Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

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Insights Into Algebra 1 - Teaching For Learning
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Topic Overview Lesson Plans Student Work Teaching Strategies Resources
Workshop 7 Direct and Inverse Variation Student Work
Student Work:

Oil Module Unit Test Sample 1

Oil Module Unit Test Sample 2
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NCTM Standards

Oil Module Unit Test Sample 1

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Teacher Commentary:

NOTE: Questions 6, 7, and 8 from both work samples are discussed below:

I believe question 6 actually gives better insight into the depth of understanding that each student has concerning direct and indirect variation than do questions 7 and 8. When asked about situations totally unrelated to classroom experiences, Haily's answers in problem 6 demonstrate a clearer comprehension of the two concepts. Her response in problem 8 shows she can perform the necessary steps to obtain a mathematical model for a data set. Although it was interesting that after making the scatterplot in 8, she did not go back to problem 7 and adjust her graph to fit the definition.

On the other hand, Heather was able to express a memorized definition to answer problem 7, and initiate a memorized series of steps to create a mathematical model in problem 8. But she was unable to finish the process in order to write the algebraic equations to fit the data. She also could not apply the concepts to correctly label the situations in problem 6. That indicates to me that she really did not understand the big picture of direct and indirect variations.

Neither of the students discussed the relationship between the independent and dependent variables: both increasing or decreasing (in a direct variation), or as one variable increases, the other decreases (in an inverse variation).

To better assess students' understanding, changes I plan to incorporate next year include:
  1. In problem 6, ask them to explain WHY they think each situation represents a direct or indirect variation.

  2. Have more detailed requirements for graphs, i.e. scatterplot vs. a connected line graph, and including labels and scales for axes. (For this test I did not take off points for not having a scale on their scatterplots. I was more concerned about the general shape of the graph. One of my goals next year is to incorporate higher expectations across the curriculum, at all grade levels, for complete graphs at all times.)
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