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

Length, Weight, and Volume

Materials Needed: Textbook

## Contents

## Why[edit]

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[edit]

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

## Warm-up[edit]

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[edit]

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