Can’t measure the height of that tree with your ruler? No problem! Let’s use ratio’s to find it’s height!
This lesson is a great modeling activity where students are able to apply ratios and proportions to real world situations. They will be using the concept illustrated above with objects they find around their school. The students will find their own height and shadow length, and use this ratio to find the heights of several tall objects. Some of these might be basketball hoops, portables, school buildings, soccer goals, railings, and even the height of their own teacher!
Standards:
6.RP.A.3 : Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
7.RP.A.2 : Recognize and represent proportional relationships between quantities.
Concepts: Ratios and Proportions, Similar Triangles
Procedures: Cross-Multiplication, Fractions, Division, One-Step Equations, Variables, Similar Triangles
Applicable Practices: #1 – Make sense of problems, #3 – Construct viable arguments and critique the reasoning of others, #4 – Model with mathematics, #5 – Use appropriate tools strategically, #6 – Attend to precision
Overview: The students will begin by measuring their own shadow and their own height. They will then have the opportunity to measure the shadows of 4 different objects outside. Using ratios, they will be able to determine the approximate height of each of the four objects. Students will also participate in a discussion concerning the differences in their answers. Some of the questions on the differences that come up might be….”Does the time of day affect the shadow length? Did you measure this object at a different time than I did? Did you measure in inches or centimeters?” These questions will create powerful discussions between the students as they journey through the application of mathematics in real-world situations.
Materials for the Teacher:
Ratios and Proportions Lesson Plan
Ratios and Proportions Worksheet
Supplementary Similar Triangles Worksheet
Created by: Rabeya Suraka, Kelsie Peterson, and Stephanie Anderson