standard_description: Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., p^(2)). For example, by truncating the decimal expansion of Ö2, show that Ö2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.
problem_activity: Activity
In this partner activity, students take turns finding a set of representations that represent the same function. As students trade roles explaining their thinking and listening, they have opportunities to explain their reasoning and critique the reasoning of others (MP3).
Launch
Arrange students in groups of 2. Partners take turns identifying representations that match, and explaining to their partner how they know they match. If necessary, demonstrate the protocol before students start working, including productive ways to agree or disagree, for example, by explaining your mathematical thinking or asking clarifying questions.
Student Facing
Your teacher will give you a set of representations. Sort them so that in each group there is a table, graph, equation, and example that all represent the same function.
Student Response
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Activity Synthesis
Much of the discussion will happen within groups. Ensure that students found correct matches, and invite selected students to explain how they know they are matches. Here are some possible discussion questions:
“Which matches were tricky? Explain why.”
“Did you need to make adjustments in your matches? What might have caused an error? What adjustments were made?”


aligns: no