## Wednesday, May 18, 2016

### Day 161: 2 way frequency tables & measuring the center

Today's estimation was the value of a bowl of nickels. It's a great followup to estimating the bowl of pennies. Students reasoned that nickels are bigger and thicker than pennies so it had to be less than 450 coins. So some said 50 less so 400 nickels than multiplied by 5. 2000 cents 20 dollars. Some students thought of it has instead of 9 rolls of pennies maybe 8 rolls of pennies. I don't want to ruin the answer. Also one student thought of it as layers and I took that opportunity to relate it to finding layers of a circle bases to find the volume of a cylinder. Tomorrow is dimes!!
I started by reviewing the trashketball lesson. I had a student volunteer and closed it out by rewriting it on the board after students broke down the clues and the steps.

To launch 2 way frequency tables I told students I had a hypothesis. I predict that students who play an instrument are more likely to play a sport. Not many students believed this. Many students play a sport and not an instrument. But in general in most classes the majority of students who played a musical instrument also played a sport except 4th period.

This task was adapted from Illustrative mathematics. I made half sheets of class rosters. I asked students what 2 questions I had to ask to everyone in the class. I labeled these at the top of 4 columns with yes no yes no below it. Then I had students think of the answer to the first and second question and to be prepared to go down the list. A few hiccups a long the way in one class but we got our data.

I asked students if it was easy to see if my hypothesis is correct. Some said yes some said no. This is when I introduced the definition of a 2 way frequency table. I showed and will reiterate the differences between joint (inside box) and marginal (outside box) frequencies. Tomorrow we will talk about relative frequencies to further analyze it.

As the standards say below students will need to describe a possible association between the two variables.

 2nd period definitely backed up my hypothesis.
 3rd period. 9/12 musical players also play a sport. Pretty good results, looks like an association.
 This is 4th period. They were the first class whose data did NOT back up my hypothesis.
 5th period. All 16 musical instrument players play a sport! Money results!

Then I asked students to think of 2 questions with yes or no answers to help you figure out an association. Students took their time but came up with some good hypotheses (some commented how it felt like science class).

People that have a cell phone are more likely to be on social media.

Students who play video games tend to go to sleep after midnight.

People that have an iPhone also probably have snapchat.

People that have Instagram in this class and people who follow me on Instagram.

People that are girls are still just as likely to play a sport than boys.

Tomorrow we will revisit and make sure students know what joint, margin, and relative frequencies are.

In accelerated students gave feedback on each other's posters. I am going to post a standings where students post their iqr or interquartile range to see who was the most consistent. (Lower the better because smaller range in 50% of data)

Then they looked at how the median of two city price listings could be the same but their means could be much different. The center can be described in 2 ways and some situations one is more effective than the other.

Then they looked at 2 medical procedures that detailed response times to an emergency. One was consistently under 15 minutes, while the other was a little more spread out. Students made arguments for each case.

 I thought it was funny that the student wrote "units!" with an arrow. I'm pretty sure they didn't want points to be taken off! Standards of mathematical practice: attend to precision.
I found this great link to 2 math board games here http://blog.mindresearch.org/blog/big-list-mathematical-board-games. The last 2 or 3 days of school I will have the substitute make these available to the students. I printed out the first 2, Achi and Dara.
 I tutor a 10th grader and these are the topics in Algebra 2. As teachers have been discussing on twitter, it's a disjointed mess of topics. I feel the Common Core standards
Regarding 2 way frequency tables, coincidentally, I saw a few math teachers discussing it. Next year I'd like to incorporate this as my notice and wonder to immerse students in the power of the data display. I do want to know what the situation is about first because I'd hate to leave them without knowing the context.

#### 1 comment:

1. Thank you for sharing and printing out the Achi and Dara board games! I look forward to hearing how the games play in your class. -Calli Welsch, Communications Specialist, MIND Research Institute