SCORE Mathematics

Standards Connections

Curve Fitting and the TI-85 Graphing Calculator

Linear and Exponential Models

BY: Cheryl Snider

Introduction: This is a step-by-step guide for using the TI-85 Graphing Calculator to do scatter plots using data obtained from sources on the Internet. Some information will model linear functions and some will be models of exponential functions.

Prior Knowledge: Knowledge of linear and exponential graphs.

Grade Level: 10 - 12

Task: Students will follow a step-by-step guide for using the graphing calculator to determine equations which best fit data graphed. Students will then gather data from various sites on the web, or they will do searches to find information necessary to complete extension assignments.

Resources:

Linear Regression Student Instruction Page

Exponential/Polynomial Student Instruction Page

Process: The students will use a graphing calculator and a step-by-step guide to enter data into the stat menu of the calculator. They will then learn how to use the correlation to determine the equation of best fit. They will be able to write an equation of best fit for data in the sample lessons and then they will be asked to analyze other data obtained from Internet sources.

Learning Advice: Since some sites are not available or they move, it is important to have students use the data provided to learn how to use their calculator. The extension assignments allow for student creativity.

Evaluation:

  • The quality and the accuracy of the graphs
  • The accuracy of the equations obtained by using the graphing calculators.

Extensions: Scavenger hunt (html) / (pdf) to search the web for data for the extension assignments.

Conclusion: Students will be able to work at their own pace and without the aid of the teacher to learn how to use the graphing calculator. Teachers can just give students the programmed guide and let students learn at their own pace.


SCORE Mathematics | | SCORE Mathematics Lessons Index | |  SCORE Mathematics Search

California Mathematics Academic Standards:

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

4.0 Students solve simple linear equations and inequalities over the rational numbers.

4.1 solve two-step linear equations and inequalities in one variable over the rational numbers, interpret the solution or solutions in the context from which they arose, and verify the reasonableness of the results

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 exist between the two variables (e.g., between time spent on homework and grade level)

Mathematical Reasoning
2.0 Students use strategies, skills, and concepts in finding solutions.

2.5 use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to explain mathematical reasoning
2.6 express the solution clearly and logically by using appropriate mathematical notation and terms and clear language; support solutions with evidence in both verbal and symbolic work

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).
7.0 Students verify that a point lies on a line, given an equation of the line. Students are able to derive linear equations by using the point-slope formula.
9.0 Students solve a system of two linear equations in two variables algebraically and are able to interpret the answer graphically. Students are able to solve a system of two linear inequalities in two variables and to sketch the solution sets.
10.0 Students add, subtract, multiply, and divide monomials and polynomials. Students solve multistep problems, including word problems, by using these techniques.
13.0 Students add, subtract, multiply, and divide rational expressions and functions. Students solve both computationally and conceptually challenging problems by using these techniques.
16.0 Students understand the concepts of a relation and a function, determine whether a given relation defines a function, and give pertinent information about given relations and functions.
18.0 Students determine whether a relation defined by a graph, a set of ordered pairs, or a symbolic expression is a function and justify the conclusion.

Algebra II
2.0 Students solve systems of linear equations and inequalities (in two or three variables) by substitution, with graphs, or with matrices.
5.0 Students demonstrate knowledge of how real and complex numbers are related both arithmetically and graphically. In particular, they can plot complex numbers as points in the plane.
12.0 Students know the laws of fractional exponents, understand exponential functions, and use these functions in problems involving exponential growth and decay.

Probability and Statistics
8.0 Students organize and describe distributions of data by using a number of different methods, including frequency tables, histograms, standard line and bar graphs, stem-and-leaf displays, scatterplots, and box-and-whisker plots.

NCTM 9-12:

STANDARD 1: MATHEMATICS AS PROBLEM SOLVING
STANDARD 3: MATHEMATICS AS REASONING
STANDARD 5: ALGEBRA
STANDARD 6: FUNCTIONS
Copyright Kings County Office of Education
August 1997
Revised June 16, 2000
SCORE Webmaster