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Making use of structure to make sense of mathematics

Making use of structure to make sense of mathematics. Kevin McLeod Connie Laughlin Hank Kepner Beth Schefelker Mary Mooney Math Teacher Leader Meeting, April 5 th and 7 th.

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Making use of structure to make sense of mathematics

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  1. Making use of structure to make sense of mathematics Kevin McLeod Connie Laughlin Hank Kepner Beth Schefelker Mary Mooney Math Teacher Leader Meeting, April 5th and 7th The Milwaukee Mathematics Partnership (MMP), an initiative of the Milwaukee Partnership Academy (MPA), is supported with funding by the National Science Foundation.

  2. Learning Intention We are learning to • Explore examples that look for and make use of structure. • To understand CCSS Math Practice #7: Look for and Make Use of Structure The Milwaukee Mathematics Partnership (MMP), an initiative of the Milwaukee Partnership Academy (MPA), is supported with funding by the National Science Foundation.

  3. Structure • What does structure mean… • of a building? • of a classroom? • in mathematics?

  4. Launch 19 x 8 • Find the product in two different way • Do not use the standard algorithm. The Milwaukee Mathematics Partnership (MMP), an initiative of the Milwaukee Partnership Academy (MPA), is supported with funding by the National Science Foundation.

  5. What is Area? • Write your answer on an index card. • Discuss your table’s answers and come to consensus.

  6. Mathematical Practice Standard #7 Look for and Make Use of Structure Mathematically proficient students look closely to discern a pattern or structure….students will see that 7 x8 equals the well remembered 7x5 + 7x3, in preparation for learning about the distributive property. • But how does structure help us make connections within and between math strands?

  7. Success Criteria • We will know we were successful when we are able to use structure to explain and justify area formulas for selected quadrilaterals.

  8. Explore: Area formula for parallelograms Follow the steps below to write a formula for the area of a parallelogram. Step 1: Use two different width straight edges to construct a large parallelogram on large patty paper. Step 2: Show how you can split the parallelogram and rearrange the pieces to form a rectangle. Compare your results with your table partners. Come to consensus as to a formula that could be used.

  9. Explore: Area formula for triangles Follow the steps below to write a formula for the area of a triangle. • Step 1: Each person at the table should construct a different large triangle on patty paper. • Step 2: Place a 2nd patty paper over the first and copy the triangle. Form a parallelogram from the two triangles. Compare your results with your table partners. Come to consensus as to a formula that could be used to find the area of a triangle.

  10. Explore: Area formula for trapezoid Step 1: Draw a large trapezoid on your patty paper. Step 2: Place a second patty paper over the first and copy the trapezoid. Form a parallelogram from the two trapezoids. Compare your results with your table partners. Come to consensus as to a formula that could be used.

  11. Explore: Area formula for trapezoid Step 1: Draw a large trapezoid on your patty paper by folding or drawing. Step 2: Explore finding the area of a trapezoid using triangles. Experiment to find as many different ways as you can to arrive at a formula for a trapezoid.

  12. What have you found? Turn and Talk at your table: How does structure of the polygons help make sense of the area formulas?

  13. Success Criteria • We will know we were successful when we are able to use structure to explain and justify area formulas for selected quadrilaterals. The Milwaukee Mathematics Partnership (MMP), an initiative of the Milwaukee Partnership Academy (MPA), is supported with funding by the National Science Foundation.

  14. Standard for Mathematical Practice

  15. Walk Away Question • When you engage your teachers in the content sessions, how are you (1) using the sessions to connect the Mathematical Practices to classrooms? or (2) using the sessions to assist you in clarifying the LESA lesson structure?

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