# Prealgebra for Two-Year Colleges/Workbook AIE/Length, area, and volume

Length, Weight, and Volume

Materials Needed: Textbook

## Why

Real-world problems almost always contain units. Some of the most common units in the U.S. are English units of length, weight, and volume.

## Learning Objectives

1. Explain the difference between length, weight, and volume, and identify appropriate English units for each.
2. Know the conversion factors for common English units of length, weight, and volume.
3. Give examples of situations in which a given operation (+, –, , ) is appropriate.

## Warm-up

You should have the following facts memorized. Complete the table. Length : ___12__ in = 1 ft ___3__ ft = 1 yd ___5280__ ft = 1 mi Weight : ___16__ oz = 1 lb ___2000__ lbs = 1 ton Time: ___60__ sec = 1 min ___60__ min = 1 hr ___24__ hr = 1 day ___30__ dys = 1 mon ___12__ mon = 1 yr ___52__ wks = 1 yr ___365__ dys = 1 yr Volume/Capacity : ___8__ fl oz = 1 cup ___2__ cups = 1 pt ___2__ pt = 1 qt ___4__ qt = 1 gal

## Activity

1) Does the situation describe a length, weight, or volume? Write L, W, or V. a) Filling you car with gasV b) Going on a dietW c) Measuring cough syrupV d) Figuring postageW e) Driving to CincinnatiL f) Building a fenceL 2) Write an appropriate English unit for measuring each of the following: a) The distance from San Francisco to Washington, D.C. miles b) The weight of an aircraft carrier tons c) The size of a soda bottle quart d) The size of a sheet of paper inches e) The amount of flour in a loaf of bread cup f) The amount of Cheerios in a box oz 3) Because of construction CalTrans needs to install 100 yds of concrete barriers along the edge of Highway 4. Each barrier is 1 yd 2 ft long. How many barriers are needed? 100 yds = 300 ft; 1 yd 2 ft = 5 ft 100/5 = 20 barriers

4) Write a realistic problem situation for 2 tons 850 lbs – 1 ton 1430 lbs. Solve the problem you wrote. A fully-loaded pickup truck weighs 2 tons 850 lbs. If the emptied truck weighs 1 ton 1420 lbs (a fact I found in the owner’s manual), then how much does the cargo weigh? 2 tons 850 lbs – 1 ton 1430 lbs = 1420 lbs

5) Write a realistic problem situation for 1 cup 4 fl oz  13. Solve the problem you wrote. I have 13 friends coming over on a hot day. I want to make enough lemonade to be able to serve each of them 1 cup 4 fl oz. How much lemonade do I need to make? 1 cup 8 fl oz  13 = 13 cups 52 fl oz = 19 cups 4 fl oz

6) Write a realistic problem situation for 3 lbs 12 oz  12. Solve the problem you wrote. At Costco, a box of 12 cans of cat food weighs 3 lbs 12 oz. How much does each can weigh? 3 lbs 12 oz  12 = 5 oz

7) Write a realistic problem situation for 24 ft 9 in + 18 ft 6 in + 24 ft 9 in + 18 ft 6 in. Solve the problem you wrote. I have a garden that is 24 ft 9 in long and 18 ft 6 in wide. What length of fencing material should I buy if I want the fence to go all the way around the garden? 24 ft 9 in + 18 ft 6 in + 24 ft 9 in + 18 ft 6 in = 84 ft 30 in = 86 ft 6 in