Calculation

Policy

Route Through Calculation

Addition Methods

Year 1
Addition on a prepared number line
LI: To add numbers together
Context: Prepared number line
SC:
  1. I can read the number sentence
  2. I can say how many 1s I need to add to the first number to get to 10
  3. I can say how many more I need to add
  4. I can jump to 10 first then I can jump for the rest of the steps
  5. I can say which number I land on and this is my answer
  6. I can check to make sure my answer is reasonable and bigger than the number I started with
  7. I can write the answer in the number sentence

7 + 5 = 7 + 3 + 2 = 10 + 2 = 12
3 2 +3 +2
1 1 1 1 1
______
123456789101112 13
Addition on a 100 square
LI: To add numbers together
Context: 100 square
SC:
  1. I can read the number sentence
  2. I can circle the biggest number
  3. I can partition the smallest number into chunks
  4. I can add on the 10s
  5. I can add on the 1s
  6. I can circle and say the number I land on and know this is my answer
  7. I can check to make sure my answer is reasonable and bigger than the number I started with
  8. I can write the answer in the number sentence
TIP: When using interactive whiteboard for step 4 and 5, highlight jumps on 100 square
26 + 17 = 43
1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10
11 / 12 / 13 / 14 / 15 / 16 / 17 / 18 / 19 / 20
21 / 22 / 23 / 24 / 25 / 26 / 27 / 28 / 29 / 30
31 / 32 / 33 / 34 / 35 / 36 / 37 / 38 / 39 / 40
41 / 42 / 43 / 44 / 45 / 46 / 47 / 48 / 49 / 50
51 / 52 / 53 / 54 / 55 / 56 / 57 / 58 / 59 / 60
61 / 62 / 63 / 64 / 65 / 66 / 67 / 68 / 69 / 70
71 / 72 / 73 / 74 / 75 / 76 / 77 / 78 / 79 / 80
81 / 82 / 83 / 84 / 85 / 86 / 87 / 88 / 89 / 90
91 / 92 / 93 / 94 / 95 / 96 / 97 / 98 / 99 / 100
10 1
1
1
1
1
1
1
Year 2
Addition on an empty number line
LI: To add numbers together
Context: Number line
SC:
1. I can circle the largest number
  1. I can break the smallest number up into chunks (favourite)
  2. I can draw a straight line using a ruler
  3. I can put the largest number on the left handside of the line
  4. I can start on the left hand side
  5. I can jump along the line using the chunks
  6. I can put the chunk on top of the jump (If children are confident without this step it can be missed out)
  7. I can write the numbers I land on under the line
  8. I can circle the answer
  9. I can check to make sure my answer is reasonable

