Bridging Through Ten

What is bridging through ten?

Bridging through ten is a way of adding two numbers when the answer goes past 10. Instead of counting on one at a time, you stop at a tidy 10 along the way, then add what is left. Ten is an easy number to build from, so the journey becomes much smoother — like crossing a river by stepping on a sturdy bridge in the middle.

The strategy has just two steps:

1. Add enough to reach 10.
2. Add the rest.

Why ten is the perfect stopping point

Our whole number system is built on tens. Adding to 10 is wonderfully easy: 10 + 3 is just 13, and 10 + 6 is just 16. You barely have to think.

So the trick is to break the second number into two pieces: the piece that completes the ten, and the leftover. To do this quickly you need your number bonds to 10 — they tell you exactly how much each number needs.

How to split the number

Take 8 + 5. The 8 needs 2 to make 10. So split the 5 into 2 and 3:

• 8 + 2 = 10 (we reached the bridge)
• 10 + 3 = 13 (we added the rest)

So 8 + 5 = 13. Why split the 5 and not the 8? Because we want to top up the 8 to a tidy 10, and the bond tells us it needs exactly 2.

Here are more sums shown the same way.

Sum	Make 10	Leftover	Answer
8 + 5	8 + 2 = 10	10 + 3	13
9 + 4	9 + 1 = 10	10 + 3	13
7 + 6	7 + 3 = 10	10 + 3	13
6 + 8	6 + 4 = 10	10 + 4	14
5 + 9	5 + 5 = 10	10 + 4	14

Worked example 1: 9 + 4

1. The 9 needs 1 to make 10 (bond to 10).
2. Split the 4 into 1 and 3.
3. 9 + 1 = 10, then 10 + 3 = 13.

So 9 + 4 = 13.

Worked example 2: 7 + 6

1. The 7 needs 3 to make 10.
2. Split the 6 into 3 and 3.
3. 7 + 3 = 10, then 10 + 3 = 13.

So 7 + 6 = 13.

Worked example 3: bridging with bigger numbers

Bridging works past every ten, not just the first one. Try 28 + 5.

1. The 28 needs 2 to reach the next tidy ten, 30.
2. Split the 5 into 2 and 3.
3. 28 + 2 = 30, then 30 + 3 = 33.

So 28 + 5 = 33. The same idea scales up to any number.

Why this strategy matters

Bridging through ten replaces slow counting with two quick, reliable steps. It also builds a deep feel for how tens hold our number system together — the very same thinking you use later in column addition and mental math. Children who bridge confidently make far fewer counting mistakes.

Try it yourself

You will need a ten frame (draw two rows of five squares) and some counters.

1. Place a number of counters on the frame, say 8.
2. Now try to add 5 more. Fill the frame to 10 first.
3. Notice how many counters spill over onto a second frame — that is your leftover.
4. Say the steps aloud: "8 plus 2 makes 10, plus 3 more is 13."
5. Challenge: Pick your own sums that cross 10 and beat your fastest time.

What's next?

Bridging pairs beautifully with other tricks. Explore mental math strategies for more, or move on to written methods in addition and subtraction.