Find Angle Measurements
10 min
Narrative
This Warm-up prompts students to visualize the idea of arranging angles around a point and adding their measurements as more pieces are added. The angles are familiar angles: 90∘, 180∘, and 270∘. Students previously arrived at these benchmarks by decomposing a full turn or 360∘. Here, they compose a full turn from 90∘ angles.
The work here familiarizes students with the context and mathematics that might be involved later in the lesson. In the subsequent activities, students will compose and decompose paper cutouts of angles to determine angle measurements.
Launch
- Groups of 2
- Display the image.
- “What do you notice? What do you wonder?”
- 1 minute: quiet think time
Teacher Instructions
- “Discuss your thinking with your partner.”
- 1 minute: partner discussion
- Share and record responses.
Student Task
What do you notice? What do you wonder?
Sample Response
Students may notice:
- The rectangle looks like a piece of paper with 3 corners torn out.
- There are 3 angles.
- The torn corner pieces fit in each angle.
- In the last two angles, the straight edge of the pieces line up with one another and the pieces share the same corner point.
Students may wonder:
- Why is the last corner not torn out?
- Would the untorn corner fit in the right angle in the bottom right?
- Are all the corner pieces the same?
- What are the angle measurements?
Activity Synthesis (Teacher Notes)
- “What do you think is the measurement of each angle?” (They look like 90∘, 180∘, and 270∘ angles.)
- “How do you know?” (If the paper is a rectangle, then the corner pieces are right angles or 90∘ each. Two of the corner pieces would be 90+90. Three pieces would be 90+90+90.)
- “What angle would we get if we add the last corner piece?” (360∘)
Standards
- 4.MD.7·Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.
- 4.MD.C.7·Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.
25 min
10 min
Knowledge Components
All skills for this lesson
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Find Angle Measurements
10 min
Narrative
This Warm-up prompts students to visualize the idea of arranging angles around a point and adding their measurements as more pieces are added. The angles are familiar angles: 90∘, 180∘, and 270∘. Students previously arrived at these benchmarks by decomposing a full turn or 360∘. Here, they compose a full turn from 90∘ angles.
The work here familiarizes students with the context and mathematics that might be involved later in the lesson. In the subsequent activities, students will compose and decompose paper cutouts of angles to determine angle measurements.
Launch
- Groups of 2
- Display the image.
- “What do you notice? What do you wonder?”
- 1 minute: quiet think time
Teacher Instructions
- “Discuss your thinking with your partner.”
- 1 minute: partner discussion
- Share and record responses.
Student Task
What do you notice? What do you wonder?
Sample Response
Students may notice:
- The rectangle looks like a piece of paper with 3 corners torn out.
- There are 3 angles.
- The torn corner pieces fit in each angle.
- In the last two angles, the straight edge of the pieces line up with one another and the pieces share the same corner point.
Students may wonder:
- Why is the last corner not torn out?
- Would the untorn corner fit in the right angle in the bottom right?
- Are all the corner pieces the same?
- What are the angle measurements?
Activity Synthesis (Teacher Notes)
- “What do you think is the measurement of each angle?” (They look like 90∘, 180∘, and 270∘ angles.)
- “How do you know?” (If the paper is a rectangle, then the corner pieces are right angles or 90∘ each. Two of the corner pieces would be 90+90. Three pieces would be 90+90+90.)
- “What angle would we get if we add the last corner piece?” (360∘)
Standards
- 4.MD.7·Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.
- 4.MD.C.7·Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.