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 (

*point*,

*line*, 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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