The pairs that make ten
A number bond to ten is a pair of numbers that add up to 10: 0 and 10, 1 and 9, 2 and 8, 3 and 7, 4 and 6, and 5 and 5. There are only six pairs. Know them by heart and every sum that crosses ten gets quicker.
A ten frame is a row of ten boxes. Put 6 counters in it and 4 boxes stay empty, so 6 + 4 = 10. The empty boxes are the partner of 6, and you can see how many there are without counting the full ones.
10 − 5 = 5, which is what 5 needs to reach ten
Find what 7 needs to reach ten.
The ten counters stay the same ten; only the split between the two parts changes. Each split is one of the pairs that make ten.
Finding the missing part
When one part is missing, as in 7 + ? = 10, take the part you know from the whole: 10 − 7 = 3. Or count on from 7: eight, nine, ten. That is three steps, so the missing part is 3.
The bonds make bigger sums quicker too. For 7 + 6, the 7 needs 3 more to make ten, so split the 6 into 3 and 3. Then 7 + 3 = 10, and 10 + 3 = 13.
Worked example: An Egg Box That Holds Ten
Question An egg box holds 10 eggs. There are 6 eggs in the box. (a) How many more eggs fit in the box? (b) Mom puts 2 more eggs in the box. How many more eggs fit now?
1.Draw a ten frame for the box. Put in 6 counters for the 6 eggs.
The egg box is a ten frame. There are 6 counters for the 6 eggs. 2.Count the empty cells: 1, 2, 3, 4. The numbers 6 and 4 make 10.
Count the empty cells: 1, 2, 3, 4. The numbers 6 and 4 make 10. 3.(a) 6 + 4 = 10. So 4 more eggs fit in the box.
(a) 6 + 4 = 10, so 4 more eggs fit in the box. 4.(b) Now there are 6 + 2 = 8 eggs in the box. There are 2 empty cells, and 8 + 2 = 10. So 2 more eggs fit.
(b) Now there are 6 + 2 = 8 eggs. 2 cells are empty, and 8 + 2 = 10. So 2 more eggs fit.
Answer: (a) 4 eggs; (b) 2 eggs
Common mistakes
- Adding the two numbers: 10 + 6 = 16. The box holds only 10 eggs. The question asks for the part that is missing from 10.
- Answering 8 in part (b). There are 8 eggs in the box now, but the question asks how many more fit, and that is the 2 empty cells.
More adding and subtracting within 20 problems, worked step by step →
Worked example: Three Bunches of Flowers with a Ten Inside
Question Lina picks 4 red flowers. She picks 5 white flowers and 6 yellow flowers. (a) How many red and yellow flowers does she pick? (b) How many flowers does she pick altogether?
1.Put 4 counters in a ten frame for the red flowers. There are 6 empty cells.
There are 4 counters for the red flowers. 6 cells of the frame are empty. 2.The 6 counters for the yellow flowers fill the 6 empty cells. The numbers 4 and 6 make 10.
The 6 yellow flowers fill the 6 empty cells. The numbers 4 and 6 make 10. 3.(a) 4 + 6 = 10. Lina picks 10 red and yellow flowers.
(a) 4 + 6 = 10 red and yellow flowers. 4.Put the 5 counters for the white flowers in a new frame.
The 5 counters for the white flowers go in the next frame. 5.(b) 4 + 5 + 6 = 10 + 5 = 15. Lina picks 15 flowers altogether.
(b) 4 + 5 + 6 = 10 + 5 = 15 flowers altogether.
Answer: (a) 10 flowers; (b) 15 flowers
Common mistakes
- Adding only the first two numbers: 4 + 5 = 9. There are three groups of flowers, and all three are added in part (b).
- Adding the 10 from part (a) to all three numbers again. The 10 is the red and the yellow flowers already, so only the 5 white flowers are added to it.
More adding and subtracting within 20 problems, worked step by step →