In this activity, students use their knowledge of , , and , and paper cutouts of some acute angles to determine the measurements of those angles. Students then use those measurements to compose and find the measurements of greater angles.

No explicit directions for finding the angles are given, so students have an opportunity make sense of the problem and use what they know about the additivity of angles to find the angle measures (MP7). If requested, give students access to rectangular sheets of paper, the square corners of which could be torn off.

This activity uses MLR5 Co-craft Questions. Advances: reading, writing.

• Invite students to share their responses and reasoning for the second question. Display the angles.
• For each angle in the second problem, record the different compositions of angles students use to find its measurement. For example:
  • To compose the angle in the first part of the problem, students may use Angles P, R, and S, or they may use 3 copies of P.
  • To find the angle in the third part of the problem, students may use 3 copies of Angle S, or they may draw a line to separate 180 of the angle and fit Angle P in the remaining space.

In this activity, students find the sizes of the angles created by folding paper several times, and reason about the resulting angles (MP7).

The first fold decomposes the paper into two congruent shapes, the edges of which line up exactly, and students can see how the fold splits two of the angles into equal halves. The subsequent folds decompose an angle into two equal angles, but this may not be obvious to students because the shapes of the two resulting parts are different. (The edges or creases that form the angles are of different lengths.) Students need to remember that the measure of an angle is not determined by the lengths of the segments that form it, and reason accordingly.

Some students may need support in folding paper precisely. Consider providing a larger sheet of paper or a straightedge to facilitate the folding.

• Invite students to share their responses and reasoning.
• “How can we tell if the first fold resulted in pairs of equal-size angles?” (The two triangles are identical and match up exactly, which means the angles in the two halves are the same.)
• “The shapes that result from the second and third folds are not the same. Do those folds produce equal-size angles as well?” (Yes. The edges of the resulting angles match up exactly and meet at the same starting point, so the angles are the same size.)
• “Which angle is greater, B or E?” (They are the same, both are . Angle B is half of 90. Angle E is twice .)