NCTM Content Standards:
Algebra
 understand patterns, relations, and functions;
 represent and analyze mathematical situations and structures using algebraic symbols;
 use mathematical models to represent and understand quantitative relationships;
 analyze change in various contexts.
NCTM Process Standards:
Problem Solving
 Build new mathematical knowledge through problem solving
 Solve problems that arise in mathematics and in other contexts
 Apply and adapt a variety of appropriate strategies to solve problems
 Monitor and reflect on the process of mathematical problem solving
Reasoning and Proof
 Make and investigate mathematical conjectures
 Develop and evaluate mathematical arguments and proofs
Communication
 Organize and consolidate their mathematical thinking through communication
Representation
 Recognize and use connections among mathematical ideas
 Recognize and apply mathematics in contexts outside of mathematics
NCSCOS:
Algebra 2
2.02 Use quadratic functions and inequalities to model and solve problems; justify results.
a. Solve using tables, graphs, and algebraic properties.
b. Interpret the constants and coefficients in the context of the problem.
Prior Knowledge required:
Students should have a working knowledge of how to use the TI-Nspire. They should
understand that a quadratic function has a parabola for its graph and the critical points are the
roots, intercepts and vertex. Students should be able to write a quadratic function give its roots
and understand how to factor and multiply terms together.
Knowledge students might gain:
Through working this activity students should understand a real world application of
quadratic functions. Students will connect the roots of a function to its algebraic representation.
Students will be able to interpret the critical points of a parabola in context. They will
understand how data analysis can be used to gather information, examine a pattern, and arrive at
a model.
Modeling the area of a rectangle
Open the file: rectangle.tns
On the first page you will see a rectangle with a perimeter of 38 units. The length, width, perimeter, and
area are shown in the upper right. You can adjust the dimensions of the rectangle by clicking and
dragging the top right corner. You can also collect data and plot points of the form (length, area) on the
graph on the right by holding control and pushing the period button for each rectangle you create.
As you explore comment on the following statements
How does the area change as the dimensions change?
How does the perimeter change as the dimensions change?
What set of dimensions appear to maximize the area?
What type of function would fit the pattern of data you collected?
Can you find the function that fits the data?
Hint: Find the roots by determining what lengths will yield and area of 0.
How well does your function fit the data?
On the second page is a graph page (Push Control right to get there). Plot your function. Go to
menu, graph type, and choose scatter plot. Make x lgh and y area. How well do they match? If they
match, find the maximum area by putting a point on the plot and moving it until it arrives at the
maximum. (menu, point on). What is the maximum area?
If the amount of fencing was 50 feet determine the function that would model the possible rectangles
that could be formed and find the maximum area.