# Final Exam

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## Objective

Students will take a two-hour final exam that consists of both individual and group work.

#### Big Idea

I want my final exam to reflect the priorities I've stated to students throughout the year. That's why kids will work together to solve problems in addition to working alone on today's test.

In the two weeks leading up to the final exam I make sure to take a moment each day and tell students what to expect, so there are no surprises when they show up today.  As I explain in this video, this two-hour exam consists of one hour of individual work, and another hour of group work.

## Part 1: Multiple Choice

60 minutes

Students spend the first hour working individually on this multiple-choice exam, which consists of 32 questions.  I try to stick to straightforward problems that assess essential knowledge and skills from this Algebra 1 course.  Take a look at the exam, and please share your thoughts and questions in the comments below.

One hour, less the few minutes it takes to get started, is enough for my students to get through these 32 problems.  In fact, some students will finish in 30-40 minutes.  For anyone with time to spare, I've prepared some bonus problems.  When students are done with the first part, they return it to me, keep their bubble sheet, and get the final eight problems, which are numbered from 33-40.  These problems come from old American Mathematics Competition exams.  The Art of Problem Solving Wiki has problems and solutions for exams dating back to 1985.

## Part 2: Group Problem Solving

60 minutes

When the first hour is up, I tell everyone to hand in everything they've got.  I project this familiar random group generator on the front board, press the sort button, and tell students that these are their final exam groups.  Then, I tell everyone that when they find their group and place to work, I'll provide a copy of the exam.

Here is Part 2, the group part of the exam.  The instructions are written on the first-page cover sheet:

• With your group, you have 60 minutes to complete this part of the exam.
• Everyone should participate in helping to solve each problem.
• Each member of your group must be the Recorder for at least one problem.  Write the name of the Recorder for each problem at the top of each page.
• Show all work on the papers provided. You may use scrap paper, but it will not be collected.
• If you make a mistake, it’s ok!  Just cross it out neatly, and continue with your solution.

I take a moment to read the instructions with students, and I take clarifying questions.

There are five problems, and here's a note or two about each one:

1. For the first problem, students must identify the error in a step-by-step solution to a linear equation, and explain how they would fix it.  While watching kids work on this during the exam, I realized that I want to use problems like this a lot more often next year.
2. The second problem is Malcolm Swan's "Hurdles Race" problem, which you can find his outrageously useful book, The Language of Functions and Graphs.  The book is available for free, online.  If you've never read it, or encountered Malcolm Swan's work elsewhere, then stop reading about this exam right now, and go take care of that!  This task is useful for assessing student understanding of graphs and the stories they tell, and it's a blast to read what kids come up with.
3. The third problem is an overtaking problem of the sort students saw during the Systems of Equations unit and as an opener last week.  One of last week's assignment options consisted of problems like these.
4. Problem #4 is a Mixture Problem, like the ones students saw two weeks ago and on another review assignment.
5. The final problem consists of four questions about a dot pattern.  We started the year with number sequences, have worked to generalize rules throughout the year, and I don't think it's possible to over-use dot patterns in an Algebra 1 course.  I think that's a nice place to conclude this course!