## Saturday, March 25, 2017

### Systems of Equations Through the Lens of Child Labor

My latest project consider the importance of social justice conversations in the classroom and how those conversations can naturally take place within the secondary mathematics classroom. With this in mind, my goal has been to write a series of social justice-inspired math activities with different high school content foci.

Here is the first. Note: I literally just finished this, and it has taken FOREVER. These are still in draft mode though, so they will likely (read: definitely) need editing. Please, if you decide to review them, let me know of any or all issues. I really want to polish these up.

Before I began teaching, I worked in Washington, D.C. at an international trade law firm. Lots of the work I did centered around labor issues in different countries, and thus I became very familiar with concerns of child and forced labor around the globe. The activity below introduces students to the issue of child labor and forced child labor blended with 3-variable and 2-variable systems of equations. This lesson is not meant to introduce the idea of systems but rather serve as a type of review activity. This lesson is meant to span 3-4 days and is built in Desmos Activity Builder as well as ThingLink and GoogleDocs.

Teacher notes: Divide the class into 8 groups of 3 or 4. Each group will be assigned a different region of the world. At the end of the lesson, each group will report back their findings concerning their region of the world.

Links to Activity (NOTE: It is important to make your own copy of this activity and then run it from teacher.desmos.com):

North America: https://teacher.desmos.com/activitybuilder/custom/588fd6f23d61c71e3aa19481
South America:https://teacher.desmos.com/activitybuilder/custom/5893cefd7548c7ff1aab520d
Europe & Oceania:https://teacher.desmos.com/activitybuilder/custom/589d25bedfd541181c3a3f26
West Africa:https://teacher.desmos.com/activitybuilder/custom/589d2dc4b776cc1b0d6f2e89
North & Central Africa: https://teacher.desmos.com/activitybuilder/custom/589d2d82b776cc1b0d6f2e73
East & South Africa: https://teacher.desmos.com/activitybuilder/custom/589d2d10b776cc1b0d6f2e67
West & Central Asia: https://teacher.desmos.com/activitybuilder/custom/589d2e36b776cc1b0d6f2eda
East, Southeast & South Asia: https://teacher.desmos.com/activitybuilder/custom/589d2dfc13dc6f5f1d6a56f3

While the students are working through these activities on their devices, the instructor needs to have the following two graphs pulled up and displayed so students can compile regional data near the end of the activity.

Counts Compiled Data Graph: https://www.desmos.com/calculator/mmsqwjskna
Percentages Compiled Data Graph: https://www.desmos.com/calculator/il0flhd0pq

Teacher Notes (Part 2): It is CRUCIAL that the instructor move about the room and push conversations as groups arrive at the interspersed reflection questions. When groups compile data onto the master graphs on the teacher device, it is also important to have comparative discussions at that juncture.

Again, please let me know of any issues or suggestions with these activities! Enjoy!

## Wednesday, November 23, 2016

Yesterday was our last day before Thanksgiving Break, and I wanted to do something a little bit holiday themed that was grounded in real-life application and still incorporated the fraction work we've been doing lately. So, I came up with the idea that we were going to cook Thanksgiving side dishes for 50 people (the school staff, local fire departments, etc.).

My students were paired up in groups of four. Each group was given a recipe for mashed potatoes (thanks Pioneer Woman), corn pudding (kids thought this sounded gross), green bean casserole (most of my students had never heard of this - WHAT!!!???!!!), and pumpkin pie. Each person was responsible for one side dish. Note: The traditional Campbell's Green Bean Recipe was hard, as it calls for cups of green beans. Note x2: Everybody thought corn pudding sounded disgusting and wanted nothing to do with that recipe.

Here are the recipes I chose (courtesy Pioneer Woman and AllRecipes.net):

Students each had a copy of the recipe, then they multiplied the ingredients up so that the recipe would serve 48-50 people (mashed potatoes serve 50, everything else 48 people). This helped students practice multiplying fractions as well as converting between mixed numbers and improper fractions. We also did a little conversion here with teaspoons to tablespoons, etc.

