# Pivot Algebra Two: Final Exam

A semester of my wild idea is in the books and I'm very happy with the results. I ironed out a lot of the problems over the summer and was able to refine the standards enough to let other people try and reproduce it.

But let's talk final act. One year ago I gave a final with equations of various types intermixed. Student performance was poor, lacking the appropriate number of solutions or leaving the problem blank.

This year I gave the final I always wanted to give (though I'm not a believer in high stakes final exams in high school).

Your first reaction might the presence of the word "review" on there. Yes, the final exam was the review, but with a bit of a twist. We have moved to 70 minute finals so I had to shrink the contents of the exam to fit the time frame. I love the idea and I don't need to see someone do 10 versions of a problem to prove they know it (or, ugh, multiple choice...bleh). A keen eye can spot the difference between a student who gets it or not with a problem or two.

Their instructions were to complete all 24 of these equations/inequalities. On exam day, they would be given 8 chosen at random and had to demonstrate the algebraic solution and graphical solution to the problem. iPads with Desmos were available for them to use during the final. A hand drawn version of the graph was all that was required.

Students had two class periods to work on this in advance. I directed them to the Desmos website if they wanted to get a head start on the graphs. I reviewed solutions to five of them in class.

Exam papers looked like this:

The night before I identified 3 sets of 8 that were reasonable (#18 is badly formed for example, so I made sure to scan the rest for issues to avoid freaked out students). Exam papers had the students name on them already to prevent any sneaky trading.

My criteria:

• Completed review was worth up to 20pts
• Each exam problem was worth up to 10pts
• Review score and exam score were combined to give a total out of 100pts
• Algebraic solution(s) should be correct
• Graph should be accurate representation (no faking a line as a quadratic)
• Intersection point(s) should match the algebraic solution(s)

Students had options. If they diligently completed all 24 problems in advance, reproducing their work would be easy. Provided they typed the equation/inequality into Desmos properly, they'd know immediately if they were right. Students could also risk it, not do the review, and figure everything out on the fly. All of them were somewhere in the middle of the extremes.

Other than some mild technical questions about how to type something in Desmos, conducting the review and the final were a BREEZE. Retention seemed pretty high and no one flinched when asked to recall the difference between an absolute value and a quadratic. You should've seen my face when a student solved a factorable quadratic like 22, 23, and 24 using the quadratic formula. They knew it was the catch all! No reminders!

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