# #17. Context with representations in high school

Posted on January 16th, 2015

From the Institute for Learning, this is Steve Miller.

In another podcast, Laurie Speranzo talked about the use of multiple representations in the middle school as a means of scaffolding student learning.

High school students also need to use context, drawings, tables, graphs, and equations to make sense of problems and mathematics.

Let's consider students who are beginning to develop their understanding of non-linear graphs. They are given the context of a vendor at the ballpark tossing a bag of peanuts to a customer. The bag of peanuts travels upward and reaches a maximum height before it begins to fall and land into the customer's hands.

A student says, "the bag of peanuts leaves my hand, goes upward to reach a maximum height of 9 feet at 2 seconds. Then it starts down and lands in the customer's hands. Hmmâ€¦I'm picturing the journey of the bag of peanuts on a graph and it looks like an upside-down U. I know this is called a parabola."

Another student says, "The values in a table give us the same U-shape but in numbers. The table starts at 0 seconds and 5 feet and at the end of the table we see 5 seconds and 0 feet because the bag of peanuts has landed. I can see the curve of the upside-down U in the table because the heights in the table read 5 ft, then 8, 9, 8, 5, and finally 0 feet. The table provides the maximum height at the time of 2 seconds and the height of 9 feet." Interesting how numbers can paint a picture of what is happening to the bag of peanuts.

We heard how students talked about and generalized the pattern they saw in the flight of a bag of peanuts. This same pattern appeared in the graph and table. Finding relationships like these can help to clarify mathematics for students.

From the Institute for Learning, this has been Steve Miller.

**Steve Miller** is a Fellow of the Institute for Learning's mathematics Disciplinary Literacy Team.

More information on Steve Miller.

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