Don’t Let Division
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Don’t Let Division Get You Down!. Created by Danielle Miller Hawk Ridge Elementary School. What is division?. An operation that tells how many groups there are and how many are in each group Repeated subtraction The inverse of multiplication. 4 6 24. 24 6. = 4.

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Don’t Let Division Get You Down!

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Don t let division get you down

Don’t Let Division

Get You

Down!

Created by Danielle Miller

Hawk Ridge Elementary School


What is division

What is division?

  • An operation that tells how many groups there are and how many are in each group

  • Repeated subtraction

  • The inverse of multiplication


What does division look like

4

6 24

24

6

= 4

What Does Division Look Like?

24 ÷ 6 = 4

A division problem can be written as a fraction.

A division problem can be written horizontally.

A division problem can be written with the traditional division sign.


Division vocabulary

Division Vocabulary

24 ÷ 6 = 4

dividend– the number being divided (total number of items)

divisor – the number by which another number is divided (# of groups)

quotient-the answer to a division problem (# of items in each group)


Don t let division get you down

4

624

24 is the…

dividend

6 is the…

divisor

4 is the…

quotient


Division methods

Division Methods

  • Draw a Picture

    • Circles and Stars

  • “Old School”

    • The Standard Algorithm

  • “New School”

    • Short Hand Division

    • Partial Quotients


Circles and stars

Read the problem

Identify the divisor (the number of groups) and draw that many circles

Identify the dividend and begin distributing out that number of stars.

Count the number of stars in one circle. This is your quotient.

6

Circles and Stars

18÷3=?

18÷3=6


Old school division the standard algorithm

Ducks (÷)

May (x)

Swim (-)

Backwards (bring )

-

-

0

0

0

“Old School” DivisionThe Standard Algorithm

2

4 80

0

8

0

0


New school division short hand division

“New School” DivisionShort Hand Division

  • Short division is similar to long division only you do the multiplication and subtraction in your head.

  • Knowing your basic facts is a must!


Steps in short division

Steps in Short Division

  • Divide into the number.

  • Place answer above # divided into

  • Multiply this answer & divisor together in your head.

  • Subtract product from 7.

  • Put your answer, 1, in front of the 4 in the dividend.

2

3 ) 7 4 8

1

3 x 2 = 6

7 - 6 = 1


Steps in short division1

Steps in Short Division

  • Divide 3 into 14.

  • Place answer above # divided into.

  • Multiply the new number & divisor together in your head.

  • Subtract product from 14.

  • Put your answer, 2, in front of the 8 in the dividend.

2

4

3 ) 7 4 8

1

2

3 x 4 = 12

14 - 12 = 2


Steps in short division2

Steps in Short Division

  • Divide 3 into 28.

  • Place answer above # divided into.

  • Multiply that answer and divisor together in your head.

  • Subtract product from 28.

  • Put your answer, 1, as the remainder.

2

4

9

R1

3 ) 7 4 8

1

2

3 x 9 = 27

28 - 27 = 1


Steps in short division3

Steps in Short Division

2

4

9

R1

Hooray! I did it!

3 ) 7 4 8


New school division partial quotients algorithm

“New School” DivisionPartial Quotients Algorithm

The Partial Quotients Algorithm uses a series of

“at least, but less than”

estimates of how many times the dividend can be divided by the divisor.


Don t let division get you down

There are at least ten 12’s in 158 (10 x 12=120), but fewer than twenty. (20 x 12 = 240)

13 R2

12

158

There are more than three 12’s (3 x 12 = 36), but fewer than four (4 x 12 = 48). Record 3 as the next guess

- 120

10 1st guess

Subtract

38

3 2ndguess

- 36

Subtract

2

13

Sum of guesses

Since 2 is less than 12, you can stop estimating. The final result is the sum of the guesses (10 + 3 = 13) plus what is left over (remainder of 2 )


Don t let division get you down

36

7,891

Did you check your work with

Multiplication?

219 x 36 = 7,884 + 7 = 7,891

Let’s try another one…

219 R7

- 3,600

100 – 1st guess

Subtract

4,291

- 3,600

100 – 2nd guess

Subtract

691

- 360

10 – 3rd guess

331

- 324

9 – 4th guess

7

219 R7

Sum of guesses


Don t let division get you down

43

8,572

Now do this one on your own…

199 R 15

- 4,300

100 – 1st guess

Subtract

4272

-3870

90 – 2nd guess

Subtract

402

- 301

7 – 3rd guess

101

- 86

2 – 4th guess

199 R 15

Sum of guesses

15


Choose the method that works for you

Choose the Method That Works For You!

  • Read the problem that you have to solve carefully and choose the best method for the problem!

  • Select the method of division that you are most comfortable with to help you.

  • Don’t forget to always check you work with multiplication.

  • If you have access to a calculator – use it – that’s what it is there for!


Don t forget

Don’t forget…

  • There is no substitution for lacking fluency with your math facts!

  • To use any of these strategies – you need to have memorized your basic addition, subtraction, multiplication and division facts.

  • Quick recall is required for success in math!

  • Keep studying! Keep practicing!


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