Post on 03-Jan-2016
description
Progression through the teaching of
calculation Year 5 - 6
Aim of ProgressionMaths has changed!!
The maths work your child is doing at school may look very different to the kind of ‘sums’ you remember. This is because children are encouraged to work mentally, where possible, using personal jottings to help support their thinking.
‘Formal’ calculations are introduced from Year 3 onwards. Even then children are encouraged to use these methods for calculations they cannot solve in their heads.
Calculation
When faced with a problem, we want children to ask themselves….
• Can I do this in my head?• Could I do this in my head using
drawings or jottings to help me?• Do I need to use a written method?• Should I use a calculator?
Addition +THE FOLLOWING ARE STANDARDS THAT WE EXPECT
THE MAJORITY OF CHILDREN TO ACHIEVE.Year 5
Following formal addition methods with carrying above the line being introduced at Year 4, children should at Year 5 should then extend the carrying method to numbers with at least four digits.
• 587 3587
+ 475 + 675 1 1_ 1 1 1___
1062 4262
Addition +Using similar methods, children will:• Add several numbers with different
numbers of digits• Begin to add two or more decimal fractions
with up to three digits and the same number of decimal points
• Know that decimal points should line up under each other, particularly when adding or subtracting mixed amounts, e.g 3.2m – 280cm
Addition +• Year 6Children should extend the carrying method to number with any
number of digits. 7648 6584+ 1486 + 5848 1 11_ 111_
9134 12432
Using similar methods, children will:• Add several numbers with different numbers of digits• Begin to add two or more decimal fractions with up to four
digits and either one or two decimal places• Know that decimal points should line up under each other,
particularly when adding or subtracting mixed amounts, e.g 401.2 + 26.85 + 0.71
Subtraction -• Year 5The teaching of subtraction continues from Year 4 where an expanded
method will have been introduced.This expanded method uses partitioning
Step 1: 754 = 700 + 50 + 4 - 286 200 + 80 + 6
Step 2: 700 + 40 + 14 (adjusting from T to U) - 200 + 80 + 6
Step 3: 600 + 140 + 14 (adjusting from H to T) - 200 + 80 + 6 400 + 60 + 8 = 468
Subtraction -
Decomposition 614 1
754 (as in your booklet, as the borrowing between the tens
- 286 and the hundreds takes place, the 5 and the 7 will be
468 crossed out)
Children should:• Be able to subtract numbers with different numbers of digits• Begin to find the number between two decimal fractions with
up to three digits and the same number of decimal places• Know that decimal points should line up under each other.
Subtraction -• Year 6If children are able by the end of year 5 to cope withdecomposition then they will continue with this method into Year 6 513 1 6467 - 2684 3783
Children should:• Be able to subtract numbers with different numbers of digits• Be able to subtract two or more decimal fractions with up to three
digits and either one or two decimal places• Know that decimal points should line up under each other.
Multiplication XYear 5As in Year 4, Year 5 children when being introduced to multiplication will
be using the Grid Method
Year 5 children will begin with HTU x U369 x 9Children are expected to approximate first369 x 9 is approximately 370 x 10 – 3700 x 300 60 9 2700 9 + 540 81 1 1___
3321
2700 540 81
Multiplication XTU x TU
72 x 38
Again children are expected to approximate first
72 x 38 is approximately 70 x 40 = 2800
x 70 2 2100
30 + 560
8 60
16 1____
2736
2100 60
560 16
Multiplication XUsing similar methods, children will be expected to multiply decimals with one decimal place. They should know that decimal points line up under each other.
e.g 4.9 x 3Approximating first4.9 x 3 is approximately 5 x 3 = 15
x 4 0.9 12 3 + 2.7 14.7
12 2.7
Year 6ThHTU x U4346 x 8Approximate first4346 x 8 is approximately 4346 x 10 = 43460
x 4000 300 40 8 32000 8 + 2400 320 48 34768
Multiplication X
32000 2400 320 48
Multiplication XYear 6HTU x TU
372 x 24Approximate first372 x 24 is approximately 400 x 25 = 10000
X 300 70 2 600020 + 14004 1200 280 40 8 _ 1__
8928
6000 1400 40
600 140 8
Multiplication xUsing similar methods, Year 6 pupils will be expected to multiply decimals with up to two decimal places by a single digit and then by two digits.
4.92 x 3
Approximate first
4.92 x 3 is approximately 5 x 3 = 15
X 4 0.9 0.02 12
3 + 0.7
_0.06
12.76
12 2.7 0.06
Multiplication XYear 6
For the higher attainers who have grasped the concept of multiplication in Year 5, the short method of multiplication will be taught.
365
x 9 5 4_
3285
Division Year 5
In Year 4, a method of division called ‘Chunking’ will be introduced as a written method.This method is carried over into Year 5 where children will use the method to solve short division questions such as
TU U Example: 196 6 32 r 4 6 ) 196 - 180 (30x) 16 - 12 (2x) 4Answer: 32 reminder 4 or 32r4
Division Year 6 Children will continue to use this method into Year 6 where they will extend it to solving HTU U and HTU TU
HTU TU Example: 972 36 27 36 ) 972 - 360 (10x) 612 - 360 (10x) 252 - 180 (5x) 72 - 72 (2x)Answer 27
Division Year 6Division using the ‘chunking’ method will be extended to solving division with decimals up to two decimal places.87.5 7 12.5 7 )87.5 - 70.0 (10X) 17.5 - 14.0 (2X) 3.5 - 3.5 (0.5X) 0
Answer: 12.5
Division A short method of division will be introduced to those children who can fully understand the chunking method. This will only be used for division of HTU by U or TU by U. 4 1369 9 = 3
9)369
By the end of Year 6, all children will have a range of calculation methods, mental and written. Selection will depend upon the numbers involved.
Children should not be made to go onto the next stage if:* they are not ready* they are not confident
Children should be encouraged to approximate their answers before calcualting and should be encouraged to check their answers after calculation.
Children should also be encouraged to consider first before they attempt the question, whether a mental calculation would be appropriate.
Time for you to have a go!!Try to use the methods explained tonight to solve each of the following questions:
1. 1654 + 465 =2. 6854 - 798 =3. 965 30 =4. 374 X 24 =