Looking for an engaging activity to introduce slope? In this investigation, students examine four different “staircases” of varying steepness. They will calculate the rise/run ratios of each staircase and analyze how the size of the ratio relates to how steep each staircase appears. Through this comparison, they begin to recognize that larger slopes correspond to steeper lines and smaller slopes correspond to flatter lines. This allows students to build an intuitive understanding of slope before being introduced to formal rules.
Next, students create their own lines that are intentionally steep and intentionally flat. Before calculating the slopes, they predict whether each new line will have a “big” slope or a “small” slope and justify their predictions using what they learned from the staircases. They then calculate the rise/run for their lines to check the accuracy of their predictions.
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This activity is designed to be highly student-driven and requires minimal teacher intervention. Students learn through hands-on investigation, visual reasoning, and comparison. It works well as an introductory lesson, a reinforcement activity, or a set of sub plans, since students can complete the tasks independently with clear written directions.
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