Session 1: Angle Basics Worksheet

Name: ____________________________ Date: ____________________

A. Angle Vocabulary

1. Vertex: the ____________________________
   
   
   
2. Angle: the figure formed by ____________________________ and ____________________________ with a common endpoint.
   
   
   
   
   
   

B. Classifying Angles

Define each angle type in your own words. (Use the Hint Box on page 2 if needed.)

• Acute angle (less than 90°): ____________________________
  
  
  
• Right angle (exactly 90°): ____________________________
  
  
  
• Obtuse angle (between 90° and 180°): ____________________________
  
  
  
• Straight angle (exactly 180°): ____________________________
  
  
  
• Reflex angle (between 180° and 360°): ____________________________
  
  
  
  
  
  

C. Measuring Angles

Use your protractor to measure each angle shown. Then record its measure and classify its type.

1. Angle 1 diagram here
   
   Measurement: __________° Type: ____________________
   
   
   
   
   
   

2. Angle 2 diagram here
   
   Measurement: __________° Type: ____________________
   
   
   
   
   
   

3. Angle 3 diagram here
   
   Measurement: __________° Type: ____________________
   
   
   
   
   
   

D. Real-World Angle Investigation

Find three objects in the classroom that form an angle. For each object:

1. Object: ____________________________
   
   Sketch the angle:
   
   
   
   Measurement: __________° Type: ____________________
   
   
   
   
   
   
   

2. Object: ____________________________
   
   Sketch the angle:
   
   
   
   Measurement: __________° Type: ____________________
   
   
   
   
   
   
   

3. Object: ____________________________
   
   Sketch the angle:
   
   
   
   Measurement: __________° Type: ____________________
   
   
   
   
   
   
   

Hint Box & Definitions

How to Measure an Angle:

1. Place the protractor’s center point on the vertex.
   
2. Align one side of the angle with the zero line of the protractor.
   
3. Read the number on the protractor scale where the other side crosses.
   
   

Angle Types at a Glance:

• Acute: less than 90°
  
• Right: exactly 90°
  
• Obtuse: between 90° and 180°
  
• Straight: exactly 180°
  
• Reflex: between 180° and 360°
  
  

Key Terms:

• Vertex: Point where two rays meet.
  
• Ray (Side): One of the two lines that form an angle.
  
• Protractor: Tool for measuring angles in degrees.

Session 1: Angle Stations

In this activity, students rotate through three hands-on stations to practice identifying, measuring, and classifying angles. Students work in groups of 3, assigning roles at each station:

• Timer: Keeps track of the 15-minute rotation.
• Recorder: Writes down measurements, classifications, and observations.
• Presenter: Shares the group’s work at the end of each station.

Total time: 3 stations × 15 minutes = 45 minutes, plus 5 minutes for transitions and 10 minutes for debrief.

Station 1: Angle Classification Puzzle (15 minutes)

Materials:

• Printed puzzle cards with angle diagrams and type labels (acute, right, obtuse, straight, reflex)
• Blank sorting mats labeled with each angle type

Tasks:

1. Spread out all puzzle cards face down and pick one card at a time.
2. Measure the angle on each card (using quick sketches or protractors).
3. Place the card on the correct sorting mat by angle type.
4. Once sorted, glue the cards in order from smallest to largest angle.

Roles:

• Timer: Signals halfway (7:30) and end of station.
• Recorder: Notes any tricky angles and how the group decided classification.
• Presenter: Summarizes the most challenging angle and the sorting strategy.

Follow-up prompt for Presenter:

Station 2: Digital Angle Tool Practice (15 minutes)

Materials:

• Devices with Digital Angle Tool
• Station worksheet for recording measures and types

Tasks:

1. Use the digital protractor to measure five on-screen angle diagrams.
2. Record each measurement and classify its type.
3. For two angles, adjust one ray and predict how the measurement and type will change—then test it.

Roles:

• Timer: Keeps track of time and reminds when 5 minutes remain.
• Recorder: Logs original, predicted, and actual measurements.
• Presenter: Demonstrates one “before and after” adjustment to the class.

Prediction & Test space:

Station 3: Real-World Angle Photo Hunt (15 minutes)

Materials:

• Classroom or hallway photo cards showing objects (door frames, window corners, book edges)
• Clipboards, protractors, and angle-type reference chart

Tasks:

1. In the room or via photo cards, identify five real-world angles.
2. Sketch each angle on your station sheet.
3. Measure with a Protractor and label each with its type.

Roles:

• Timer: Ensures all five angles are recorded before time is up.
• Recorder: Draws quick sketches and records measurements/types.
• Presenter: Chooses one object and explains why its angle matters in the real world.

