SWBAT demonstrate understanding of algebraic reasoning by creating and writing solutions for rational and radical problems.

Let your students write their own test and see just how tough they can be!

5 minutes

I begin this review lesson by asking my students to list all the key terms and topics we've covered in this unit on the board. ** **I expect them to come up with a list similar to the one I've given below, but if they leave out any key pieces, I ask leading questions to have them included. For example, "Do you remember the lesson on ...?" filling in the blank with an example from whichever section they've forgotten. When all the terms and topics are posted, I group them into four sections; radical equations, rational equations, extraneous solutions, and graphing; then tell my students to discuss and review the definition of each term with their right shoulder partner. **(MP6)** I close this section of the lesson by telling my students that tomorrow's test will be individual and will have an assortment of free-response problems for them to solve.

**key topics/terms:** extraneous solutions, graphical solutions, absolute value equations, exponential equations, rational equations, radical equations

**possible vocab from previous classes/lessons:** numerator, denominator, radicand, index, radical sign, divisor, dividend

40 minutes

At times my students complain that they didn't study the right stuff or that the test didn't ask the right questions, so this activity lets them see testing from the other side. I explain that they will be writing test questions and give them the Exam Questions Rubric to look over. I check understanding using fist-to-five let them know they can discuss ideas with classmates, but they must each create their own questions and solutions. **(MP1, MP2, MP4)**

The most difficult part of this lesson for me is not being able to put the test together until the evening before the exam! I worried the first time or two that I tried this because I wasn't sure my students would put in the effort to write good questions, but apparently the incentive to have their questions included on the exam is enough to inspire most of them. My video explains the positive benefits of letting go and giving my students some control over the assessment content.

5 minutes

I wrap up this section by giving each student a notecard and asking them to reflect on whether today's activity helped them feel more assured about their understanding or not and how/why.

If you would like more specific feedback you might try questions like the following:

- How did writing test questions help you understand rational equations?
- How did writing test questions help you understand radical equations?
- How did writing test questions help you understand extraneous solutions?
- How did writing test questions help you understand graphing solutions?
- If you could do this again for another test would you choose to do so? Why or why not?