Unit 8, Lesson 10
Ways to Find Angle Measurements (Optional)
Grade 4
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This Warm-up encourages students to look for and make use of structure in an image to identify the lines of symmetry it has (MP7). Students could try to find all the segments or angles that are the same size as a way to identify lines of symmetry, but keeping track of all the pieces can be rather impractical. Instead, students could pay attention to the composition of the image— a five-sided figure on the outside and a five-point star on the inside, where all of the five parts are the same—and use that insight to determine the number of lines of symmetry.
How many lines of symmetry do you see? How do you see them?
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This activity serves several goals. Students continue to practice visualizing and drawing a complete shape given a line of symmetry and one half of the shape. As they do so, they practice drawing angles of certain measurements. Students also use symmetry to reason about unknown angle measurements in two-dimensional figures.
For the drawing portion of the activity, assign a different figure for each group member to start with and ask students to draw as precisely as possible (MP6). Provide access to protractors and patty paper (MP5). Most students are likely to find Andre’s figure the most challenging to draw. Differentiate the starting drawing for each student as needed.
Clare, Andre, Elena, and Noah each have a piece of paper with 1 line of symmetry. When they fold their papers along the line of symmetry, they all produce the same shape. The dashed line represents the folding line.
Draw the figure of the unfolded paper that each student had. Be as precise as possible.
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In this activity, students apply their understanding of symmetry and knowledge of angles to find angle measurements in a more complex line-symmetric figure. Students use what they know about the measurement of a straight angle and the measurement of a full rotation of a ray around a point to find the unknown angles. As needed, review the measurements of benchmark angles (
Origami is the Japanese art of folding paper.
Here is a diagram of an origami fish that has 1 line of symmetry.
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“Today we saw that lines of symmetry can be handy for finding unknown angle measurements.”
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“Here are two V-shaped figures—one has line symmetry and the other does not. In each diagram, one angle measurement is known.”
“Can you find the size of each angle marked with a question mark? Why or why not?” (Yes for the first one, but no for the second. The first one has a vertical line of symmetry, so the two unknown angles are the same size. In the second figure, the two angles are different sizes.)
“How would you find the angle measurements in the first figure?” (The two unknown angles plus
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