"History shows that mathematical creativity is not privy to any particular culture, time period, civilization, or gender. The wealth of amazing ideas and contributions that were developed over the centuries is truly incredible and exciting to explore."
We're in the middle of the chapter introduction. Pappas is describing how so many different groups of people contributed to mathematics throughout history. She repeats the chart from page 142 showing how to count in several different numeration systems -- except for some reason, this chart counts up to 12 rather than 11.
Pappas also mentions how the concept of zero developed, independently by the Babylonians and Mayans before used in our Hindu-Arabic system.
We have reached the end of the U of Chicago text. Typically, in my first blog post after the last chapter test, I write about my most popular post of the past year. This year, it's no contest -- my number one post is my review of the movie Hidden Figures. This post has over 300 hits, nearly four times its closest competitor. Most likely, many people were searching for information about the movie and stumbled across my post.
In a way, Hidden Figures represents the truth of the Pappas quote at the start of this post. Creativity in math is not limited to any culture or gender, which is why Katherine Johnson was able to find success in math.
In the past, I would devote an entire post to the worksheet I created from my most popular entry. But of course, there is no worksheet associated with that post -- unless you count the extra credit page that I made for my students. I don't post it though, since I didn't save any copies of it.
Instead, we go straight to the next thing I usually do after completing the book -- test prep. In the past, I'd post worksheets based on the PARCC Practice Exam. But recall that I live in California, which administers the SBAC, not the PARCC. It's silly to continue posting PARCC questions when I live in one of the SBAC states -- with my students actually taking the SBAC.
In fact, I'm going to post eighth grade SBAC test prep questions this year, since I did choose after all to focus on eighth grade this year. And besides, some of the eighth grade questions are ultimately related to geometry anyway.
The reason I favored PARCC over SBAC is because the former is easier to access. Even though both tests are given on the computer, the PARCC website has a written practice test -- which I used the first two years of this blog. The SBAC website forces you to take the practice test at once -- and it's impossible to reach Question 33 (the last practice question) without answering the first 32. This is very inconvenient for setting up worksheets based on one or two questions at a time.
In the past, I reviewed only one question each day. There is less time available, so this time I'll review two questions per day. And yes, I know that my students finished the SBAC last week, and most teachers reading this have probably finished state testing as well, but I'm posting these worksheets now anyway.
Question 1 of the SBAC Practice Exam is on exponents:
1. Enter the value of n for the equation 5^n = 5^11 * 5^3.
This question is straightforward for those who remember the laws of exponents. To multiply powers we just add exponents, so the correct answer is 11 + 3 = 14.
Question 2 of the SBAC Practice Exam requires a graph:
2. The distance (d) in meters a car travels in t seconds is shown in the table.
d t
10 1
20 2
30 3
40 4
50 5
Use the Add Arrow tool to graph the proportional relationship between the distance (d) traveled by a car and the time (t).
This question is tricky because the distance is shown on the y-axis even though the table lists distance in the left column, where the x-values usually are given. The scale on the distance axis is 10 while the scale on the time axis is 1, so the graph ends up looking like the identity function even though its slope is officially 10, not 1.
SBAC Practice Exam Question 1
Common Core Standard:
Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 32 × 3-5 = 3-3 = 1/33 = 1/27.
SBAC Practice Exam Question 2
Common Core Standard:
Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.
Commentary: In this section, I'll write about how my own eighth graders dealt with these questions as they faced them. Naturally, many of them forgot the laws of exponents. This might have been a good time to sing my exponents song -- the eighth grade verse of my parody of the UCLA fight song. The graphing was a little tricky because of the x-y reversal.
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