Thursday, October 22, 2015

Day 36: Complete Graphs, Graphing & Generic Rectangles

Today's estimation was how many red vines in Mr. Stadel's hand. I liked how one student grabbed a handful of pens from his supplies, counted them, and then rounded up. I thought that was a creative strategy. They will use that clue to estimate how many are in the whole package.

Today started with a Silent Board game. It was nice to discuss how students saw the rule after seeing students mistakes. I commended students willing to make a mistake and also how that mistake provided a valuable clue for them and the rest of the class.

Then they analyzed three graphs with errors on them. This lead to them understanding 3 aspects that make a complete graph:

1. The x and y axes are labeled with number intervals or else you don't know the coordinates.

2. The line must extend all the way left and right and also have arrows on each end. (we also discussed what it was called without arrows. At least one student knew it was called a line segment. Then I offered a bonus question. What if it ends on one side and extends with an arrow? They knew it was called a ray)
3. The x and y axes must be labeled.

Then students were instructed to graph y=-x+1, y=0.5x+2, and y=x^2-4. I asked students how you could read y=-x+1 after seeing mistakes in 2nd period. They only knew one way, so I asked them when we brainstormed the meaning of minus, how do we properly say -(-3)? Students remembered that that is called the opposite of -3. So, the equation can be read, "y equals the opposite of x plus 1". I had them copy that. I asked them what is your first step before you graph a rule? They said make a table. I showed them a horizontal table, but also made a T symbol and showed you can make a T chart, which is a vertical table. I also said you always want to include 0, but include two numbers to the left and right of zero for a complete graph, so x values of -2 through positive 2.

Evelina's graph was nice and compact, no wasted space!

Then students graphed, I circulated and asked clarifying questions, especially those who numbered axes in the wrong order. They also analyzed how the graphs were the same and different. They also labeled their x and y intercepts with coordinates. I also did some community building with mathographies with 15 minutes to go.

Jarren was moving along quite nicely on all 3 graphs! Next stop: labeling x and y intercepts.
In accelerated we discussed the pattern for fractions with a denominator of 9. I threw at them, what would 4/9 be then? What about 9/9? They said 1. I said is there another way based on the pattern? They said .9 repeating. This proves that .9 repeating is equivalent to 1.

We also read the math notes box aloud that introduced the vocabulary polynomials and binomials. They worked on distributive property, and then were introduced to generic rectangles to multiply binomials.

So each week I build community in my class with letters they wrote to me at beginning of year. I said stay standing if you are helpful in groups, if you love classic video games like Zelda, stay standing if your birthday is August 3rd. Then we honor that student with 3 second clap and I ask them to elaborate about themselves. Well my accelerated class is same 32 kids from last year so one said how come we don't get to find out more about you? So I gave them all a post it note and said sign their name on it and ask me one appropriate question and I'll read it and answer it to the class each week. One question was why do I love game of thrones so much? This week was can you beat Harrison in an arm wrestling match? With 2 minutes to go in class I had to oblige. Very fun. I won but not easily. Haha.

Here is a link to an arm wrestling match between myself and my student Harrison:

1 comment:

  1. We all lost our voices afterwards due to all the cheering for Harrison (Alexis)