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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. 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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  1. Constructing the Meaning of Division Math Alliance June 29, 2010 Beth Schefelker, DeAnn Huinker, Melissa Hedges & Chris Guthrie

  2. 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.

  3. 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!

  4. 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?

  5. Meaning of Division • Turn and Talk: • What is division? • Beckmann • Two natural ways to interpret division and both are useful.

  6. 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?

  7. You might say the answer is “the same.” But is it?

  8. 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

  9. 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?”

  10. 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

  11. 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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