Explaining how we Explaining how we teach teach

mathematics, and mathematics, and what you can do what you can do to help your child to help your child

become a become a confident confident

mathematician.mathematician.

Fawkham C.of E. Primary School

Welcome to Welcome to multiplication and multiplication and

divisiondivision

Multiplication and Division •Calculation methods

•Using and applying: using the calculation methods in situations that have

meaning.

•Vocabulary: vital and constantly referred to through all our

teaching.

We use a consistent, progressive approach

•KS1 – Focus on mental calculation

strategies•KS2 - Mental calculation strategies and a standard written method

Starting to understand multiplication: Starting to understand multiplication:

Begin to relate addition to combining 2 groups of objects, counting all the objects.

Activities:Count out 3 cakes. Now count out 3 more cakes. How many cakes are there altogether?

There are 4 cars in the garage 4 more arrive.

How many cars are in the garage now.Know how to use the relevant vocabulary:

Understanding multiplication

Know by heart addition doubles of all numbers to at least 10 then to 20.

Activities:There are 6 counters in the red cup and 6 counters in the blue cup. How many counters are there altogether? Can you record this to show me what you did?

What is double 4?Which two numbers would make a total of 8, 12, 14?

What is double 10?What is double 4? How could we work out double 14?

Double and halve dart board

Understanding multiplication Understand the operation of multiplication as

repeated addition or as describing an arrayarray.

I have 12 counters. I have 12 counters.

How could I arrange them into How could I arrange them into equal rows?equal rows?

Arrays are a useful visual tool for Arrays are a useful visual tool for multiplication and divisionmultiplication and division

What number What number sentences sentences could you write could you write to go with this to go with this array?array?

2 x 6 = 12 6 x 2 = 12

6 + 6 = 12

2 + 2 + 2 + 2 + 2 + 2 = 12

We can also say that 12 ÷ 6 = 2 and 12 ÷ 2 = 6

Can you think of any other ways Can you think of any other ways to arrange the 12 counters? to arrange the 12 counters?

What number What number sentences could sentences could

you write to go with you write to go with this array?this array?

4 x 3 = 123 x 4 = 12

4 + 4 + 4 = 12

3 + 3 + 3 + 3 = 12

We can also say that 12 ÷ 4 = 3 and 12 ÷ 3 = 4

Multiplication using jumps along a number line(repeated addition).

0 5 10

+5

+5

0 2 4 6 8 10

+2

+2

+2

+2

+2

2 x 5

means jumps of 2 made 5 times

or 2 jumps of 5 (5 x 2)

0 x 6 = 01 x 6 = 62 x 6 = 12 3 x 6 = 18 4 x 6 = 245 x 6 = 306 x 6 = 36 7 x 6 = 428 x 6 = 489 x 6 = 5410 x 6 = 60

0 x 2 = 0

1 x 2 = 2

2 x 2 = 4

3 x 2 = 6

4 x 2 = 8

5 x 2 = 10

6 x 2 = 12

7 x 2 = 14

8 x 2 = 16

9 x 2 = 18

10 x 2 = 20

Multiplication facts are absolutely vital for

progress with maths.

The children need to know them thoroughly, so that they can use the knowledge not just in multiplication problems, but also in division,

fractions, percentages, ratio etc.

It is important that they learn division alongside multiplication.

Multiplication can be seen as repeated addition4 + 4 + 4 + 4 + 4 = 4 x 5

(make 20)

Division can be seen as repeated subtraction.20 – 4 – 4 – 4 – 4 – 4 = 0

(How many 4s have we taken away?) so 20 ÷ 4 = 5

Times table awardsTimes table awardsBy the time the children come into year 3 they should already be confident with the 2, 5 and 10 times tables.

To help motivate the children to learn their times tables in class 2 we have times table awards.

For being able to recite the times table they earn a bronze sticker.

For being able to answer random questions from the times table they earn a silver sticker.

For being able to answer division questions, word problems, fraction questions using that times table they earn a certificate with a gold sticker that is presented in front of the school.

0 x 2 = 01 x 2 = 22 x 2 = 4 3 x 2 = 6 4 x 2 = 8 5 x 2 = 106 x 2 = 12 7 x 2 = 148 x 2 = 169 x 2 = 1810 x 2 = 20

0 x 2 = 0

1 x 2 = 2

2 x 2 = 4

3 x 2 = 6

4 x 2 = 8

5 x 2 = 10

6 x 2 = 12

7 x 2 = 14

8 x 2 = 16

9 x 2 = 18

10 x 2 = 20

0 x 6 = 01 x 6 = 62 x 6 = 12 3 x 6 = 18 4 x 6 = 245 x 6 = 306 x 6 = 36 7 x 6 = 428 x 6 = 489 x 6 = 5410 x 6 = 60

Speed racesSpeed racesBy the time the children leave year 2 they should know their number bonds (as listed last week), doubles etc.

