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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 &amp; Chris Guthrie. Learning Intentions &amp; Success Criteria. We are learning to… Use contextual situations to explore 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

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?

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

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