Bridging through 10
National Curriculum: this is in the Year 2 programme of study, part of key stage 1 (Years 1 and 2). Schools have to teach the key stage 1 programme by the end of Year 2, and can introduce content earlier or later within it.
Children in Year 2 are 6 or 7, and turn 7 during the school year.
What it is
Bridging through 10 means crossing a ten by stopping at it on the way. 8 + 5 is worked as 8 + 2 to make 10, then 3 more, which gives 13. Subtraction goes the same way in reverse: 13 − 5 is 13 − 3 to get back to 10, then 2 more off, which gives 8.
Two things have to be in place first: the pairs that make 10, so that 8 needs 2 comes back without thinking, and splitting the second number into the two pieces the crossing needs, so 5 becomes 2 and 3. A child with both crosses ten without counting. A child missing either one counts on in ones instead, usually on fingers, and the count is where the wrong answers come from.
This is where addition stops being counting and starts being built out of facts, so it is worth working on rather than waiting out. The same crossing turns up in 36 + 27, in every column addition that carries, and in mental subtraction for the rest of primary school.
When children learn it
Children meet crossing ten with numbers within 20 in Year 1. Year 2 is where it is expected to be secure and where it gets used constantly: adding two two-digit numbers such as 36 + 27 crosses a ten in the ones column. Fingers used for 8 + 5 after Year 2 point at this skill rather than at carelessness, because the crossing is being counted rather than known.
What it looks like when it goes wrong
These patterns come up again and again in children's answers on this skill. Each one points at a specific missing idea, not carelessness.
- Counting all from one. Asked 8 + 5, they hold up 8 fingers, then 5 more, then count the whole lot from one. The answer comes out right, and slowly. Counting on from the larger number is the step before bridging, and a child still counting all has not taken it yet.
- Crossing ten by counting in ones. 8 + 5 answered as 12 or 14. They count on past ten in ones and the count slips, often at ten itself. The answer is close, which is why this reads as carelessness rather than as a method that has not been learned.
- The answer stops at ten. 8 + 5 answered as 10. They made the ten and stopped there: reaching ten was treated as arriving, and the 3 that was still to be added never went on.
- The ten is left behind. 8 + 5 answered as 3. The 5 was split into 2 and 3 correctly and the ten was made, but only the leftover 3 was said. The ten they built is not being counted as part of the answer.
How to help at home
- Ask the bond first: what does 8 need to make 10? If that does not come back straight away, practise the pairs to 10 on their own for a few days. Bridging cannot be quicker than the bond inside it.
- Ask for the split out loud before the answer: in 8 + 5, which part of the 5 makes the ten? A child who says 2 and 3 has the method. A child who cannot is counting, whatever answer comes out.
- Two ten frames, or an egg box with ten spaces and some loose counters, make it visible: fill the ten, let the rest spill over, and read off ten and three. Say the calculation next to what they can see.
- Practise the matching subtraction on the same day: 8 + 5 = 13, so 13 − 5 = 8, worked as 13 − 3 − 2. Children often have the addition half of the bridge and not the subtraction half.