The Arizona STEM Acceleration Project

Trigonometry with Contractors

The Use of Trigonometry for Contractors

A 10-11 grade STEM lesson

Author: Karen Larsen

Date: 01/04/2023

Notes for teachers

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• The original for this lesson takes two 50-minute class periods and involves a local contractor as a presentation for the first class period. It can be modified to a single class period with a brief overview of contractors if needed.

• Groups were used originally for less materials.

• A module on trigonometry and special right triangles should be taught sometime in the past month before this lesson.

List of Materials

• Medical gloves
• Sharpies
• A board or clipboard or flat item for each class.
• At least 5 books of the same type for each group. these will be used for stacking and changing the angle of the board.
• Ruler or tape measurer.
• A smooth item such as a phone or block.

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Standards

Standards for Geometry

• G.SRT.6 Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.

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• G.SRT.7 Explain and use the relationship between the sine and cosine of complementary angles.

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Standards

Standards for Mathematical Practice

• MP.5 Use appropriate tools strategically.

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• MP.7 Look for and make use of structure.

Objectives:

• Allow students to apply trigonometric ratios to a real world situation.

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• Introduce students to possible STEM career paths that are local and and available to them

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• Give students more confidence in their mathematical ability by use of technological and physical tools.

Agenda (1-2 class periods)

Day 1: (50 min) A local contractor that many of the students know will come in and present how trigonometry is used in his work. He will be showing them the hand rule and showing them the use of special right triangles on specific projects he has done.

Day 2:

• (2-3 min)The students will split into groups.
• (10 min) The students will study a little about snow load code for roofs in Arizona at the following website. https://myroofhub.com/roof-pitch/ (one computer to a group).
• (25 minutes) The students will use books and clipboards to examine the possible pitch angles that are possible and how large a roofs frame must be.
• (5-10 minutes)Write a small paragraph about what sort of roof they would build on their own home.

Intro

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Have you ever sat in a math class and wondered if anyone uses this math in real life? Much of the math you are learning in the trigonometry module is how people make a living. Here to explain to you about how he uses math in his Career is Alonzo Mclaws. He owns his own contracting business here in Joseph City and employs more than 20 people on his crews. He doesn’t consider himself a mathematician and wants you to understand how you can have a stable STEM career without being a genius.

Trigonometry in Your Palm Activity Day 1 Instructions

• Students can do this individually or in groups.

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Step 1: Have students put a glove on their non-writing hand.

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Step 2: Have them spread their fingers so that the pinky is pointing straight up and the the thumb roughly makes a 90 degree angle pointing to the right.

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Step 3: have them draw an x axis up their pinky and y axis on the thumb them connect them on the palm or back of the hand. That point will be your origin.

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Step 4: Draw a line up each finger and label the pointer 30 degrees, the middles finger 45 degrees, and 60 degrees on the ring finger.

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Step 5: Explain how this can be used as good estimation of the basic trigonometric angles at any time.

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• This website has ideas for questions you might ask for testing the concept.

https://geometrycoach.com/the-unit-circle-hand-trick/

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Credit for the Picture:GeometryCoach.com

Building a Roof Activity Day 2 Instructions

• Students should do this in groups to encourage brainstorming.

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Step 1: the students will split into groups of about 3 or 4.

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Step 2 : The students will study a little about snow load code for roofs in Arizona at the following website. https://myroofhub.com/roof-pitch/ (one computer to a group).

Step 3: The students will use books and clipboards to examine the pitch angles that are possible and how large a roof’s frame must be and discuss lengths of roof and general truss and pros and cons of steeper roofs vs. less sloped roofs. Remember for calculation the kids will need to know height and distance from clipboard to books. (In my class we used wood and saw horses as we were building a project)

Step 4: The students will write a small paragraph about what sort of roof they would build on their own home.

• The picture to the right isn’t exactly what we are looking at but shows an idea of the book stacking.

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Assessment

Formative: The hands-on activity is to go along with previously learned concepts and have trigonometry questions embedded in the recording sheets that can be used to decide if the concept is being grasped.

Summative: A general module test. I use the McGraw- Hill Reveal Geometry Exams and then modify them to my needs. You could also use the written paragraph as an assessment.

Differentiation

• Rather than having students figure out the exact angles just talk about if it looks steeper or less steep than the last angle. Have them sort which one seemed the steepest and relate this analysis to if the cell phone or object you were using slid off of the board or stayed.
• Another great hands on idea is having them go to the school gym and walk on the inclined treadmill and change the slope. Talk about if it seems to take more energy to stay on the treadmill when it is steeper and relate that back to the roof with snow.

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Remediation

Extension/Enrichment

• Build a structure. My students ended up designing and building a small shed for our agriculture department. They had to find the pitch of the roof and then actually decide together as a class which design was best. We contacted suppliers and got quotes and had the materials delivered and worked with the agriculture clubs and wood working class to build the shed.

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Works Cited

M. (2019, June 30). The Unit Circle - Hand Trick. GeometryCoach.com. https://geometrycoach.com/the-unit-circle-hand-trick/

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