5 6 r = 2 28 ÷ 5 = 5 remainder 3 ( so carry the 3)
5 7 28 32
32 ÷ 5 = 6 remainder 2 - so write r = 2
H T U
3 0 7
x 3 5
1 5 3 5
3
9 2 1 0
2
We start with the units.
5 x 7 = 35 ~ place 5 and carry 3
5 x 0 = 0 + 3 (carried) ~ place 3
5 x 3 = 15 ~ place 15
FIRST Place a 0 in the units
3 x 7 = 21 ~ place 1 and carry 2
3 x 0 = 0 + 2 (carried) ~place
2
9 8 4 5
3 x 3 = 9 ~place 9
Now add the two together
312
3 936
Finally we move onto the more challenging decimal answers and maybe dividing
by a 2 digit number depending on their ability.
0 7
6 4 45
5 . 5
3 3 . 30