Tuesday, April 14, 2015

PARCC Practice Test Question 1 (Day 146)

Today begins a day-by-day look at each of the questions on the PARCC Practice End-of-Year (EOY) assessment, in order to prepare students for the Common Core tests.

Originally, I was considering giving some extra lessons that aren't directly related to the Common Core Standards here -- earlier I mentioned spherical non-Euclidean geometry. But I've changed my mind, because I want to make sure that -- since this is a Common Core blog -- every question that appears on the PARCC Practice EOY is covered on this blog. This will serve as a review for the students preparing to take the computerized exams.

If I cover one question each day, then I will finish this review in time for finals -- but of course, not in time for the actual PARCC EOY that this is supposed to prepare the students for. Still, it's helpful for me to post a discussion of each of the PARCC questions before the students begin the text -- and it also provides me with some guidance regarding what to highlight next year, if we notice that a certain idea occurs repeatedly on the PARCC but inadequately in my previous lessons.

I've mentioned numerous times that I live in California, an SBAC state -- yet I keep talking about PARCC over and over again. Once again, this is because there is no EOY exam for SBAC, only a single exam covering algebra and geometry at the end of junior year. So students in PARCC states have to take two full tests in geometry, while those in SBAC states only have to take one -- and it might not be until nearly a year or two after the student has finished Geometry. So there is much more material to cover for PARCC than for SBAC. My hope is that by covering the PARCC questions, the SBAC will automatically be covered as well.

To make things clear, the following link is my source for the PARCC Practice EOY exam:

So let's begin. Question 1 of the PARCC Practice EOY exam is on similarity:

1. The figure shows Triangle ABC ~ Triangle DEF with side lengths as indicated.

(The figure shows AB = 21, AC = 27, BC = x, DE = 7, DF = 9, EF = 5.)

What is the value of x?

This question is very straightforward. The triangles are similar, so students should set up a proportion to find the missing side length. There is enough information to set up more than one proportion -- for example, we could have x/5 = 21/7 or x/5 = 27/9, among others. Solving any of these proportions gives the correct answer as x = 15.

I admit that there are some terrible questions on the PARCC practice test, and we'll be discussing these questions on the blog in due course. But Question 1 is not one of these bad questions. This is a skill-based content problem, no more than that. Because this question requires only a simple numerical answer, 15, students will have no problem entering it on the computer. In short, maybe if all of the questions were like this one, then there wouldn't be so many students opting out of the tests.

This is my plan for the worksheets for these PARCC questions. We begin with the PARCC practice question as it is written. Then there are additional questions just like the PARCC question. If the question is as simple as today's, then I will just give several more problems of increasing difficulty for the students to answer -- a traditionalist worksheet for a traditional question. If the question is a more difficult multi-part question, then a second problem with the same parts will be given.

Here on the blog, I will give the corresponding section of the U of Chicago text for each question and the key theorem or formula used to solve the problem. This is followed by some additional commentary on specific questions that appear in the U of Chicago text, or an announcement that this exact question doesn't appear in the text.

So, without further ado, here is my worksheet for Question 1:

PARCC Practice Test Question 1
U of Chicago Correspondence: Section 12-5, Similar Figures
Key Theorem: Similar Figures Theorem

If two figures are similar, then:
(b) corresponding lengths are proportional.

Common Core Standard:
CCSS.Math.Content.HSG.SRT.B.5
Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

Commentary: The question in Section 12-5 most like the PARCC question is Question 23, but Question 22 is not that far off, the main difference being that the similar triangles are parts of cones. In the SPUR section at the end of the chapter, Questions 11 and 12 are also not that far off, the main difference being that it is not directly stated that the triangles are similar, although enough information is given to prove that they are similar.