##
* *Reflection: Gradual Release
Introducing Angles - Section 1: Concept Development

As I was reading the section that I was going to have students read, I was monitoring my thoughts in order to distill what things students would have to make sense of in order to fully understand the reading. Then I created a handout with questions that would facilitate this process. I was really pleased with how this simple supplement enhanced the reading experience and helped students to get a lot more out of it than they would have just reading on their own.

See the following video for a student work sample that typifies what the students and I got out of this exercise.

*Gradual Release: Helping students to read for understanding*

# Introducing Angles

Lesson 7 of 14

## Objective: SWBAT define angles and identify their parts; SWBAT create and interpret notation and diagrams involving angles; SWBAT identify real-world examples of angles and angular measures

#### Concept Development

*30 min*

In this section, we develop some pretty basic, but important, knowledge related to angles. The medium for this section is the Introducing Angles PowerPoint slideshow. The style of the PowerPoint is to not explicitly call out the concepts and relationships, but rather to provide examples that students can use to make inferences. So I don't say much as I'm going through the slides. Instead, I show the cases, and then focus my energy on stirring up a good classroom dialogue. I focus on developing students' ability to speak articulately using complete sentences, conveying complete thoughts, and using academic vocabulary where appropriate.

So for example, when asked to share their conjecture about the meaning of the arc symbols on the angles in the slides, a student might say, "it shows that they're congruent". I would help this student to revise their statement to something more like "I infer that placing matching arc symbols on two angles indicates that those angles are congruent."

Throughout the PowerPoint presentation, I also pause frequently to check for understanding using student whiteboards. For example, after the slide on complementary angles. I might ask the students to draw a diagram that shows complementary angles. Or I might give them an angle measure, and ask them to indicate the measure of its complement.

#### Resources

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#### Investigating Real Angles

*30 min*

For this section, we head to the computer lab to complete the Real Angles activity. In part 1, I have students investigate one of the most widely used forms of angular measurement: Latitude and Longitude.

Next, students create a PowerPoint slideshow that illustrates the terminology from this lesson using real-world images.

#### Resources

*expand content*

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- UNIT 1: Community Building, Norms, and Expectations
- UNIT 2: Geometry Foundations
- UNIT 3: Developing Logic and Proof
- UNIT 4: Defining Transformations
- UNIT 5: Quadrilaterals
- UNIT 6: Similarity
- UNIT 7: Right Triangles and Trigonometry
- UNIT 8: Circles
- UNIT 9: Analytic Geometry
- UNIT 10: Areas of Plane Figures
- UNIT 11: Measurement and Dimension
- UNIT 12: Unit Circle Trigonmetry
- UNIT 13: Extras

- LESSON 1: Origins of the Geometric Universe
- LESSON 2: Line Segments
- LESSON 3: Distances in the Coordinate Plane
- LESSON 4: Exploring Midpoint Quadrilaterals
- LESSON 5: Investigating Points, Segments, Rays, and Lines
- LESSON 6: Formative Assessment Day 1
- LESSON 7: Introducing Angles
- LESSON 8: Angle Measurements
- LESSON 9: Basic Constructions
- LESSON 10: Measuring to find Perimeter and Area
- LESSON 11: Finding Perimeter and Area in the Coordinate Plane
- LESSON 12: Geometry Foundations Summative Assessment Practice Day 1 of 2
- LESSON 13: Geometry Foundations Summative Assessment Practice Day 2 of 2
- LESSON 14: Introduction to Transformations