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Algebra 1 Lesson

Discovering Slope and Constant Rates of Change (The Staircase Dilemma)

Shared by A STEM Educator

8th or 9th GradeBuilding Thinking ClassroomsCCSS.MATH.CONTENT.8.EE.B.5, CCSS.MATH.CONTENT.8.EE.B.6, CCSS.MATH.CONTENT.HSF.IF.B.660 min
Learning Objective

Students will define slope as rise over run, calculate the rate of change between two points using , identify constant rates of change in tables and graphs, and interpret the real-world meaning of positive, negative, zero, and undefined slope.

Lesson Overview

Students move from intuitive comparisons of steepness using staircase ratios, through formal slope calculations from coordinates and tables, to interpreting positive/negative/undefined slopes in real-world contexts. The lesson follows Building Thinking Classrooms protocols with visibly random groups at vertical non-permanent surfaces.

Materials

  • Vertical whiteboards (VNPS) or large chart paper taped to walls
  • One dry-erase marker per group (BTC: only one marker to encourage collaboration)
  • Visibly random grouping cards or app
  • Printed or projected WODB slide (4 lines on coordinate grids)
  • Desmos Classroom activity link (teacher-projected or student devices)
  • Exit slip half-sheets (printed)
  • Homework 'Keep-It-Thinking' sheets

Scaffolded Task Progression

1Task 1
The Staircase Dilemma (Anchored Problem): Which staircase is the steepest? How can you prove it mathematically without just guessing by eye?

- Staircase A rises 4 feet over a horizontal distance of 6 feet.
- Staircase B rises 5 feet over a horizontal distance of 5 feet.
- Staircase C rises 6 feet over a horizontal distance of 8 feet.

Create a single number that rates the steepness of each staircase so that a higher number always means steeper. Show your reasoning on the whiteboard.
2Task 2
Now plot each staircase on a coordinate grid, starting each at the origin . The horizontal axis is the run (feet forward) and the vertical axis is the rise (feet up). Plot the starting point and ending point of each staircase.

For each staircase, identify the coordinates of the landing point, then confirm your steepness ratio using the coordinates.


[ Interactive graph / diagram — available in the full lesson ]

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