## "Graph Zooming" Teacher Support

Graph Zooming Archived PoW || Student Version

Graph Zooming is no longer the current ESCOT Problem of the Week. The student version allows teachers to use the problem with their students without giving the students access to the archived answers. Teachers can use the link to the archived problem to get ideas of student thinking.

[Standards]  [Activities]  [Lessons]  [Dr. Math]  [Vocab]  [Other Resources]

Graph Zooming asks students to explore the concept of scale in mathematics and apply it to everyday experiences.

This ESCOT PoW could be used as an introductory exploration of scale in graphing.

If you have something to share with us as you use any of the links or suggestions on this page (something you tried and changed or a new idea), we would love to hear from you. Please email us.

Alignment to the NCTM Standards - Grades 6-8

Number & Operations
- understand numbers, ways of representing numbers, relationships among numbers, and number systems

Geometry
- use visualization, spatial reasoning, and geometric modeling to solve problems
- specify locations and describe spatial relationships using coordinate geometry and other representational systems

Problem Solving
- solve problems that arise in mathematics and in other contexts

Communication
- communicate mathematical thinking coherently and clearly to peers, teachers, and others
- use the language of mathematics to express mathematical ideas precisely

Connections
- recognize and apply mathematics in contexts outside of mathematics

Possible Activities:

Pre-Activities
- Read and discuss the scale page on Ursula Whitcher's Chameleon Graphing site.

Suggested by Susan Socha:

Have students look at a commercial map site, choose a location (maybe the city where their school is located) and start zooming in, noting the scale at the bottom. Here are some sites to use:

I tried this with Expedia and after typing in Swarthmore, I zoomed in until I could see the street where the Math Forum is located. I watched the scale. It's really cool, because you can zoom out to miles, and zoom in to yards. It would be great to ask the kids why you would need both kinds of maps. When do you need a big picture, and when do you need details?

Post-Activities
- Have students graph y = x. Explain why the graph of y = x can be seen in all three scales. Challenge students to write another function that can be seen in all three scales and explain why.

- Have students discuss why the graphs of y = 1x + 10 and y = x appear to be parallel. Are they really parallel? Provide a convincing argument.

- For algebra students: graph a function that would pass through the intersection of the first two functions.

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Related Lessons Online:

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Resources to use with students:

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