SCORE Mathematics

Standards Connections

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DISCOVERING GROWTH PATTERNS

A Web Activity Comparing Linear and Exponential Growth

Emilie Mason 
SCORE Mathematics Institute 
Fresno, California 
August 11-15, 1997

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Introduction:

The differences between linear (arithmetic) and exponential (geometric) growth functions are emphasized in this lesson. A student page instructs students to locate four specific sites on the Internet. After data is collected on the student worksheet, pattern predictions are made. Graphing the collected data is done using ClarisWorks or Microsoft 3.0 spreadsheet or by using pencil and grid paper. Student description and analysis concludes the lesson.

Prior Knowledge:

Experience graphing data points, previous discussion of linear (arithmetic) and exponential (geometric) functions, basic computer skills.

Grade Level:

7 to 9, pre-algebra or algebra 1

Objective:

By the end of this data collection and graphing lesson students will see the differences between linear (arithmetic) and exponential (geometric) growth.

Materials:

Computer with Internet access, printer, pencil, paper, calculator. Grid paper and ruler if graphing is done with pencil.

Time:

Two or three class periods.

Process:

  1. Review linear and exponential growth functions.
  2. Review plotting data points and graphing.
  3. Discuss Internet search procedures.
  4. Have students access Student Instructions. Review.
  5. Have students print out Student Worksheet (html) / (pdf) or provide copies to students.
  6. Students collect data on worksheets, make predictions, graph data points.
  7. Students write descriptions, comparing similarities and differences of graphs, reflecting on predictions and outcomes.
  8. Conduct discussion and review.

Evaluation:

For evaluation, collect data collection worksheets, graphs, and descriptions.

Extensions:

Brainstorm with students other situations where linear and exponential growth may exist. If time permits, allow search time on the Internet to see if sites can be located which allow for further investigation of these growth patterns.

Conclusion:

From this lesson students will discover that linear and exponential growth patterns exist in diverse situations. Connections are made between functions and patterns studied in class and the environment. Computers and the Internet will be used as tools for discovering these connections.

Related Internet Resources

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California Mathematics Academic Strands:

Grade 7:
Algebra and Functions
1.0 Students express quantitative relationships using algebraic terminology, expressions, equations, inequalities and graphs.

1.5 represent quantitative relationships graphically and interpret the meaning of a specific part of a graph in terms of the situation represented by the graph

3.0 Students graph and interpret linear and some non-linear functions.

3.1 graph functions of the form y = nx2 and y = nx3 and use in solving problems
3.3 graph linear functions, noting that the vertical change (change in y-value) per unit horizontal change (change in x-value) is always the same and know that the ratio ("rise over run") is called the slope of a graph

Statistics, Data Analysis, and Probability
1.0 Students collect, organize, and represent data sets that have one or more variables and identify relationships among variables within a data set by hand and through the use of an electronic spreadsheet software program.

1.2 represent two numerical variables on a scatterplot and informally describe how the data points are distributed and any apparent relationship that exists between the two variables (e.g., between time spent on homework and grade level)

Mathematical Reasoning
1.0 Students make decisions about how to approach problems.

1.2 formulate and justify mathematical conjectures based upon a general description of the mathematical question or problem posed

Grade 8-12:
Algebra I
6.0 Students graph a linear equation and compute the x- and y- intercepts (e.g., graph 2x + 6y = 4). They are also able to sketch the region defined by linear inequality (e.g., they sketch the region defined by 2x + 6y < 4).

Algebra II
12.0 Students know the laws of fractional exponents, understand exponential functions, and use these functions in problems involving exponential growth and decay.

 

NCTM 5-8:

Standard 1 Mathematics as Problem Solving
Standard 2 Mathematics as Communication
Standard 3 Mathematics as Reasoning
Standard 4 Mathematical Connections
Standard 5 Number and Number Relationships
Standard 7 Computation and Estimation
Standard 8 Patterns and Functions
Standard 9 Algebra

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