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Addition and Subtraction of Fractions

By Laura Campbell,2014-04-30 23:50
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Addition and Subtraction of Fractions

    Making Sense of Adding and

    Subtracting Fractions

    January MTL Meeting

    January 20 & 28

    Marshall Complex

Core Content Development Team

    DeAnn Huinker

    Connie Laughlin

    Kevin McLeod

    Mary Mooney

    Beth Schefelker

    Melissa Hedges

Assisting MTLs

    Frelesha LeFlore

    Cecile Labecki

Learning Intentions:

    ; Develop “operation sense” related

    to adding and subtracting common

    fractions.

    ; Understand how estimation should

    be an integral part of fraction

    computation development.

Success Criteria:

    At the end of this session you will be able to:

     Justify your thinking when adding

    and subtracting fractions using

    concrete models and estimation

    strategies.

    Types of Rational Numbers:

    ; Part-whole comparisons

    ; Quotients

    ; Operators

    ; Ratios and Rates

    ; Measurement

No pencils please!

For each expression below…

    (1) Estimate the sum and the difference for the expressions below. (2) Justify how you know your estimate is in the ballpark.

    No computing please!

    49/99 11/34 16/25 + 9/14

    Background on Fraction Computation

; Read page 160 only.

    ; What ideas from the reading support

    the work we’ve been engaged in

    during the past 2 sessions around

    fractions?

From:

    Van de Walle, J. & Lovin H. (2006). Teaching Student Center Mathematics:

    Grades 3-5. pp. 160-161. New York: Pearson Education.

    Three Models Used to

    Work With Fractions

    Set model (Mariah's Kittens)

Linear model (Taking a Run)

    1 mile 2 miles 3 miles 4 miles

     Finding ? of 4 miles

Area Model (Spaghetti Problem)

     ? ? ? ?

     4 packages of meat each weighing ? lbs

    Folding Fraction Strips

    Fold fraction strips to represent the following:

    ; one whole ; eighths

    ; halves ; thirds

    ; fourths ; sixths

    As you fold, discuss with your partner how you know that your fraction strips are accurate.

    Folding fraction strips is so time consuming. Why do it?

Turn and talk:

     What was the benefit of folding

    your own fraction strips?

     In what way would the cognitive

    demand be affected if we were to

    hand you a pre-printed set of

    strips?

    Exploring Operation Sense Using

    Benchmark Fractions

    Using your fraction strips, work through the following and have several examples for each:

    ; If you add 2 fractions and the sum is greater

    than ?, what can you say about the fractions?

    ; If you add 2 fractions and the sum is greater

    than 1, what can you say about the fractions?

    ; If you add 2 fractions, and the sum is more than

    1 ?, what can you say about the fraction?

    What conversations did you have with your partner that helped to develop a

    generalization about all three contexts?

Making connections to

    whole number operation sense…

    In what ways does this reasoning mirror the thinking we are asking children to develop as they work with whole numbers?

    If you add 2 whole numbers together and the sum is larger than 10, what do you know about those 2 numbers? What about 100? What about 150?

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