Point, Point, Slope

Boost your students’ facility with calculating slope through this open-middle challenge:

Challenges

1. Use four different digits (from 2-9) to create two points which determine a line with the greatest possible slope.
2. Use four different digits (from 2-9) to create two points which determine a line with the least possible slope.
3. Use four different digits (from 2-9) to create two points which determine a line with a slope as close to zero as possible.

Lesson Notes

Display the image with a projector. To help students think more flexibly, encourage them to create and use paper number tiles (2-9) as they explore.

When students think they’ve found the answer to one of the challenges, ask them to describe their approach and justify their reasoning. When they’re ready, encourage them to tackle the next challenge (or to create their own remix of the task).

I’ve excluded 0 and 1 from the list of available digits to increase the level of difficulty for the challenges. Add them back in, or further reduce the pool of digits, to adjust the level of difficulty for your students.

Note: If these lesson notes sound familiar, it’s because I’ve more or less stolen them from Two Fractions, another task I created with an open middle.

Extensions

1. How many different pairs of points can you create (using four different digits, from 2-9) with the same slope?
2. Use six different digits (from 0-9) to create three points which lie on the same line.
3. Is it possible to create two points which determine a line with slope zero? Undefined slope? Explain.

Resources

• Image (with directions)
• Image (without directions)
• Desmos graph (may support exploration, visualization)

Standards

• CCSS 8.EE.B
  Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

More Lessons

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