eg + 142=
100 10 1
10 1
10
10
+100+10+10+10+10 +1 +1
______
327427 437447 457467 468
eg + 23=
10 1
10 1
1
+10+10+1+1 +1
______
36 46 56 57 58
Smaller numbers can be used to help children become familiar with the method – normally a mental
method would be used with smaller number.
Addition by partitioning
LI: To add numbers together
Context: Partitioning
SC:
  1. I can read the number sentence
  2. I can write down the partitioned numbers under the question
  3. I can put the partitioned numbers into columns (one digit in one box)
  4. I can put my addition sign on the right hand side
  5. I can start adding from the units column
  6. I can put my answers together
  7. I can check to see if the answer is reasonable
434+252
400 200
30 50
4 2
H T O
400 + 30 + 4
200 + 50 + 2 +
______
600 + 80 + 6
______
Answer is then combined = 686
384+252
300200
80 50
4 2
300 + 80 + 4
200 + 50 + 2 +
______
500 + 130 + 6
______
500 + 100 + 30 + 6
______
Answer is then combined = 636
Year 3
Formal written method for addition
LI: To add numbers together
Context: Formal Written Method
SC:
  1. I can put the headings for each column at the top
  2. I can put the question into columns (one digit in one box)
  3. I can put my addition sign on the right hand side
  4. I can start adding from the right hand side
  5. I can check to see if there are any ways to make it easier (number bonds, doubles, triples)
  6. I can put any carries under the next column
  7. I can check to see if there are any carries I need to add
  8. I can check to see if the answer is reasonable
789 + 642 =
H T O
7 8 9
6 4 2 +
1 4 3 1
¹ ¹
Year 4
Formal written method for addition
LI: To add numbers together
Context: Formal Written Method
SC:
  1. I can put the headings for each column at the top
  2. I can put the question into columns (one digit in one box)
  3. I can put my addition sign on the right hand side
  4. I can start adding from the right hand side
  5. I can check to see if there are any ways to make it easier (number bonds, doubles, triples)
  6. I can put any carries under the next column
  7. I can check to see if there are any carries I need to add
  8. I can check to see if the answer is reasonable
789 + 642 =
H T O
7 8 9
6 4 2 +
1 4 3 1
¹ ¹
Year 5
Formal written method for addition
LI: To add numbers together
Context: Formal Written Method
SC:
  1. I can put the headings for each column at the top
  2. I can put the question into columns (one digit in one box)
  3. I can put my addition sign on the right hand side
  4. I can start adding from the right hand side
  5. I can check to see if there are any ways to make it easier (number bonds, doubles, triples)
  6. I can put any carries under the next column
  7. I can check to see if there are any carries I need to add
  8. I can check to see if the answer is reasonable
789 + 642 =
H T O
7 8 9
6 4 2 +
1 4 3 1
¹ ¹
Year 6
Formal written method for addition
LI: To add numbers together
Context: Formal Written Method
SC:
  1. I can put the headings for each column at the top
  2. I can put the question into columns (one digit in one box)
  3. I can put my addition sign on the right hand side
  4. I can start adding from the right hand side
  5. I can check to see if there are any ways to make it easier (number bonds, doubles, triples)
  6. I can put any carries under the next column
  7. I can check to see if there are any carries I need to add
  8. I can check to see if the answer is reasonable
789 + 642 =
H T O
7 8 9
6 4 2 +
1 4 3 1
¹ ¹

Route Through Calculation

Subtraction Methods

Year 1
Subtraction on a prepared number line
LI: To subtract/take away one amount from another
Context: Prepared number line
SC:
  1. I can read the number sentence
  2. I can circle the biggest number in the number sentence
  3. I can find the biggest number on the number line
  4. I can say how many 1s I need to take away to get to 10
  5. I can jump to 10 and I can jump for the rest of the steps
  6. I can say which number I land on and this is my answer
  7. I can check to make sure my answer is smaller than the number I started with
  8. I can write the answer in the number sentence

12 - 5 = 7
2 3 -3 -2

1 1 1 1 1
______
123456789101112 13
Subtraction on a 100 square
LI: To subtract/take away one amount from another
Context: 100 square
SC:
  1. I can read the number sentence
  2. I can circle the biggest number
  3. I can partition the smallest number into chunks
  4. I can subtract the 10s
  5. I can subtract the 1s
  6. I can circle and say the number I land on and know this is my answer
  7. I can check to make sure my answer is reasonable and smaller than the number I started with
  8. I can write the answer in the number sentence
TIP: When using interactive whiteboard for step 4 and 5, jumps can be highlighted on 100 square
43 – 17 = 26
1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10
11 / 12 / 13 / 14 / 15 / 16 / 17 / 18 / 19 / 20
21 / 22 / 23 / 24 / 25 / 26 / 27 / 28 / 29 / 30
31 / 32 / 33 / 34 / 35 / 36 / 37 / 38 / 39 / 40
41 / 42 / 43 / 44 / 45 / 46 / 47 / 48 / 49 / 50
51 / 52 / 53 / 54 / 55 / 56 / 57 / 58 / 59 / 60
61 / 62 / 63 / 64 / 65 / 66 / 67 / 68 / 69 / 70
71 / 72 / 73 / 74 / 75 / 76 / 77 / 78 / 79 / 80
81 / 82 / 83 / 84 / 85 / 86 / 87 / 88 / 89 / 90
91 / 92 / 93 / 94 / 95 / 96 / 97 / 98 / 99 / 100
10 1
1
1
1
1
1
1
Year 2
Subtraction on an empty number line
LI: To subtract/take away one amount from another
Context: Number line
SC:
1. I can circle the largest number
  1. I can break the smallest number up into chunks
  2. I can draw a straight line using a ruler
  3. I can put the largest number on the right handside of the line
  4. I can start on the right hand side
  5. I can jump along the line using the chunks
  6. I can write the result after subtracting each chuck, as I go along
  7. I can cross off each chuck as I subtract it
  8. I can put the chunk on top of the jump
  9. I can write the numbers I land on under the line
  10. I can circle the answer
  11. I can check to make sure my answer is reasonable

