#### Table of Contents

## When do students learn the 12 times table?

The 12 times table forms part of the Year 4 national curriculum in the UK (approx 8 years old).

By the end of Year 4, all students should know all their times tables 1-12 and in June 2021 students will be tested nationally for the first time with something called the “Multiplication Tables Check” (here’s a link to a lot of information on the MTC).

In Years 5 and 6, students will use this knowledge to approach problems in geometry, fractions,.., and of course in more difficult multiplication problems.

## What do students need to know before learning the 12 times table?

Before learning their 12 times table, students should know:

- how to add 12 to any number (year 1)
- the concept of multiplication (i.e. 3 groups of 12 objects)
- the 2, 3, 4, 6 and 10 times tables
- place value and exchanging units
- how to use manipulatives to workout a particular times table.

## How are times tables taught in schools now?

Learning times tables is one of the few things that most people remember from their schooling and those that possess a good knowledge will always proudly demonstrate it.

20 years ago, and still in a number of Asian countries, times tables are memorised by chanting and repeated testing.

Nowadays, teachers spend a lot of time making times tables fun to learn using games such as Times Tables with Emile, using songs and dance or involving other subjects (cross-curricular learning).

They still use worksheets, songs and dances, but the emphasis is on understanding.

## Separate into Three Groups

The 12 times table is intimidating due to the size of the numbers involved. But it can be broken down into three manageable groups. The first group can be calculated by adding 12’s and is a great place to start

### Group 1

- 1 x 12 = 12
- 2 x 12 = 24
- 3 x 12 = 36
- 4 x 12 = 48
- 5 x 12 = 60

### Group 2

- 6 x 12 = 72
- 7 x 12 = 84
- 8 x 12 = 96
- 9 x 12 = 108
- 10 x 12 = 120

### Group 3

- 11 x 12 = 122
- 12 x 12 = 144

Things to notice:

The pattern in the ones: 2, 4, 6, 8, 0, 2, 4, 6, 8, 0, 2, 4 (The last digit repeats).

Can any of your students spot this pattern?

Can any of your students explain why?

Can any of your students explain why the last digit must be even? (potentially key stage 4 level work – see the here)

## Working it out from 10's and 2's.

As 12 = 10 + 2, the 12 times table can be worked out by 12 x number = (number x 10) + (number x 2)

12 x 1 = (10 x 1) + (2 x 1) = 10 + 2 = 12

12 x 2 = (10 x 2) + (2 x 2) = 20 + 4 = 24

12 x 3 = (10 x 3) + (2 x 3) = 30 + 6 = 36

12 x 4 = (10 x 4) + (2 x 4) = 40 + 8 = 48

12 x 5 = (10 x 5) + (2 x 5) = 50 + 10 = 60

12 x 6 = (10 x 6) + (2 x 6) = 60 + 12 = 72

## Times Table Facts

Always remember that there are only 12 x 12 (144) maths facts to learn for the national curriculum.

Once you remove the 1 and 10 times tables that leaves 102 maths facts.

Know your 2, 3 and 5 times tables and then there’s 60 maths facts left – fewer than half the 144.

Regular practice with Times Tables with Emile will lead to all your students wanting to practice them and knowing all their times tables in no time at all.

## 12 Times Table Games & Activities

### Get them to Work it Out

Give students manipulatives such as buttons, pasta or dried beans.

As they will eventually need 144 manipulatives, it may mean working in groups and being prepared for a bit of a sweep up.

Get them in their groups to write down the 12 times table up to 12 x 12. Then check with adjacent groups.

Hopefully this exploration of the 12 times table will help embed their understanding of what the 12 times table is.

(To reduce mess, and the number of manipulatives required, you may want to explore up to 5 x 12 instead.)

### View and Read Aloud

Work through their results as a class. Ask if anyone can see any patterns like the repeating last digit.

### 12 Times Table Grid

Ask students to complete an empty multiplication grid. It’s quite a useful exercise in itself to see where some students are struggling.

The grid could be selectively empty in the 9 row or column.

It can also be useful to remind children that they can reverse the order of a multiplication to make it an easier calculation.

### 12 Times Table Worksheet

Use the free worksheet that can be found here to check on understanding and comprehension by leaving the multiplication grid with the students.

### Prepare for the MTC

Practice for the MTC with MTC with Emile for FREE. It looks exactly the same as the DfE’s MTC, allows teachers to choose which times tables, how long to answer and track student progress.

### Times Tables with Emile

Play online games at home on mobiles, tablets or computers. Compete to see who is the fastest and best at their times tables with Times Tables with Emile and explore the mysterious planet of Meso.

### SNAP!

Really simple, really easy.

Print off this worksheet once for every pair of children:

If you liked this, please share!

## Why the last digit must be even.

Any three-digit number can be expressed as a sum of the hundreds, tens and ones. (This is the basis of place value.)

So if p is a 3 digit number, p = (a x 100) + (b x 10) + (c x 1), where a, b and c are whole numbers between 0 and 9.

If p is a multiple of 12, then p = 12 x q where y is a whole number between 0 and 12.

Or similar to before let q = (d x 10) + (e x 1), where d and e are whole numbers between 0 and 9.

If p =12 x q and q = (d x 10) + (e x 1)

Then:

p = 12 x q = 12 x ((d x 10) + (e x 1))

Change 12 for 2 x 6

p = 12 x q = 6 x 2 x ((d x 10) + (e x 1))

Bring 2 inside the brackets:

p = 6 x ((2 x d x 10) + (2 x e x 1))

Remove the x1 because it has no effect:

p = 6 x ((2 x d x 10) + (2 x e))

As we’re only interested in the last digit, we must focus on 2 x e (as 12 x d x 10 >10 where d is a whole number between 0 and 9), where e is a whole number between 0 and 9.

The last digit in p must therefore always be an even number (i.e. it is divisible by 2).