This lesson is the first in a series of lessons in which students create shapes with given conditions. During these lessons students think about what conditions are needed to determine a unique figure, in preparation for future work with congruence in grade 8 and high school. These lessons continue the language used in grade 6: two polygons are identical if they match up exactly when placed one on top of the other.
In this lesson, students experiment with making polygons of various numbers and combinations of side lengths, using cardboard strips and metal fasteners. The goal of the lesson is to help students see that sometimes lots of different shapes are possible under given constraints about side lengths, and that at other times, with different constraints, it might be that only one shape is possible or that no shape is possible. In this lesson, students do not try to formulate general rules about what side lengths are possible; in the next lesson, they formulate such a rule for triangles.
- Comprehend that two shapes are considered “identical copies” if they can be placed on top of each other and match up exactly.
- Recognize that four side lengths do not determine a unique quadrilateral, but that three side lengths can determine a unique triangle.
- Use manipulatives to create a polygon with given side lengths, and describe (orally) the resulting shape.
Let’s build shapes.
For the activities in this lesson and the next, you will need slips cut from copies of the What Can You Build? blackline master. Prepare 1 copy for every 2 students. These slips can be reused from one class to the next. To make the slips sturdier, it is recommended to copy them onto card stock. If card stock is not available, consider gluing each copy to light cardboard, such as a cereal box. Also if possible, copy each set of slips on a different color of paper, so that a stray strip can quickly be put back.
After the slips are cut, punch holes into the endpoints of each segment. A standard hole punch makes holes that are a little larger than needed for the metal paper fasteners, causing the cardboard strips to wiggle around. If possible, find a way to punch holes that are slightly smaller than the size of a standard hole punch.
Put each set of strips in an envelope. Prepare to distribute at least 12 metal paper fasteners (i.e., brass brads) to each group.
Note: If using the digital version of every activity, the strips and fasteners will not be needed.
- I can show that the 3 side lengths that form a triangle cannot be rearranged to form a different triangle.
- I can show that the 4 side lengths that form a quadrilateral can be rearranged to form different quadrilaterals.