Friday, January 8, 2016

Day 78: Systems: Equal Values, Fraction Buster & LSRL with TI 83s

Today's estimation was the Eternal Peace Memorial. A lot of students underestimated. Some said it was 5 Mr. Joyce's tall, so round up and use 6 feet and multiply by 5 to get 30 feet. It seemed like the accelerated class had higher than the answer estimates and saw the scale of the perspective.

Students were to revise their pre-test, after spending a day and half completing their posters. Here are a couple examples I picked out:

I like how these students used sharpie to emphasize their connections.
I feel I should have emphasized why the bottom 2 right are infinite solutions and prove it by manipulating their equations. IE writing x+2y=8 from standard form to y=mx+b form.

Here you can see Kyle C wrote his equations, and set them equal to each other using the Equal values method. Then he decided to multiple everything by 6 to use the Fraction Busters method. You can see he checked for their height on the right.
Some students are more comfortable making the fractions have like denominators and working with them that way, and I made sure to honor these types of solving strategies first before showing Fraction busters, when possible.
Here students observed what the graphs of the systems looked like after solving using algebra. Some students pluggred in 42 days, for 6 weeks, while I loved hearing students who reasoned that at 30 days they were the same height, and since 2/3 is a greater growth rate than 1/2, Plant A will have to be taller after 42 days.
Notice how this student also subtracted 5 from both sides first, but decided to eliminate one fraction at a time. I asked him how he could have eliminated them both at the same time with the LCD. He realized that number would be 6.
Here J showed his intermediate step of multiplying the two fractions properly by 6/1. One whole group forgot to multiply the whole numbers and noticed how that changed everything.

In accelerated students worked on a problem about number of pizza toppings and prices from 8 local pizzerias. They wanted to figure out how to predict the price of a 2 topping pizza. One student wanted to get the average price per topping by dividing. Another student suggested we plot the data and get a line of best fit to predict the price of a 2 topping pizza. We went with that plan.

Students worked in pairs with a TI 83 or + calculator between them and I showed them how to input the x and y values (toppings and price, respectively) in the L1 and L2. Some of my calculators had the L1 and L2 headers not there, so that's something I have to trouble shoot.

I would say there was 80% success rate with plotting the data and writing out the Line of Regression with the variables. I will post my instruction posters on the blog on Monday.
I need to look up this error.
And this one.
Not sure about this one.

Students used the TRACE function on the LSRL to find what y= when x=2 on the line. I think students appreciated the simplicity of yesterdays Desmos lesson in how easy it was to input data, and to write in y1~mx1+b.

On Monday students will match residual graphs to scatterplots. Then they will look at the residual plots of the data from Friday.

Note to self: Desmos: Polygraph Systems of Equations during extra time with Chromebooks.

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