Small facts
Single-digit addition and subtraction until the answer is instant.
Best in your head · no pen, no calculator why?
the idea
Every small sum and difference comes from the same 55 addition facts, all the pairs from 0 + 0 up to 9 + 9. Subtraction is those facts read backward: 15 − 8 asks what goes with 8 to make 15.
The goal is recall, not counting. Counting on your fingers is slow, and it is easy to land one off. Lean on two anchors you already know, ten and doubles. Every other fact is one short step from one of them. After a few rounds, the answer just arrives.
techniques
Make ten
- Take the bigger number and ask how much it needs to reach 10.
- Take that much away from the smaller number.
- The answer is 10 plus what is left.
worked example
8 + 7
- 8 needs 2 to reach 10.
- 7 − 2 = 5 left over.
- 10 + 5 = 15.
Answer: 15
Doubles and near doubles
- Know the doubles cold: 6 + 6 = 12, 7 + 7 = 14, 8 + 8 = 16, 9 + 9 = 18.
- For numbers one apart, double the smaller one.
- Then add 1.
worked example
7 + 8
- Double the smaller one: 7 + 7 = 14.
- Add 1: 14 + 1 = 15.
Answer: 15
Go through ten
- Count up: read 15 − 8 as "8 plus what makes 15?"
- Jump from the small number to 10, then from 10 to the big number. Add the two jumps.
- Or count back through ten: 15 − 5 = 10, then 3 more back is 7.
worked example
15 − 8
- 8 up to 10 is 2.
- 10 up to 15 is 5.
- 2 + 5 = 7.
Answer: 7
watch out for
- Adjusting a double the wrong way: 8 + 7 is one less than 8 + 8, not one more.
- Counting back and counting the starting number too. That makes the difference one too big.
- Adding in a missing-number problem. In 6 + ? = 13 the answer is the gap between 6 and 13, not their sum.
practice
Sums to 18
worked example
8 + 7
Answer: 15
- Near double: 7 + 7 = 14, and one more is 15.
Differences under 20
worked example
12 − 4
Answer: 8
- Back to ten first: 12 − 2 = 10, then 2 more back is 8.
- Check: 4 + 8 = 12.
Missing addend
worked example
7 + ? = 15
Answer: 8
- Count up through ten: 7 → 10 is 3, 10 → 15 is 5, and 3 + 5 = 8.