Lesson 13

The purpose of this lesson is for students to find unknown angle measurements by composing or decomposing known measurements, and to see that an angle is not determined by the length of the segments that form it.

In this lesson, students use tactile tools to find angle measurements and observe more clearly that angles are additive. They compose and decompose angles by arranging paper cutouts, by folding paper or tracing, and by drawing diagrams. Students arrange smaller angles whose sizes are unknown into larger angles with familiar sizes and features (\(90^\circ\), \(180^\circ\), and \(360^\circ\)). Once the measurement of an angle is known, they use it to find those of other angles. For example, if two copies of angle \(x\) form a right angle, angle \(x\) must be \(45^\circ\). If another angle, \(z\), can be decomposed into three of these \(45^\circ\) angles, then \(z\) must be \(135^\circ\).

Encourage students to continue to collect, define, and illustrate new terms to support communication and reasoning at the end of each lesson.

• Create 4 copies of each angle (\(p\), \(q\), \(r\), and \(s\)) from the blackline master for each group of 2–4 students.
• Cut out the angles in advance, or prepare scissors and extra time for students to cut out the angles.
• If using patty paper instead of cutouts of the angles, each student needs 1–2 sheets of patty paper.

The work of finding angle measurements in this lesson offered opportunities to reason about equal groups. Did you hear students use this type of reasoning? What were some other ways students reasoned about the angle sizes?