In Class 2 we revise these, then move onto ensuring that they can recall mixed up times tables with the added pressure of time.

They answer 50 questions in 3 minutes, if they get them all right they move onto the next list next time. If they get less than 48 correct they get the same list again next time.

They are rewarded with merit marks when they improve their best score.

Know by heart the multiplication tablesthen use these facts to derive new facts

Two numbers multiplied together make 20. What could the two numbers be?A baker puts 5 buns in each of 10 rows. How many buns are there?How would you write 5 + 5 + 5 + 5 as a multiplication calculation?Using the numbers 2, 4, 15, 30 and 60. Work out six different multiplication calculations.Do you know 4 x 3? Can you work out 4 x 30? 40 x 30?

Hit the button

Tables wheel

Multiplying and dividing by 10 and 100

We learn how to move the digits.The bully 10 or 100 pushes the digits over.

Multiply by 10 move the digits one place to the leftMultiply by 100 move the digits two places to the left

Divide by 10 move the digits one place to the rightDivide by 100 move the digits two places to the right.

Moving the digits over demonstration

10

Written multiplication method

Division goes alongside multiplication Division as sharing

To start with the children learn to share objects into equal groups

Then write the number sentence; 6 shared between 2 is 3 each, 6 ÷ 2 = 3We use visual images, record jottings and use number sentences for division.

Division as grouping or chunking (repeated subtraction)

20 spots in groups of 5 (columns).20 spots in groups of 4 (rows).

Using a number line20 ÷ 5 = 4

20 divided into groups of 5 equals 4

0 5 10 15 20

The family of sums

4 x 5 = 20

5 x 4 = 20

20 ÷ 4 = 5

20 ÷ 5 = 4

Using arrays

Division on a number line

Or this one

Division methods with remainders.

The children need to know when to round the remainder up or down, e.g. How many boxes do we need? How many boxes will we fill?

Useful tricks:Useful tricks:Knowing that the two times table is also the doubles number bonds that they should already know (all answers are even numbers).

4 times table is double the two times table (all answers are even numbers).

8 times table is double the four times table (if they can double two digit numbers quickly in their head this is a useful skill) (all answers are even numbers).

6 times table is double the 3 times table (all answers are even numbers).2 x 6 = 12, 4 x 6 = 24, 6 x 6 = 36, 8 x 6 = 48 (this only works for the even multiples)

Multiples of the 5 times table always end in 0 or 5.

Little rhymes that help with some of the trickiest multiplication facts:

5, 6, 7, 8 56 is 7 x 8

I ate and I ate till I was sick on the floor 8 times 8 is 64.

These are some of the activities that we carry out, trying to make learning

tables fun and keep the children motivated.

Number grids

Function machines

Matching pairs

When the children can add 10 quite quickly in their head and can take away 2 they can work out their 8 times table.

Add 10 and take away 2 to work out the answers to the 8 times tables.

+10-2

+8

8 x table8 x table

9 x table9 x table 0 x 9 = 00 x 9 = 0 1 x 9 = 91 x 9 = 9 2 x 9 = 182 x 9 = 18 3 x 9 = 273 x 9 = 27 4 x 9 = 364 x 9 = 36 5 x 9 = 455 x 9 = 45 6 x 9 = 546 x 9 = 54 7 x 9 = 647 x 9 = 64 8 x 9 = 728 x 9 = 72 9 x 9 = 819 x 9 = 8110 x 9 = 9010 x 9 = 90

Digit sumsDigit sums 00 9 0 + 9 = 99 0 + 9 = 918 1 + 8 = 918 1 + 8 = 927 2 + 7 = 927 2 + 7 = 936 3 + 6 = 936 3 + 6 = 945 4 + 5 = 945 4 + 5 = 954 5 + 4 = 954 5 + 4 = 963 6 + 3 = 963 6 + 3 = 972 7 + 2 = 972 7 + 2 = 981 8 + 1 = 981 8 + 1 = 990 9 + 0 = 990 9 + 0 = 9

Finger trick

Thank you for reading this. We hope you find it useful.

Wizard number

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