Thursday, January 14, 2016

Day 82: Translations & Reflections, & R Squared

Today was estimating the number of words in the Gettysburg address. I liked that students used the statue of the eagle at the bottom to say that was about 5 rows, and then counting how many eagles to go up. Most kids thought there were 5 to 7 words on average in each row. I demonstrated that they were all using the basic principle of the area of a rectangle.

We started by reviewing how to move a point 10 units to the right and 12 units up. A common misconception was when an x coordinate increased by 28 they thought that meant 28 up. We discussed why it wasn't and what it actually would do. We summarized these concepts on T charts for translating and reflecting. Multiplying one coordinate by negative 1 was a big jump for a lot of students.

The eagle reasoning.

I tried to stress that yes, to translate or reflect you can count squares and see how far up down left or right to go, but that can easily result in careless mistakes. If you actually look at the coordinates, and see where the point will end up, then you can count and confirm it.

A lot of students needed to be reminded to write the change in coordinates as an equation.

Here was the agenda for both classes:

Agenda for both classes. I posted simple goals at the bottom of each agenda, did not review those enough.
Here is the work from yesterday and the type of assessment on the test tomorrow. Plotting a triangle, translating it, reflecting it, and finally rotating it.
I later added arrows in parentheses to stress the wording of each direction of movement / translation.
Here's a student's work who successfully reflected over the x-axis.

Here's a later class with arrows added. They finished the sentences in the bottom left, and all on the right.
And some more details about reflecting. After starting one sentence, students told me what to write for reflecting over the x-axis.

I liked this reasoning. Students were making comparisons to the bricks that make up the wall of the Gettysburg address.
In accelerated students analyzed the r squared value of a sample class data of shoe size and height. Students were asked to come up with other reasons for the variability of the data.

Then they analyzed a data set that ended up having an R squared value of 1. They realized it was actually not a scatterplot then because it was points on the LSRL line. Students used TI 83 calculators to analyze it. Then they looked at a situation that had no association, and an R and R squared value of 0. They said it looked like a random assortment of points.

The students' thinking.

After school a student used that Photomath app.. and still didn't understand it. Though I give him credit for trying to figure it out in some way while he was waiting.
This is tomorrow's estimation.

1 comment:

  1. That poster along the top of your whiteboard for the estimations is genius. Super nice to have a consistent location/procedure for those tasks.