33. Division of Fractions U.S. teacher’s approach Flip and multiply Answers don’t match Confused division by 2 with division by 1/2
34. Division of Fractions Chinese teacher’s approach Gave mathematically accurate story problem Explained the mathematics behind the operation Gave multiple mathematical constructs for division of fractions
37. Prototype for lesson construction Touchable visual Discussion: Makes sense Of concept 1 2 Learn to Record these ideas V. Faulkner and DPI Task Force adapted from Griffin Symbols Simply record keeping! Mathematical Structure Discussion of the concrete Quantity Concrete display of concept
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39. Prototype for Lesson Construction 1 2 Symbols Simply record keeping! Mathematical Structure Discussion of the concrete V. Faulkner and NCDPI Task Force adapted from Griffin Quantity Concrete display of concept
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41. For each Cup of Beans— I get two portions if I divide by 1/2
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44. Division of Fractions: Bean Party! Division as Repeated Subtraction 1 2 2 ½ / ½ V. Faulkner and DPI Task Force adapted from Griffin “ Why does this constant amount of beans “looks like it is getting bigger”? Division as repeated subtraction Quantity Concrete display of concept Mathematical Structure Discussion of the concrete Symbols Simply record keeping!
56. Prototype for Lesson Construction The Idea of the Unit 1 2 V. Faulkner and NCDPI Task Force adapted from Griffin Quantity Concrete display of concept Mathematical Structure Discussion of the concrete Symbols Simply record keeping!
57. Imagine that one of your students comes to class very excited. She explains that she has discovered that as the perimeter of a closed figure increases the area also increases. She shows you a picture to explain what she is doing. P = 16cm A = 16 cm 2 P= 24cm A = 32cm 2 How would you respond to this student? 4 cm 4 cm 4 cm 8 cm
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61. Perimeter = 16 units Area = 16 square units Perimeter = 24 units Area = 32 square units A Condition in which Student’s Claim is supported
