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.

| |
| |

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? ___

| | | | | | | |
| | | | | | | |
| | | |

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

| | | | | | | | | | | |
| | | | | | | | | |
| | | | | | | | | |
| | | | | | | | | |

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

FREE math homework help on www.PhatMath.com

40 Math forums for grades K-12 & College
Post/view math problems & solutions
Blogs for students, parents, teachers

- Learn subtraction concept
- fact families
- memorize basic facts
- word problems
- colorful pages.
- download & print.
Self-teaching worktext.

Download today!

Times Tales

Learn the upper
times tables with
mnemonic stories.

Learn more!

Download Math Mammoth Multiplication 2
self-teaching workbook.
* Understand multi-digit
multiplication
* Plenty of word problems!
* Students practically learn
on their own.

HOMESCHOOL MATH NEWSLETTER

Homeschool Math Newsletter comes out once monthly, and includes math teaching articles and tips, Math Mammoth news, and all kinds of little "tidbits" such as math news, interesting links, or humor. The content is equally good for all of us who teach math (not just homeschooling parents).

When you subscribe, you will alsoreceive a GIFT of over 280 FREE math worksheets and sample pages from Math Mammoth books for grades 1-8.

Note: This is a double opt-in list. You will FIRST get an email that asks you to confirm your email address. PLEASE check also your SPAM/JUNK folder for this confirmation email.

The newsletter service is by Aweber.com. Your email address will not be shared, sold, or distributed to anyone else.

Check out these short video clips from my favorite band - Rockabilly.US. They play oldies, Elvis, country, and top hits of the 50s and 60s. It's a show with large band, costumes, choreography, little skits, "Kid Kritters", 6 dancing/singing girls, junior dancer troupe, etc.
"Be My Baby" originally by the Ronettes	Impossible Dream (Elvis song)
Most importantly, the band wants to use the uplifting and energetic music to bring some fun, happiness and encouragement into people's lives. They're doing it selflessly to help others, and don't get paid for any of it themselves. And I admire that! => See more video clips at YouTube

Division as repeated subtraction Free lesson plan from HomeschoolMath.net

Example problems

HOMESCHOOL MATH NEWSLETTER

Division as repeated subtraction
Free lesson plan from HomeschoolMath.net