Eg – 132 = 335
100 10 1
101
10
-1 -1 -10-10-10-100

______ 336 337 347 357 367 467
Subtraction by partitioning
LI: To subtract/take away one amount from another
Context: Partitioning
SC:
  1. I can write down the partitioned numbers under the question
  2. I can put the partitioned numbers into columns (one digit in one box)
  3. I can put my subtraction sign on the right hand side
  4. I can check to see if I need to exchange (look for the classic subtraction error)
  5. I can start subtracting from the right hand side (ones column)
  6. I can put my answers together
  7. I can check to see if the answer is reasonable
789-246
700200
80 40
9 6
H T O
700 + 80 + 9
200 + 40 + 6 -
______
500 + 40 + 3
______
Answer is then combined = 543
552-348
500300
50 40
2 8
H T O
40 12
500 + 50 + 2
300 + 40 + 8 -
______
200 + 0 + 4
______
Answer is then combined = 204
Year 3
Formal written method for subtraction
LI: To subtract/take away one amount from another
Context: Formal Written Method
SC:
  1. I can put the headings for each column at the top
  2. I can put the question into columns (one digit in one box)
  3. I can put my subtraction sign on the right hand side
  4. I can start subtracting from the right hand side
  5. I can subtract from the top number to the bottom number (when starting this method or if a child is having difficulty draw an arrow at the side of the sum showing direction)
  6. I can check to see if I need to exchange
  7. I can check to see if the answer is reasonable
874 - 523 =
H T O
8 2 4
5 2 3 -
3 5 1
932 – 457 =
H T O

9 3 2
4 5 7 –
4 7 5
Year 4
Formal written method for subtraction
LI: To subtract/take away one amount from another
Context: Formal Written Method
SC:
  1. I can put the headings for each column at the top
  2. I can put the question into columns (one digit in one box)
  3. I can put my subtraction sign on the right hand side
  4. I can start subtracting from the right hand side
  5. I can subtract from the top number to the bottom number (when starting this method or if a child is having difficulty draw an arrow at the side of the sum showing direction)
  6. I can check to see if I need to exchange
  7. I can check to see if the answer is reasonable
874 - 523 =
H T O
8 2 4
5 2 3 -
3 5 1
932 – 457 =
H T O

9 3 2
4 5 7 –
4 7 5
Year 5
Formal written method for subtraction
LI: To subtract/take away one amount from another
Context: Formal Written Method
SC:
  1. I can put the headings for each column at the top
  2. I can put the question into columns (one digit in one box)
  3. I can put my subtraction sign on the right hand side
  4. I can start subtracting from the right hand side
  5. I can subtract from the top number to the bottom number (when starting this method or if a child is having difficulty draw an arrow at the side of the sum showing direction)
  6. I can check to see if I need to exchange
  7. I can check to see if the answer is reasonable
874 - 523 =
H T O
8 2 4
5 2 3 -
3 5 1
932 – 457 =
H T O

