SOLs Covered: 8.9 Pythagorean Theorem; 8.6 Surface Area & Volume
Math Unit: 15 Pythagorean Theorem; 16 Surface Area & Volume
Daily Agenda: Feb. 27-28 & March 1-3, 2023
Upcoming Assessments: Quiz 3.03 Surface Area & Volume (A-Mon. 3/6; B-Tues. 3/7); Unit 4 Test (A-Wed. 3/8; B-Thurs. 3/9)
Happy Friday, folks! I've got a family gathering later, so let's get straight into this week's math happenings. The B-day students got the same review of rectangular prisms and cylinders that the A-day students got last week. Tuesday and Wednesday were spent exploring what happens when you change an attribute (a.k.a. dimension; length, width, or height). The students discovered that the volume changes by the same factor the dimension changed and though the surface area didn't change by the same factor, it did increase or decrease accordingly. We talked about how they could determine the scale factor by which a prism was adjusted either by setting up the changing attributes or the two volumes as a ratio; the ratio should be greater than one if the shape is getting bigger, but less than one if the shape is getting smaller.
The kids found that aspect of the topic pretty easy, but the square-based pyramids and cones we moved onto Thursday and Friday were a little intimidating at first, predominately because the formulas are a little more complex and some of the dimensions aren't immediately obvious. We walked through the process of how to do the problems "old school" style, which for me means starting by copying the formula (some folks skip this, but I find it prevents students from missing parts and will help them not have typos on the calculator), identifying which values are needed, plugging them into the formula, and then calculating the final surface area and/or volume. As mentioned, the kids were a little freaked out when they realized that some of the necessary dimensions were not provided, but we then discussed how they would sometimes need to find the missing values for height (h, altitude) or slant height (l) (occasionally the side of the square or the radius) using the Pythagorean theorem we just covered. The slant height would form the hypotenuse (c) while the height (along with half the square's side or the radius) would form the legs. There are also parts of the pyramid formula that require the use of other formulas, specifically the square formulas since we're only required to work with square-based pyramids at this stage. All of this makes for very complex problems, but the kids got the hang of it and while they groaned at all the details needed to set up their Desmos calculators after the "old school" method was covered, they appreciated how easy that made solving the rest of their work.
Speaking of Desmos, I plan to add some "Desmos Hacks" documents to the unit folders to help students remember how to set up the different problems. While I'm able to help them now, no one can tell them how to set it up the day of the SOL test, so they need to remember that for themselves. They will have access to the formula sheet, but the won't have any reminders for how to set up the formulas nor what additional elements need to be included. I plan to add these to other units where relevant and as I think of new things, so as students start their reviewing at home, they'll be able to reference these guides as well.
Well, that should cover everything for this week. As always, please let me know if you have any questions. Hope you all have an amazing weekend!