A B C

Solutions for Session 10, Part A

See solutions for Problems: A1 | A2 | A3

Problem A1

 a. Answers will vary. Some ideas: The challenge of feeling a shape but not looking at it, and of describing its properties without using its name simultaneously, requires students to practice with vocabulary like "sides" and "vertices" but also keeps the lesson from seeming like a vocabulary lesson. Also, the fact that students have different roles -- feeling and describing, listening and drawing -- keeps the focus on communication rather than just on the words. b. We see students learn new terms like "trapezoid," but with meaning and context and relating it to other things they know. (It's half a hexagon.) c. Throughout the lesson, students work on solving a problem that involves discovering what the properties of a shape are. In other words, they think about what makes a square a square, a triangle a triangle, etc. d. One of the big ideas that students encounter in this lesson is the idea of classification. In this lesson, we see how students begin to develop a sense of classification of polygons based on their properties. Classification is an idea that progresses through grade levels.

 Problem A2 People have very different, and often very strong, opinions about the use of context in mathematics classrooms. It is important to present students with a variety of lessons. Students can be engaged by problems that are not context-based, as well as by those with real-world connections.

 Problem A3 In this lesson, students describe just one shape rather than a design made of several shapes. Also, students feel the shapes without looking and draw the shapes that are described. This gives them the opportunity to touch, draw, describe, and listen to descriptions of the shapes.