Algebra – We came back from our Winter Break (aka Christmas Vacation when I was in school) and started chapter 5 in the CPM Core Connections Algebra Book. It’s on Sequences and I’m looking forward to teaching it because it’s so different from the 1 section that would be on sequences in the old Algebra book I’ve used.
We started out by representing exponential growth by looking at bunnies reproducing. There were several different situations that we looked at, drew patterns for and graphed. Next came dropping a bouncy-ball from different heights and seeing what the rebound rate was (it was raining that day, so we had to go into the “Jungle Hallway” – see the pics). We calculated the “rebound ratio” and figured out that this was the slope of the line.
The next day we used the bouncy-balls again, except this time they caught the ball at the top of the rebound, recorded that height, then dropped it from there again. This graph was ball bounce to bounce height – and showed exponential decay! It was pretty cool.
Math 7 – We decided to finish up proportions and come back later to equations again. We (awesome co-teacher-Maddy and I) need to do more work with using inverse operations to solve equations that have fraction answers. Our kids are really good at “undoing” or “looking inside” the equations to find the answer when it’s an integer, but we want to work more on just “using inverse operations to solve the equation” so they have another resource when the equation isn’t as “nice”. So… we did big white board review of proportions – we gave the kids a situation and they had to write the proportion from it and solve it – and equations, and some area and perimeter. (We started reviewing area and perimeter in homework, so put a perimeter question on our test.) Wednesday we used Mr. Orr’s awesome post on a site he found “Internet in Real Time”. The link to the original site wasn’t working so I found another one that showed the numbers changing (go look at his post!), then froze it at one second. The kids made up problems on the white boards (if there are 214 tweets per second, how many tweets would there be in a day?) and then walked around the room looking at the different questions. Then I called on a few kids and they picked one of the problems and we all solved it – and explained how they solved it. I NEVER had to explain how to figure out how many seconds were in a day! They said 60 x 60 x 214 because there are 60 seconds in a minute and 60 minutes in an hour, then times that by 24 for the hours in a day. WooHoo!! On Thursday we did some more proportion problems and then on Friday they took a team test. We started out by having the kids work in pairs, then they could check their results with the pair across from them. And, a lot didn’t finish, so they’ll finish today.
I think the reason they didn’t finish is because we are still discussing the homework everyday, but that is so great! This week one problem was to write a situation for 157 – 162 and the student that was explaining it said he lent his mom $157 and then spent $162 ( so -157 – 162) and got -319. Hands went up. He called on a student who said it wasn’t -157, just 157. The boy explaining said, “But you can’t take away 162 from 157, it doesn’t make since. You can’t spend more than you have.” I said “What if you reversed the problem?” So then he wrote -162 + 157 and said, “Oh, it’s -5.” I loved that 1) kids questioned his answer, and 2) he thought about it making sense when writing his story and 3) realized he could have reversed it. This is the best homework, and use of homework I have ever done.
Math 7 Accelerated – We also started a new chapter, Chapter 4 in the CPM Core Connections 3 book. It’s on patterns and equations, tables and situations, and tying them all together. The groups all had patterns that were all quadratic, and we were working on “seeing the pattern number in squares and rectangles in the patterns”. It was pretty cool seeing the different ways the kids “saw” the patterns. We spend a few days doing it – and used Fawn’s site www.visualpatterns.org for some extra examples. On Friday we started talking about y=mx+b and where the m and b are shown in the patterns. It is so much fun watching the kids “see” the growth.