1. 1 Don’t Let Division Get You Down! Created by Danielle Miller Hawk Ridge Elementary School

2. 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

3. 3 What Does Division Look Like? 24 ÷ 6 = 4 4 6 24 24 6 = 4 A division problem can be written horizontally. A division problem can be written as a fraction. A division problem can be written with the traditional division sign.

4. Division Vocabulary 2464 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)

5. dividend divisor quotient 4 6 24 24 is the… 6 is the… 4 is the…

6. Division Methods Draw a Picture –Circles and Stars “Old School” –The Standard Algorithm “New School” –Short Hand Division –Partial Quotients

7. 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. 18 ÷ 3 = ? 6 18 ÷ 3 = 6

8. “Old School” Division The Standard Algorithm 2 4 80 D ucks (÷) M ay (x) S wim (-) B ackwards (bring ) 8- 0 0 0 0 - 0 0

9. “New School” Division Short 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!

10. 10 Steps in Short Division 3 ) 7 4 8 2 3 x 2 = 6 7 - 6 = 1 1 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.

11. 11 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. 3 ) 7 4 8 2 3 x 4 = 12 14 - 12 = 2 1 4 2 Steps in Short Division

12. 12 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. 3 ) 7 4 8 2 3 x 9 = 27 28 - 27 = 1 1 4 2 9 R1 Steps in Short Division

13. 13 3 ) 7 4 8 2 Hooray! I did it! 49 R1 Steps in Short Division

14. “New School” Division Partial 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.

15. 15 12 158 There are at least ten 12’s in 158 (10 x 12=120), but fewer than twenty. (20 x 12 = 240) 10 1 st guess - 120 38 Subtract 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 3 2 nd guess - 36 2 13 Sum of guesses Subtract 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 ) 13 R2

16. 16 Let’s try another one… 36 7,891 100 – 1st guess - 3,600 4,291 Subtract 100 – 2 nd guess - 3,600 7 219 R7 Sum of guesses Subtract 219 R7 691 10 – 3 rd guess - 360 331 9 – 4th guess - 324 Did you check your work with Multiplication? 219 x 36 = 7,884 + 7 = 7,891

17. 17 Now do this one on your own… 43 8,572 100 – 1st guess - 4,300 4272 Subtract 90 – 2 nd guess -3870 15 199 R 15 Sum of guesses Subtract 199 R 15 402 7 – 3 rd guess - 301 101 2 – 4th guess - 86

18. 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!

19. 19 Don’t forget… There is no substitution for lacking fluency with your math facts!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.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!Quick recall is required for success in math! Keep studying! Keep practicing!Keep studying! Keep practicing!