I always make two versions of a test and pass them out checkerboard style. The goals for this unit were to ensure that students all have the skills to simplify algebraic expressions and solve equations and inequalities as well as model simple situations with these skills. This test directly reflects those goals. Each problem relates to one of the learning objectives as seen in the Practice Test.
This test was created with Kuta Software, an amazing resource that I would highly recommend.
Unintended but illuminating, a major theme to the struggles I encountered in correcting this test is Math Practice 6. I was expecting modeling (Math Practice 4) to be the overwhelming issue, but was pleasantly surprised with my students success in this arena. Many students obviously understood the mathematics but made small errors in the accuracy of their answers. This leads me to the necessity of focusing on Math Practice 6 more discretely in the next unit. To illuminate these issues, I have included three sample problems as well as my plans to build up these skills in future lessons.
The fourth problem on the test gave the students an equation to solve that had no solution. The correct solution is shown in Problem 4A. This was one of the major ideas in Cake Pops Day 4. Some students would get to 0 = 28 and not know where to go from there like in Problem 4B. We related this problem to its graphical solution and this will be visited again during the Functions Unit. Particularly in the Modeling Systems lesson, I intend to have the students connect the idea that the graph of the two sides of an equation with no solution never intersect. I also had many students, particularly those who struggled with solving equations make the mistake of not canceling out the variables properly as highlighted in Problem 4C. While both of these mistakes point to some structural misunderstandings (Math Practice 7), I have also noticed that the students do not strive for the exact answer and often seem satisfied with “close” answers like 0 = 28.
The sixth problem asked students to use their calculator to find the solution to an equation containing a cube. I had many students struggle with precision here. Some would provide both the x and y values without indentifying which provided the correct solution like in Problem 6A. Others would approximate the solution to an imprecise approximation like in Problem 6B. Fortunately, we will be solving equations graphically many more times this year. I plan to provide them an opportunity to explore and discuss the precision of these answers in context in lessons like Modeling with Systems of Equations.
One other place I found precision issues was in representing inequalities, particularly the multiple representations of compound inequalities. Problem 14 is a perfect example of this. I did have several representations I did accept as correct, such as Problem 14A and Problem 14B. While B is the most accurate, I made the decision to include answers like A as acceptable as a scaffolding measure since this is our first test. I intend on tightening that definition of precision as the year progresses. Many students did not properly read this problem and gave me answers like Problem 14C. I have found that misreading directions is one of the biggest issues with precision in mathematics. My goal is through repeated practice and peer critique, the students’ attention to exact directions will improve and lead to improvements to accuracy.
Early in the next chapter, we will be discussing linear functions. In preparation for this, my students will be taking a Pre Assessment on Parallel and Perpendicular Lines as soon as they finish their test. This lesson is from the Mathematics Assessment Project. I collect it at the end of class and use it to prepare for the lesson on Parallel and Perpendicular lines.
I offer a variety of extra credit puzzles puzzle for students who finish early and have no make up work to complete. This includes, but is not limited to; sudoku, mathdoku, logic problems, picture mazes, and pixel puzzles. A couple of my favorites are: Griddlers and Concept is puzzles
Both sites offer a number of free puzzles as well as purchasable books. Pixel Puzzles are a particular favorite. The Mathdoku are also great. They can increase a student's numeracy abilities if done regularly.