In this activity, students create their own figures that have certain symmetry-based attributes. Students are given a pair of parallel segments on a grid. They then add more segments to create figures with one, two, and zero lines of symmetry.

To create their own figures, students rely on their understanding of symmetry and parallel lines. They consider where possible lines of symmetry could be, how many segments to add, and where to place them. Students may also experiment, rely on familiar shapes and their lines of symmetry, or imagine a line of symmetry and what it would tell them about the figure. As they do so, they look for and make use of structure (MP7).

• “What was your process for creating a figure that has only __ line(s) of symmetry?”
• “How could you check if your figure has more or fewer lines(s) of symmetry? How could you change your figure to have exactly __ line(s) of symmetry?”

• Invite students to share their drawings and how they determined how and where to add segments.
• “Which parts of the figure did you pay attention to when drawing? How did you make sure your drawing has line symmetry?“ (The segment lengths, angles, and distances from the line of symmetry all have to be the same on both sides of a line of symmetry.)
• “What was tricky about creating figures with line symmetry in this task?” (It was hard to figure out what to draw to get the exact number of lines of symmetry.)

In this activity, students apply their understanding of symmetry, parallel and perpendicular lines, and types of quadrilaterals to create shapes with certain attributes on isometric dot paper. The arrangement and equal spacing of the dots give students structure for drawing parallel and perpendicular lines and to determine symmetry.

• Invite students to share their drawings. Highlight that many different drawings are possible for each description.
• “How did you make sure that the first two figures have line symmetry?” (Check that the figure has a line that splits it into two halves that mirror one another and match up when folded.)
• “How did you create parallel sides and know that they are indeed parallel?” (Use the spacing of the dots to draw segments that are the same distance apart.)
• “How did you create segments that are perpendicular?” (Connect dots that line up vertically and those that line up horizontally.)
• “What parts, specifically, did you need to draw to create a rectangle?” (2 sets of parallel segments—the same length for opposite sides—and 4 right angles)