1
Lesson Overview
Lesson Title:
Match Your Graph
Abstract:
A CBR (Calculator Based Ranger) unit sends out an ultrasonic pulse and measures
the time which passes until that pulse returns after bouncing off the closest object.
The CBR also computes and stores velocity and acceleration data.
In the warm-up, students track each other walking toward and away from the CBR.
Grade Level or
Course Name:
Materials:
Preparation:
Duration:
Virginia DOE
SOLs
In the activity, students are presented with multiple graphs, one at a time. All
graphs are comprised of line segments. By walking forward and backwards and
differing rates, each student tries to duplicate the graph. The given graph is shown
in solid line segments. At different stages of the experiment, the students are
presented with questions which require them to explore their understanding of rates
of change.
Grades 9-12
Algebra, PreCalculus, Calculus
CBR unit
TI-83/84 series calculator with Easy Data application
Calculator-to-Calculator Data Cable
CBR to Computer video cable
Projector Screen
Masking Tape
Meter Measuring Stick
Worksheet Questions
 Ensure that the classroom has a clear path of approximately 20 feet (6 meters)
from a wall
 At one-yard (or one-meter) intervals, mark the floor with masking tape
45-60 minutes
(Delete those all which do not apply.)
Algebra II
Functions
AII.7
The student will investigate and analyze functions algebraically and
graphically. Key concepts include
a) domain and range, including limited and discontinuous domains and
ranges;
b) zeros;
c) x- and y-intercepts;
d) intervals in which a function is increasing or decreasing;
e) asymptotes;
f) end behavior;
g) inverse of a function; and
h) composition of multiple functions.
Graphing calculators will be used as a tool to assist in investigation of
functions.
GMU COMPLETE: Center for Outreach in Math Professional Development and Educational Technology
2
Algebra, Functions & Data Analysis
Algebra and Functions
AFDA.1 The student will investigate and analyze function (linear, quadratic,
exponential, and logarithmic) families and their characteristics. Key
concepts include
a) continuity;
b) local and absolute maxima and minima;
c) domain and range;
d) zeros;
e) intercepts;
f) intervals in which the function is increasing/decreasing;
g) end behaviors; and
h) asymptotes.
AFDA.3 The student will collect data and generate an equation for the curve
(linear, quadratic, exponential, and logarithmic) of best fit to model realworld problems or applications. Students will use the best fit equation to
interpolate function values, make decisions, and justify conclusions with
algebraic and/or graphical models.
AFDA.4 The student will transfer between and analyze multiple representations of
functions, including algebraic formulas, graphs, tables, and words.
Students will select and use appropriate representations for analysis,
interpretation, and prediction.
Mathematical Analysis
MA.3
The student will investigate and describe the continuity of functions,
using graphs and algebraic methods.
Content
Standards
A-CED.2 Create equations that describe numbers or relationships.
A-REI.2 Understand solving equations as a process of reasoning and explain the
reasoning.
F-IF.1
Understand the concept of a function and use function notation.
F-IF.2
Understand the concept of a function and use function notation.
F-IF.4
Interpret functions that arise in applications in terms of the context.
F-IF.6
Interpret functions that arise in applications in terms of the context.
F-IF.9
Analyze functions using different representations.
F-LE.5
Interpret expressions for functions in terms of the situation they model.
S-ID.7
Interpret linear models
Process
Standards:
Common Core Mathematical Practices
1.
2.
3.
4.
5.
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Use appropriate tools strategically.
GMU COMPLETE: Center for Outreach in Math Professional Development and Educational Technology
3
NCTM Process
Standards
1. Problem Solving
 Build new mathematical knowledge through problem solving
 Monitor and reflect on the process of mathematical problem solving
3. Communication
 Organize and consolidate their mathematical thinking through
communication
 Communicate their mathematical thinking coherently and clearly to peers,
teachers, and others
 Analyze and evaluate the mathematical thinking and strategies of others
 Use the language of mathematics to express mathematical ideas precisely
4. Connections
 Recognize and use connections among mathematical ideas
5. Representation
 Create and use representations to organize, record, and communicate
mathematical ideas
 Use representations to model and interpret physical, social, and
mathematical phenomena
GMU COMPLETE: Center for Outreach in Math Professional Development and Educational Technology