Illuminations: Representing Data

Representing Data

Skin Weight

In this lesson, students complete a chart by multiplying or dividing a given value, compare two categories in a line graph, and identify number patterns.

Learning Objectives
 

Students will:

  • complete a chart by multiplying or dividing a given value
  • compare two categories of information in graphic form (line graph)
  • identify number patterns

Materials
 
Two colored crayons for each student (preferably red and blue)
A local newspaper or Internet news source
Graph Paper
Skin Weight Activity Sheet

Instructional Plan

Write the following chart on the chalkboard or overhead:

 

Start
Finish
96
8
144
12
12
1
120
10
36
3

 

Ask students how they would get to start from finish. Most students will say that you can simply divide the start number by 12 to arrive at the finish number. Some students may say that you can also multiply the finish number by 12 to get the start number.

Write the following chart on the chalkboard or overhead:

 

Start
Finish
17
85
100
500
31
155
12
60
5
25

 

Once again, ask students how they would get to start from finish. Most students will say that you can simply multiply the start number by 5 to arrive at the finish number. Some students may say that you can also divide the finish number by 5 to get the start number.

(Note: You may wish to include some numbers with decimals or fractions in your chart.)

Distribute the Skin Weight activity sheet to each student.

Skin Weight Activity Sheet Skin Weight Activity Sheet

Discuss the rule of thumb on the Activity Sheet to the students. Give an example: "The weight of a 320-pound man's skin is determined by dividing 320 by 16." Thus, his skin weighs 20 pounds.

 

 

Give students time to individually complete the chart. As a class, make sure all students have completed the chart correctly before continuing.

Explain how to plot the graphs using a blue crayon for the body weight and a red crayon for the weight of the skin. Give students time to complete the graph using Graph Paper.

Graph Paper Graph Paper

In pairs, discuss the completed graphs. Circulate through the classroom to verify the accuracy of the graphs.

Assessment Options
 

You may wish to collect the Skin Weight activity sheet as a means of assessment. Solutions to the chart are as follows:

  1. 160, 10
  2. 64, 4
  3. 100, 6.25
  4. 88, 5.5
  5. 128, 8
  6. 8, 0.5
  7. 48, 3
  8. 232, 14.5
  9. 36, 2.25
  10. 144, 9

Extensions
 
  1. In the sports section of the newspaper (or Internet news source), find the weights of ten different athletes. Figure the weights of their skins and then rank the weights from highest to lowest. What is the difference between the highest and the lowest?

NCTM Standards and Expectations
 
Data Analysis & Probability 6-8
  1. Formulate questions, design studies, and collect data about a characteristic shared by two populations or different characteristics within one population.
  2. Select, create, and use appropriate graphical representations of data, including histograms, box plots, and scatterplots.
  
1 period   

NCTM Resources

Principles and Standards for School Mathematics
National Council of Teachers of Mathematics Thinkfinity Verizon Foundation
More and Better Mathematics for All Students
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