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Establishing Number Sense Through Alternate Strategies

Establishing Number Sense Through Alternate Strategies. 5 th GRADE DIVISION Created by Christine M. Nobley. STANDARDS. GPS 2011-2012 M5N3b. Explain the process of division including situations where divisors are whole numbers and decimals. CCGPS 2012-2013

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Establishing Number Sense Through Alternate Strategies

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  1. Establishing Number Sense Through Alternate Strategies 5thGRADE DIVISION Created by Christine M. Nobley

  2. STANDARDS GPS 2011-2012 M5N3b. Explain the process of division including situations where divisors are whole numbers and decimals. CCGPS 2012-2013 MCC5.NBT.6 Find the whole number quotients of whole numbers with up to 4 digit dividends and 2 digit divisors using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division.

  3. “Students with good number sense can think and reason flexibly with numbers, use numbers to solve problems, spot unreasonable answers, understand how numbers can be taken apart and put together in different ways, see connections among operations, figure mentally, and make reasonable estimates”. Burns, M. (2007)

  4. DEALING OUT (SHARING)by one 30 5 I I I I I I I I I I I I I I I I II I II I II I II I II I II I II I II I II I II

  5. 2 2 2 2 2 2 2 2 2 30 5 2 2 2 2 2 2 DEALING OUT By multiples

  6. REPEATED ADDITION • Uses existing addition skills • Helps with multiplication skills • Limited view of division 18 3 18 3 12 0 6 9 15 3 + 3 + 3 + 3 + 3 + 3

  7. REPEATED SUBTRACTION • Uses existing subtraction skills • Most kids not as proficient in subtraction 18 3 18 15 12 9 6 3 0

  8. 84 6 • Divide 6 into 8, subtract, get 2, bring down 4? • 6 X 10= 60 6 X 4= 24 14 • ½ of 84 = 42 ½ of 6= 3 • 42 3 = 14 so 84 6 = 14 • Half of 84 is 42. 42 divided by 6 = 7. • 7 X 2= 14.

  9. COUNTING ON • Uses knowledge of addition or subtraction • Large numbers time consuming 6 12 42 18 24 30 36 48 54 60 66 72 78 84

  10. HALF THEN DOUBLE • Can only use if dividend is even 24 4 12 4 = 3 Double that = 6 108 6 54 6 = 9 Double that = 18 8662 41 4331 41 Clearly, this strategy is not helpful. 91 7 Strategy not helpful because 91 is odd

  11. PROPORTIONAL REASONING 100 50 = 2 10 5 = 2 2 1 = 2 50 25 = 2 8 2 = 4 48 12 = 4 4 1 = 4 24 6 = 4 288 16 144 8 72 4 36 2 = 18

  12. SINGLE DIGIT ARRAYS • Shows how to build up to the dividend • Uses existing multiplication knowledge 300 7 300 7 10 10 10 2 10 7 70 70 70 70 6 left over 14

  13. 3 DIGIT BY 2 DIGIT ARRAY 884 26 10 10 10 2 2 26 260 260 260 52 52

  14. MULTIPLYING UP • Builds on strengths in multiplication • Relates multiplication to division 960 15 15 x 10 = 150 15 x 20 = 300 15 x 30 = 450 15 x 30 = 450 15 x 4 = 60 15 x 10 = 150 15 x 10 = 150 15 x 10 = 150 15 x 10 = 150 15 x 10 = 150 15 x 4 = 60 15 x 20 = 300 15 x 20 = 300 15 x 2 = 30 15 x 2 = 30

  15. DISTRIBUTIVE PROPERTY 65 5 645 20 (30 + 30 + 5) 5 (600 + 40 + 5) 6 + 6 + 1 = 13 30 + 2 = 32 R 5 132 12 (120 + 12) 12 120 12 12 12 10 + 1 = 11

  16. PARTIAL QUOTIENTS 18 468 • Uses friendly multiplication facts • x 2 • x 5 • x 10 - 180 10 288 - 180 10 108 • 90 5 • 18 - 18 1 0 Answer = 26

  17. PARTIAL QUOTIENT • http://www.youtube.com/watch?v=qWstA8EZr2w

  18. STANDARD ALGORITHM 177 885 -5 38 -35 35 -35 0 Divide Multiply Subtract Bring Down

  19. REVIEW OF DIVISION STRATEGIES • Dealing Out/Sharing • Repeated Addition • Repeated Subtraction • Counting Up • Half then Double • Proportional Reasoning • Rectangular Arrays • Multiplying Up • Distributive Property • Partial Quotients

  20. “By abandoning the rote teaching of algorithms we are not asking children to learn less, we are asking them to learn more” (Fosnot & Dolk, 2001, p.102).

  21. Partial quotients method for division. (August 26, 2009). Retrieved June 21, 2012 from http://www.youtube.com/watch?v=qWstA8EZr2w

  22. HOW CAN I PRACTICE? • http://www.sophia.org/partial-quotients-algorithm-tutorial • http://www.slideshare.net/guestb30cd4/partial-quotients • http://www.williston.k12.sc.us/kees/KEES%20Curriculum/MAPLessonPlans/Num&Oper/221-230/Day08.pdf • http://teachmath.openschoolnetwork.ca/wordpress/grade-5/division/distributive-property-for-division/ • http://www.youtube.com/watch?v=4o_5PUZ4wvU • http://eternaltreasures.hubpages.com/hub/MATHEMATICS-Shortcuts-in-Multiplication-Division-Addition-Subtraction-secrets-in-mental-math-calculation-speed • http://www.teachertube.com/viewVideo.php?title=Partial_Quotients_Division&video_id=20032 http://www.youtube.com/watch?v=By9Kwoz8oT4 5 • http://www.youtube.com/watch?v=340UK0aox1I • http://www.youtube.com/watch?v=FJ-P5c_bZlc • http://www.youtube.com/watch?v=hCKd3C4P6Uk

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