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A mathematically proficient student makes sense of quantities and their relationships in a given problem situation, looks for principle s applicable to that problem, and takes the problem situation to a general situation.

Second step: For example, in a right triangle ABC, with the right angle at vertex C, when the 2 legs and hypotenuse are given, in several settings, one observes and then derives: Students conduct 3 rate experiments: The math textbooks are backwards. Published December 14, 2011 By Ms.

Comprehensive reasoning—to think abstractly and quantitatively separately and then together, develops when teachers employ a range of questions to help students focus on understanding quantities e. In these clips, Cabana analyzes groups' work in terms of logical flow and carefulness of organization, trying to make a guess about what they really understand.

All of these problems are equivalent and develop a deeper understanding of numbersense, quantitative reasoning and mental arithmetic. Condon refers his students to strategies for comparing rates, asking the students to use these strategies with new data.

Which is more—5 quarters or 8 pennies?

Base Ten Number Line. A middle childhood teacher might ask her students to reflect on what each number in a fraction represents as parts of a whole. Search this site: To find out more, including how to control cookies, see here: Only with a great deal of scaffolded questioning and examples can a teacher achieve this with all students.

Mathematical understanding results from the practice of these justifications and, in the process, procedural skills are strengthened, particularly when mathematical tasks experienced by students are of sufficient richness. Site hosted by Education Development Center, Inc.

This site uses cookies. When students answer a word problem by labeling each component of their equation, they are reasoning quantitatively.

I am a quadrilateral, But I am also a rhombus. It goes beyond the ability to merely find the value of the unknown say, x in the equation. They bring two complementary abilities to bear on problems involving quantitative relationships: Intro to Physics.

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