##
* *Reflection: Connection to Prior Knowledge
Angle Measurements - Section 1: Concept Development

In the past, I had assumed that most, if not all, students came into a high school geometry course knowing how to use a protractor. I was surprised to find out that many of my students- even the advanced ones- did not come in knowing how to use this tool.

I found myself giving the spiel on how to use a protractor to one student students, and then another, and so on, until finally wised up to the fact that I should just train all students to use protractors before requiring them to do so on their own.

Of course there were students who did know how to use a protractor. For these students, I tried to add an extra level of sophistication to the presentation so that they could take something away from it that they didn't already know. Particularly, I introduced the notion of initial side and terminal side of an angle, terminology which students will encounter as they progress into more advanced courses.

So, to generalize, I found that today's students have not had a whole lot of experience using rulers, protractors, compasses so they need explicit training on how to use these tools correctly. Failing to incorporate this training at the beginning causes lots of wasted time and energy explaining things one-on-one that could be explained once to the whole class.

*The need for tool training*

*Connection to Prior Knowledge: The need for tool training*

# Angle Measurements

Lesson 8 of 14

## Objective: SWBAT measure angles using a protractor and create angles to specifications; SWBAT classify angles and identify complementary and supplementary angle pairs.

#### Concept Development

*10 min*

This is the first time students are using protractors in my class. So the first order of business is demonstrating how to use the protractor. First I establish some vocabulary: initial side, vertex, and terminal side.

Then I show the steps:

1. Place the "sight" of the protractor at the vertex of the angle.

2. Zero the protractor on the initial side of the angle.

3. Determine the intersection of the terminal side with the protractor's measurement scale (noting that sometimes it's necessary to extend the terminal side).

Students often ask about whether they should use the upper or lower numbers on the protractor. I answer this two ways:

1. Remember that starting from the initial side of the angle (which is determined by the measurer) you should start at zero, not 180, on the measurement scale.

2. You should know intuitively whether the angle you're measuring is acute or obtuse, so choose the reasonable one.

After this basic refresher on protractors, it's time for students to get some hands on experience.

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#### Hands On Training

*20 min*

For this section, I hand each student a protractor and the Measuring Angles resource. Students work on this independently with help from their neighbors as needed.

I walk around making sure that students are using proper notation, e.g. m∠PST=20 degrees and not just "20".

I also make sure that students are being precise with their measurements. If a student has been imprecise, I say "Show me how you measured angle ABC again...is the angle measure exactly 140 degrees, or can we be more precise?"

On the back side of the handout, I go around with my protractor measuring students angles to make sure that they have been precise. And on the last two problems, I am making sure that students have not neglected the *non-congruent *constraint.

#### Resources

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In this section, I introduce some basic anatomy concepts related to range of motion. This section gives students an opportunity to see some real-life applications of angle measures in a fun, relaxed atmosphere.

I start with some physical exercises that demonstrate the different types of joint movement.

Flexion/Extension: I model extending my forearm, then flexing it. Then I have student do it. To check for understanding, I ask the students to show me neck extension....now neck flexion.

Rotation: I demonstrate neck rotation. Then I ask students, "Are there any other joints in your body that you can rotate?"

Abduction/Adduction: I demonstrate arm abduction (toward the midline) and arm adduction (away from the midline), then ask student to demonstrate leg adduction and leg abduction.

I also show students an online animation that demonstrates these anatomical movements.

Time permitting, we might also do some basic 'Simon Says' with anatomical movements..."Simon says demonstrate hip flexion" and so forth.

Finally I introduce the concept of range of motion, using neck extension/flexion as an example. I explain that it's an important way for physical therapists and doctors, for example, to measure joint health.

Then organize students into groups of three and give each group the Cooperative Activity_Measuring ROM. I'm not prescriptive when it comes to the methods students use to measure joint angles. I want them to be creative. It's not the accuracy that is of primary importance in this exercise, but rather the awareness of the angles they are attempting to measure.

#### Resources

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#### Reflection and Discussion

*15 min*

Each student writes a reflection on what they learned in the lesson and discusses the methods they used to measure range of motion.

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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