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The ideas in this division lesson are taken from Division 1 ebook. Only a few examples of each problem type are shown; you should make more problems of each kind for the student.

Division as repeated subtraction
Free lesson plan from HomeschoolMath.net

Remember how MULTIPLICATION is repeated addition:

5 × 4 = 4 + 4 + 4 + 4 + 4 = 20.

Let's draw one group of four...
Draw another group of four to the picture.
And another group.
And another group.
And yet one more group.

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You drew or added __ groups of four.

Let's reverse the process. You start out with 20 sticks.

Make one group of four. In your mind, "move it away" from the picture.
Form another group of four. Again, "move it away" in your mind, or subtract it from the picture. Keep forming groups of four till you have none left.
How many groups did you make? ___

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20 − 4 − 4 − 4 − 4 − 4 = 0

This is repeated subtraction. You subtract 4 repeatedly, or many times, till you hit zero. Each subtraction is forming a group of 4. How many groups did you form? How many times did you subtract? That is the answer to the division problem 20 ÷ 4.

Try it yourself: Separate groups, but in your mind 'move them away' or subtract.

42 ÷ 3

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42 ÷ 14

DIVISION is repeated subtraction:

20 ÷ 4 = ??

20 − 4 − 4 − 4 − 4 − 4 = 0.
I subtracted 4 five times,
so 20 ÷ 4 = 5.

84 ÷ 21 = ??

84 − 21		1
63 − 21		1
42 − 21		1
21 − 21		1
0		4

I subtracted 21 four times,
so 84 ÷ 21 = 4

Often, it is handier to actually add instead of subtract:

Since 13 + 13 = 26,
13 goes to 26 two times.
So 26 ÷ 13 = 2

Since 21 + 21 + 21 + 21 = 84,
21 goes to 84 four times.
So 84 ÷ 21 = 4

Example problems

1. Write a multiplication sentence AND a division sentence that fits the addition/subtraction facts.

5 + 5 + 5 = 15
15 − 5 − 5 − 5 = 0

__ ÷ __ = __

12 + 12 + 12 + 12 = 48
48 − 12 − 12 − 12 − 12 = 0

__ ÷ __ = __

23 + 23 + 23 = __
__ − 23 − 23 − 23 = 0

__ ÷ __ = __

40 + 40 = __
__ − 40− 40 = 0

__ ÷ __ = __

2. Write a subtraction sentence for each division sentence.

45 ÷ 15 = __

45 −

32 ÷ 8 = __

32 −

Multiplication is repeated addition, and it is like jumps on the number line.

5 × 4 = 20. Five jumps of 4 gets you to 20.

Division is repeated subtraction. You make jumps of four backwards from 20 till you hit 0:

20 ÷ 4 = 5. 20 − 4 − 4 − 4 − 4 − 4 = 0
Five jumps of 4 gets you from 20 till 0.

What division is illustrated here?

2. Draw jumps backwards to illustrate the division sentences.

30 ÷ 5 =

28 ÷ 4 =

42 ÷ 6 =

4. Solve using repeated subtraction OR adding up to the number being divided.

40 ÷ 20 = __

90 ÷ 30 = __

30 ÷ 15 = __

52 ÷ 13 = __

34 ÷ 17 = __

69 ÷ 23 = __

45 ÷ 15 = __

90 ÷ 15 = __

90 ÷ 18 = __

5. If 12 × 2 = 24, then 13 × 2 is __ How about division? Use the previous problem to help you solve the next one.

a.
24 ÷ 2 = __

26 ÷ 2 = __

28 ÷ 2 = __

30 ÷ 2 = __

d.
60 ÷ 2 = __

66 ÷ 2 = __

70 ÷ 2 = __

78 ÷ 2 = __

6. Try the same kind of thing when dividing by 3.

a.
30 ÷ 3 = __

36 ÷ 3 = __

39 ÷ 3 = __

d.
81 ÷ 3 = __

90 ÷ 3 = __

99 ÷ 3 = __

Next lesson: Zero and one in division

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Division as repeated subtraction Free lesson plan from HomeschoolMath.net

Example problems

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Free lesson plan from HomeschoolMath.net

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