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Partial Quotients Method in Relation to Core Standards

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Partial Quotients Method in Relation to Core Standards

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GRADE 4: NUMBERS AND OPERATIONS OF BASE 10
Use place value understanding and properties of operations to perform multi-digit arithmetic.
Partial Quotients Method of division helps students reach this goal by being able to see how the quotients are lined up and understanding the dividend as a whole.

GRADE 5: NUMBERS AND OPERATIONS OF BASE 10
Perform operations with multi-digit whole numbers and with decimals to hundredths.
Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

The Partial Quotients Method of division helps students reach this standard by helping them to explain the place value through a calculation as seen through the viewing of the dividend and the partial quotients as they are added up for the answer.

TO LEARN MORE ABOUT THE CORE STANDARDS OF MATHEMATICS PLEASE VISIT:
http://www.corestandards.org/Math/

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Partial Quotients Method Compared to Long Division

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Partial Quotients Method Compared to Long Division

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One thing that partial quotients allows students to do is to better understand place value. As students are taught to view the dividend as a whole and not as an individual number like in long division. This is also seen on the other side of the vertical line drawn, where the quotients are added and listed by place value as well. Additionally, the Partial Quotients Method allows for students to improve their estimation skills. With all of this in mind it is easier to transition to long division once students understand what the numbers represent.

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https://drive.google.com/open?id=0B22X6w7PTVZVdnBPR1hqamJwUjAhttps://drive.google.com/open?id=0B22X6w7PTVZVdnBPR1hqamJwUjA

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Comparison to the "standard" method of subtraction.

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Comparison to the "standard" method of subtraction.

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Visual Explanation of Expanded Subtraction

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Visual Explanation of Expanded Subtraction

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Expanded Subtraction and how it relates to the Common Core

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Expanded Subtraction and how it relates to the Common Core

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The Expanded Method of subtraction can be related to the common core standards for children in mainly grade 2.  In this grade they are required to learn how to "use addition and subtraction within one hundred so solve one- and two- step problems involving situations of adding too, taking from, putting together, taking apart, and comprising, with unknowns in all positions by using drawings and equations with a symbol for the unknown number to represent."
So when looking at the expanded form, we see children solving subtraction by "taking apart" each number being subtracted in order to visually understand it. In relation, using base blocks is another great way for kids to visually understand subtraction. In addition, using base blocks also covers "using drawings..for the unknown number to represent" part of the common core.