Calculations at
Holy Cross
Multiplication and division
Multiplication
Mental strategies:
• Doubling
• Multiplication facts – by Year 3 up to 12 times table
• Multiplying by 10, 100 or 1000
• Using known facts – if I know 3 x 7 = 21, what else
do I know?
30 x 7 = 210, 300 x 7 = 2100, 0.3 x 7 = 2.1 etc
Multiplication
Mental strategies:
• Closely related facts
13 x 11 = (12 x 11) +( 1 x 11)
•
Partitioning
23 x 4 = (20 x 4) + (3 x 4)
= 80 + 12
= 92
• Using factors
8 x 12 = 8 x 4 x 3
Multiplication
Stage One
• Count in patterns (e.g. 2s and 10s and begin to
count in 5s).
• Look at equal sets of objects:
• Begin to use multiplication vocabulary
Multiplication
Stage Two
• Begin to use jottings
• Learn that multiplication is the same as repeated
addition:
3 times 5 is 5 + 5 + 5 = 15 or 3 lots of 5 or 3 x 5
Number Lines
Multiplication
Stage Two
• This can be shown on number beads too:
3x5
Multiplication
Stage Two
• Commutativity – know that 5 x 3 is the same as
3 x 5.
• On a number line:
3x5
or
5x3
Multiplication
Stage Two
• Using arrays:
The following array, made of four columns and two rows,
could be used to represent the number sentence:
2x4=8
Multiplication
Stage Three
• Empty number lines
• Scaling:
Multiplication
Stage Three
• Using symbols to stand for unknown numbers to use
the inverse in calculations:
How many 5s can go into 20?
How many 3s can go into 18?
Multiplication
Stage Four
• Grid method (partition to break multiplication into chunks)
using arrays
6 x 14
Multiplication
Stage Four
• Grid method without arrays for TU x U:
23 x 8
(20 x 8) + (3 x 8)
160 + 24
= 184
Multiplication
Stage Four
• Expanded multiplication (in columns but linked with
grid method):
23 x 8
Multiplication
Stage Four
• Short multiplication, starting with least
significant digit TU x U:
23 x 8
Multiplication
Stage Five
• Grid method - HTU x U
Note: Children will approximate first
346 x 9 is approximately 350 x 10 = 3500
346 x 9
Multiplication
Stage Five
• Long multiplication using grid method - TU x TU
Note: Children will approximate first
72 x 38 is approximately 70 x 40 = 2800
72 x 38
Multiplication
Stage Five
• Long multiplication with fewer recordings - TU x TU
Multiplication
Stage Five
•
Long multiplication with fewer recordings - TU x TU
1
Multiplication
Stage Six
• Short multiplication - ThHTU x U
• Long multiplication – HTU x TU:
Multiplication
Stage Six
•
Long multiplication – HTU x TU:
2
1
Multiplication
Stage Six
• Multiplication of decimal numbers:
4.92 x 3
4.92
x 3
14.76
2
Multiplication
By the end of Year 6 girls will:
• have a range of calculation methods,
mental and written in a range of contexts
• approximate before calculating
• check their answers after calculating
• consider if a mental calculation would be
appropriate before using written methods
Division
Mental strategies:
•
•
•
•
•
•
Doubling and halving
Deriving and recalling division facts
Using and applying division facts
Dividing by 10,100 and 1000
Use of factors
Use related facts:
Given that 14 x 11 = 154 ,
what is 154 ÷ 14, or 154 ÷ 11?
Division
Stage One
• Understand equal groups and share items out:
12 shared between 3 equal groups
• Begin to use division vocabulary
Division
Stage Two
Use jottings to:
• Share equally
Division
Stage Two
Use jottings to:
• Group (repeated subtraction):
Division
Stage Two
Use jottings to:
• Repeated subtraction on number line/bead strings:
3
3
3
3
Division
Stage Three
• Repeated subtraction using number line:
4
4
4
4
• and for division with remainders:
4
4
Division
Stage Four
• Repeated subtraction to subtract multiples of the divisor:
Division
Stage Four
• Vertical method (or chunking) TU ÷ U:
72 ÷ 3
KNOWN FACTS
1x3=3
2x3=6
10 x 3 = 30
Division
Stage Four
Rounding up and down:
• Make sensible decisions about rounding up and
down according to context.
e.g. I have 62p. Sweets are 8p each. How many can I buy?
Answer: 7 (the remaining 6p is not enough to buy another
sweet).
Apples are packed into boxes of 8. There are 62 apples.
How many boxes are needed?
Answer: 8 (the remaining 6 apples still need to be placed
into a box).
Division
Stage Five
• Subtracting larger multiples of the divisor e.g. 30 x
Division
Stage Five
•
Formal short division
145 ÷ 5
029
5 145
1 4
847 ÷ 5
169 r 2
3 4
5 847
Division
Stage Six
• Long division HTU ÷ TU
972 ÷ 36
Division
Stage Six
• Long division HTU ÷ TU
972 ÷ 36
Known facts
027
36 972
72
252
36 x 2 = 72
36 x 10 = 360
36 x 5 = 180
36 x 7 = 252
Division
Stage Six
• Division with decimals up to 2 d.p.
15.65 ÷ 5
03.13
1
1
5 15.65
Division
By the end of Year 6 girls will:
• have a range of calculation methods,
mental and written in a range of contexts
• approximate before calculating
• check their answers after calculating
• consider if a mental calculation would be
appropriate before using written methods