Learning addition and substraction facts

Here is the structure of the process of learning addition and subtraction facts.

Addition

“Doubles”
1) 5 + 5 = ________2) 9 + 9 = ________
“Doubles plus 1” “Doubles minus 1”
3) 5 + 6 = 5 + 5 + 1 = ________4) 8 + 7 = 8 + 8 – 1 = ________
“Counting on (start at x and count-up by y)”
5) 7 + 2 = ________6) 8 + 3 = ________
“Breaking–down Numbers”
7) 6 + _____ = 9 8) _____ + 7 = 11
“How far apart are two numbers?” “How far is it from x up to y?”
9) How far apart are 6 and 10? __10) How far is it from 9 up to 12? ____
“Combinations that make 10”
11) 8 + 2 = ________12) 6 + 4 = ________
“10 plus a number”
13) 10 + 7 = 1714) 10 + 9 = 19
“10 plus what number”
15) 10 + _____ = 1616) 10 + _____ = 19
“Putting it all together”
17) “8 + 6 = ”: 8 plus how much makes 10 (2) ...[6 – 2 = 4]...10 plus the left–over (4) ... 10 + 4 = 14
18) “9 + 7 = ”: 9 plus how much makes 10 (1) ...[7 – 1 = 6]...10 plus the left–over (6) ... 10 + 6 = 16

Substraction

Subtraction has two aspects:

  • the notion of “how much is left,” and
  • the notion of “how far apart are the two numbers” (how far is it from the smaller number up to the bigger number.)

Use the notion of “how much is left” when the numbers are fairly far apart, and count down.

For example, “12 – 3” is best thought of “counting down from 12 by 3.”

On the other hand, use the notion “how far apart are the two numbers” when the numbers are fairly close to each other, and count up.

For example, “12 – 9” is best thought of “how far is it from 9 up to 12.”

After a good deal of practice with both methods, the right one will automatically come to mind as you are doing problems.

Try these:

  • Which method would you use for “100 - 98”? (CIRCLE ONE)
    HOW FAR APARTHOW MUCH IS LEFT
  • Which method would you use for “100 - 3”? (CIRCLE ONE)
    HOW FAR APARTHOW MUCH IS LEFT
  • Which method would you use for “100 - 87”? (CIRCLE ONE)
    HOW FAR APARTHOW MUCH IS LEFT
  • Which method would you use for “100 - 15”? (CIRCLE ONE)
    HOW FAR APARTHOW MUCH IS LEFT

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