12

TitleEarly algebra ideas about binomial expansion, Stephanie's interview six of seven, Clip 5 of 11: Developing the correspondence between towers 4-cubes tall, selecting from two colors, Pascal's Triangle and the symbolic algebraic expansion of (a+b) to the 4th power

DescriptionIn the fifth clip in a series of eleven from the sixth of seven interviews, 8th grader Stephanie responds to questions from researchers Carolyn Maher and Robert Speiser about the correspondence...

13

TitleEarly algebra ideas about binomial expansion, Stephanie's interview four of seven, Clip 6 of 9: Explaining the algebraic and geometric representations of (a+b) squared and the algebraic expansion of (a+b) cubed.

DescriptionIn the sixth clip in a series of nine from the fourth of seven interviews in which 8th grader Stephanie explores Early Algebraic Ideas about Binomial Expansion, Stephanie explains her algebraic and...

14

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...

15

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...

16

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...

17

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...

18

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...

19

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...

20

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...

21

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...