Saturday, January 9, 2016

Day 79: Transformations Intro Screencasting & Residual Plots



Today's estimation is how tall is Jefferson's house at Monticello. Some students thought it was 5 Mr. Joyce's tall so 5*6 after rounding my height up to 6 feet. Some students thought it was about 7 short students tall (7*5).

Analyzing the LSRL before getting predicted values. (accelerated class)

I collected students pre tests they could revise and their follow up worksheet for their FAL Classifying Systems.

Volunteers read the introduction to 6.1.1 for Rigid Transformations. We did an example together with students telling me what to do, what button to press, while I showed them my colorful posters describing the buttons.

This year, instead of students copying down the steps on the left of the transformations, students worked in pairs and recorded a screen cast explaining their steps. I also asked them to write a reflection to accompany their video post. I think they can go back and improve these tomorrow. I'm contemplating doing Polygraph: Transformations after they practice it in their composition books on a coordinate plane tomorrow.

Students worked in pairs on solving key lock puzzles using rigid transformations.
  1. In pairs you will login to one of your google accounts. The blog post will later be posted to this persons.
  2. First you will install a Chrome extension called "Snagit".
  3. Then you will practice by solving the first 3 key puzzles together.
  4. After you've practiced together, you will record a screen cast of either a Wall, Star, or Challenge puzzle.
  5. Once you've picked one, you'll record yourselves solving it. Start off by talking about your plan, and then executing it using the Translate (slide), Rotate (turn), and Reflect (flip) buttons.
  6. After you've recorded it, go to your blog at Blogger and post a reflection of what you learned and a link to your video.
Check out my students work at @joycemathletes .

Here students were collaborating solving the key lock puzzles.
Here's a sample made by the students above:


In accelerated students first matched 3 scatterplots to their correct residual plots. Students inferred that the horizontal axis of the residual plot represented the line of best fit, or LSRL. They noticed that the further the residuals were from 0, the further the actual data points were away from the predicted values on the line. I was pleased with their interpretation.

Sample problem from class.

Then I showed students how to input their L2 or Y coordinate values from Friday into their TI 83 graphing calculators L3 column as the equation "a*L1+b". Then I asked them how you calculate residuals. They said it's actual minus predicted. So, what expression represents that? They said L2 is the actual and L3 is the predicted, so do L2 - L3. We put that expression in L4.

We then plotted it by going to STAT PLOT and turning Plot 2 on and setting its y coordinate to L4, but keeping the L1 value the same, just like how they matched it up.

I asked them if the model for the pizza toppings and prices was a good linear fit. They said that since the residuals were close to the horizontal line at y=0 on the x-axis, then it must be a good fit. It's a strong association.

I made posters to help students. I want a student with neater writing to re-do my posters so they're easier to read and follow, but this is what I came up with so far:

Thanks to Sarah on twitter for the inspiration for this poster... which motivated me to make the others.
One of the most basic features of a graphing calculator: input x y table data.
Students were bummed how much more complicated it was to make an LSRL calculate predicted values

Oh I almost forgot. Students predicted what it would be if you added all the residuals together. They said zero because the data above the line, cancels out to zero with the data below the line, and the LSLR has the least squares of those residuals (last part hard to explain)

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