Unit 6, Two Day Exam
Lesson 21 of 21
Objective: SWBAT demonstrate what they've learning during the five weeks of this Quadratic Functions unit.
A defining feature of the second half of this unit is that students have been encouraged to work at their own pace and to choose the work that best suits their needs each day. At the end of the unit, I want to have a clear picture of how well and to what extent each student has mastered the five learning targets:
- 6.1: I can find the product of two polynomials.
- 6.2: I can factor a quadratic expression to reveal the roots of the function it defines.
- 6.3: I can complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.
- 6.4: I can graph a quadratic function and show all of the following features: roots, the vertex, the axis of symmetry, and the y-intercept.
- 6.5: I can solve a quadratic equation by any appropriate method, including factoring, completing the square, and using the quadratic formula.
I give the exam in two parts, over two days. On each part of the exam, there are some questions that test basic procedural skills and knowledge of quadratic functions. These questions provide a baseline for whether or not kids mastered the essentials. Then, for each learning target, there are more complicated versions of each sort of problem, that require students to demonstrate a deeper level of mastery or the ability to make deeper connections.
When I grade the exam, I'll grade each student on the mastery of each learning target, which is not the same thing as recording the percentage of right answers. On the first section of the short answer exam, for example, there are five pairs of polynomials to be multiplied. The first two are of the most basic sort that we've studied since the first week of the unit, and if students can give perfect answers to these but not the next three, I'll give them a 2 on SLT 6.1, because they've demonstrated a basic ability to multiply simple binomials. A "2" translates to a 70 on a report card grade, even though 2/5 would represent getting 40% of the problems correct. The fifth problem is much more challenging, and represents a bigger challenge. Although I'd love for all students to be confident and able to give a correct answer to that problem, I don't consider it as essential an outcome in an Algebra 1 course as I do the first two.
Some problems appear on both tests, and it's useful for me to see when students can apply their knowledge to one form of a problem and not the other. Just for fun, I use the same exact expressions a few times. For some examples, compare:
- #16 on Day 1 to #2 on Day 2
- #2 on Day 1 to #3 on Day 2
- #8 on Day 1 to #5 on Day 2
Day 1: Short Answer
On the first part of the exam there are 20 short-answer problems, most of which are in the form of basic exercises without context. My goal was to make this part of the exam as straightforward as possible for each of the first four Student Learning Targets. I want a snapshot of how well each student has mastered the essentials. Each section of this exam starts with a very simply example or two before building in complexity.
Some students will take the entire 42 minute period to complete this exam, and others will breeze through it pretty quickly. For those that finish early, I've prepared an optional set of ten quadratic equations to solve as evidence of mastery on SLT 6.5 (Unit 6 Exam SLT 6.5). This requires students to draw on their knowledge of the other SLTs.
I'll keep the SLT 6.5 part of the exam available for any students who finish early on Day 2 as well.
Day 2: Multiple Choice
On the second part of the exam there are 25 multiple choice questions. I made this exam with a free account on Problem-Attic.com, which makes it easy to sift through released test items from many different state exams.
The purpose of this part of the exam is to give students practice as they develop the literacy skills essential to success on such tests. Over the years, I've gone back and forth about using multiple-choice exams in my own courses. When I think about the hoops kids have to jump through, taking state exams and the SAT, for example, my idealism about sticking solely to projects and performance-based assessments is tempered. I'll still pursue those latter goals, but I'd never want it to be at the expense of my students. I find it's a fair trade-off to dedicate a half-dozen days each year to this sort of practice, while in conversations with students avoiding the expression disproportionate faith in these exams. We'll see what the Common Core exams hold. I'm looking forward to seeing how our practice might shift in the coming years.