Lesson 1

Relationships of Angles

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 ( $180^\circ$), and “all the way around” angles ($360^\circ$), 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.

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 $180^\circ$ and $360^\circ$ 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.

Let’s examine some special angles.

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.

I can find unknown angle measures by reasoning about adjacent angles with known measures.
I can recognize when an angle measures $90^\circ$, $180^\circ$, or $360^\circ$.

Building On

Addressing

7.G.A
7.G.B

Building Towards

adjacent angles

Adjacent angles share a side and a vertex.

In this diagram, angle $ABC$ is adjacent to angle $DBC$.
right angle

A right angle is half of a straight angle. It measures 90 degrees.
straight angle

A straight angle is an angle that forms a straight line. It measures 180 degrees.