Counting on and counting back

Mathematics · Addition & Subtraction · ages 6-7

Name ______________________ Date ____________

You count back to work out 12 − 3. Which number do you start at?
- 3
- 9
- 12
Lena says counting on is a way to add. Is Lena right?
Circle one: True False
Subtract 12 - 3 by counting back from 12. What is 12 - 3?
Answer: ______________
To add 8 + 3 by counting on, where do you start counting?
- 1
- 8
- 3
Tom says 12 - 3 = 9 because he counted back 3 from 12. Is Tom right?
Circle one: True False
What is 15 - 6?
Answer: ______________
What is 9 + 5? Hint: make 10 first.
- 14
- 13
- 15
- 12
Nina adds 5 + 4 by counting on. She starts at 5 and counts on 4 more. What does she say?
- 6, 7, 8, 9
- 5, 6, 7, 8
- 9, 10, 11, 12
Ben adds 4 + 7 by counting on. He starts at 4 and counts on 7 more. Would it be faster to start at 7 instead?
- Yes, fewer hops to count
- No, it would take longer
- It does not matter
What is 20 - 5?
Answer: ______________

Answer key

For grown-ups. Fold this page away before handing over the rest.

12 · Start at 12, the number you are subtracting from, then count back 3.
True · Lena is right. Counting on adds by steps forward.
9 · 12 minus 3 equals 9. Count 11, 10, 9.
8 · Counting on means starting at the first number, 8, then counting up 3 more.
True · Tom is right. Counting back 3 lands on 9.
9 · 15 minus 6 equals 9.
14 · 9 needs 1 to make 10, leaving 4. 10 + 4 = 14.
6, 7, 8, 9 · Starting at 5, the next four counts are 6, 7, 8, 9. So 5 + 4 = 9.
Yes, fewer hops to count · Starting at the bigger number, 7, means only 4 hops instead of 7. Counting on still works either way, but starting big is faster.
15 · 20 minus 5 equals 15.