The purpose of this activity is for students to use a protractor to measure angles. In previous lessons, students learned to read the measurement of an angle with a protractor already in position. Now they decide where to place the tool, how to align it with the vertex and the rays of the angle, and which set of numbers on the protractor to use.

Some of the figures in the activity explicitly show angles formed by two rays. In others, students are asked to find and measure the angles within polygons. In both cases, students may find it necessary to extend one or both rays of an angle so that it can be measured more effectively or precisely (MP6). Doing so reinforces the idea that the size of an angle is not determined by the length of the segments that frame it, but by the space between the rays that compose the angle.

Monitor for and select to share in the Activity Synthesis students with the following approaches:

• Align the rays of an angle to tick marks on the protractor and count from one ray to the other in the same way that students used the clock face to estimate angle measurement in earlier lessons.
• Don’t align either ray of an angle to or  on the protractor and instead find the difference of the numbers where the two rays land on the protractor.
• Align one ray of an angle with the  line or the  line on the protractor and always read from the scale that starts with .

The approaches are sequenced from more intuitive to more conventional to elicit the different ways students may position a protractor and use it to determine the measure of angles. In addition to how to position the tool, prompt students to explain which set of numbers to use and whether their measurements make sense. Aim to elicit both key mathematical ideas and a variety of student voices, especially students who haven’t shared recently.

• Invite previously selected students to share in the given order. Record or display their work for all to see.
• Connect students’ approaches by asking:
  • “How are the ways of measuring the same, and how are they different?” (We had to line up both rays on the protractor to measure the angles. Where we placed the protractor and how we used the numbers on it were different.)
  • “What are some benefits of aligning one ray of an angle with  on the protractor?” (The measurement can be identified right away: it’s the number where the second ray lands on the protractor. Aligning the first ray with a non-zero number means having to count or subtract two numbers before finding the measurement.)
• Connect students’ approaches to the learning goal by asking:
  • “No matter which way you choose, how can you tell if your measurement was reasonable? How can you make sure your measurements make sense?” (Compare them against a familiar angle, like . If an angle looks greater than a right angle, it can’t be less than .)

In this activity, students fold paper to form right angles and learn that intersecting lines that create 4 right angles are perpendicular lines. They then identify perpendicular segments in two-dimensional figures and explain how they know the segments are perpendicular.

To create four right angles that share the same vertex by folding generally means making two folds through the same point. The first fold, which can be done in any way (as long as it goes through point P, in this case), creates two straight angles. The second involves folding through the point again such that the edges formed by the crease of the first fold match up exactly, creating two equal halves or two angles.

While students have experience with folding paper to partition a shape or an angle, some may need support in folding precisely. Consider providing a straightedge to facilitate the folding.

This activity uses MLR2 Collect and Display. Advances: conversing, reading, writing.

• “What statement could we write to explain to another student what perpendicular lines are?” (Lines that intersect and create 4 right angles.)
• Remind students that they can use words or phrases from their personal word walls in their responses.
• Invite students to share the perpendicular lines they created by folding.
• “How can you be sure that the creases from your folding are perpendicular or created angles?” (My first fold makes two angles. My second fold splits each of those into two equal angles, so each one must be . We can measure each angle with a protractor.)
• “In the last problem, how did you know which shapes have perpendicular sides?” (By measuring the angles with a protractor, or by comparing them with a square corner.)