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DescriptionIn this edited and narrated episode from the Private Universe Project in Mathematics, five tenth-grade students consider two different problems. FIRST PROBLEM STATEMENT: “Choosing from two colors...
DescriptionResearcher Amy Martino posed two related tasks to the students that highlighted the difference between additive and multiplicative reasoning. First, she asked the students: If we call the orange...
DescriptionDuring this clip, the students discuss a task that had been posed by Erik: If I call the blue rod one, what rod will I call one half? A lively discussion centering on the definition of one half...
TitleIntroducing fraction equivalence and an exploration of fraction comparison, Clip 3 of 4: Proportional Reasoning Continued
DescriptionThe students work on the task: If the orange rod is called fifty, what number name would I give the white rod? Sarah and Beth offer an answer immediately, and are questioned by researcher Amy Martino...
TitleWord problems with addition and subtraction, Stephanie's group, Clip 9 of 9: Reasoning about the solution to problem 4 with the teacher
DescriptionIn the final clip of the series of nine in a first grade classroom, four children: Stephanie, Gerardo, Sean and Aaron, explain their reasoning about problems 4 of a set of 6 problems to their teacher,...
TitleIntroducing Fraction Equivalence and an Exploration of Fraction Comparison, Clip 2 of 4: An introduction to proportional reasoning.
DescriptionResearcher Amy Martino asked the students to assign a number name to the white rod when the orange rod was called ten. After discussing the problem with their partners, the students joined in a whole...
DescriptionAmy Martino leads a whole class discussion during which they talk about ways of writing number sentences for two problems: 1) How many one sixths are in one? and 2) How many one twelfths are in one?...
TitleEarly algebra ideas about binomial expansion, Stephanie's interview one of seven, Clip 5 of 9: Beginning to make sense of (x + y)(x + y)
DescriptionIn the fifth clip in a series of nine from the first of seven interviews focusing on Early Algebraic Ideas about the binomial expansion researcher Carolyn Maher asks Stephanie to multiply (x + y)(x +...
DescriptionResearcher Amy Martino posed two related tasks to the students. In this clip, the students work on designing a rod that can be called one half when the blue rod is called one. Erik and Alan discuss...