Adding Is Counting On

You have 3 apples in a bag. At the market you buy 4 more and put them in the same bag. How many apples are in the bag now? You could tip them all out and count from one. But there is a quicker way, and it works for any numbers.

Putting groups together

Adding means putting groups together and finding how many there are altogether. We write it with a plus sign:

3 + 4 = 7, said "three plus four equals seven".

The answer, 7, is called the sum.

Three apples in one group and four apples in another, joined together into one group of seven apples. Under them: 3 + 4 = 7

Counting on

You don't have to count all seven apples from one. You already know there are 3 in the bag. So start at 3 and count on, one for each new apple: "four, five, six, seven". That is counting on.

On the number line, counting on is hopping to the right: start at 3 and take 4 hops. You land on 7.

A number line from 0 to 10. A dot sits on 3, and four green hops go to the right from 3 to 7: 3 + 4 = 7

The order doesn't matter

Is 3 + 4 the same as 4 + 3? Put 3 apples and 4 apples on a table. Whether you look at them from left or from right, there are 7. So 3 + 4 = 4 + 3. This is true for any two numbers you add.

That gives a handy trick: start from the bigger number. For 2 + 9, start at 9 and count on just two: "ten, eleven". Much quicker than starting at 2 and counting on nine.

Making ten

In the Ones, Tens and Hundreds lesson we saw that ten ones make a ten. Adding gets easier if you fill up a ten first.

Take 8 + 5. Eight needs 2 more to make ten. So split the 5 into 2 and 3:

8 + 2 = 10;
10 + 3 = 13.

So 8 + 5 = 13.

Two boxes of ten squares each. The first box has 8 blue dots and 2 orange dots, so it is full: ten. The second box has 3 orange dots. Ten and three make 13

Place value helps with bigger numbers too. 30 + 40 is 3 tens and 4 tens: 7 tens, which is 70. You add tens just like ones.

Try it at home

Put 6 coins in one pile and 5 in another. Count on from 6 to find how many there are altogether. Then count on from 5. Same answer?
Use "making ten" for 9 + 4 and 7 + 6. Answers below.

Answers: 9 + 1 + 3 = 13; 7 + 3 + 3 = 13.

Words to know

adding - putting groups together to find how many there are altogether
plus sign (+) - the sign for adding
sum - the answer to an adding sum, like 7 in 3 + 4 = 7
counting on - starting from one number and counting forward, one for each thing added

Big idea

Adding puts groups together. Start from the bigger number and count on, or fill up a ten first. The order you add in never changes the answer: 3 + 4 = 4 + 3.