The Arizona STEM Acceleration Project

Similarity and Laser Beams

Similarity and Laser Beams

An 8th - 10th grade STEM lesson

Susin Hall

June 17, 2024

Notes for teachers

I used this lesson for my 8th grade Geometry class.

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I only took one day for this lesson but would have preferred two days.

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We had already been covering similarity and indirect measurement in class and this was a final lesson to wrap it all up.

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Part of our class time was for the students to experiment with the laser beams and mirror reflection (easy tie to the science standard at this point)

List of Materials

• 30 Pcs Small Mirrors for Kids Unbreakable Shatterproof Mirror 6 x 4 Inches Round Corners Plastic Mirrors Square Double Sided Preschool Classroom Mirror DIY Crafts (Bright Colors) available at Amazon for $31.99
• Laser Pointers (available on Amazon)..green and red work best, purple was hard to see. Three pack is $8.99
• Targets (attached a sample of some, but really any you want will work)

Standards

Mathematics:

CCSS.MATH.CONTENT.HSG.SRT.B.5

Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

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Standards for Mathematical Practices (MP)

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*Model with mathematics.

*Use appropriate tools strategically.

*Attend to precision.

*Look for and make use of structure.

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Science and Engineering Practices (a dimension of the Arizona Science Standards)

• ask questions and define problems
• develop and use models
• plan and carry out investigations
• analyze and interpret data
• use mathematical and computational thinking
• construct explanations and design solutions

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Science:

8.P4U1.4 Develop and use mathematical models to explain wave characteristics and interactions. ● A simple wave has a repeating pattern with a specific wavelength, frequency, and amplitude. ● A sound wave needs a medium through which it is transmitted. ● When light shines on an object, it is reflected, absorbed, or transmitted through the object, depending on the object's material and the frequency (color) of light.

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Objectives:

Students will be able to

• demonstrate knowledge of similar triangles
• solve problems using proportions and set up necessary equations

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Key Vocabulary: Similarity, Indirect Measurement

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Agenda

Sample day

Bellwork (5-10 minutes)

DESMOS: Laser Challenge • Activity Builder by Desmos Classroom (technology activity)

Classwork (10-35 minutes)

Similarity and Laser Beams Activity

Closure (5 minutes) turn and talk to a neighbor; ask a question based on either what they learned during the DESMOS activity or the classwork portion.

I used the DESMOS activity over a couple of days as opening bellwork.

I only spent ONE day on the classwork. I would have liked at least one more day.

Essential Question for this portion of the unit

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How can the geometric relationships that come from proving triangles similar be applied in problem solving situations?

Hands-on Activity Instructions

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• Place students in groups of 2 (no more than 3).
• Each student picked up a target, mirror and laser pointer.
• Idea was for each group find a place to place the given target (I gave each group the same target, but might be fun to give different targets).

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• We had done a mirror activity with measuring the flagpole on our campus using mirrors. This was a chance for students to create their own problem based on what we have learned.
• This activity the students were to decide where they wanted to place their target (could be inside the classroom or right outside).
• Then they placed the mirror in a designated spot and took required measurements (see next slide).

Student sketch:

• Shows placement of mirror.
• Distance from mirror to ground below target.
• Distance from ground below to bullseye
• Height of student from ground to bottom of pointer.
• Then had to calculate where student should stand to point the laser at the mirror in order to reflect and hit the target.

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Possible

Target:

7

6

5

4

3

2

1

Assessment

• Checking if students were able to accurately set up the problem and hit the bullseye was the informal assessment.
• If I had another day, would have liked to give students the opportunity to work through some of the other students problems.
• Formal assessment

Differentiation

Delta Math: Geometry Similar Triangles skill sets

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Quizizz: Indirect Measure lessons and quizzes

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Geogebra:

Indirect Measure practice

Remediation

Extension/Enrichment

Would your Rather

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Which one doesn't belong

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Billiards

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Using same activity add it finding the angle of depression.

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