Then, students had to write-up their recipe on an index card along with summarized steps. I shared with them that it is common, when sizing up a recipe, that you record the final amounts so you don't have to re-do all the calculations again.
Next, students had to make a grocery list using the template below:

To find prices, we used the website of our local grocery chain, Food City. They have pick-up grocery ordering, so every item is searchable on-site and includes pricing information.

Note x3: Kids really don't know much about grocery shopping. Multiple kids thought pot pie was an acceptable pie shell. When students needed something like 2 tablespoons of cinnamon, they thought they'd need to buy 2 bottles of cinnamon spice. In other words, this was a very practical, helpful exercise for students. However, they desperately need more work with things like this. Making a note for later...

## Monday, August 29, 2016

### Segment Addition Exploration with Cuisenaire Rods

This weekend, I was working on a special project, and I was pushing myself to develop a conceptually rigorous activity for the segment addition postulate. When you search for segment addition postulate activities, you find a lot of problem sets, a lab or two on paper and Geogebra, and a few other odds and ends. Don't get me wrong - some of these are great. However, I really like for kids to build conceptual understanding through hands-on exploration. So, I wrote the following activity:

First, students are given a set of Cuisenaire Rods. They will need 2 lime rods, 2 orange rods, 2 red rods, 2 fuchsia rods, and 1 of every other color. This exploration will likely work best in groups, so you could easily give one group of students a set of rods, rather than each student a set. Note: If you don't have Cuisenaire Rods, You could probably cut down some popsicle stick or something. It'll just be a lot of cutting.

First, explain to students that this is a complete set of Cuisenaire Rods:
It is their job to find the length of each rod without using a ruler. Instead, they will have the actual rods to manipulate at their desks as well as corresponding algebraic expressions for the length of many rods.

Next, students will need access to the problems. I have the problems in a PowerPoint file, but I'm thinking each group probably needs a handout at their seat so they can work at their own pace. Regardless, here are the questions as a converted PDF file. If you want the PowerPoint, click HERE.

Ask the kids to work through the problems and solve. You will need to circulate around the room and prompt students when they are stuck. This activity will likely come easily to some and less easily to others.

After students have successfully solved for the lengths of these bars, the should check their solutions against the whole set to see if their solutions make sense. They could also double check themselves with a ruler( Note: measurements are all in cm).

Then, the last four slides of the PowerPoint is hopefully where the geometric representations and algebraic thinking gels. What similarities did students notice? Differences?

The last three slides takes you through the three different types of problems encountered in the activity and asks students to discuss how they viewed and solve that particular type of problem.

I am excited about trying this lesson in a classroom soon. Special thanks to @pamjwilson and @mrdardy for their help in developing this activity.

## Sunday, August 28, 2016

If you are interested in this post have haven't read Teaching Segment Addition with Types, I strongly recommend you skim that first before reading this post.

Now, moving on to the fourth day of segment addition and betweeness postulates, the students just needed to practice.To do this, students completed some Socrative Practice problems using the three types. Basically, each problem becomes two questions. In the first question, students must classify the type of Segment Addition problem. Then, in the second accompanying question, students must apply the strategy needed to correctly solve that particular type of segment addition problem.  Here is an example:

If you would like to use this Socrative practice assignment, just use the following code: SOC-17443219

Teaching kids to first identify the type, recall the strategy, and then solve in this very systematic way proved so beneficial for my kids and for further applications later on in the year.

### Teaching Segment Addition with Types

In the past, as I had planned for segment and angle addition topics, I would almost always expect a bumpy ride. I always started the unit off with a lab/discovery activity but found my students could not transfer what they had learned in the lab to different types of segment addition problems. Therefore, I chose to give them additional guidance so as to smooth the seemingly difficult transition for them between algebraic reasoning alone and the marriage of algebraic and geometric reasoning.

