Establishing Number Sense Through Alternate Strategies 5 th GRADE DIVISION Created by Christine M. Nobley

STANDARDS GPS M5N3b. Explain the process of division including situations where divisors are whole numbers and decimals. CCGPS 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.

“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)

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

DEALING OUT By multiples

REPEATED ADDITION Uses existing addition skills Helps with multiplication skills Limited view of division

REPEATED SUBTRACTION Uses existing subtraction skills Most kids not as proficient in subtraction

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

COUNTING ON Uses knowledge of addition or subtraction Large numbers time consuming

HALF THEN DOUBLE Can only use if dividend is even = 3 Double that = = 9 Double that = Clearly, this strategy is not helpful Strategy not helpful because 91 is odd

PROPORTIONAL REASONING = = = = = = = = = 18

SINGLE DIGIT ARRAYS Shows how to build up to the dividend Uses existing multiplication knowledge left over

3 DIGIT BY 2 DIGIT ARRAY

MULTIPLYING UP Builds on strengths in multiplication Relates multiplication to division 15 x 10 = x 4 = x 20 = x 2 = x 30 = x 4 =

DISTRIBUTIVE PROPERTY ( ) = ( ) = ( ) = 32 R 5

PARTIAL QUOTIENTS Uses friendly multiplication facts x 2 x 5 x

PARTIAL QUOTIENT r2w r2w

STANDARD ALGORITHM Divide Multiply Subtract Bring Down

REVIEW OF DIVISION STRATEGIES 1.Dealing Out/Sharing 2.Repeated Addition 3.Repeated Subtraction 4.Counting Up 5.Half then Double 6.Proportional Reasoning 7.Rectangular Arrays 8.Multiplying Up 9.Distributive Property 10.Partial Quotients

“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).

Partial quotients method for division. (August 26, 2009). Retrieved June 21, 2012 from

HOW CAN I PRACTICE? /Day08.pdf 230/Day08.pdf for-division/ for-division/ Division-Addition-Subtraction-secrets-in-mental-math-calculation-speed Division-Addition-Subtraction-secrets-in-mental-math-calculation-speed