How far to the next ten?
To add 47 + 8, look first at how far 47 is from the next ten. The next ten after 47 is 50. 47 ends in 7, and 7 + 3 = 10, so 47 needs 3 more to reach 50.
10 − 5 = 5, which is what 5 needs to reach ten
Find what 7 needs to reach ten.
Ten counters split into two parts. With 7 on the left, 3 are on the right: 7 + 3 = 10, so 3 is what 7 needs to reach ten.
Split the number you are adding
Split the 8 into the 3 that reaches 50 and the rest: 8 = 3 + 5. The first hop is 47 + 3 = 50.
The first hop, 3, takes 47 to 50.
Then the rest
3 of the 8 have been used, so 5 are left. 50 + 5 = 55, so 47 + 8 = 55. Adding 5 to 50 is easy, because 50 has no ones.
From 50, add only what is left of the 8. Adding the whole 8 again gives 58, which counts the 3 twice. The two hops together must make the number being added: 3 + 5 = 8.
A hop of 3 reaches 50, and a hop of 5 lands on 55. The two hops together are 8.
Through a hundred
The same move works at a hundred, because 100 is a ten too. For 96 + 7, 96 needs 4 more to reach 100, since 6 + 4 = 10. Split the 7 into 4 and 3: 96 + 4 = 100, and 100 + 3 = 103.
A hop of 4 reaches 100, and a hop of 3 lands on 103.
Worked example: More People Get On a Train
Question A train has 58 people on it. At the first station 27 more people get on. At the second station 38 more people get on. No one gets off. (a) How many people are on the train after the first station? (b) How many people are on the train after the second station?
1.58 needs 2 more to reach the next ten, which is 60. So split 27 into 2 and 25.
58 needs 2 more to reach 60, so 27 is split into 2 and 25. 2.(a) 58 + 2 = 60 and 60 + 25 = 85, so there are 85 people on the train after the first station.
(a) 58 + 2 = 60 and 60 + 25 = 85 people. 3.85 needs 15 more to reach 100. So split 38 into 15 and 23.
85 needs 15 more to reach 100, so 38 is split into 15 and 23. 4.(b) 85 + 15 = 100 and 100 + 23 = 123, so there are 123 people on the train after the second station.
(b) 85 + 15 = 100 and 100 + 23 = 123 people.
Answer: (a) 85 people; (b) 123 people
Common mistakes
- Jumping 2 to reach 60 and then adding the whole 27 to get 87. The 2 is part of the 27, so only 25 is left to add.
- Splitting 38 into 15 and 13. The two parts must add up to 38, and 15 + 13 is only 28. The right split is 15 and 23.
More adding and subtracting in your head problems, worked step by step →