Sketch & Measurement space:

Debrief (10 minutes)

1. Each group’s Presenters share one highlight from each station.
2. Class discussion: How do measurements and classifications help us in everyday tasks?
3. Exit question: Which station helped you most—and why?

IEP Supports:

• Provide printed role cards and visual checklists at each station.
• Allow extended time or a scribe for Recorder as needed.
• Offer sentence starters for Presenter (e.g., “Our most challenging angle was… because…”).

Angle Bingo

Objective: Reinforce angle vocabulary, measurement skills, and classification in a fun, collaborative game.
Grade: 10th
Duration: 20–30 minutes
MTSS Tier: Tier 1 (All students, with IEP supports)

Materials

• Bingo boards (5×5 grids) pre-filled with a mix of:
  • Angle types (acute, right, obtuse, straight, reflex)
  • Degree measures (30°, 45°, 60°, 90°, 120°, 135°, 150°, 180°, 210°, 270°)
  • Definition phrases (e.g., “an angle less than 90°”)
  • Key vocabulary (vertex, ray, protractor, measure with protractor)
• Calling cards with the same 25 items (shuffle and draw)
• Markers or chips for covering squares
• Prize tokens (optional)

Setup

1. Create or print one Bingo board per student (see template below).
2. Provide each student with 20–25 markers.
3. Shuffle the calling cards and place them face down.
4. Explain that the first student to mark five in a row (horizontally, vertically, or diagonally) shouts “Bingo!” and wins that round.

How to Play

1. The teacher (Caller) draws one calling card and reads it aloud, for example:
   • “45°”
   • “An angle between 180° and 360°”
   • “Obtuse angle”
2. Students look for the matching term on their boards. If they have it, they place a marker on that square.
3. Continue drawing and calling cards until a student covers five squares in a row.
4. The first student to call “Bingo!” must read back the five terms they covered.
5. Check their board against the called list—if correct, award them a token and clear all boards for the next round.

Sample Calling List

• acute angle
  - right angle
  - obtuse angle
  - straight angle
  - reflex angle
  - an angle less than 90°
  - an angle exactly 90°
  - an angle between 90° and 180°
  - an angle exactly 180°
  - an angle between 180° and 360°
  - 30°
  - 45°
  - 60°
  - 90°
  - 120°
  - 135°
  - 150°
  - 180°
  - 210°
  - 270°
  - vertex
  - ray
  - protractor
  - measure with protractor
  

Bingo Board Template (Example)

Create additional boards by shuffling the 24 items (center is FREE).

IEP & Accessibility Supports

• Visual aids: Include icons next to terms (e.g., a small right-angle square).
• Reading support: Provide CALLING CARDS with both text and picture cues.
• Extended time: Allow students extra processing time to locate squares.
• Peer helpers: Pair students so one can assist with scanning the board.
• Choice of response: Permit students to point or place a token if writing is a challenge.

Variations & Extensions

• Speed Round: First to cover four corners wins.
• Definition-Only Call: Read only definitions—no measures or types.
• Student Caller: Rotate the Caller role among students for practice reading angle vocabulary.
• Math Discussion: After each Bingo, ask the winner to share a real-world example of one covered angle type.

Enjoy practicing angles in a competitive, supportive classroom challenge!

Session 1 Answer Key

This key provides correct answers, explanations, and scoring notes for the Session 1 Quiz.

Question 1 (Multiple Choice)

Prompt: Which of the following best describes an angle?

A. A figure formed by two rays with a common endpoint
B. A line segment with two endpoints
C. A three-dimensional shape
D. A point in space

Correct Answer: A. A figure formed by two rays with a common endpoint

Explanation: An angle is defined as the figure formed by two rays (sides) that share a common endpoint (vertex). Options B, C, and D describe other geometric objects.

Scoring: 1 point for correct selection; 0 points for any other choice.

Question 2 (Open Response)

Prompt: In your own words, define an acute angle and give its degree range.

Model Answer:
An acute angle is an angle whose measure is greater than 0° and less than 90° (i.e., between 0° and 90°).

Key Elements for Full Credit (2 points):

• Definition: States it is less than 90°
• Degree range: correctly identifies “between 0° and 90°” or “less than 90°”

Partial Credit (1 point):

• Correct definition but missing the explicit range (e.g., “an angle less than 90°” without stating the lower bound)
• Correct range but incomplete definition language

No Credit (0 points):

• Incorrect definition (e.g., describes obtuse or right angles)
• No mention of degree range

Question 3 (Multiple Choice)

Prompt: Which of the following angle measures represents an obtuse angle?

