Process Standards definition and examples - Green Hills AEA

Process Standards as Proposed by NCTM
Note: Expect overlapping among process standards within given examples.
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
Example:
The Green family is planning a one-week vacation in Florida and needs
to rent a car while there. They researched and found the following
options.
*Weekly Rate 1 $329 per week, unlimited mileage.
*Weekly Rate 2 $219 per week, plus 12 cents per mile.
**Daily Rate 1
**Daily Rate 2
*Partial week charged at a full week's price.
$50 per day, unlimited mileage.
$40 per day plus 3 cents per mile.
**Partial days charged at a full day's price.
The Greens don't know exactly how far they will drive but estimate that it will be between 500
and 1000 miles. They must decide which plan to choose. Explore the four options below.
Make a Table
Things to Do
Fill in a table like the one below with the costs of each option.
Comparison of Total Rental Car Costs per Week Based on Mileage Driven
Make a Graph
Total Miles Driven in Week 500 600 700 800 900 1000
Cost at Weekly Rate 1
Cost at Weekly Rate 2
Cost at Daily Rate 1
Cost at Daily Rate 2
Draw and compare graphs of the four options.
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Prepared by Colleen Confer

Analyze the Graph
1. Each graph should contain six points. Is it appropriate to connect
the points on the graphs to make lines? Explain why or why not.
2. Do all of the points of each graph lie on a straight line? What is a
function called that has a graph which is a straight line?
3. Which of the lines is steepest? What is the slope of that line?
Which of the functions grows at the fastest rate? Which of the
functions grows at the slowest rate? What is its slope ?
4. If you extend the lines through the y axis, would any of the lines
go through the origin? Explain why or why not.
5. What is significant about the points where the graphs intersect?
Write the Functions
Write the Total Week's Rental Car Cost as a function of the Number of Miles Driven
for each of the options.
Write a Paragraph
Based on the best economics, explain under what conditions the Green Family should
choose each option.
http://math.rice.edu/~lanius/Algebra/rentacar.html
Reasoning and Proof
Recognize reasoning and proof as fundamental aspects of mathematics
Make and investigate mathematical conjectures
Develop and evaluate mathematical arguments and proofs
Select and use various types of reasoning and methods of proof
Example:
Students research various epidemics that have devastated the world population at
various points in history. They then share and calculate statistics obtained in their
research and develop graphs comparing and contrasting how different epidemics
affected the global population.
http://www.nytimes.com/learning/teachers/lessons/19980908tuesday.html
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Prepared by Colleen Confer

Communication
Organize and consolidate their mathematical thinking through
communication
Communicate their mathematical thinking coherently and clearly to peers
Analyze and evaluate the mathematical thinking and strategies of others
Use the language of mathematics to express mathematical ideas properly
Example:
It's the night of the big game. You're in the locker room. The coach is pumping the
team up. "Now, I know you people are nervous. That's okay, in fact, that's what we
want. You're going to perform better on the court if you're a little nervous".
Does the graph above confirm what the coach told you?
Here are some questions for you based upon the graph.
1. Write a statement that describes performance as stress increases.
2. Which part of the graph illustrates where stress is highest? What is
performance at that point? Which part of the graph illustrates where
performance is highest? Which part of the graph illustrates where
performance is increasing? Which part of the graph illustrates where
performance is decreasing?
3. Notice that the graph is symmetric about a vertical line. What would
you say this indicates about performance?
4. What if this was a graph of your bank balance over a year. Describe
what the graph would indicate about your saving and spending
practices.
http://math.rice.edu/~lanius/Algebra/stress.html
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Prepared by Colleen Confer

Connections
Recognize and use connections among mathematical ideas
Understand how mathematical ideas interconnect and build on one another
to produce a coherent whole
Recognize and apply mathematics in contexts outside of mathematics
Example: Students learn about the impact of the recent J.P. Morgan/Chase
Manhattan merger. By studying the recen t financial performance of the two
banks, students will predict how the merger will affect the new company's
financial performance. Students will then create an annual report for the new
company based on their predictions.
http://www.nytimes.com/learning/teachers/lessons/20000914thursday.html
Representation
Create and use representations to organize, record, and communicate
mathematical ideas
Select, apply, and translate among mathematical representations to solve
problems
Use representations to model and interpret physical, social, and
mathematical phenomena
Example: A group of students has $60 to spend on dinner. They know that the
total cost, after adding tax and tip, will be 25 percent more than the food prices
shown on the menu. How much can they spend on the food so that the total cost
will be $60?
$60
Tax and Tip
Cost of Food
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Prepared by Colleen Confer