Thursday, September 24, 2015

Review for Chapter 2 & 3 Quiz (Day 21)

It's time for me to post a review for some sort of quiz or test today. But before I post the assessment from last year, let's remember how I've changed the units from last year from this year. Unit 1 (Introduction to Geometry), which consisted of Chapters 1 and 2 last year, was really only Chapter 1 this year.

And so I posted last year's "Chapter 1 Quiz" as this year's Unit 1 Test. Unit 2 (Reflections) was only Chapter 4 last year, but this year consists of Chapters 2 through 4. This means that at this point last year I posted my "Test for Chapters 1 and 2" (i.e., for Unit 1 last year), but this year what I need is a quiz for Chapter 2 and 3 (since Unit 2 doesn't end until after Chapter 4).

Let's recall why I changed the units around in the first place. One thing about long weekends like Labor Day and Columbus Day is that students -- who often don't study over three-day weekends -- forget what they've learned. Meanwhile, three-day weekends give teachers more time for grading. So I reorganized my units so that Unit 1 would end at Labor Day weekend and Unit 2 would end at Columbus Day weekend. So my philosophy is, any time that students are unwilling to study (as in three-day weekends, vacation weeks), that's when teachers should be grading tests. The Middle Start Calendar that this blog is following gave us only enough time

Some may argue that this makes the Unit 2 title, "Reflections," a misnomer. In some ways, the material of Chapters 2 and 3 prepare us for the study of reflections in Chapter 4 -- after all, students can't know that reflections preserve angle measure until they've learned what angles are and how to measure them. So in some ways, Chapters 2 and 3 go along with "Reflections" -- but we just as easily could consider this to be introductory material that belongs in Unit 1 (as we did last year).

Now I called the assessment that I posted last year the "Test for Chapter 1 and 2." This test includes material from Lessons 3-1 through 3-3 (which we still want), but it also contains Chapter 1 stuff (which we might not want anyone, since it already appeared on the Unit 1 Test). Also, I originally posted this as a test with 20 questions, but we wouldn't want our quiz to last that long -- especially since we don't have a three-day weekend to grade them this time.

We could give our students only the second page instead, since this page contains all of the Chapter 2 and 3 questions we'd like to give. Before our students wonder why the questions are numbered starting with 12, we could change that 12 to 2 and add an extra question at the start -- possibly on area or perimeter since I added that extra lesson to this unit. It's too bad that I can't make Question #12 into an area problem. After all, it's about equilateral triangles and notice that an equilateral triangle with sides of length 2 has height sqrt(3) -- and we wouldn't want to explain where the sqrt(3) comes from at this point in time.

This is what I wrote last year about today's review worksheet. Recall that this worksheet contains problems from all three chapters. Teachers may wish to give only questions from Chapters 2 and 3 -- and of course, the worksheet assigned to the students should correspond to the questions you plan on giving them for the quiz the next day. Of course, there's no harm in giving students the extra review questions for Chapter 1 even you plan on giving them only Chapters 2 and 3 on tomorrow's quiz:

Here is the rationale for which questions I decided to include on this review worksheet -- just as I did for the Chapter 1 Quiz, these problems come directly from the "Questions on SPUR Objectives" appearing at the end of each chapter.

For Chapter 1, I begin with Question 21, the three undefined terms (pointline, and plane), and then move on to Questions 26 and 32, two of the properties from arithmetic/algebra (Multiplication Property of Inequality and Substitution Property of Equality). Next are Questions 36-37, order on the number line -- except that I made the distances whole numbers, not decimals, and also I omitted point V from the second question, which serves no purpose other than to confuse and frustrate the students. Question 39 directs students to find the two points R on the number line that are the right distance from Q, and Question 41 is another distance question. Finally, I jumped to Question 61, another absolute value question similar to one that appeared on the Chapter 1 Quiz.

For Chapter 2, I begin with Question 16, which asks why the following definition is not a good definition of triangle: "A triangle is a closed path with three sides." The problem is, what exactly is a "closed path"? We're not allowed to give definitions containing words that also themselves need definitions. Question 20 asks the students to rewrite a statement in if-then form, then Question 30 reminds students that just because a conditional p=>q is true, it doesn't mean that its converse q=>p must be true.

Then I move on to questions for which the students need to draw pictures. I back up to Question 4 in Chapter 2, an equilateral triangle, and then Question 6, a convex octagonal region, and then Question 9, a midpoint quadrilateral -- but I decided to make the quadrilateral convex for less confusion. Question 25 asks for a counterexample to an oversimplified definition of quadrilateral, and finally Question 42 is a different sort of drawing -- the students must draw a simple polygon hierarchy.

The first two questions in Chapter 3 also involve drawing -- first Question 4 asks for two complementary angles with the same measure, and then Question 10 asks for a 92-degree angle. Now is a good time to point out what materials are needed to complete this review worksheet -- for starters, students should use a protractor to measure out the 92 degree angle, and probably a straightedge as well. Notice that the previous question requires students to draw two 45-degree angles -- best done using the protractor as well. But a previous question asks for an equilateral triangle. Now the students could construct it using a straightedge and compass -- recall that this is one of the Common Core constructions -- but they don't do learn how to do so until at least Chapter 4. Or the students could use the protractor to measure out 60-degree angles, since the angles of an equilateral triangle measure 60 degrees -- but they don't learn this until Chapter 5. So for now, I believe that the U of Chicago text expects the students simply to freehand a triangle that is approximately equilateral. The key is whether the students know what an equilateral triangle is, not whether they know its angle measures or how to use a compass to construct it.

The final two questions from Chapter 3 are Questions 13 and 23, but as usual, I modified these. I changed the minus sign in Question 13 into a plus sign so that x doesn't end up negative. The question is now more natural sounding -- what is the supplement of a 12-degree angle? In Question 23 I dropped the variable z and changed 17 to an even number, since students will have to divide by 2.

And so here is my review worksheet for Chapters 1, 2, and the first half of 3:

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