Illuminations: Measuring Up

Measuring Up

Unit Overview

Lesson 1

Lesson 2

Lesson 3

Lesson 4

Lesson 5

Lesson 6

Lesson 7

Off the Scale

Students use real-world examples to solve problems involving scale as they examine maps of their home states and calculate distances between cities.

Learning Objectives

Students will:

set up and solve problems dealing with scale by writing proportions
recognize examples of scales being used in real-life situations
examine a map of their home states to determine distances between cities using a scale

Materials

Overhead Transparencies and Pens
Maps of birth states of students
Rulers
Map Activity Sheet

Instructional Plan

To assess students' prior knowledge, have the students brainstorm ideas about where they might use a scale to enlarge or reduce the size of something. List these ideas on the board or on an overhead projector.

To begin the lesson, give the students a copy of their state map and have them locate the legend. Maps of individual states are available at Maps of the United States. Another site is located here. Alternatively, students can find their own state map.

Give pairs of students a ruler and have them figure out distances between given cities. Use the Teacher Resource Sheet, Map activity sheet, as a guideline to creating your own worksheet.

Map Activity Sheet

Students should use the map's scale to complete information about the miles and the inches. Work with the students on setting up proportions to compute unknown distances using their scale factors. Be sure that when the students are setting up the proportions, they do actual distances over each other, and the scale distances over each other (the scale distances or one of the actual distances will be represented by x). Once the proportions are set up, the students can simply solve for x in their proportions.

Questions for Students

What mathematics are involved in enlarging something? Reducing something?

[Proportions, similarity, scale factor.]

What mathematics do you use to convert inches to miles (on the map) using the scale on the map?

[Scale, conversion factor].

What steps do you take to convert miles to feet? How about miles to yards?

[To convert miles to feet, divide miles by 5,280. To convert miles to yards, divide miles by 1,760.]

Assessment Options

At this point in the unit, students should be able to do the following:
- Set up and solve proportions
- Apply proportions in a variety of instances
- Apply what they have learned about making conversions and use distances on maps to convert their units to actual distances
You can assess these objectives by verbally asking the students to glance at an atlas and use their conversion factors to approximate the distance between certain cities. Once they make an estimate, have students set up their proportions to verify their guesses.

Extensions

You can extend the activity by having the students select a comic strip from the newspaper. They should mark off their comic in ¼-inch squares. If they write light enough with their pencil, they can erase the grid after the comic is drawn.
Then have students mark off an 8 1/2 × 11 inch sheet of paper in one-inch squares. Have students draw each box from their comic onto their paper, enlarging the comic strip. You may consider drawing out a one-inch by one-inch grid on a transparency to show the students exactly how to measure and mark the grid with their rulers.

Teacher Reflection

Are the students able to make reasonable estimates using the scale in the map's legend?
Are the students able to connect the use of scales to real-world situations?
Is further review of the metric and customary conversion factors necessary?

NCTM Standards and Expectations

Measurement 6-8

Select and apply techniques and tools to accurately find length, area, volume, and angle measures to appropriate levels of precision.
Solve problems involving scale factors, using ratio and proportion.
Use common benchmarks to select appropriate methods for estimating measurements.
Understand both metric and customary systems of measurement.
Understand relationships among units and convert from one unit to another within the same system.

This lesson was developed by Katie Carbone.