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TitlePizza problems with four and five toppings, Clip 1 of 6: Approaching the problem

DescriptionThis clip is the first of six featuring four grade 11 students, Robert, Stephanie, Shelly, and Amy Lynn, as they construct and justify solutions to the Pizza Problem. This clip focuses on Stephanie...

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2 Analytics found

TitlePizza problems with four and five toppings, clip 5 of 6: Explaining solutions

DescriptionIn this fifth of six clips, four 11th grade students reconsider Pascal's Triangle as it relates to the Pizza Problem and connect this problem with the Towers Problem. As the students summarize their...

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2 Analytics found

TitlePizza problems with four and five toppings, clip 3 of 6: Why does it work?

DescriptionThe third of 6 clips focuses on the four 11th grade students as they map the numbers of pizza choices to the rows of Pascal’s Triangle and attempt to make sense of the addition rule with the...

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TitleEarly algebra ideas about binomial expansion, Stephanie's interview three of seven, Clip 2 of 7: Explaining the meaning of area of a square with concrete materials

DescriptionIn the second clip in a series of seven from the third of seven interviews in which 8th grader Stephanie explores Early Algebraic Ideas about Binomial Expansion, the researcher, Carolyn Maher, asks...

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TitleEarly algebra ideas about binomial expansion, Stephanie's interview three of seven, Clip 1 of 7: Revisiting earlier ideas about the square of the quantity (a + b)

DescriptionIn the first clip in a series of seven from the third of seven interviews in which 8th grader Stephanie explores Early Algebraic Ideas about Binomial Expansion, Stephanie arrives with several pages of...

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TitleEarly algebra ideas about binomial expansion, Stephanie's interview three of seven, Clip 6 of 7: Expanding (a+b) cubed algebraically.

DescriptionIn the sixth clip in a series of seven from the third of seven interviews in which 8th grader Stephanie explores Early Algebraic Ideas about Binomial Expansion, Stephanie uses her numerical...

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TitleEarly algebra ideas about binomial expansion, Stephanie's interview three of seven, Clip 5 of 7: Testing the partial symbolic expansion of the cube of (a+b) for a=3 and b=7.

DescriptionIn the fifth clip in a series of seven from the third of seven interviews in which 8th grader Stephanie explores Early Algebraic Ideas about Binomial Expansion, Stephanie is asked by researcher...

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TitleEarly algebra ideas about binomial expansion, Stephanie's interview four of seven, Clip 3 of 9: Describing the volume of (a+b) cubed using math manipulatives.

DescriptionIn the third clip in a series of nine from the fourth of seven interviews in which 8th grader Stephanie explores Early Algebraic Ideas about Binomial Expansion, researcher Carolyn Maher presents...

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TitleEarly algebra ideas about binomial expansion, Stephanie's interview seven of seven, Clip 3 of 7: Investigating the algebraic generalization for building Unifix-cube towers n-tall with exactly two red cubes from towers with exactly one red cube.

DescriptionIn the third clip in a series of seven from the seventh of seven interviews, 8th grader Stephanie continues to investigate the construction of Unifix towers four-cubes tall, selecting from red and...

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TitleEarly algebra ideas about binomial expansion, Stephanie's interview seven of seven, Clip 6 of 7: Making sense of the Pascal Triangle addition rule with Unifix cube towers .

DescriptionIn the sixth clip in a series of seven from the seventh of seven interviews, 8th grader Stephanie first revisits her investigation of the number of duplicates that would be produced when building...