Algebra CP – We finished our chapter on exponential functions and had our test. Most of the kids are doing really well, some are better at finding the constant multiplier (b) when given a table than if they are reading it in a situation. They just want to say, “Oh, 6.25% increase? That means b must be 6.25.” What? No! Add that to your 100%, then change it to your decimal. We’ll still work on it, and the homework still has them finding the exponential functions so I think it will be okay.
Our current chapter is on Quadratic Functions. We’ve started factoring, and everything is through the generic rectangle (we did use algebra tiles initially, then moved on to the rectangle. I’ve used the generic rectangle before and the X to help factor before, but 1) I had never thought about the diagonals in the rectangle (see picture below – Casey’s Pattern) and 2) had never included the x’s when thinking about “what multiplies to this and adds to that”. CPM really ties everything together so well, so the generic rectangle and the X make sense, and there are patterns in them… honestly when I used them 8-10 years ago they were just “a trick”, or way to help factor, we didn’t explain any of the Why, just the How!
Math 7CP – Last week we did a couple of days review then took the Trimester 2 Benchmark from our district. We aren’t going in the same order as the book, and haven’t taught inequalities yet, however there were 5 problems about inequalities on the Benchmark. So, we gave the kids those answers, then calculated their scores out of 20 questions instead of 25 questions. Overall our kids did really well. Unfortunately, most of the questions were DOK Level 1 on the test, and we’ve really been trying to do more DOK Level 2, and even some Level 3 questions with our kids. But that’s why they thought it was pretty easy and did so well. We also looked at the Grade 7 Math Performance Task on the CASSPP Released Questions so we could talk about everything that is looked for. The kids are getting better at reading the questions to make sure they’re answering everything, and they really need to do that on the Performance Task! Hopefully the one on the actual test is as interesting as this one was so the kids get into doing it.
This week we started Unit 7, Geometry. We began with circles, and on 3.14.17 did the measuring the circle to find the diameter and circumference (using string and rulers) to derive pi. One group was really close with their measurements, others not quite as accurate, but our class average was 3.25, which is pretty good! The next day we did the Fractions Circle activity by Illuminations (scroll down to see this activity, it’s the second one). We did this last year too and really like it – it’s better than cutting the paper plate apart! I didn’t have enough time to have them understand how the “base” of the cut-up-and-glued-on-as-a-rectangle-shape was 1/2 of the circumference, so 1/2 of pi(d), which would be pi(r), since 1/2 of the diameter is the radius. So the next day we continued and I think it was a little clearer. One of our mixed review problems for homework on Wednesday was: “4. A bicycle wheel has a diameter of 60 inches. In one turn, how far does the wheel travel in feet and inches?” (it’s a really big bike LOL). I had RTI that day and a lot of kids were asking questions on that problem, so they totally weren’t relating the circumference to the distance. Soooo, as I was taking a shower the next morning I was thinking about what I could do to help them see this relationship. I thought about bringing in an orange and using a slice of it, but decided a banana would be better. This is what happened the next day: I had kids come up and explain how they did problems 1-3, then I talked about problem 4. I brought up a small knife and my banana and cut a slice about the width of my little finger from the center of the banana (one student says “you’re wasting food”). I told the class, “This is my wheel.” Then I marked a green line on the peel, and told the class, “OK, now we need to see how far the wheel travels until this green line is on top again.” So I rolled the banana slice along my paper until the green line appeared again, and made a line for how long that was (I’d marked where we started). Then I cut along the line, ate the banana slice (“No, I’m not wasting food”) and opened up the peel to show that it was the same length as the line! Then I made it a circle again! I think this helped the kids see that the distance traveled in one turn was the circumference. I ate a little more of the banana and other kids wanted a bite so the rest of the banana was disposed of without any waste. (HA! I showed you, you 7th grade boy!) I liked this idea, and I’d definitely do it again. We worked on circumference and area problems for the rest of the week, and took a little group quiz today. When we were doing the problems I’d give them the diameter or radius and have them draw me that circle, with the correct line. Then they had to write down the other measurement (d or r) and the formula for the Circumference and fill in the numbers and find the answer. Same for Area. I told them each problem would be 2.5 points – 1 point for the formula, one for the correct answer, and 1/2 for the measurement. So if they just write the answer they only get 1 out of 2.5 points. Today when going over the HW neither kid had the equation or the measurement. I had them write them on their paper, and reminded them that I need to see the formulas! The CAASPP expects the students to be able to “know and use the formulas” and doesn’t put them on the test (PARC does). After that we did a few more review questions then did the Historic Bicycle Task from MARS as a group quiz. I helped them convert the measurements some because they’d have to recreate it again in the last problem….it looks like about 1/2 understand so we’ll keep working on it!
Math 7 Accelerated – We also started a new chapter! Last week we finished Ms. Pac-Man on Tuesday (I was out at the UCSB Math Leadership Cadre) and then used grade 7 TEAM UP! cards to do review for a few days. We’re learning the 8th grade standards so the kids can be accelerated to honors algebra 1 next year but they are still going to be tested on the 7th grade standards so we need to review/teach some more before the testing starts at the end of April.
This week we started on our Data Analysis and Slope Chapter. The first couple of days we made and talked about circle graphs, categorical data vs. numeric data, and reviewed Box Plots (AKA Box and Whisker Graphs). Yesterday and today we started slope, revisiting y = mx + b and comparing and finding slope on a graph today. The groups worked pretty independently today and I walked around and joined a few of the groups. I think it was a good day for them because they got to work at their pace in their groups. Happy St. Patrick’s Day!
Here’s a picture of what my backyard looked like this morning. We’ve had so much rain and now it’s warm so there are flowers galore!