Download Maths Meeting (2015) Parents

Multiplication
Year 1
A range of concrete and pictorial representations should be used with
teacher support.
Examples:
• Using songs/rhythms to begin counting in 2’s, 5’s and 10’s
• Using pictures of shoes/socks to count in 2’s
• Using fingers/gloves to count in 5’s
• Using coins to count up in 2's (2p coins), 5’s (5p coins) and 10’s (10p
coins).
Multiplication
Year 2
Continue using a range of concrete and pictorial representation should be
used as well as physical representations of sharing, grouping, arrays and
patterns.
Examples:
• Practical problem solving activities involving equal groups of 2, 5 and 10
objects e.g. 3 groups/lots of 2 cars is 6 cars
• Concrete representations of grouping
• Using bead strings to model groups of a certain number
• Counting repeated groups of a certain amount
• Using arrays
Multiplication
Year 3
Teach informal methods before moving onto the formal written method.
Partitioning
Example:  24 × 5
2 4
×
5
= (2 0 × 5) + (4  ×  5)
=  1 0 0 +  2 0
=  1  2 0
Multiplication
Year 3
Grid Method
Example:  45 × 7
280
280 + 35 = 315
35
Multiplication
Year 4
Use the formal written method, short multiplication to multiply a 2/3 digit
number by a 1-digit number.
Expanded Column Method
•
•
•
•
Line up the ones and the tens
Multiply the ones (by 6 in this example).
Multiply the tens (by 6 in this example).
Add the amounts together.
Multiplication
Year 5
Use the formal written method, long multiplication to multiply a 3/4 digit
number by a 2-digit number.
Example
2
Multiplication
Year 6
Use the formal written method, long multiplication to multiply up to 4digit numbers by a 2-digit number, including money and decimals.
Example 4.02 × 73 =
Multiply 4.02 by 100 = 402
Work out 402 x 73 using long
multiplication. 402 × 73 = 29346
Divide the answer by 100
29346 ÷ 100 = 293.46
Division
Year 1
Practical hands-on activities with a high profile given to developing
mathematical language together with visual images, concrete and pictorial
representations of sharing, grouping, arrays and patterns.
Examples:
•
•
•
•
•
•
Sorting objects given into equal groups.
Counting repeated groups of the same size
Understand division as sharing
Practical problem solving activities involving combining groups of 2’s, 5’s and 10’s
Using practical objects to answer questions such as: How many 2’s make 12?
Using bead strings to model grouping
Division
Year 2
A range of concrete and pictorial representation should be used as well as
physical representations of sharing, grouping, arrays and patterns.
Examples:
• Grouping objects into groups
• Using sorting trays, asking children to sort objects into groups including 3’s.
• Using bead strings to model grouping
• Using repeated subtraction as a form of grouping
• Using practical objects to pose questions such as, “How many groups of 5
can I make with 20 counters?”
Division
Year 3
Repeated subtraction involving remainders.
Division
Year 4
Use the formal written method of short division to divide a 2-digit number
by a 1-digit number and a 3-digit number by a 1-digit number.
Children to write remainders as whole numbers.
Division
Year 5
Use the formal written method of short division to divide up to 4-digit
numbers by a one-digit number, giving the answer with a remainder or as a
fraction.
Example: 4321 ÷ 4 =
remainder
remainder
divisor
divisor
Division
Year 6
Divide numbers up to 4 digits by a two-digit whole number using the
formal written method of long division and interpret remainders as whole
number remainders, fractions or by rounding as appropriate for the context.
Example: 422 ÷ 15 =
422 children need to travel by mini
bus for a school trip.
Each mini bus can hold 15 pupils.
How many mini buses are needed?
Round answer up to 29 mini buses.
Pupils are also expected to show remainders as a decimal.
Continue until there are no
remainders left or give the answer
to the nearest decimal place e.g.
28.1 (to 1 d.p).
0  5
Multiplying and Dividing by 10, 100 and 1000
When multiplying or dividing by 10, 100 or 1000, the children need to use
their knowledge of place value to understand the digits move, not the
decimal point.
36 x 10 =
3 6
3 6 0
one space to the left
36 ÷ 10 =
3 6
3 6
one space to the right
3.6 x 1000 =
3 6
3 6 0 0
three spaces to the left
0.6 ÷ 100 =
0 6
0 0 0 6
two spaces to the right
Multiplication Tables
In Year 2 – pupils should be taught to recall and use multiplication and
division facts for the 2, 5 and 10 multiplication tables, including recognising
odd and even numbers.
In Year 3 – pupils should be taught to recall and use multiplication and
division facts for the 3, 4 and 8 multiplication tables.
In Year 4 – pupils should recall multiplication and division facts for
multiplication tables up to 12 × 12.
Multiplication Tables
Knowing multiplication facts and their corresponding division facts is key
for so many other mathematical areas…
• Mental calculations such as 400 x 8 = 3200 knowing 4 x 8 = 32 and then multiplying by 100
• Mental calculations such as 6.4 ÷ 8 = 0.8 knowing 64 ÷ 8 = 8 and then dividing by 10
• Word problems i.e. converting measures to solve a word problem e.g. A ribbon is 2m long, it is cut into 4
pieces, how long is each piece of ribbon, in centimetres? 1. Convert 2m into cm [2 x 100 = 200cm]
2. Divide 200 by 4 = 50 because 20 ÷ 4 = 5 then
multiply the answer by 10
3. 50 cm
• Finding equivalent fractions
x3
3
x3
• Problems involving ratio and proportion
A bag contains red, blue and green balls.
How many blue balls will there be if there are 60 green balls?
x12
blue : green
7:5
x12
? : 60
7 x 12 = 84 blue balls
Strategies to learn Multiplication Tables at home
Flash cards (multiplication on one side, the answers on the other)
Commutative law 8 x 5 = 40 so 5 x 8 = 40 also.
Missing number questions ____ x 6 = 42
Knowing corresponding division facts 42 ÷ 6 = 7 because 6 x 7 = 42
If you know 8 x 9 = 72, what other facts do you know?
• 90 x 8 = 720
• 0.9 x 8 = 7.2
• 800 x 90 = 72 000
• 72 ÷ 9 = 8
• 7.2 ÷ 9 = 0.8
• 720 ÷ 80 = 9