Adjacent Angles
5 min
Teacher Prep
Setup
Narrative
The purpose of this Warm-up is for students to estimate degree measures based on angles that are familiar. In the first two rows, an angle that is close to either a right angle or a straight angle is given, and students could use this as a reference angle for the other angles in the row.
Asking students to share estimates that are too low and too high gives students a low-stakes opportunity to share a mathematical claim and the thinking behind it (MP3).
As student discuss with their partner, monitor for students who use phrases such as:
- “a little more than 90 degrees”
- “almost a straight line”
- “a little less than 360 degrees”
Launch
Display the image for all to see. Ask students to silently think of a number for the angle measure that they are sure is too low, a number that they are sure is too high, and a number that is about right, and to write these down.
Then, invite students to share their estimates and a short explanation for the reasoning behind their estimate. (Too low: 30 degrees, since that is an acute angle and this angle is obtuse. Too high: 170 degrees, since that would be almost a straight angle. About right: 115 degrees, since it’s a little more than a right angle.)
Arrange students in groups of 2. Do not supply protractors or pattern blocks; let students know that in this activity they are estimating the degree measure of each angle.
Give students 2 minutes of quiet work time followed by a partner and whole-class discussion.
Student Task
Estimate the degree measure of each indicated angle.
Sample Response
- Angle CAB measures about 90 degrees, since it looks close to a right angle.
- Angle FDE measures about 80 degrees, since it’s a little less than a right angle.
- Angle GHI measures about 95 degrees, since it's a little more than a right angle.
- Angle JKL measures about 180 degrees, since it looks like a straight angle.
- Angle MNO measures about 175 degrees, since it’s a little less than a straight angle.
- Angle PQR measures about 185 degrees, since it’s a little more than a straight angle.
- Angle STU measures about 270 degrees, since it looks like a right angle added to a straight angle.
Activity Synthesis (Teacher Notes)
Display the angles for all to see. For each angle, ask a few students to share their estimate and their reasoning, and record the estimates near the displayed angle. If a student is reluctant to commit to an estimate, ask for a range of values. If time allows, ask students, “Based on this discussion, does anyone want to revise their estimate?”
After sharing estimates for the angle measures, ask students what tools they might use to know for sure how many degrees an angle measurement is. (A protractor is a tool to measure angles.) Ask students how they could use a protractor to find the measure of angles like STU or VWZ when the protractors usually only go to 180. (Find the measure of the angle that is less than 180, and subtract it from 360. Draw a straight angle from one side, then measure the remaining portion and add that measure to 180 degrees.)
Standards
- 4.MD.C·Geometric measurement: understand concepts of angle and measure angles.
- 4.MD.C·Geometric measurement: understand concepts of angle and measure angles.
- 7.G.B·Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
- 7.G.B·Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
20 min
10 min
Knowledge Components
All skills for this lesson
No KCs tagged for this lesson
Adjacent Angles
5 min
Teacher Prep
Setup
Narrative
The purpose of this Warm-up is for students to estimate degree measures based on angles that are familiar. In the first two rows, an angle that is close to either a right angle or a straight angle is given, and students could use this as a reference angle for the other angles in the row.
Asking students to share estimates that are too low and too high gives students a low-stakes opportunity to share a mathematical claim and the thinking behind it (MP3).
As student discuss with their partner, monitor for students who use phrases such as:
- “a little more than 90 degrees”
- “almost a straight line”
- “a little less than 360 degrees”
Launch
Display the image for all to see. Ask students to silently think of a number for the angle measure that they are sure is too low, a number that they are sure is too high, and a number that is about right, and to write these down.
Then, invite students to share their estimates and a short explanation for the reasoning behind their estimate. (Too low: 30 degrees, since that is an acute angle and this angle is obtuse. Too high: 170 degrees, since that would be almost a straight angle. About right: 115 degrees, since it’s a little more than a right angle.)
Arrange students in groups of 2. Do not supply protractors or pattern blocks; let students know that in this activity they are estimating the degree measure of each angle.
Give students 2 minutes of quiet work time followed by a partner and whole-class discussion.
Student Task
Estimate the degree measure of each indicated angle.
Sample Response
- Angle CAB measures about 90 degrees, since it looks close to a right angle.
- Angle FDE measures about 80 degrees, since it’s a little less than a right angle.
- Angle GHI measures about 95 degrees, since it's a little more than a right angle.
- Angle JKL measures about 180 degrees, since it looks like a straight angle.
- Angle MNO measures about 175 degrees, since it’s a little less than a straight angle.
- Angle PQR measures about 185 degrees, since it’s a little more than a straight angle.
- Angle STU measures about 270 degrees, since it looks like a right angle added to a straight angle.
Activity Synthesis (Teacher Notes)
Display the angles for all to see. For each angle, ask a few students to share their estimate and their reasoning, and record the estimates near the displayed angle. If a student is reluctant to commit to an estimate, ask for a range of values. If time allows, ask students, “Based on this discussion, does anyone want to revise their estimate?”
After sharing estimates for the angle measures, ask students what tools they might use to know for sure how many degrees an angle measurement is. (A protractor is a tool to measure angles.) Ask students how they could use a protractor to find the measure of angles like STU or VWZ when the protractors usually only go to 180. (Find the measure of the angle that is less than 180, and subtract it from 360. Draw a straight angle from one side, then measure the remaining portion and add that measure to 180 degrees.)
Standards
- 4.MD.C·Geometric measurement: understand concepts of angle and measure angles.
- 4.MD.C·Geometric measurement: understand concepts of angle and measure angles.
- 7.G.B·Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
- 7.G.B·Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.