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learn › Mental Arithmetic

Small facts

lesson · about 3 minutes

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.

more of the idea

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 The two numbers add up to more than 10.
Making ten: 8 + 7A number line. 7 chips: 2 of them take 8 up to 10, and the other 5 carry on to 15. 8 + 7 = 15.020101075 left+2+5815
  1. Take the bigger number and ask how much it needs to reach 10.
  2. Take that much away from the smaller number.
  3. The answer is 10 plus what is left.

example 8 + 7

  1. 8 needs 2 to reach 10.
  2. 7 − 2 = 5 left over.
  3. 10 + 5 = 15.

Answer: 15

more: Make ten

Doubles and near doubles The two numbers are the same, or one apart.
Near doubles: 7 + 8Two bars, 7 and 8 long. The shared 7 of each doubles to 14; the 1 left over makes 15.78+17 + 7 = 1414 + 1 = 15
  1. Know the doubles cold: 6 + 6 = 12, 7 + 7 = 14, 8 + 8 = 16, 9 + 9 = 18.
  2. For numbers one apart, double the smaller one.
  3. Then add 1.

example 7 + 8

  1. Double the smaller one: 7 + 7 = 14.
  2. Add 1: 14 + 1 = 15.

Answer: 15

more: Doubles and near doubles

Go through ten A subtraction or missing number where the big number is 10 or more.
Counting up from 8 to 15A number line. A jump of 2 from 8 to 10, then A jump of 5 from 10 to 15. Together: 7.5+2+5810152 + 5 = 7
  1. Count up: read 15 − 8 as "8 plus what makes 15?"
  2. Jump from the small number to 10, then from 10 to the big number. Add the two jumps.
  3. Or count back through ten: 15 − 5 = 10, then 3 more back is 7.

example 15 − 8

  1. 8 up to 10 is 2.
  2. 10 up to 15 is 5.
  3. 2 + 5 = 7.

Answer: 7

more: Count up to subtract

watch out for · 3 traps

practice

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Sums to 18

worked example

8 + 7

  1. Near double: 7 + 7 = 14, and one more is 15.

Answer: 15

Differences under 20

worked example

12 − 4

  1. Back to ten first: 12 − 2 = 10, then 2 more back is 8.
  2. Check: 4 + 8 = 12.

Answer: 8

Missing addend

worked example

7 + ? = 15

  1. Count up through ten: 7 → 10 is 3, 10 → 15 is 5, and 3 + 5 = 8.

Answer: 8

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