A. 45°
B. 90°
C. 120°
D. 180°

Correct Answer: C. 120°

Explanation: Obtuse angles measure between 90° and 180°. 120° falls in this range. 45° is acute, 90° is right, and 180° is straight.

Scoring: 1 point for selecting 120°; 0 points otherwise.

Question 4 (Open Response)

Prompt: List the steps for measuring an angle using a protractor.

Model Steps (3–4 points total):

1. Place the protractor’s center (origin) on the angle’s vertex.
2. Align one ray of the angle with the protractor’s zero line (baseline).
3. Read the measurement on the protractor where the other ray crosses the numbered scale.
4. Record the degree measure and classify the angle if requested.

Scoring Rubric:

• 4 points: All four steps correctly stated in logical order.
• 3 points: Three of four steps correctly stated.
• 2 points: Two clear, correct steps.
• 1 point: One correct step or a partially correct description.
• 0 points: No accurate steps provided.

Question 5 (Multiple Choice)

Prompt: An angle measures exactly 180°. How is this angle classified?

A. Acute
B. Right
C. Straight
D. Reflex

Correct Answer: C. Straight

Explanation: A straight angle measures exactly 180°. Reflex angles measure more than 180° up to 360°.

Scoring: 1 point for “Straight”; 0 points otherwise.

Question 6 (Likert Scale)

Prompt: How confident are you in your ability to classify angles correctly?

1 – Not confident at all
2 – Slightly confident
3 – Moderately confident
4 – Very confident
5 – Extremely confident

Correct Answer: No single correct answer.
Purpose: A self‐reflection item to gauge student confidence and inform instructional adjustments.

Usage Notes:

• Responses can guide targeted support in subsequent sessions.
• Look for students selecting 1 or 2 to offer additional scaffolding or peer support.

End of Answer Key for Session 1 Quiz.

Session 2: Angle Relationships Worksheet

Name: ____________________________ Date: ____________________

A. Vocabulary

1. Complementary angles: two angles whose measures sum to _______________.
   
   
   
   
   
   

2. Supplementary angles: two angles whose measures sum to _______________.
   
   
   
   
   
   

3. Vertical angles are _________________________________________________________.
   
   
   
   
   
   

4. Adjacent angles are ________________________________________________________.
   
   
   
   
   
   

B. Identifying Relationships

For each diagram, write the type of angle pair (complementary, supplementary, vertical, or adjacent).

1. [Diagram: two angles sharing a vertex that form a right angle]
   Relationship: ____________________________
   
   
   

2. [Diagram: two angles forming a straight line]
   Relationship: ____________________________
   
   
   

3. [Diagram: two angles opposite each other at the intersection of lines]
   Relationship: ____________________________
   
   
   

4. [Diagram: two angles sharing one side but not overlapping]
   Relationship: ____________________________
   
   
   

C. Solving for Unknown Angles

Show your work: write an equation using the given relationship, then solve for the variable.

1. ∠A and x are complementary. ∠A = 35°.
   Equation: ___________________________________
   Solution: x = ______°
   
   
   
   
   
   

2. ∠B and x are supplementary. ∠B = 120°.
   Equation: ___________________________________
   Solution: x = ______°
   
   
   
   
   
   

3. In intersecting lines, ∠1 = (3x – 15)° is vertical to ∠2 = (x + 45)°.
   Equation: ___________________________________
   Solution: x = ________
   
   
   
   
   
   
   
   
   
   
   

4. ∠3 and x are adjacent and form a right angle. ∠3 = (2x + 10)°.
   Equation: ___________________________________
   Solution: x = ________
   
   
   
   
   
   
   
   
   
   
   

D. Real-World Application

Find or imagine a real-world example that shows complementary or supplementary angles.

1. Object or scenario: ____________________________
   
   
   

2. Sketch the angles below:
   
   
   
   
   
   
   
   
   
   
   

3. Describe the relationship and measures:

   • Relationship type: _______________
   • Approximate measures: Angle A = ____°, Angle B = ____°
   • Check: ____° + ____° = _______°
   • Why this matters: ________________________________________________________
     
     
     
     
     
     

Hint Box & Formulas

• Complementary: m∠1 + m∠2 = 90°
• Supplementary: m∠1 + m∠2 = 180°
• Vertical: m∠1 = m∠2 (they are opposite and equal)
• Adjacent: share a common side and vertex; interior regions do not overlap

Use these equations to set up your work in Section C.

Back to Lesson Plan | Use the Digital Angle Tool for diagrams and practice measuring online.