Count on from the bigger number
To add 8 + 5, start at 8 and count on 5 more: nine, ten, eleven, twelve, thirteen. The fifth count lands on 13, so 8 + 5 = 13. The 8 is counted already, so the first count is nine, not eight.
Start from the bigger number. For 3 + 9, start at 9 and count on 3: ten, eleven, twelve. The order you add in does not change the total, and three counts are quicker than nine.
Move the marker from 8, one step at a time. Each step to the right adds 1, and the fifth step lands on 13.
Make ten first
Counting on five times is slow, and one slip spoils it. There is a quicker way, through 10. 8 needs 2 more to make 10, because 8 and 2 is a number bond to ten. So split the 5 into 2 and 3, and add the 2 first: 8 + 2 = 10.
The first hop, +2, takes 8 up to 10.
Then add what is left
2 of the 5 have been used, so 3 are left to add. Ten and 3 more is 13. Written in one line: 8 + 5 = 8 + 2 + 3 = 10 + 3 = 13.
The two parts of the split must make the number being added: 2 + 3 = 5. Once the 2 has filled the ten, add only the 3 that is left, not the whole 5 again.
A hop of 2 reaches 10, and a hop of 3 reaches 13. The two hops together are the 5.
Any sum that crosses ten
The same two steps work for every sum that crosses ten. For 9 + 4, 9 needs 1 to make 10, so split the 4 into 1 and 3: 9 + 1 = 10, and 10 + 3 = 13. For 7 + 5, 7 needs 3, so split the 5 into 3 and 2: 7 + 3 = 10, and 10 + 2 = 12.
Taking away checks an addition. 8 + 5 = 13, so 13 − 5 takes you back to 8.
Worked example: Stickers Added by Making Ten First
Question Ali has 8 stickers. His teacher gives him 5 more stickers. (a) How many of the new stickers make his 8 stickers up to 10? (b) How many stickers does Ali have altogether?
1.Put 8 counters in a ten frame for the 8 stickers. There are 2 empty cells.
There are 8 counters for the 8 stickers. 2 cells of the frame are empty. 2.(a) The numbers 8 and 2 make 10. So 2 of the new stickers fill the frame.
(a) The numbers 8 and 2 make 10, so 2 of the new stickers fill the frame. 3.Split 5 into 2 and 3. The 2 filled the frame. Put the other 3 counters in a new frame.
Split 5 into 2 and 3. The other 3 new stickers go in the next frame. 4.(b) 8 + 5 = 8 + 2 + 3 = 10 + 3 = 13. Ali has 13 stickers altogether.
(b) 8 + 5 = 8 + 2 + 3 = 10 + 3 = 13 stickers altogether.
Answer: (a) 2 stickers; (b) 13 stickers
Common mistakes
- Filling the frame with 2 counters and then adding all 5 again to get 15. The 2 counters are part of the 5, so only 3 more are added.
- Splitting 5 into 2 and 2. The two parts must make 5, and 2 + 3 = 5.
More adding and subtracting within 20 problems, worked step by step →
Worked example: Cookies Baked and Eaten, One Fact Family
Question Mom bakes 7 round cookies and 5 star cookies. (a) How many cookies does Mom bake altogether? (b) The family eats the 5 star cookies. How many cookies are left?
1.Put in 7 counters for the round cookies. Put in 5 counters for the star cookies.
There are 7 counters for the round cookies and 5 counters for the star cookies. 2.(a) 7 + 3 = 10, and 2 more make 12. So 7 + 5 = 12. Mom bakes 12 cookies altogether.
(a) 7 + 3 = 10, and 2 more make 12. 7 + 5 = 12 cookies. 3.The family eats the 5 star cookies. Cross out the 5 counters for the star cookies.
The 5 star cookies are eaten, so the 5 star counters are crossed out. 4.(b) The 7 round cookies are left. 7 + 5 = 12, so 12 − 5 = 7. There are 7 cookies left.
(b) The 7 round cookies are left. 7 + 5 = 12, so 12 − 5 = 7.
Answer: (a) 12 cookies; (b) 7 cookies
Common mistakes
- Taking 5 away from 7 in part (b) to get 2. The family eats 5 of the 12 cookies, so the subtraction is 12 − 5.
- Counting back 5 from 12 and saying 12 as the first count, which gives 8. The first cookie eaten leaves 11. The fact 7 + 5 = 12 gives 12 − 5 = 7 with no counting back.
More adding and subtracting within 20 problems, worked step by step →