Profit Predicting

   Contents

 Task

In this problem, students will read from a graph showing the profits that a group of friends makes for different numbers of customers. Students will use points on this graph to predict the location of additional points and are asked to informally make sense of the slope of a linear relationship.

 GPS Addressed (click [+] to expand)

    [-] M6A2. Students will consider relationships between varying quantities.
     

    a. Analyze and describe patterns arising from mathematical rules, tables, and graphs.
    c. Use proportions (a/b = c/d) to describe relationships and solve problems, including percent problems.
    d. Describe proportional relationships mathematically using y = kx, where k is the constant of proportionality.
    e. Graph proportional relationships in the form y = kx and describe characteristics of the graphs.
    g. Use proportional reasoning (a/b = c/d and y =kx) to solve problems

    [-] M6P1. Students will solve problems (using appropriate technology).
      a. Build new mathematical knowledge through problem solving.
    b. Solve problems that arise in mathematics and in other contexts.
    [-] M6P3. Students will communicate mathematically.
      a. Organize and consolidate their mathematical thinking through communication.
    b. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.
    c. Analyze and evaluate the mathematical thinking and strategies of others.
    [-] M6P4. Students will make connections among mathematical ideas and to other disciplines.
      a. Recognize and use connections among mathematical ideas.
    b. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.
    [-] M6P5. Students will represent mathematics in multiple ways.
      a. Create and use representations to organize, record, communicate mathematical ideas.
    b. Select, apply, and translate among mathematical representations to solve problems.

 Video (duration: 19:56)

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Use these questions to guide your thinking about some of the important teacher ideas in the lesson featured in the video clip.

  1. What is the teacher's role in encouraging student communication of mathematical ideas?
  2. How is the teacher gauging students’ current understandings and building from those understandings?
  3. In what ways does the concept of slope appear in this lesson?
  4. Consider the GPS standards listed with this video. How does the lesson featured in this video address each of these?
  5. What makes this lesson different from lessons you have taught on this topic? What is similar between this lesson and lessons you have taught?

 Classroom Materials / Lesson Outlines