Thursday, January 7, 2016

Day 76: Classifying Solutions to Systems & Data Predictions

Today's estimation was estimating my height. Some students had heard me say it before, and I loved students that saw me walk by my door where I have 2 meter sticks taped on top of each other for 200 centimeters. They said I walked by and they saw me at about 180. They were pretty accurate. The lowest estimate was 5'10" I believe. Still saw some students use decimals, after making the same mistake day 1. The highest I got was... 6"7"? No, I am not as tall as Dan Meyer, thanks. Some students compared themselves to my height, Ryan in the picture, or the tree next to me

I had students spend 5 minutes completing cards C1 to C6 of the FAL: Classifying Solutions. In some classes we went over 1 card, and it revealed misconceptions with multiplying by -1/2, adding integers, and switching the variables x and y at times. The lesson had started though with whiteboards to go over substituting a variable for x to find y, and writing it as an ordered pair solution (x,y). I asked what does x=5 and y=17 mean in relation to the graph of the equation y=3x+2? Some students said it was point, and it was difficult to articulate that it was a point on the graph of the line of the equation.

We started out on whiteboards solving for y when given x. It's not pictured, but it revealed multiplying by a negative and adding integers. In this picture, students get the bigger challenge of solving for x when given y. This really showed who was proficient or not solving two step equations.

I had to point out how this student M was showing A that you couldn't subtract 2 from both sides if the +2 was in parentheses. A was a little resistant to learning they were wrong about it. I liked how M was willing to point with their pencil at her classmate's work.
We finished with some closure, and had students label their table number on the cards. Tomorrow they will match the arrows on a poster with the 6 cards.

Here we an see the upper and lower boundary lines of the line of best of y=5x+25. The residual was 25, so students added and subtracted 25 from the y-intercepts. They reasoned data predictions would generally fall in between these two lines.

In accelerated we started where we left off with Jason showing us his scatterplot. He had skipped a multiple of 25 when making his graph and it didn't affect the data and I wanted to make a point of not getting another student's work because I asked how we could fix it. He drew his slope triangle to interpret his slope based on the scale of his axes and found his y-intercept of 25.

We heard different predictions of the humanoids height based on different equations. Most students had a slope of around 5.

Then students started on the Desmos activity I created, LSRL's based on the start of the Golden State Warriors season.

Some of students notices and wonders.

Students had different predictions of what the data represented and a lot of students predicted correctly.

The other objective was for students to make a manual line of best fit, and look what it looked like with overlay. Today and tomorrow we will discuss how these inconsistencies lead to a need for the best line of best fit, or the Least Squares Regression Line.

Look at the overlay:

After seeing the x/y table of Warriors rosters. Not labeled.
Notice all the different lines of best fit.

I forgot to have students tweet what they learned from the lesson.

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