9 3 2
4 5 7 –
4 7 5
Year 6
Formal written method for subtraction
LI: To subtract/take away one amount from another
Context: Formal Written Method
SC:
  1. I can put the headings for each column at the top
  2. I can put the question into columns (one digit in one box)
  3. I can put my subtraction sign on the right hand side
  4. I can start subtracting from the right hand side
  5. I can subtract from the top number to the bottom number (when starting this method or if a child is having difficulty draw an arrow at the side of the sum showing direction)
  6. I can check to see if I need to exchange
  7. I can check to see if the answer is reasonable
874 - 523 =
H T O
8 2 4
5 2 3 -
3 5 1
932 – 457 =
H T O

9 3 2
4 5 7 –
4 7 5

Route Through Calculation

Multiplication Methods

Year 1
Multiplication using arrays
LI: To multiply amounts together
Context: Arrays
SC:
  1. I can read the number sentence using the words “lots of” eg 3 x 4 is the same as 3 lots of 4
  2. I can make the array using objects/dots

* * * *

* * * *

* * * *
  1. I can count how many there are altogether in the array.
  2. I can check my answer is reasonable
  3. I can write the answer in the number sentence
Multiplication on an empty number line
LI: To multiply numbers together
Context: Number line
SC:
  1. I can draw an empty number line
  2. I can put my start number on the number line (0)
  3. I can circle the number I am going to count up in (the number I am multiplying by)
  4. I can count up in the number I am multiplying and write the number of jumps as I go
  5. I can write the numbers I land on under the line
  6. I can say which number I land on and this is my answer
  7. I can check to make sure my answer is reasonable

16 x 4 = 64
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
______
0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60
Year 2
Multiplication on an empty number line by chunking
LI: To multiply numbers together
Context: Number line by chunking
SC:
  1. I can draw an empty number line
  2. I can put my start number on the number line (0)
  3. I can circle the number I am going to count up in (the number I am multiplying by)
  4. I can choose the chunks I am going to use
  5. I can find out how big the chunk will be I am going to jump in
  6. I can jump in the chunk
  7. I can say which number I land on and this is my answer
  8. I can check to make sure my answer is reasonable
16 x 4 = 64


