How high can ladders safely reach? Safety experts recommend placing a ladder one foot away from a building for every four feet of height. This ratio keeps everyone from homeowners to fire-fighters safe, but it also limits how high they can reach.
Students use the Pythagorean Theorem to determine the maximum height ladders can safely reach and discuss the implications for fire safety and building construction.
Students will
Use Pythagorean Theorem to solve real-world problems
Model real-world scenarios geometrically
Before you begin
Students will need to be fluent in ratio language.
How hard is it to steal second base in baseball? Students use the Pythagorean Theorem and proportions to determine whether a runner will successfully beat the catcher's throw.
Topic:
Geometry (G), Ratios and Proportional Relationships (RP)
When you buy a bigger TV, how much more do you really get? Students use the Pythagorean Theorem and proportional reasoning to investigate the relationship between the diagonal length, aspect ratio, and screen area of a TV.
Topic:
Geometry (G), Similarity, Right Triangles, and Trigonometry (SRT)
How accurate are police speed guns? Students use rates and the Pythagorean Theorem to examine the accuracy of LiDAR guns used to catch speeding drivers.
Topic:
Expressions and Equations (EE), Geometry (G), Ratios and Proportional Relationships (RP)
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Mathalicious lessons provide teachers with an opportunity to teach standards-based math through real-world topics that students care about.
How have video game consoles changed over time? Students create exponential models to predict the speed of video game processors over time, compare their predictions to observed speeds, and consider the consequences as digital simulations become increasingly lifelike.
Topic:
Building Functions (BF), Interpreting Categorical and Quantitative Data (ID), Interpreting Functions (IF), Linear, Quadratic, and Exponential Models (LE), Seeing Structure in Expressions (SSE)