Counting On from a Number

A faster way to add

When you add, you do not always have to count everything from one. There is a quicker way called counting on.

Counting on means: start at a number, then count forward to add more. You keep the first number in your head and just carry on counting.

Counting all vs counting on

Imagine 6 marbles in a bag and 3 more in your hand. How many altogether?

The slow way (counting all): tip them out and count every marble from the start: "one, two, three... nine." That works, but it takes a while.

The quick way (counting on): you already know the bag has 6. So just say "six" and count on the 3 in your hand: "seven, eight, nine." Nine! You never had to count the first six.

Counting on is faster because you trust the first number and only count the rest.

Always start with the bigger number

Here is a smart tip. When you count on, start with the bigger number. That way you have fewer numbers to count on.

For 2 + 7, do not start at 2 and count on 7. Instead, swap them: start at 7 and count on just 2 — "eight, nine." Same answer, much less work! Adding numbers in either order gives the same total — that handy fact is called commutativity.

Keep track with your fingers

How do you know when to stop counting on? Use your fingers! Lift one finger for each number you count on. When all your fingers are up, you stop.

To add 3, you will lift 3 fingers as you say "seven, eight, nine" — and the last word is your answer.

Worked example 1: 8 + 2

The bigger number is 8, so start there. Count on 2, lifting a finger each time:

Say "eight"... then "nine" (one finger), "ten" (two fingers).

Two fingers are up, so stop. You landed on 10. So 8 + 2 = 10.

Worked example 2: 5 + 4

Start at the bigger number, 5. Count on 4:

"five"... "six" (1), "seven" (2), "eight" (3), "nine" (4).

Four fingers up — stop. The answer is 9. So 5 + 4 = 9.

Worked example 3: swapping to make it easy

Work out 3 + 6. The bigger number is 6, so swap and start there. Count on 3:

"six"... "seven" (1), "eight" (2), "nine" (3).

The answer is 9. By starting with 6, you only counted on 3 instead of 6.

A quick table

Sum	Start at	Count on	Answer
7 + 1	7	8	8
9 + 2	9	10, 11	11
4 + 3	4	5, 6, 7	7
6 + 4	6	7, 8, 9, 10	10

Why counting on matters

Counting on shows that you can hold a number in your head — a big step in becoming a confident mathematician. It is quicker and more accurate than counting everything from one, and it leads straight into mental adding.

It builds nicely on knowing one more and one less, because counting on is really just "one more, and one more, and one more." When you are ready, use it to power through our lesson on addition and subtraction.

Try it yourself

Play Hide and Count On. You need a small box or cup and some counters.

1. Put some counters in the box, say 7, and tell your partner how many are hidden.
2. Place a few more counters on the table, say 3.
3. Your partner says the hidden number — "seven" — and counts on the ones they can see: "eight, nine, ten."
4. Open the box and count everything to check. Did you get the same answer?
5. Challenge: Always start with the bigger number. If the box has 2 and the table has 8, start at 8!

What's next?

Once counting on feels natural, learn an even quicker adding trick in our lesson on making 10 to add.