A whole and its two parts
A number bond shows a whole and the two parts it splits into. 9 splits into 4 and 5: the whole is 9, and the parts are 4 and 5. Put the two parts together and you get the whole again, 4 + 5 = 9.
Taking away asks for a missing part. You know the whole is 9 and one part is 4. What is the other part? That question is written 9 − 4, and it is read "9 take away 4".
The whole is 9 and one part is 4. The other part is the question.
Take the part you know from the whole
Start with all 9 and take away the 4 you know. What is left is the other part. 9 birds sit on a fence and 4 fly off: 5 are left on the fence, so 9 − 4 = 5.
There are 9 squares. Take away the 4 gold ones, and the 5 white ones are left.
Take the part you know from the whole: 9 − 4 = 5. The parts 4 and 5 make 9 again.
Or count up
Another way to find the missing part is to count up from the part you know to the whole. Start at 4 and count on to 9: five, six, seven, eight, nine. That is five counts, so the missing part is 5.
From 4 to 9 is a hop of 5, so 9 − 4 = 5.
Less than the whole
What is left is always less than the whole, because a part has gone. If an answer comes out bigger than the number you started with, the numbers were added instead: 9 + 4 = 13, and 13 is more birds than were ever on the fence.
Worked example: Birds on a Fence and Some Fly Off
Question There are 9 birds on a fence. Then 4 birds fly off. (a) How many birds are left on the fence? (b) Then 2 more birds fly off. How many birds are left now?
1.Draw a ten frame. Put in 9 counters for the 9 birds.
One counter is one bird. There are 9 counters for the 9 birds. 2.4 birds fly off. Cross out 4 counters.
4 birds fly off, so 4 counters are crossed out. 3.(a) Count the counters that are not crossed out. There are 5. So 9 − 4 = 5. There are 5 birds left.
(a) 5 counters are not crossed out. 9 − 4 = 5 birds are left. 4.(b) Cross out 2 more counters. So 5 − 2 = 3. There are 3 birds left now.
(b) 2 more counters are crossed out. 5 − 2 = 3 birds are left.
Answer: (a) 5 birds; (b) 3 birds
Common mistakes
- Adding the two numbers: 9 + 4 = 13. The birds fly off, so there are fewer birds on the fence, not more.
- Taking 2 away from 9 in part (b) to get 7. Only 5 birds were still on the fence, so take 2 away from 5.
More adding and subtracting within 20 problems, worked step by step →
Worked example: Toy Cars with One Part Missing
Question Sam has 15 toy cars. 8 of the cars are red. The rest are blue. (a) How many blue cars does Sam have? (b) Sam gets 2 more blue cars. How many blue cars does he have now?
1.Put 15 counters in two ten frames for the 15 cars. There are 10 in the first frame and 5 in the next.
There are 15 counters for the 15 cars: 10 in the first frame and 5 in the next. 2.Mark 8 of the counters for the red cars. The other counters are the blue cars.
8 of the counters are the red cars. The other counters are the blue cars. 3.(a) Count on from 8. 2 more make 10, and 5 more make 15. 2 + 5 = 7, so 15 − 8 = 7. Sam has 7 blue cars. Check: 8 + 7 = 15.
(a) Count on from 8: 2 more make 10, and 5 more make 15. 2 + 5 = 7, so 15 − 8 = 7 blue cars. 4.(b) Sam gets 2 more blue cars. So 7 + 2 = 9. He has 9 blue cars now.
(b) Sam gets 2 more blue cars. 7 + 2 = 9 blue cars.
Answer: (a) 7 blue cars; (b) 9 blue cars
Common mistakes
- Adding the two numbers: 15 + 8 = 23. The 8 red cars are part of the 15 cars already, so they are taken away from 15.
- Adding 2 to 15 in part (b) to get 17. That is all of Sam's cars. The question asks for the blue cars only, so add 2 to 7.
More adding and subtracting within 20 problems, worked step by step →