Which bonds, in which order
Each stage reuses the stage before. A child who knows 3 and 7 make 10 can be shown that 30 and 70 make 100 and 0.3 and 0.7 make 1 in the same breath. Point out the pattern; do not teach each set from scratch.
- Bonds to 5, then to 10: the foundation, usually in the first year of school.
- Bonds to 20: built from bonds to 10 (if 3 and 7 make 10, then 13 and 7 make 20).
- Bonds to 100 in tens (30 and 70), then any pair (35 and 65).
- Bonds to 1,000 in hundreds, and decimal bonds to 1 (0.3 and 0.7), for older children.
1. Ten frame fill
Draw a ten frame (two rows of five boxes). Put some counters in, and ask how many more fill it. Five counters and five empty boxes, seven counters and three empty. The frame shows the bond without any counting on fingers, and children soon see the empty spaces as a number in their own right.
2. Rainbow bonds
Write 0 to 10 in a row. Draw arcs joining 0 to 10, 1 to 9, 2 to 8, 3 to 7 and 4 to 6, each a different colour, with 5 alone in the middle. The picture shows that every bond has a partner and that there are only six pairs to learn. Children colour their own rainbow and keep it in their book.
3. Flip cards
Cards numbered 0 to 10. Flip one; the child says the partner that makes 10. Time a run through the whole pack and try to beat it tomorrow. Later, use the same cards for bonds to 20 (flip 4, say 16) with no change to the equipment.
4. Make ten with dice
Roll a die and say the number needed to make 10. Two dice: add them, then say the number needed to make 20. This one takes thirty seconds and fits into any spare moment.
5. Domino match
Spread dominoes face up. Find every domino whose two halves make a given total (all the ones that make 6, then 7, then 8). Dominoes show the bond as two groups of dots, which is exactly what a number bond is.
6. Missing part
Show a whole and one part in a part-whole diagram (a circle for the whole with two circles for the parts) and hide the other part. The whole is 10, one part is 6, what is the missing part? Swap which part is hidden. Then hide the whole instead and give both parts, so children see the same diagram works for addition and subtraction.
7. Bond snap
A pack of cards numbered 0 to 10, two of each. Deal and play snap, but a snap is two cards that make 10 rather than two matching cards. Fast, noisy, and children play it without being asked.
8. Hundred square hunt
On a hundred square, point to a number and ask for its bond to 100. Children notice that the tens digits make 9 and the ones digits make 10 (35 and 65, 42 and 58), unless the number ends in zero, when the tens make 10 (30 and 70). Spotting that rule is the whole lesson.
9. Bond ladder
Write a number at the bottom rung. Each rung up, add to reach the next multiple of ten, then the next: from 37, add 3 to reach 40, add 60 to reach 100. Older children ladder up to 1,000. It is bonds to 10 and bonds to 100 chained together, and it is exactly how mental subtraction works.
10. Oral warm-up
No equipment. Say a number, the child says the bond. Keep a steady rhythm and mix the target total: bond to 10, bond to 20, bond to 100. Two minutes at the start of every maths lesson for a term produces instant recall in nearly every child.
When to move on
A child knows a set of bonds when they can answer any one in under two seconds without counting. Until then, keep playing. Once bonds to 10 are that secure, start bonds to 20 and keep the bonds to 10 games as a warm-up rather than dropping them.