This lesson comes from the Math Assessment Project:

Mathematical goals

This lesson unit is intended to help you assess how well students solve problems involving measurement and in particular, to identify and help students who have difficulty:

• Computing measurements using formulas.
• Decomposing compound shapes into simpler ones.
• Using right triangles and their properties to solve real-world problems.

Introduction

The unit is structured in the following way:

• Before the lesson, students attempt the task individually. You then review their work and formulate questions for them to answer, in order to improve their work.
• At the start of the lesson, students work individually to answer your questions. Next, they work in small groups on the same task, to produce better collective solutions than those they produced individually. Throughout their work they justify and explain their decisions to each other.
• In the same small groups, students critique some student responses to the Glasses task, provided in the Sample Responses to Discuss. They correct errors in those responses.
• In a whole-class discussion, students discuss their own solutions and explain how to correct the common misconceptions seen in the Sample Responses to Discuss.
• Finally, students work on their own again to improve their individual solutions.

Note: This lesson includes extension questions and hint cards

This lesson corresponds to the following  standard(s):

• Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems 
• Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
• Solve real-world and mathematical problems involving area, volume, and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. (The examinee will demonstrate an understanding by applying geometric methods in modeling situations.).