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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?. 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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  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. 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.

  4. 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)

  5. 4 624 24 is the… dividend 6 is the… divisor 4 is the… quotient

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

  7. 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

  8. Ducks (÷) May (x) Swim (-) Backwards (bring ) - - 0 0 0 “Old School” DivisionThe Standard Algorithm 2 4 80 0 8 0 0

  9. “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!

  10. 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

  11. 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

  12. 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

  13. Steps in Short Division 2 4 9 R1 Hooray! I did it! 3 ) 7 4 8

  14. “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.

  15. 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 )

  16. 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

  17. 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

  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. 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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