Skip counting is a great way to start multiplication. By learning to count up in groups of numbers, students can start practicing their times tables. Skip counting involves skipping the amount of numbers you're counting up in.

For example, if you are skip counting in 2s and start at 0, you would count **0**, [1], **2**, [3], **4**... and so on.

If you are skip counting in 5s starting at 0, you would count **0**, [1], [2], [3], [4], **5**, [6], [7], [8], [9], **10**... and so on.

For example:

1 becomes "one"

2 becomes "two"

10 becomes "ten"

20 becomes "twenty"

45 becomes "forty-five"

129 becomes "one hundred and twenty nine"

Fractions can be a tricky concept for students to first grasp. Starting with splitting up shapes and foods like pizza or cake is a great introduction to fractions.

To start with, it's important to break down what a fraction is: a small part of a whole.

It's also important to understand the parts of a fraction. The bottom number is called the "denominator" and tells us how many pieces there are in total. The top number is called the "numerator" and tells us how many pieces we actually have. So if we take 2 slices of a pizza that has 8 slices, we have 2/8 of the pizza!

+ means to add or plus

- means to subtract or minus

× means to multiply or times

÷ means to divide

= means to be the same, two quantities have the same value

Using logical reasoning, students can guess the number based on initial information.

For example:

The number I'm thinking of is a multiple of 4, greater than 16 but smaller than 24. (I am 20)

I am an even number. I have a five in the tens place. You do not say me when you count by tens. I am greater than 0 but less than 54. (I am 52)

Tom 16. Emma is 1 year younger than Tom and 3 years younger than Matt. How old is Matt? (Matt is 18)

Doubling is the process of making twice as much of something, or two lots of it. For example, if I wanted to double 6 sweets, I would add another 6 sweets to make 12. I would have twice as much as I did before.

Halving is the process of splitting into two groups and removing one of them. If I wanted to halve my 6 sweets, I would split them into 2 groups of 3, and get rid of one group. I would be left with 3 which is half of 6.

Subtracting requires us to find the difference between two numbers. Practicing subtracting single digit numbers from ten helps us to learn quick facts that support larger digit subtraction.

Subtracting single digit numbers from 10 is also part of number bonds to 10. Number bonds to 10 are all the single digit numbers that add up to 10, such as 3 + 7. We can flip our addition number bonds to 10 to help with subtracting from 10.

3 + 7 = 10

So....

10 - 3 = 7

Here are the other ways we can subtract numbers from 10:

10 - 1 = 9

10 - 2 = 8

10 - 3 = 7

10 - 4 = 6

10 - 5 = 5

10 - 6 = 4

10 - 7 = 3

10 - 8 = 2

10 - 9 = 1

10 - 10 = 0

Just like number bonds to 10, number bonds to 100 can be helpful for quick addition. Here they are:

10 + 90 = 100

20 + 80 = 100

30 + 70 = 100

40 + 60 = 100

50 + 50 = 100

60 + 40 = 100

70 + 30 = 100

80 + 20 = 100

90 + 10 = 100

Using logical reasoning, students can guess the numbers based on initial information.

The sum of two numbers is 10, and their difference is 0. What are the two numbers? (The two numbers are 5 and 5)

The sum of two numbers is 17. The product of the two numbers is 66. What are the two numbers? (The two numbers are 11 and 6)

Multiplying any numbers by 3 digits or more can be a little more complex and require more steps than multiplying by single digit numbers. However, multiplying by large numbers is still based on basic knowledge of times tables.

Let's look at an example and break it down.

If we have the question 34 x 23 = ?

We automatically know that this question is not covered by our times tables to 12 but we can use our basic times tables knowledge by splitting up the question.

We can start by splitting the question into two:

34 x 20 = ?

34 x 3 = ?

We have split 21 into 20 and 1. We can split it up even further though.

30 x 20 = ?

4 x 20 = ?

30 x 3 = ?

4 x 3 = ?

This is a little simpler to work out and a lot closer to our basic times tables knowledge!

We know:

30 x 20 = 600

4 x 20 = 80

30 x 3 = 90

4 x 3 = 12

Now we can add up the four answers to give our final answer:

34 x 23 = 782!

You may have heard of long multiplication, where larger numbers such as these are stacked on top of each other as a method of multiplying larger numbers. Long multiplication is essentially what we've just worked out, just written in a different view. It involves breaking the numbers down and multiplying step by step.