Overview

When it comes to area and volume, there's just no substitute for experience. Join us as we use a little hands-on detective work in the Module 2.1 to investigate volumes using proportional reasoning.

The motivating CAHSEE release question for this module is the following:

A cereal manufacturer needs a box that can hold twice as much cereal as the box shown below. Which of the following changes will result in the desired box? (V = lhw)

A. Double the height only.

B. Double both the length and width.

C. Double both the length and height.

D. Double length, height, and width.

California Mathematics Content standards addressed in this question include:

Measurement and Geometry (7th)

2.0 Students compute the perimeter, area, and volume of common geometric objects and use the results to find measures of less common objects. They know how perimeter, area, and volume are affected by changes of scale.

2.3 Compute the length of the perimeter, the surface area of the faces, and the volume of a three-dimensional object built from rectangular solids. Understand that when the lengths of all dimensions are multiplied by a scale factor, the surface area is multiplied by the square of the scale factor and the volume is multiplied by the cube of the scale factor.

2.4 Relate the changes in measurement with a change of scale to the units used (e.g., square inches, cubic feet) and to conversions between units (1 square foot = 144 square inches or [1ft.²] = [144ft.²]; 1 cubic inch is approximately 16.38 cubic centimeters or [1 in.³] = [16.38 cm³])

Objectives

In Unit 2.1 The Cereal Box, you will:

  • deepen your understanding of mathematical concepts in Pre-Algebra, including
    • the use of formulas to find the volumes of prisms and cylinders; and
    • how changes in dimensions of a prism result in changes in its volume
  • focus on new instructional strategies, including
    • using models (specifically models of prisms with wooden cubes);
    • using sentence strips and pair-problem solving; and
    • generating and testing hypotheses