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Constructing the Meaning of Division. Math Alliance June 29, 2010 Beth Schefelker, DeAnn Huinker, Melissa Hedges & Chris Guthrie. Learning Intentions & Success Criteria. We are learning to… Use contextual situations to explore the meaning of division

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Constructing the meaning of division

Constructing the Meaning of Division

Math Alliance

June 29, 2010

Beth Schefelker, DeAnn Huinker, Melissa Hedges & Chris Guthrie


Learning intentions success criteria
Learning Intentions & Success Criteria

We are learning to…

  • Use contextual situations to explore the meaning of division

    You will be successful when…

  • Explain why the various division procedures are valid based on the meaning of division.


Planning a vacation
Planning a vacation…

Four friends are going on vacation together. They decide to rent an RV. The cost for the RV is $640.00. They agree to equally split the cost. How much will each friend pay?

No U.S. standard algorithm please!


Sharing strategies
Sharing strategies…

  • Share your strategy with your neighbor.

  • What language was used to explain the strategy?

    Now…

  • Use place value models to demonstrate your strategy.

  • How did the place value models

    • support your use of concept-based language?

    • push you to visualize the situation differently?


Meaning of division
Meaning of Division

  • Turn and Talk:

    • What is division?

  • Beckmann

    • Two natural ways to interpret division and both are useful.


Consider the following
Consider the following:

Context #1

Evan has 24 apples. He put them into bags containing 6 apples each. How many bags did Evan use?

Context #2

Evan has 24 apples. He shares them equally among 6 friends. How many apples will each friend get?

What is the answer in each context?

How might a young child

model each problem?



Two interpretations for division
Two Interpretations for Division

  • Context #1 – Measurement

    Evan has 24 apples. He put them into bags containing 6 apples each. How many bags did Evan use?

    • Known: Size of group

    • Unknown: Number of groups

  • Context #2 – Partitive

    Evan has 24 apples. He shares them equally among 6 friends. How many apples with each friend get?

    • Known: Number of groups

    • Unknown: Size of groups


8 2 4
8 ÷ 2 = 4

Javier has 8 marbles. He equally shares them with his friend Jesús. How many marbles will each boy get?

Partitive asks “how many are in each group?”

Javier has 8 marbles. If he puts 2 marbles in each bag, how many bags will he need?

Measurement asks “how many groups?”


Identifying division situations
Identifying Division Situations

  • Read each problem.

  • Act out each problem with the counters using the “Division Work Mat.”

  • Identify if the problem is a measurement or partitive situation.

  • Draw a sketch. Write an equation. Label each accordingly


Homework
Homework

  • Homework

    • Read pp. 289-293 from Beckmann

    • Complete these problems following the instructions in the book:

      • p. 187 #1

      • p. 191 #1a, #1b, #1e

  • Due July 6, 2010


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