Line of Best Fit Assessment Review

As students enter the room, I ask each student to grab a marker and his/her graphing calculator. As they do, I give out the previous lesson's partner quiz Linear Fit Partner Quiz.docx. We spend about 5 minutes grading and another 5 minutes discussing misconceptions. 

Here is how partner quiz swap's work:

1. Each partnership gets another partner's quiz
2. They must identify themselves as the graders for the other group's quiz. They write something simple, like "This quiz has been graded by __________ . " I often print this out on quizzes if I know we will be doing a swap later. 
3. I go through each question on the board and give grading instructions along the way. 
4. If a question is correct, students mark it with a check and write something encouraging, doodling is definitely allowed. 
5. If a question is incorrect, students mark it with an X and write something encouraging and something helpful, like the algorithm behind the correct answer or a reason as to why their choice was incorrect. 
6. At the end, students give a holistic score (this simplifies the whole process). A 4 is reserved for absolutely no errors. A 3 means that their was some minor error. A 2 could mean that there was a major error or several minor errors. A 1 means that there were more errors than correct answers. (In terms of grading, I use these scores as part of their class participation grade and use the linear function g(x) = 60 + 10x, where x is the grade 1,2,3 or 4. This scale tends to be fair.) 
7. After we grade, students deliver the quizzes back to each partnership and they have 5 minutes to discuss their results. 

Next, I give students 5 minutes to discuss and solve the previous exit ticket: Line of Best Fit Exit Ticket. Most students need time to review how to solve the problem and discuss what constitutes a reasonable answer. I use this time to help students use the graphing calculator. For this problem, the technology can really help to support a student's thinking. 

We then solve the problem together, as a class. To bring up the connection between their intuition and the graphing calculator, we solve it intuitively and with the graphing calculator. The goal is to find profit after 18 months and we tend to agree that a number around 12,000 seems reasonable. We discuss strategies to quickly use the calculator to test out one's intuition. One common strategy is to draw the line and estimate the profit at 18 months, then find the equation with the calculator and compare the two results. We can adjust our line to fit the result on the calculator, but for many students sketching first is a beneficial start to the problem. 

Another strategy is to average the x and y values independently to get the point (x bar, y bar) that the line of best fit must pass through. This tends to help students in their work.  Each student then grades their Exit Ticket on a 4 point scale. The process is the same as for grading partner quizzes (see the previous section) except they are now grading individual work. 

I would give them another individual assessment here, but I like to give them at least one day before I assess them again. Otherwise I am afraid they are just regurgitating what they heard in class, rather than what they understand. So instead I give a second partner quiz and circulate as they work, addressing misconceptions where I can: Partner Quiz 2.docx

I like to review this partner quiz right away. There are two questions and the second is much easier than the first. So we tend to review the first question as a class. 

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The biggest issue we tend to discuss here is "what is being asked?" The idea is simple, as houses move further from the best, the price goes down. This brings out the idea of why we should get a negative slope and then how we can use this line of best fit to predict how much a house should cost when it is 3 blocks from the beach. However, students can't access the problem unless they decode the question itself. If they can't figure out what they are solving, the process seems meaningless. So we discuss the relationship between distance from the beach and price and discuss how they can sort through all the distractors (we call all the extra fluff "garbage.") 

The second major misconception in this question is that students don't understand the typical procedure for acceptable rounding. This happens on two levels:

• First students don't understand that "round" typically means to only round your final result. So we show how different the answers look between estimating the whole time and when you just round at the end. This is an issue for my students and comes up on their standardized tests, but we discuss the logic of distinguishing estimating and rounding and leave it at that. They understand that some processes tend to apply only to the reality of testing. 
• Second, I use this as an opportunity to revisit typical rounding strategies. We review the problem as it stands, "rounding to the nearest dollar," but revisit it by asking, "what would the answer be if we were rounding to the nearest tenth or hundredth?" This review always tends to help. 

Students finish by scoring their work and submitting to me for review.