Coordinate Geometry Unit Review and Test
Lesson 4 of 4
Objective: SWBAT demonstrate mastery of this unit's concepts.
As the students enter the room, I hand back their Check for Knowledge, on which I have made corrections and/or comments. I also ask that the students take out their homework problem, the last problem on the previous lesson's problem set.
After answering any questions about the Check for Knowledge, I ask for volunteers to display their solutions to problem 7 on the homework. This is a problem that can be solved in a variety of very different ways, by closely examining the structure of the figure (MP 7), and merits, I think, a good deal of discussion.
If it appears that a fair number of the students are struggling, I hand out one Final Review Problem, a problem covering just about all of the concepts taught in this unit. I ask that the groups work together on the first section of the question, using whiteboards for their work. Then the class comes together for discussion, everyone proceeds to the next section, and so on.
I hand out the unit test, straight edges, compasses, and a generous amount of graph paper. (One of the questions involves a circle and the students like to have the compass for this question.) I stress that the students need read the questions carefully, to take their time, and to answer each question completely.
This test includes two problems that are quite challenging for the students (numbers 2 and 3). This is because the questions give no hints as to how the students should approach the problems (MP1), and because they require a good deal of justification (MP3). I think these two problems are really important in that they help set the tone for the year; therefore, after I hand the test back, I allow the students to rework and hand these two problems in as many times as it takes for them to do the problems well. (I also allow this to improve their grade.)
To help keep students who finish the test first engaged, I hand out the Post-Test Problem when a student hands in his or her test. Here are some alternatives you could use as a way to have students persevere in solving problems (MP1).
Ken-Ken: My students are hooked on Ken-Ken! It's similar to Sudoku, but with mathematical operations. Will Shortz books are my favorite because they are just the right size to photocopy, but there are lots of sources available. Here's a sample. Ken-Ken can also be found on NCTM's Illuminations site.
NCTM's magazines: The NCTM magazines always include challenging problems. In Mathematics Teaching in the Middle School, it's the Palette of Problems; in Mathematics Teacher, it's the Calendar Problems. Another NCTM source is Problems to Ponder.
24 Game: I use the original single digit set (there are many different varieties of cards available), and write the numbers from one card of each level on the board or on a handout. I believe it is now an iTunes app as well.
As we did in the first unit, we begin the third unit with the Anticipation Guide. The front page consists of true/false questions, while the back page lists the vocabulary for the unit. I give the students a few minutes to complete the anticipation guide, we discuss it very briefly as a way to set up our work in the next unit, and then I ask them to keep it in their folders. We will revisit the guide at the end of the second unit, at which time they reevaluate their answers on the true/false based on the knowledge that they hopefully gained over the course of the unit, and examine their mastery of the vocabulary.