Unit 8, Lesson 9
Symmetry in Action (Optional)
Grade 4
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This Warm-up prompts students to carefully analyze and compare attributes of two-dimensional figures with attention to the number of sides, symmetry, and presence of parallel and perpendicular lines. In making comparisons, students have a reason to use language precisely (MP6). The activity enables the teacher to observe the attributes that students notice intuitively and hear the terminologies they feel comfortable using.
Which 3 go together?
4 shapes. A. 4 sides. 1 pair of parallel sides. 2 right angles. B. kite, 2 pairs of equal length sides. 1 right angle between the two shorter sides. C. 2 vertical sides connected to two curves, one at the top, one at the bottom. D. 6 sided figure, shaped like a sideways V, 2 right angles.
To Copy (from Blackline Masters)
Before and After Shapes
In this activity, students are given the result of folding a figure along one or more lines of symmetry and they are asked to reason about the original figure. No lines of symmetry are specified, so students must consider all sides of a folded figure as a possible line of symmetry and visualize the missing half accordingly.
The first question offers opportunities to practice choosing tools strategically (MP5). Some students may wish to trace the half-figures on patty paper, to make cutouts of them, or to use other tools or techniques to reason about the original figure. Provide access to the materials and tools they might need.
During the Activity Synthesis, discuss the different ways students approach the second question. Consider preparing cutouts of Figures A–F to facilitate the discussion. (The figures are provided in the blackline master.)
Mai has a piece of paper. She can get each of these 2 shapes by folding the paper once along a line of symmetry. What is the shape of the unfolded paper?
Diego folded a piece of paper once along a line of symmetry and got this right triangle.
Which shapes could the paper have before it was folded? Explain or show your reasoning.
Previously, students reason about line-symmetric figures that have been folded once along a line of symmetry. In this activity, students encounter figures that have been folded more than once, each time along a line of symmetry, and reason about the perimeter of the original figure. They think about how a given set of expressions could represent the original perimeter of a twice-folded figure, looking for and making use of structure (MP7).
Jada folded a piece of paper along a line of symmetry and got this rectangle.
Kiran folded a different piece of paper twice—each time along a line of symmetry. Kiran’s folds created the same rectangle as Jada’s did.
Show that each expression could represent the perimeter of Kiran’s unfolded paper.
“Today we practiced visualizing shapes that have been folded along a line of symmetry and reasoning about the perimeter of the original shapes.“
Display:
“Suppose this right triangle is a result of folding once along a line of symmetry. What strategies could we use to determine the possible shapes before they were folded?” (Reflect the triangle along each of the sides—mentally, using tracing paper, or cutting out two copies of the triangle and arranging them so they mirror each other.)
“To find the perimeter of the original shape, could we just double the perimeter of the folded shape? Why or why not?” (No, because there is one side—along the folding line—that is not part of the perimeter of the original shape.)
“What could be the perimeters of the original shapes that fold into this triangle?” (If folded along the longest side: it will be 28, or
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