standard_description: Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.
problem_activity: Warm-up
This warm-up prepares students for the Info Gap activity that follows. First, students brainstorm what information they would need to know to solve a problem that involves constant speed. Then, the teacher demonstrates the process of asking a student why they need a specific piece of information before sharing it with them, in preparation for students following this procedure with their partner in the next activity.
Launch
Give students 1 minutes of quiet think time to brainstorm what information they would need to know to solve the problem, followed by a whole-class discussion demonstrating the procedure for the Info Gap activity.
Student Facing
Consider the problem: A person is running a distance race at a constant rate. What time will they finish the race?
What information would you need to be able to solve the problem?
Student Response
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Activity Synthesis
Ask students:
"What specific information do you need?"
"Why do you need that information?"
Share each piece of information with the class after a student specifically asks for it (and explains why they need to know it).
The race is 10,000 meters long.
The race started at 9:15 a.m.
In 1 minute, the person ran
\(156\frac{1}{4}\)
meters.
An equation relating distance and time is given by
\(d = 156\frac{1}{4} \boldcdot t\)
where
\(d\)
represents distance in meters and
\(t\)
represents time in minutes.
It takes 32 minutes for the person to run 5,000 meters.
The person runs at a pace of 6.4 minutes per kilometer (or 1,000 meters).
After you share each piece of information, ask the class whether they have enough information to be able to solve the problem. When they think they do, give them 2 minutes to solve the problem and then have them share their strategies. (The person should finish the race at 10:19 a.m.)
Tell students that they will be working in groups of two in the next activity and that they will be using the same procedure that you just demonstrated to solve a problem.


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