MDTP Written Response Items are developed to help students improve their written communication of mathematics. Students must be given enough time to think about the problem and to carefully and clearly answer the questions that are asked. As the rubrics indicate, simple numerical solutions are not adequate. The items are meant to be used within one class period with no outside work done as a prerequisite. (For example it is not appropriate to use any of these problems as a “Problem of the Week”)

Scoring student work and providing useful information about that work to your students will take time. We encourage you to read the students’ responses critically, looking for a variety of methods that might be discussed in class. It might also be helpful to give students an opportunity to rewrite some of their responses

A sampling of the items appropriate for our functions topics goals may include:

- Coordinate Graphing: locate points in the coordinate plane given their coordinates or a fixed distance from a given point. This requires an understanding of the coordinate system and its notation, as well as the concept of distance between points.
- Island: use population growth information to determine the population of an island at two specific times and to estimate the years in which the population will reach specific levels, one of which is the year when the needs of the population exceed the living space. Both estimates must be supported by explanations.
- Laps: Perform operations with fractions, mixed numbers, and decimals. An understanding of rates is necessary for each task.
- Punch: recognize and represent relationships expressed in a table of amounts needed to make various quantities of fruit punch from water and fruit juice concentrate.
- Age-Height: draw an approximating line for a set of data points, to use this line to find either coordinate given the other, and to recognize possible errors in arbitrary extrapolation.
- Inequality: find ways of describing a geometric region using algebraic inequalities. This requires an understanding of the coordinate plane, algebraic notation, linear graphs, and inequalities.
- Salary: make comparisons between the initial and final amounts of a salary that is affected by a decrease followed by an increase of the same percentage rate.

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