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101
Transcript
Student Work
Analytic icon 1 Analytic found
TitleIntroducing fraction equivalence and an exploration of fraction comparison, Clip 4 of 4: Finding the number name for the difference between one half and one third
Date Created1993
DescriptionDuring this small group activity, the students revisited the task: Which is larger, 1/2 or 1/3, and by how much? Some of the students attempted to solve the task using balance beams, but most reverted...
102
Transcript
Student Work
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...
103
Transcript
Student Work
TitleEarly algebra ideas about binomial expansion, Stephanie's interview seven of seven, Clip 2 of 7: Generating Unifix-cube towers 4-tall from exactly two to exactly three red cubes and from exactly three yellow cubes to the tower with all four yellow cubes.
DescriptionIn the second clip in a series of seven from the seventh of seven interviews, 8th grader Stephanie first predicts the number of Unifix-cube towers with exactly three red cubes to be generated from the...
104
Transcript
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...
105
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...
106
Transcript
Student Work
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...
107
Transcript
Student Work
Analytic icon 1 Analytic found
TitleEarly algebra ideas about binomial expansion, Stephanie's interview six of seven, Clip 1 of 11: Stephanie revisits combinatorics notation for building towers
DescriptionIn the first clip in a series of eleven from the sixth of seven interviews, 8th grader Stephanie revisits her earlier exploration of particular algebraic ideas about binomial expansion with...
108
Transcript
Student Work
TitleEarly algebra ideas about binomial expansion, Stephanie's interview seven of seven, Clip 5 of 7: Developing numerical representations for each case for the number of Unifix-cube towers 5-tall and 6-tall selecting from red and yellow cubes.
DescriptionIn the fifth clip in a series of seven from the seventh of seven interviews, 8th grader Stephanie and researcher Carolyn Maher extend their earlier investigation of how to represent the number of...
109
Transcript
Student Work
TitleEarly algebra ideas about binomial expansion, Stephanie's interview seven of seven, Clip 4 of 7: Investigating numerical and algebraic representations for each case for the number of Unifix-cube towers 4-tall selecting from red and yellow cubes.
DescriptionIn the fourth clip in a series of seven from the seventh of seven interviews, 8th grader Stephanie and researcher Carolyn Maher investigate how to numerically represent the number of Unifix towers for...
110
Transcript
Student Work
Analytic icon 1 Analytic found
TitleEarly algebra ideas about binomial expansion, Stephanie's interview six of seven, Clip 4 of 11: Developing the correspondence among towers, selecting from two colors, Pascal's Triangle, and the symbolic algebraic expansions of (a+b) squared and (a+b) cubed
DescriptionIn the fourth clip in a series of eleven from the sixth of seven interviews, 8th grader Stephanie remembers that she had figured out the expanded algebraic expressions for (a+b) for powers up to 6. ...