How to Teach Addition and Subtraction:
Bridging Through Tens Method

1. What is the bridging through tens method?

When a child counts “8 plus 6” on their fingers, they go one at a time: 8, 9, 10, 11, 12, 13, 14. It works - but only up to a point. With numbers above 20, finger counting becomes too slow and unreliable to be useful.

Bridging through tens teaches children to think about numbers structurally. Instead of counting in ones, the child splits the calculation into two simpler steps, using the nearest ten as a “stepping stone”.

Why is this better? Because the child understands what they are doing - they are not guessing or counting mechanically. The same pattern works for 28 + 7, 47 + 8 or 93 + 14. Once the principle is learned, it scales to any range of numbers.

2. Step by step: teaching addition

Always start with numbers within 20, then extend to 100 only once the first range is solid. Here are the three stages to work through in order.

Stage 1 - Number bonds to 10

Before learning the method, the child must know their number bonds to 10 fluently: 1+9, 2+8, 3+7, 4+6, 5+5, 6+4, 7+3, 8+2, 9+1. This is the foundation - without it, the method will feel slow and frustrating. Drill these pairs every day for a week before moving on.

Stage 2 - Bridging a ten (within 100)

Once within 20 feels easy, move to two-digit numbers. The principle is identical - the nearest ten, not always 10.

Stage 3 - Mental calculation

At first the child writes or says each step aloud. This is normal and necessary. Over time the steps compress - after a few weeks the child sees 38 + 7 and says “45” almost immediately, because they feel that 40 is 2 away and 5 remains. This is the breakthrough moment: fluency built on understanding, not rote learning.

3. Step by step: teaching subtraction

Subtraction with bridging works on the same principle, except the child “steps down” to the nearest ten below, rather than climbing up.

4. Common mistakes parents make - and how to avoid them

Most difficulties do not come from a child being “bad at maths”. They come from a handful of recurring mistakes in the way the skill is introduced.

Mistake 1 - Skipping number bonds to 10

If the child has to think about how much 7 needs to reach 10, the method will feel too slow and they will give up. Number bonds to 10 must be automatic - like the alphabet. Before starting the method, check these are truly fluent.

Mistake 2 - Moving to larger numbers too soon

When within 20 is shaky, many parents push ahead to within 100 - because that is what the curriculum says or because classmates seem to be there. Go back to basics. A solid foundation within 20 means the jump to 100 happens naturally - and much faster than forcing it.

Mistake 3 - Introducing column addition too early

Column addition is convenient but it teaches digit manipulation - not number understanding. A child who immediately does “8 plus 6, write 4 carry 1” often has no idea what that means in reality. Bridging should come before column methods, not instead of them - it builds the conceptual base that makes written methods meaningful.

Mistake 4 - Worksheets instead of play

A sheet of 20 sums demotivates even adults. Children aged 6-9 learn through play, movement and context. Ten minutes of a good maths game is worth more than forty minutes at a workbook.

5. Activities and games in practice

Here are some proven ways to practise the method - without worksheets and without boredom.

The “make ten” game

A parent calls out a number from 1 to 9, the child says the partner to 10 as fast as possible. Parent: “7!” - child: “3!”. Parent: “4!” - child: “6!”. Play during car rides, tidying up, cooking. Keep it to 2-3 minutes - short and fast.

The hundred chart

Draw or print a 1-100 number grid with your child. Colour in the calculations you are practising together. Seeing the structure of the tens visually is enormously helpful for children who learn better through pictures than through symbols.

LEGO tens

Use strips of 10 bricks as a physical representation of tens. “How many bricks does this strip need to be full?” Physical contact with number is irreplaceable for younger children (ages 6-7).

Maths games online

A well-designed maths game does something a worksheet cannot: it gives instant feedback, rewards progress, and makes the child want to come back. When choosing a game, check whether it requires the child to show their reasoning - not just enter a final answer. That one difference is what separates practice from understanding.

• Instant feedback - child knows immediately whether they are right
• Progressive difficulty - starts within 30, extends to 100
• Practises steps, not just answers - method, not mechanical responses
• Short sessions - 5-10 minutes is optimal for children aged 6-9