Students will be able to
- calculate the rate of change
- use the rate of change to interpret data in real-life graphs
Common Core State Standards: 8.F.B.4, 8.F.B.5
Vocabulary: Slope, rate of change, ratio, constant slope, constant rate of change
Materials: Printed copies of the graphs
1. Introduction (10 minutes, whole group)
This lesson uses interactive graphs that present the relative inequality in health, education, and economics between African Americans and white Americans, a full 50 years after Dr. Martin Luther King, Jr.’s famous “I Have a Dream” speech. (If possible, distribute printed copies of these graphs to students for easier reference.) While many students will likely have heard of Dr. King and his iconic speech, they may not know as much about the March on Washington for Jobs and Freedom or of the civil rights struggle that led to the historic gathering in the summer of 1963. This lesson provides an opportunity for students to learn more about the context, people, and issues behind the graphs themselves.
To introduce the mathematics part of the lesson, review slope and rate of change with students. Slope is calculated by finding the ratio of vertical change to horizontal change for two points on a line. Remind students that the slope of a line is the same between any two points on that line. This is called a constant slope, or a constant rate of change. (Make sure students interpret this phrase in the correct way. A constant rate of change does not mean that the rate is constantly changing—it means that it is a single, constant rate.)
Many real-life functions do not have constant rates of change, however. Use the Unemployment Rate graph as an example. There have been big fluctuations in the unemployment rate between 1965 and 2012, and the change has certainly not been constant over that entire period. Ask students to identify which periods showed the greatest increase in African American unemployment rates, as indicated by the most extreme spikes. (They should find two periods: 1979–1983 and 2007–2010.) Then, calculate the rate of change during those periods.
2. Activity (10 minutes, pairs or small groups)
In small groups, have students construct an answer to the following question: What story do the graphs tell about economic and social equality over the past 50 years?
To answer the question, students should pick at least two graphs to analyze. They should do the following:
- Describe the overall trend in the data from 1963–2012.
- Describe the story that the data tell in terms of the issue of equality between blacks and whites.
- Calculate the rate of change for each function during each decade (or periods of extreme change).
- Use the rate of change to explain how living, economic, or social conditions measurably changed from decade to decade.
By the end of the activity time, students should be able to form some sort of evidence-based argument about whether economic and social equality between whites and blacks has changed since 1963.
3. Conclusion (10 minutes, whole group)
Have each group present its argument, referencing data, the rate of change, and trends in the graph. Use the following questions to push students’ thinking:
● Have economic and social opportunities for blacks actually increased, or have they just kept pace with those for whites?
● Looking at the data, are there any specific areas where you would expect opportunities for blacks to eventually eclipse those for whites?
Continue to bring the conversation back to the issue of the rate of change. Specifically, if opportunities for whites and blacks are both experiencing the same rate of change, then is the opportunity gap changing at all?
Activity Extension: Discuss the issue of economic equality—Why is it so important, and why has it been so elusive despite major societal and political changes since 1963? Put aside the mathematical conversation for the conclusion of the class and ask students what they think is needed for equality to become a reality, and not just a dream.