I came up with three primary types of Betweeness problems. While not every problems fits nearly into one of these three categories, most do. And, by teaching my students and classifying the different kinds of geometric relationships that could exist helped them to build a firmer geometric reasoning foundation almost immediately. The difference between this lesson and lessons in prior years was quite large.

The three primary types were differentiated in the slides I gave in class. A PDF of those slides is included below:

I introduced these types over the course of two days. On the first day, we only did Type I and then quite a bit of practice. On the second day, we did Type II and III problems and practice. Then, on day three, the types were combined. Students had to classify the problems by type and then solve them. The practice sheet for their notebooks was the following:

I will definitely continue to teach the Betweeness postulates like this, simply because it helps kids catch onto the geometric reasoning layer so quickly.

## Saturday, April 2, 2016

### Making Shifting & Scaling of Data Sets Visual

Shifting and Scaling of Data in statistics is not a hard concept. However, I think it's a concept where kids can easily grasp the procedural side of the idea but really have no visual/conceptual linkage concerning what is actually happening to the data distribution. This year, I set out to make a quick, interactive Smart Notebook file that could help students see how the distribution is affected by different shifting and/or scaling attempts. The file is not complex, but it was truly effective at helping kids understand. Keep in mind that the blocks are interactive and moveable. In class, I actually move each one and then we quickly analyze the median and range to understand relationships between shifting/scaling and measures of center(location) and spread.

Slide 1

Slide 2

Slide 3

Slide 4

## Saturday, January 9, 2016

### Teaching AP Statistics Through Video Gaming

I applied for and received a grant this year that allowed me to purchase an XBox One with Kinect for my AP Statistics class. I think lots of people thought I was a crazy person, but I can't really determine a better way for kids to really understand data and different statistical ideas than creating their own data through a medium they are deeply familiar with and are curious about.

I received the materials and games I'd purchased before Christmas. During break, I wrote our first activity using the console. We are in the last few days of the regression unit, and so I wrote a Forza project to help kids review the main concepts of linear regression.

I purchased Forza 5 and decided that it would be fairly easy to do a linear regression of lap time versus placement. The premise is that the management of the particular track I selected is interested in developing a model for future aspiring drivers. The purpose of the model is to predict the ability of these aspiring drivers to compete on the current circuit, and particularly at the track I chose.

Each of my students received a letter from the track management team to both sign up as a driver and to work on the statistical analysis for the project.

Kids signed up for an after-school timeslot to complete a test lap. I used Sign Up Genius to do this.

The kids completed one practice lap and then completed their timed trial. We recorded each person's placement and time in a Google Form.

After I had all the data, I did a little regression analysis myself. I threw out all my kids that were last (there were 16 total racers on each lap). You'll see that in my write-up, I ask kids to ponder WHY I did that. If you think about it, it makes sense. You could barely be in 16th place, or you could order a pizza, take a shower, drink a pop, and still be 16th.

When I did the regression with sixteenths removed, it was very clear that there were two separate linear patterns, and when analyzed, they were very interesting. It turns out that the game went MUCH easier on the first four racers (this was on a brand new game/console post-tutorial races). When you remove those, it's obvious that post the introductory races, the pattern is incredibly linear. I forget the values, but I'm thinking that the coefficient of determination was somewhere around 97.8% with a lovely residual plot.

Here is the write-up the kids are assigned:

Almost all the kids have LOVED this project, and having this self-created data that they are genuinely interested really boosts the inquiry and depth of thought/analysis.

Even more fun is when one classmate races DURING class, we use our model to predict his/her placement and then calculate the residual. So. Much. Fun.

I hope this is the first of many AP Stats projects using the XBox. If you have any thoughts as to others I might do (especially in inference), help a girl out and let me know!

Note: If you decide to do this project, I left a few important things off of the handout. (1) Have students describe the scatterplot (2) Have students interpret the y-intercept (3) Have students analyze residual plot for fit.