Constructing the meaning of division
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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

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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?


You might say the answer is the same

You might say the answer is “the same.”

But is it?


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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