Page 143 - IM_FL_Geometry_Print Sample

Why: The purpose is to lower the bar for entry into a mathematical task for all students with these two low-stakes questions; by thinking about them and responding, students gain entry into the context and might get their curiosity piqued. Taking steps to become familiar with a context and the mathematics that might be involved is making sense of problems (MP1).
Launch
Keep students arranged in groups of 2. Display this image of a point, a tangent through the point, and a radius through the point for all to see:
Ask students to think of at least one thing they notice and one thing they they wonder about the image. Record their responses on or near the image. If not mentioned by students, ask students to conjecture what might be happening with the angles at point . Students should come away with the conjecture that the radius is perpendicular to the line . If possible, demonstrate what happens when moving point along the circle using dynamic geometry software. Ask students if their conjecture about the angles at point seems to be true regardless of its location along the circle.
Give students 5-8 minutes of quiet work time before asking them to share their reasoning with their partner. Tell students that if there is disagreement, they should work together to reach agreement.
Student Task Statement
Here’s a circle with radius and a line that intersects the circle in only one point, point , without crossing. When a line intersects a circle at only one point without crossing, it is called a tangent line.
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Teacher Guide