A Measure of Slope
This lesson unit is intended to assess students’ understanding of the four quadrants of the coordinate plane, while at the same time introducing them to a mathematical understanding of slope. The task helps students to link their intuitive understandings of steepness to a more precise, calculated measure of slope.
This lesson unit is structured in the following way:
- Before the lesson, students work individually on an assessment task, Steepness, which is designed to reveal their current understandings with regard to slope. You then review their work and create questions for students to answer in order to improve their solutions.
- In the lesson, students work in small groups on a collaborative task in which they put line segments into order of slope. They then examine some sample student work and critique the measures of slope used there.
- Then students try to construct a better measure of slope.
- In a follow-up lesson, students receive your comments on the assessment task and use these to attempt the similar task, More Steepness, approaching it with insights that they have gained from the lesson.
- Each student will need a copy of the task sheets Steepness and More Steepness. Also give them a sheet of squared paper or graph paper.
- Each small group of students will need copies of the cut-up Card Set, the four pieces of sample student work and a sheet of squared paper or graph paper.
- There are projector resources for whole-class use. Have protractors, tracing paper and more graph paper available.
Time needed15 minutes before the lesson, a 90-minute lesson, and 15 minutes of the following lesson. Timings given are approximate and will depend on the needs of your class.
This lesson involves a range of mathematical practices from the standards, with emphasis on:
- MP1: Make sense of problems and persevere in solving them
- MP2: Reason abstractly and quantitatively
- MP3: Construct viable arguments and critique the reasoning of others
This lesson asks students to select and apply mathematical content from across the grades, including the content standards:
- a_measure_of_slope.pdf ( 2952.5K PDF/Acrobat 21 Mar 2014)
- l88_a_measure_of_slope_slides_beta.ppt ( 13410K MS PowerPoint 24 Mar 2014)
A draft Brief Guide for teachers and administrators (PDF) is now available, and is recommended for anybody using the MAP Classroom Challenges for the first time.
We have assigned lessons to grades based on the Common Core State Standards for Mathematical Content. During this transition period, you should use your judgement as to where they fit in your current course.
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