In Topic B, students work extensively with a ruler, compass, and protractor to construct geometric shapes, mainly triangles (7.G.A.2). The use of a compass is new (e.g., how to hold it, and to how to create equal segment lengths). Students use the tools to build triangles, provided given conditions, such side length and the measurement of the included angle (MP.5). Students also explore how changes in arrangement and measurement affect a triangle, culminating in a list of conditions that determine a unique triangle. Students understand two new concepts about unique triangles. They learn that under a condition that determines a unique triangle: (1) a triangle can be drawn and (2) any two triangles drawn under the condition will be identical. It is important to note that there is no mention of congruence in the CCSS until Grade 8, after a study of rigid motions. Rather, the focus of Topic B is developing students’ intuitive understanding of the structure of a triangle. This includes students noticing the conditions that determine a unique triangle, more than one triangle, or no triangle (7.G.A.2). Understanding what makes triangles unique requires understanding what makes them identical.
Grade 7 Mathematics Module 6, Topic B, Overview
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