Learning Module 2 of the Illinois State text is called "Show Me the Numbers." Recall that the first four modules are identical in all three grade-level texts.
In this project, students are to take wheels of various sizes and shapes. They measure how far the wheel goes from one to five revolutions, and then display the information on a graph. And so just as the first module has them practicing tables, the second has them practicing their graphing.
Today I decide to do the project only with eighth graders. This is because the sixth graders are having some major behavior issues, and the seventh graders meet only for music on mixed-up Wednesdays. I have only two types of objects with wheels -- some small Hot Wheels and some larger toy cars that I purchased at the 99 cents store for a quarter each.
Again, the reason for doing projects is that it's always more interesting to record data and graph it than it is to just to graph some meaningless numbers. This is why I hope that not allowing the sixth graders to participate will be an effective punishment -- I tell them about all the fun the older students are having and they're missing because of their behavior.
As it turns out, the Hot Wheels are sized such that after five revolutions, the car will have traveled a little less than ten inches. So each revolution is about two inches, and the students end up graphing the points (1, 2), (2, 4), (3, 6), (4, 8), and (5, 10) -- in other words, the equation y = 2x. If the students are using the centimeter side, then five revolutions are almost 25 centimeters, and so the points end up being (1, 5), (2, 10), (3, 15), (4, 20), and (5, 25) -- the equation y = 5x.
The bigger cars are a little harder to measure. I believe that five revolutions are supposed to be about 35 centimeters, so the points should be (1, 7), (2, 14), (3, 21), (4, 28), and (5, 35) -- in other words, the equation y = 7x. But the problem is that the students often placed the back wheels at zero but measured the distance from the front wheels. The length of the car is about 10 cm, and so the graphed points were closer to (1, 17), (2, 24), (3, 31), (4, 38), and (5, 45). But this is no problem -- now the students are graphing linear equations like y = 7x + 10 that don't pass through the origin!
One group finishes quickly, and so I decide to have them use the mousetrap cars from Module 1 as a third set of wheels to measure. The mousetrap cars have three wheels -- one tiny wheel in front and two larger wheels in rear. I tell this group to measure using the larger rear wheels, since the front wheel will probably give a graph much like that for Hot Wheels. As it turns out, five revolutions using these larger wheels are almost two meters! So the graph ends up being (1, 40), (2, 80), (3, 120), (4, 160), and (5, 200). I tell the students to graph them on the same set of axes -- so if the graph is just large enough to graph (5, 45) from the previous car, it can barely show (1, 40).
The plan is for the seventh graders to perform the project tomorrow. The sixth graders will still make a graph -- except it's using the older kids' data, since they won't be allowed to use the toy cars.
In fact, the next page in the sixth grade traditional text after is a graph for some strange reason. Out of the blue, the students are asked to graph y = x + 5 and y = 7x. So today, I have the students graph the equation y = x + 5 as an introduction to graphing -- that is, I told them all about what the x and y-axes are as well as the origin.
I don't have time to show them y = 7x today -- but then again, tomorrow I'm giving them the data from the toy cars, and hey, isn't one of them y = 7x (if measured from zero correctly)? So in the end, I really am having them graph y = 7x from the text!
Recall that on Wednesdays, I give my eighth graders a science period. Today I decide to go to the next physical science lesson from Sarah Carter, on scientific notation:
http://mathequalslove.blogspot.com/2016/09/scientific-notation-ordering-cards.html
Some students figure out the order quickly after just one hint -- when I tell them that if the exponent is positive, the number is greater than one. Oops -- I probably should have done what Carter suggested and had a second set of cards ready for them.
Today is a two-day post, so let me give my plans for tomorrow. It's an assessment day -- eighth graders get a General Quiz, seventh graders get a Dren Quiz, and sixth graders get a test (after we finish graphing). The eighth grade test will be on converting rational numbers from decimal to fraction form and back -- and includes one question where they must name an irrational number.
Each day, I will continue to link to the "A Day in the Life" poster assigned to today. Again, there are many middle school teachers participating, but the poster for the 14th is a high school teacher -- in fact, it's none other than Tina Cardone, the creator of the "A Day in the Life" challenge. Here is her post for September 14th:
http://drawingonmath.blogspot.com/2016/09/day-in-life-sept-14.html
Cardone writes that she gives her Honors Algebra I students a "challenging puzzle" -- it took me a while to figure out that she's referring to the famous "four fours" puzzle, where one tries to write the numbers from 1 to 100 using four fours.
Also, I think it's interesting that Cardone has even fewer students than I do -- just 60, which must be a rarity at a public high school such as hers.
My next post will be on Friday.
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