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Constructing the Meaning of DivisionPowerPoint Presentation

Constructing the Meaning of Division

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### Constructing the Meaning of Division

### You might say the answer is “the same.”

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
You will be successful when…

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

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…

- 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

- Turn and Talk:
- What is division?

- Beckmann
- Two natural ways to interpret division and both are useful.

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?

But is it?

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

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

- 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
- 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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