Today started off with another silent board game. I was surprised that out of the whole class, roughly 5 to 8 in each class figured out the rule and could contribute. I think the issue is students can multiply by a negative, but then when adding a positive to a negative they are not fully proficient. We will definitely be spending a day some point soon on adding and subtracting integers using plus and minus tiles along with a number line.
The lesson then continues with Mr. Wallis' tip table. I asked students what background knowledge they knew about giving tips at restaurants and how much they should be. Some students knew that it is money you give to the waiter based on how good the service is. They also knew that it was a percentage of the dinner bill. Students contribute 8 typical prices for a dinner for two at a restaurant. This gave me a chance to share with students that at the dinner where I proposed to my wife it cost me $180. They calculated and were amazed that on a 15% tip I payed the waiter $27. I told students in small groups that the wait staff was very attentive and helpful and I gave them more of a 20% tip.
Students calculate the various tip amounts, estimate some tips, and then re-familiarized themselves with dependent and independent variables and how the y axis is always the dependent variable. We related it back to the height of John's giant redwood tree depends on what? The years it's growing they answered. I also related it back to the Newton's Revenge problem where the dependent variable was their reach, which depended on their height.
Students graphed it, and then didn't get much further than that. It was Wednesday, short day.
In accelerated, we discussed the first problem with getting the dimensions of an algebra tile collection. Haley caught a mistake in my drawing and the class gave her a hearty clap for noticing.
Then students worked together on building the collections. They worked together pretty well. I must say, I walked around and didn't interrupt much because they were busy the entire time. I've taken some pictures of some of their collections as they follow:
Here students were given (2+x+y)(x+4) and came up with this figure! You can see that the sum of it's parts is what you get from multiplying it, which is x^2+6x+xy+4y+8
Here they are in the process of building a collection...
And the finished product with all tiles turned over to the positive side. They were given (x+xy+2)(2x+5) and came up with 2x^2+9x+2xy+5y+10.
Students really enjoyed using the manipulatives. They did complain that it takes awhile to set it up with the tiles, but it makes it quite easy to combine the like terms. It also helps students who are kinesthetic learners and like hands-on learning.