Alg2 Lesson 4T.3: Angles in the Coordinate Plane

Lesson 4T.3: Angles in the

Coordinate Plane

Obj: I can determine when two angles are coterminal.

EQ: How do I know when angles are
coterminal?

Lesson Goals:
● Creative Thinking
● Talk through controversies and conflict
● Recognize and reduce ambiguity
● Encourage thinking based on formulas and prior info
● Help explain ideas to each other
● Own your ideas and work
● Record ideas in your journal
● Answer Questions on Slides
● Follow your team roles

Roles:
Facilitator
Scribe
Resourcer
Includer

Facilitator

• Make sure that all peers are staying on task.

• Give advice or suggestions to resolve the problem.

• Be sure everyone is able to explain.

Resourcer

• Make sure peers are getting the materials needed.

• Make sure that all materials are put away neatly.

• Make sure that peers are logged in to the needed site.

• Help troubleshoot any technology difficulties that may arise.

Scribe

• Make sure peers organize their results on their own papers.

• Remind peers to use color, arrows, and other math tools to communicate your mathematics, reasons, and connections.

• Be ready to join the teacher for a huddle.

Includer

• Make sure that all peers are talking about their work.

• Helps keep peers’ voice volume low.

• Encourages everyone to ask questions.

• Communicates conflicts or questions to the teacher.

● Check off tasks & skills on calendar.

● Select skills to work on.

● Work on Deltamath.

Remember to work on the following too…

Part 1: Rotating a Crane

Handout 4T.3A: Rotating a Crane

Aspect Construction Company is
developing a multiuse building that will
have four distinct regions: a retail area, a
fitness center, a residential area, and a
parking garage. The base of the building
is a square in which each region takes up
one quarter of its footprint. The crane
used for construction is located on a
tower at the center of the main building.
The crane’s arm does not move up and
down; the materials are picked up by a
counterweight system. The arm turns with a radius of 30 meters (m) and always picks up materials from the loading dock and rotates to drop them off. An overhead view of the building follows:

The crane’s angle of rotation is in standard
position because its vertex is at the origin and
one of its rays lies along the positive x-axis. The
ray that lies along the positive x-axis is called
the initial ray. The other ray is called the terminal ray.

Drag and Drop

If you know that an angle is in
standard position, then you know the location of the ​vertex and the ​

Placeholder

ray. This means that the location of the ​

Placeholder

ray would be ​

Placeholder

to determine because the degree of rotation begins from the positive x-axis.

In a problem with multiple angles in standard position, their shared ​

Placeholder

ray might make it ​

Placeholder

to tell the angles apart.

Drag these tiles and drop them in the correct blank above

initial

terminal

hard

easy

Multiple Choice

How might we differentiate between rotating 1 radian counterclockwise and 1 radian clockwise?

• Counterclockwise is always 0 radians regardless of direction.
• Both directions can be represented as positive angles.
• Use positive for counterclockwise and negative for clockwise.
• Use negative for counterclockwise and positive for clockwise.

Compare and contrast the angles graphed in your journal.

Part 2: Creating Coterminal

Angles

Multiple Choice

How do we indicate a clockwise rotation of the crane?

• We indicate a clockwise rotation of the crane with a negative angle measure.

• We indicate a clockwise rotation of the crane with a positive angle measure.

Multiple Choice

What are coterminal angles?

• Angles that differ by integer multiples of 360 degrees.

• Angles that are complementary to each other.

• Angles that differ by 180 degrees.

• Angles that are always less than or equal to 90 degrees.

Multiple Select

Which of the following are coterminal angles to 45º?

• 225º

• -675º

• 405º

• 945º

• -135º

Handout 4T.3.B: Practice with Coterminal Angles

Random Question of the Day Time

https://wheelofnames.com/4ke-epz We’ll spin the wheel as a class and spend a minute or so
discussing our answers.