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Similar Figures / Indirect Measurement: Using Similar Triangles to Find Heights

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1 MB|14 pages
Product Description
The Mirror Lesson: This product teaches students how to use properties of similar figures, mirrors, and proportions, to determine the heights of indoor and outdoor objects via indirect measurement. It is one of several follow-on products to Ratios, Rates, and Proportions Galore! These products focus on real-world applications of ratios, rates, and proportions. They include Percent Proportions, Dimensional Analysis, Similar Figures and Indirect Measurement - The Outdoor Lesson, and will soon be expanded to include discounts and markups and more!

In this real-world application of similar figures and proportions, a simple mirror and a meter stick are the only tools you need to conduct this lesson! This product includes:

Preparing for the Mirror Lesson – Warm-up Questions: To prepare the students to take and use measurements, you will first review ratio and proportion concepts and begin to explore similarity via a series of “warm-up” questions (answer key provided). This product assumes the students have some prior knowledge of ratios and proportions, either through Ratios, Rates, and Proportions Galore! or through some other means, but also offers this review before the students dive into similarity and indirect measurement.

Preparing for the Mirror Lesson - Notes and Exploration: This pictorially illustrated, guided note-taking activity immediately follows the warm-up activity. It provides a quick and meaningful way for the teacher to review the definition of and requirements for similarity, explain the concept of indirect measurement, and then show the students how to use similarity and mirrors to indirectly calculate the heights of a variety of objects. NOTE: If you have already conducted Similar Figures and Indirect Measurement - The Outdoor Lesson, you may want to bypass the first page of this section as there is some overlap with the notes in these two products.

The Mirror Lesson: Having been thoroughly prepared, the students are now instructed to venture to various places and take measurements of the student, the student to the mirror, and the mirror to the object. The first object is designated as “The Wall in the Hall”, but the other two, which can be either indoor or outdoor objects, are deliberately left to the teacher discretion. Flagpoles, trees, the height of the school building, the height of the gymnasium, etc., are all possible objects to be measured indirectly. Students work in groups to measure the appropriate distances , draw pictures and fill in values on a pre-printed worksheet, then perform calculations to determine the approximate heights of the three objects.

The Mirror Lesson – Follow-Up Questions: Students are asked to think critically about their measurements and calculations, providing reasons why their estimated heights might be inaccurate, and analyzing the advantages and disadvantages of direct and indirect measurement. These questions provide input for the class discussion at the end of the mirror lesson activities.

The Mirror Lesson – Compilation of Class Data: As a final step in exploring the wonders of indirect measurement, each group of students writes their estimated heights in a common table which allows the class to see the numbers from all groups simultaneously. The teacher then facilitates a class discussion regarding what the height estimates are, whether they are reasonable, what could have caused inaccuracies and inconsistencies in the estimates, and what could be done differently in future such experiments.

These activities work together in a fun and meaningful way to show the value and versatility of using properties of similar figures and proportions to solve real-world problems.

Good luck in your use of The Mirror Lesson!

Related Products:

In addition to the related products described above, feel free to check out a growing number of other products that use poetry, songs, games, worksheets, and assessments to make math fun and help students to learn a variety of common core math standards.

Click here to view Algebraic Equation Products
Click here to view Divisibility Rule Products
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Click here to view Fraction Products
Click here to view Geometry Products
Click here to view Integer and Order of Operations Products
Click here to view Probability Products
Click here to view Ratio-Rate-Proportion Products
Click here to view Riddle Card Products that Help Retain Math Essentials

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Terms of Use:

Copyright © Barry Schneiderman. This product is to be used by ONE teacher (the purchaser) for his or her classes only. Any reproduction of this material is limited to the purchaser for his or her classes. Beyond this usage, it may not be reproduced, republished, or copied in any way without written permission of the publisher. It may not be distributed to other teachers, a school department, a school, or a school district. This product may not be posted on any website, including but not limited to classroom websites, school websites, or district websites, without written permission of the publisher. Failure to follow the terms of usage represents a copyright violation per the Digital Millennium Copyright Act (DMCA). To receive written permission to copy or post this product beyond the terms of use, ask Barry Schneiderman a question on Teachers Pay Teachers.
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Teaching Duration
2 days
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