______
0 40
Grid method for multiplication (2digit by 1 digit)
LI: To multiply numbers together
Context: Grid method for 2 digit x 1 digit
SC:
  1. I can write the partitioned numbers down
  2. I can draw the correct grid
  3. I can put the partitioned numbers into the correct place on the grid
  4. I can say the question I am going to do
  5. I can multiply the numbers together (check for any easy steps)
  6. I can circle the amounts I need to add
  7. I can make my addition question using the answers (don’t forget to look at the SC to help
make the addition)
  1. I can add my numbers together
  2. I can check to make sure my answer is reasonable
23 x 4
20 3
X 2 0 3 8 0
4 8 0 1 2 1 2 +
9 2
Year 3
Grid method for multiplication (2digit by 2 digit – can be used for 3digit)
LI: To multiply amounts together
Context: Grid method for 2 digit x 2 digit (can be used for 3 digit)
SC:
  1. I can write the partitioned numbers down
  2. I can draw the correct grid
  3. I can put the partitioned numbers into the correct place on the grid
  4. I can say the question I am going to do
  5. I can multiply the numbers together (check for any easy steps)
  6. I can circle the amounts I need to add
  7. I can make my addition question using the answers (don’t forget to look at the SC to help
make the addition)
  1. I can add my numbers together
  2. I can check to make sure my answer is reasonable
36 x 43
30 40
6 3
X 3 0 61 2 0 0
40 1200 240 2 4 0
3 90 18 9 0
1 8
______
1 5 4 8
______
1
Short multiplication
LI: To multiply amounts together
Context: Short multiplication
SC:
  1. I can put the numbers into columns
  2. I can multiply the digit in the ones column with the multiplier
  3. I can write the answer in the equals row
  4. I can remember to put any carries under the equals row of the tens column
  5. I can multiply the digit in the tens column with the multiplier
  6. I can remember to add any carries
  7. I can write the answer in the equals row
  8. I can remember to put any carries under the equals row of the hundreds column
  9. I can multiply the digit in the hundreds column with the multiplier
  10. I can remember to add any carries
  11. I can write the answer in the equals row
342 x 7 =
multiplier
H T O
3 4 2
7 x
______
2 3 9 4
² ¹
Year 4
Short multiplication
LI: To multiply amounts together
Context: Short multiplication
SC:
  1. I can put the numbers into columns
  2. I can multiply the digit in the ones column with the multiplier
  3. I can write the answer in the equals row
  4. I can remember to put any carries under the equals row of the tens column
  5. I can multiply the digit in the tens column with the multiplier
  6. I can remember to add any carries
  7. I can write the answer in the equals row
  8. I can remember to put any carries under the equals row of the hundreds column
  9. I can multiply the digit in the hundreds column with the multiplier
  10. I can remember to add any carries
  11. I can write the answer in the equals row
342 x 7 =
multiplier
H T O
3 4 2
7 x
______
2 3 9 4
² ¹
Year 5
Short multiplication
LI: To multiply amounts together
Context: Short multiplication
SC:
  1. I can put the numbers into columns
  2. I can multiply the digit in the ones column with the multiplier
  3. I can write the answer in the equals row
  4. I can remember to put any carries under the equals row of the tens column
  5. I can multiply the digit in the tens column with the multiplier
  6. I can remember to add any carries
  7. I can write the answer in the equals row
  8. I can remember to put any carries under the equals row of the hundreds column
  9. I can multiply the digit in the hundreds column with the multiplier
  10. I can remember to add any carries
  11. I can write the answer in the equals row
342 x 7 =
multiplier
H T O
3 4 2
7 x
______
2 3 9 4
² ¹
Long multiplication
LI: To multiply amounts together
Context: Long multiplication
SC:
  1. I can put the numbers into columns
  2. I can multiply the digit in the ones column with the multiplier in the ones column
  3. I can write the answer in the equals row
  4. I can remember to put any carries under the equals row of the tens column
  5. I can multiply the digit in the tens column with the multiplier in the ones column
  6. I can remember to add any carries
  7. I can write the answer in the equals row
  8. I can remember to put any carries under the equals row of the hundreds column
  9. I can multiply the digit in the hundreds column with the multiplier in the ones column
  10. I can remember to add any carries
  11. I can write the answer in the equals row
  12. I can draw another equals row below
  13. I can put a zero in the ones column of this equals row
  14. I can multiply the digit in the ones column with the multiplier in the tens column
  15. I can write the answer in the equals row
  16. I can remember to put any carries under the equals row of the tens column
  17. I can multiply the digit in the tens column with the multiplier in the tens column
  18. I can remember to add any carries
  19. I can write the answer in the equals row
  20. I can add together the answers in each equals row
124 x 26 =
multipliers
H T O
1 2 4
2 6 x
_____
7 4 4
¹ ²
2 4 8 0 +
3 2 2 4
¹ ¹
Year 6
Long multiplication
LI: To multiply amounts together
Context: Long multiplication
SC:
  1. I can put the numbers into columns
  2. I can multiply the digit in the ones column with the multiplier in the ones column
  3. I can write the answer in the equals row
  4. I can remember to put any carries under the equals row of the tens column
  5. I can multiply the digit in the tens column with the multiplier in the ones column
  6. I can remember to add any carries
  7. I can write the answer in the equals row
  8. I can remember to put any carries under the equals row of the hundreds column
  9. I can multiply the digit in the hundreds column with the multiplier in the ones column
  10. I can remember to add any carries
  11. I can write the answer in the equals row
  12. I can draw another equals row below
  13. I can put a zero in the ones column of this equals row
  14. I can multiply the digit in the ones column with the multiplier in the tens column
  15. I can write the answer in the equals row
  16. I can remember to put any carries under the equals row of the tens column
  17. I can multiply the digit in the tens column with the multiplier in the tens column
  18. I can remember to add any carries
  19. I can write the answer in the equals row
  20. I can add together the answers in each equals row
124 x 26 =
multipliers
H T O
1 2 4
2 6 x
_____
7 4 4
¹ ²
2 4 8 0 +
3 2 2 4
¹ ¹

Route Through Calculation