We started off by consolidating yesterday’s work on the three times table. Ioan and Finny had learnt the song from Numberblocks to help them remember the multiplication facts.

## Method

We went on to make this harder, by removing the Numberblocks and leaving only the associated props for each character, that were mentioned in the song.

They were still able to recall the three times table without the Numberblocks themselves.

### The relationship between the 3 times table and 6 times table

I gave them some sticky labels which just said ‘1×6’, ‘2×6’, ‘3×6’ etc. and asked them to describe any relationships they could see between the 3 and 6 times tables.

While Finny was building characters, Ioan looked at the base ten representation of the 3 times table and compared what the 6 times table would be.

Multiplication is repeated addition. You take one number and add it together a number of times. This is why multiplication is sometimes called “times“.

The multiplication process below is explained in more detail in the post ‘Two Times Table Shoe Shop‘.

### Observation 1: The multiples of 6 are double the multiples of 3

multiple is a number that can be divided by another number evenly without leaving a remainder. Multiples are basically the answers from any times table question, e.g. with the equation 3 × 4 = 12, 12 is a multiple of both 3 and 4.

The multiples of the 6 times table are double the multiples of the 3 times table.

Example: 3 multiplied by 4

3 multiplied by 4 means 3 + 3 + 3 + 3 = 12. We took the number 3 and added it together 4 times. So, 3 x 4 = 12.

For 6 multiplied by 4, the 3 in the previous example is doubled.

6 + 6 + 6 + 6 = 24. We took the number 6 and added it together 4 times. Therefore, 6 x 4 = 24.

24 is double 12.

### Observation 2: The multiples of 3 are half the multiples of 6

This is the inverse of the previous observation.

Example: 6 multiplied by 4

6 multiplied by 4 means 6 + 6 + 6 + 6 = 24. We took the number 6 and added it together 4 times. So, 6 x 4 = 24.

For 3 multiplied by 4, the 6 in the previous example is halved.

3 + 3 + 3 + 3 = 12. We took the number 3 and added it together 4 times. Therefore, 3 x 4 = 12

12 is half of 24.

### Observation 3: Every other multiple of 3 is also a multiple of 6

Ioan noticed that every second multiple of 3, is also a multiple of 6.

Finny remembered it as all the even numbers, when multiplied by 3, are multiples of 6.

2 x 3 = 6 and 1 x 6 = 6

4 x 3 = 12 and 2 x 6 = 12

6 x 3 = 18 and 3 x 6 = 18

8 x 3 = 24 and 4 x 6 = 24

10 x 3 = 30 and 5 x 6 = 30

12 x 3 = 36 and 6 x 6 = 36

### Inventing Numberblocks characters

Ioan and Finny worked out their own characters for the second half of the six times table. As with the three times table above, the idea was to have an object associated with each multiplication fact, so that we could go on to move the numberblocks and the item would still remind them of the answer.

It didn’t matter what the shape of the numberlock was, or the object they chose to associate it with. It just needed to be something that meant something to them.

#### New multiplication facts: 6 x 6 = 36

36 could be either a square or a step shape.

#### 7 x 6 = 42

42 had just got out of bed and was wearing a dressing gown and had a red mug of tea.

#### 8 x 6 = 48

Finny loved 48. He was sat in a rocking chair, patting his pet pigs. If he wants to go on a ride his pigs pull him along, like a sleigh.

#### 9 x 6 = 54

56 is a dreamer who likes patterns. He sleeps a lot and has a teddy bear.

#### 10 x 6 = 60

Sixty was given six of the ’10’ juggling balls. They pointed out that this was double 30, which was 10 x 3. Later on, Finny made a magic mirror, to show that if you put 10 x 3 = 30 in front of the mirror, it doubled in to 10 x 6 = 60.

Giggles always follow this pair around during our maths work.

Once the numberblocks characters were removed, we were left with an assortment of objects which wouldn’t mean anything to anyone else, but helped as a visual reminder of the multiplication facts to Ioan and Finny when asking each other multiplication facts out of order.

## 4 days later

After a few days break, we came back to consolidate the work on the 6 times table. This was to see how much they had retained.

The giggles at the start were them recovering from me tripping over and nearly landing on top of them.

A very tired Cici had come over to watch them Ioan and FInny. This time they had to do the multiplication facts out of order.

## DfES National Curriculum (2013)

### Numeracy Year 4 programme of study

#### Number – multiplication and division

• recall multiplication and division facts for multiplication tables up to 12 × 12