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Solving for Angles

Solving for Angles. Unit of Study: Angles Global Concept Guide: 2 of 2. Content Development.

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Solving for Angles

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  1. Solving for Angles Unit of Study: Angles Global Concept Guide: 2 of 2

  2. Content Development • In Day 1 of this GCG, “students investigate what happens when an angle is separated into smaller angles. They use measurements of the angles to find and make generalizations about the angle relationships. As students decompose and compose angles, they will be able to conclude that the sum of an angle is equal to the sum of the measure of its parts. (TE p. 413A)” • Students further explore angle measure as additive on Day 2. They learn they can use a bar model to solve problems involving angle measurement. “Students apply algebra skills to the concepts of this lesson. They draw a bar model that shows the relationship between the whole, the given angle measure, and the unknown angle measure. Then they can use the bar model to write an equation to help find the unknown angle measure. (TE p. 435A)” They should use a variable to stand for the unknown angle measure in the equation. ~Go Math Throughout GCG 1 and 2, it is important to reinforce angle and triangle classification, and the naming of angles

  3. Refer to the Enrich/Reteach/Intervention slide at the end of this PowerPoint for ideas to differentiate instruction throughout this GCG as needed.

  4. Essential Question: How can you use known angle measures to find unknown measures? • Engage students by giving them a piece of construction paper and a protractor. Instruct students to use their protractor to draw a large angle, ⦟ABC, that measures exactly 70˚. Students should decompose that angle by separating it into two parts, beginning by cutting from vertex B and continuing to cut between the rays. This will form two angles; the two angles do not need to be congruent and all students do not need to decompose the angle the same way. Students should use a protractor to measure one of the angles. Challenge students to find the measure of the other angle WITHOUT using a protractor . • While students are solving, monitor, looking for students with 3 different correct angle measures. Select one student who can clearly explain how they were able to solve for their missing angle measure., and then use a protractor to check their angle. Invite the other 2 selected students to share their angle measures. Ask HOT questions to facilitate a discussion to help students see that the measure of an angle is equal to the sum of its parts. Also, discuss how they can record an equation to show ⦟ABC as the sum of its parts. (See “Investigate” TE p. 431 as reference.) • Ask students, “What if you had cut ⦟ABC into three parts? Work with a partner to figure out what the measure of the three smaller angles could be without cutting the angle or using a protractor.” Facilitate whole group discussion on various different ways partners decided to decompose the angle. • Show students #4 SE p. 433. Ask students what the total measure of the three angles will be and how they know. Students should then use a protractor to find the measure of the angles and record the sum of the angles as an equation. • Students should then apply their understanding that angle measures are additive to complete Lesson 11.4 problems referenced in the GCG.. • By the end of Day 1, students should demonstrate understanding that angle measure is additive. • Evidence of Learning: In journal, write a sentence that compares the measure of an angle to the sum of its parts. (See #3 TE p. 432 for possible response) Day 1

  5. A Day 2 Set the stage for students by reading the Window Pane scenario. Students should work with a partner to create a bar model and write a matching equation. Look for different possible equations, and give students the opportunity to justify their equations. Show students the possible equations from Window Pane, and facilitate a discussion as to whether each equation could be used and why. B • EQ: What strategies can you use to solve angle measurement problems? • Engage : Show students figure A and B from “Window Pane” without displaying the possible equations. • Students should solve #8 from Lesson 11.4 SE p. 434, buy creating a bar model and writing an equation prior to solving. Ask questions to facilitate a whole group discussion to ensure students realize that the sum of the angles must be 180˚, because it is a straight angle. • Students should continue practicing with Lesson 11.5 angle problems referenced in the GCG. • By the end of Day 2, students should be able to apply their understanding of benchmark angles and the additive property of angles to solve for missing angle measures. • Evidence of Learning: Pentagon Problem

  6. Enrich/Reteach/Intervention • Reteach • Go Math Reteach Book p. R86, R87 • Core • Cameron’s Problem- students make conjectures about the relationship between angle measures • Birthday Cake- unknown angle measure performance task • Fruit Picker – students use additive property of angles to play this online game • Enrich • Degrees of Separation (E86), Unknown Measures (E87) • Angles in a Circle- unknown angles in a circle performance task • Fruit Picker – students use additive property of angles to play this online game

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