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181
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Student Work
TitleEarly algebra ideas about binomial expansion, Stephanie's interview six of seven, Clip 2 of 11: Stephanie rebuilds Unifix towers 1-cube, 2-cubes, 3-cubes and 4-cubes tall, selecting from two colors
DescriptionIn the second clip in a series of eleven from the sixth of seven interviews, 8th grader Stephanie continues her exploration of early algebraic ideas about binomial expansion with researchers Carolyn...
182
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Student Work
Analytic icon 1 Analytic found
TitleEarly Algebra Ideas About Binomial Expansion, Stephanie's Interview Six of Seven: Clip 7 of 11: Generating towers 4-cubes tall, selecting from blue and green cubes, from towers with exactly one green cube to towers with exactly two green cubes.
DescriptionIn the seventh clip in a series of eleven from the sixth of seven interviews, 8th grader Stephanie is asked by researchers Carolyn Maher and Robert Speiser to consider how the Unifix-cube towers...
183
Transcript
Student Work
Analytic icon 1 Analytic found
TitleEarly algebra ideas about binomial expansion, Stephanie's interview six of seven, Clip 3 of 11: Comparing towers, selecting from two colors, built inductively and corresponding to the addition rule of Pascal's Triangle
DescriptionIn the third clip in a series of eleven from the sixth of seven interviews, 8th grader Stephanie continues a discussion of ideas about binomial expansion with researchers Carolyn Maher and Robert...
184
Transcript
Student Work
Analytic icon 1 Analytic found
TitleEarly algebra ideas about binomial expansion, Stephanie's interview six of seven, Clip 10 of 11:
Developing mathematical expressions for generating the number of towers 4-cubes tall selecting from green and blue cubes for exactly 2 green cubes, exactly 3 green cubes, and for 4 green cubes
DescriptionIn the tenth clip in a series of eleven from the sixth of seven interviews, 8th grader Stephanie works with researchers Carolyn Maher and Robert Speiser to synthesize her ideas about how to build the...
185
Transcript
Student Work
Analytic icon 1 Analytic found
TitleEarly algebra ideas about binomial expansion, Stephanie's interview six of seven, Clip 9 of 11: Beginning to generalize mathematical expressions to generate cases for towers 4-cubes tall selecting from green and blue cubes
Descriptionn the ninth clip in a series of eleven from the sixth of seven interviews, 8th grader Stephanie is asked by researchers Carolyn Maher and Robert Speiser to describe mathematically how she has...
186
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Student Work
TitleEarly algebra ideas about binomial expansion, Stephanie's interview six of seven, Clip 8 of 11: Working backwards from towers 4-cubes tall selecting from blue and green cubes, with exactly two green cubes, to towers with exactly one green cube
DescriptionIn the eighth clip in a series of eleven from the sixth of seven interviews, 8th grader Stephanie is asked by researchers Carolyn Maher and Robert Speiser to revisit her set of six Unifix cube towers...
187
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Student Work
TitleEarly algebra ideas about binomial expansion, Stephanie's interview six of seven, Clip 11 of 11:
Extending ideas about generating towers 4-cubes tall selecting from green and blue cubes to towers 5-cubes tall with exactly 1 green cube and connecting to Fermat and Pascal
DescriptionIn the final clip in a series of eleven from the sixth of seven interviews, 8th grader Stephanie is challenged by researchers Carolyn Maher and Robert Speiser to extend her ideas about how to build...
188
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Student Work
TitleEarly algebra ideas about binomial expansion, Stephanie's interview seven of seven, Clip 1 of 7: Stephanie revisits generating Unifix-cube towers 4-tall from exactly one to exactly two red cubes.
DescriptionIn the first clip in a series of seven from the seventh of seven interviews, 8th grader Stephanie revisits her earlier exploration of how to generate Unifix-cube towers across cases with researchers...
189
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TitleRevisiting construction of large models to compare fractions, Clip 1 of 5: Which is larger, two thirds or three fourths, and by how much?
DescriptionIn the first of five clips from this classroom session, the researcher, Amy Martino, provided the students with an opportunity to briefly discuss a task that they had been working on during the...
190
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Student Work
Analytic icon 3 Analytics found
TitleContinuing to explore fraction comparisons, Clip 4 of 7: Michael and Brian find four models to compare one half and three fourths
DescriptionIn the fourth clip Michael and Brian worked together to compare one half and three fourths. Michael built a model of an orange and red train, two dark green rods, and four light green rods. He then...