Page 141 - IM_FL_Geometry_Print Sample

Why: This is a teaching routine useful in many contexts whose purpose is to give all students enough time to think about a prompt and form a response before they are expected to try to verbalize their thinking. First they have an opportunity to share their thinking in a low-stakes way with one partner, so that when they share with the class they can feel calm and con dent, as well as say something meaningful that might advance everyone’s understanding. Additionally, the teacher has an opportunity to eavesdrop on the partner conversations so that she can purposefully select students to share with the class.
Launch
Arrange students in groups of 2. Give students 5-8 minutes of quiet work time before sharing their responses with a partner. Follow with a whole-class discussion.
Student Task Statement
Jada and Diego discuss distance between a point and a line from the warm-up.
Diego draws his path from the point to the Jada constructs a segment from to that is
line, segment .
perpendicular to .
1. Which path from to is shorter, Jada’s or Diego’s? Explain your reasoning.
2. What would change if Diego picked a di erent point? What would stay the same? 3. What is the shortest path from a point to a line? Explain your reasoning.
Student Response
1. Jada’s path is shorter than Diego’s because Diego’s path forms the hypotenuse of a right triangle in which Jada’s path is one of the legs.
2. The further away Diego’s point, is from Jada’s point , the longer his path would be. Unless he picked the exact same point as Jada his path would always be longer.
3. The shortest path from a point to a line is that formed by making a right angle to the line because any other path would form a hypotenuse and thus by the Pythagorean Theorem it would be longer.
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Teacher Guide