Students were introduced to angles in grade 4, when they drew angles, measured angles, identified angles as acute, right, or obtuse, and worked with adding and subtracting angles. Earlier in grade 7, students also touched on angles briefly in their work with scale drawings. Now they begin a more detailed study of angles.
In this lesson, students gain hands-on experience composing, decomposing, and measuring angles. They refresh their memory about the relationship between right angles, straight angles ( \(180^∘\)), and “all the way around” angles (\(360^∘\)), and they fit pattern blocks around a point to find out the angles at their vertices. They use simple equations they learned about in the previous unit to solve for angles.
Lesson overview
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1.1 Warm-up: Visualizing Angles (5 minutes)
- There is a digital applet in this activity.
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1.2 Activity: Pattern Block Angles (15 minutes)
- Includes "Are you Ready for More?" extension problem
- There is a digital applet in this activity.
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1.3 Activity: More Pattern Block Angles (10 minutes)
- There is a digital applet in this activity.
- 1.4 Optional Activity: Measuring Like This or That (10 minutes)
- Lesson Synthesis
- 1.5 Cool-down: Identical Isosceles Triangles (5 minutes)
Learning goals:
- Comprehend and use the word “degrees” (in spoken and written language) and the symbol ∘ (in written language) to refer to the amount of turn between two different directions.
- Recognize \(180^∘\) and \(360^∘\) angles, and identify when adjacent angles add up to these amounts.
- Use reasoning about adjacent angles to determine the angle measures of pattern blocks, and justify (orally) the reasoning.
Learning goals (student facing):
- Let’s examine some special angles.
Learning targets (student facing):
- I can find unknown angle measures by reasoning about adjacent angles with known measures.
- I can recognize when an angle measures \(90^∘\), \(180^∘\), or \(360^∘\).
Required materials:
- scissors
- pattern blocks
- blank paper
- straightedges
- protractors
Required preparation:
- Prepare one set of pattern blocks for each group of 3–4 students, include blocks consisting of at least 3 yellow hexagons and 6 of each of the other shapes.
Glossary:
- adjacent angles - Adjacent angles share a side and a vertex. In this diagram, angle \(ABC\) is adjacent to angle \(DBC\).
- straight angle - A straight angle is an angle that forms a straight line. It measures 180 degrees.
- right angle - A right angle is half of a straight angle. It measures 90 degrees.
- Access the complete Grade 7 glossary.
Standards:
- This lesson builds on the standards: CCSS.4.MD.C.6MS.4.MD.6MO.4.GM.B.5CCSS.4.MD.C.7MS.4.MD.7MO.4.RA.A.2
- This lesson builds towards the standards: CCSS.7.G.BMO.7.GM.BCCSS.7.G.B.5MS.7.G.5MO.7.GM.B.5 MS.7.G
IM 6–8 Math was originally developed by Open Up Resources and authored by Illustrative Mathematics, and is copyright 2017-2019 by Open Up Resources. It is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0). OUR's 6–8 Math Curriculum is available at https://openupresources.org/math-curriculum/.
Adaptations and updates to IM 6–8 Math are copyright 2019 by Illustrative Mathematics, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
Adaptations to add additional English language learner supports are copyright 2019 by Open Up Resources, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
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