Students did their last 4 estimations this week, with dot talks starting on Monday. Plan is for 20 days straight of number talks starting with 5 dot talks that I will post the google slide for. The 15 days after will be a mixture or progression of addition, subtraction, multiplication, and division. I will use the book Making Number Talks Matter as a framework.
Students worked on the Newton's Revenge problem and reasoned that the heights of the roller coaster riders and their heights from their fingertips to the seat would be important to measure. Students realized that taller people tend to have longer reaches. After measuring their group they submitted their data via a Google form. I was then able to display the data for their class, and later manipulate it in the Desmos calculator.
In this estimation, some students saw the container as layers of cups, with 3 layers of 4 being a common idea.
Here students are graphing their height (x) versus their reach (y) and analyzing why the graph is not setup properly for numerous reasons using CPM's prompts.
Looking at the data as the google form submits to a google sheet.
This was an amazing estimate. Too bad they subtracted 20!
This was a bummer to read in an Mathography. As I said at open house, if you were not good at math as a kid, please refrain from telling that to your child. It gives them an excuse to not try after making mistakes.
Students think pair shared, then shared with the class what they knew about proportional relationships. Students had a hard time explaining how a table can show proportionality. Some students said a constant rate, and you can get the unit rate or price of it.
In Math 6 support students had to measure their pace, then see how long a million of their paces would be. Then they were prompted to write it in the biggest units. When I asked them what other ways car speed is measured besides miles per hour they came up with kilometers per hour. The method above is how my 8th grade science teachers taught us conversions. Think of a giant one and the units cancelling and the units you want being in the numerator and the ones you are "trying to get rid of" as the denominator.
A nicely scaled graph.
A good table and graph. Shows a constant rate, but needed to think further to realize it wasn't passing through the origin so it wasn't proportional. On Monday I want to take a closer look at the table to this problem to help students clearly define proportionality in their learning logs.
It'd be nice if the variables were defined, but a clear table and graph.
Clearly defined variables.
For the above graph I asked students if they agreed with this table or the tables output 42 for the input of 20 days. The wording of the problem was key. The puppy's weight wasn't doubling EVERY 10 days, just the first 10 days. From there, you assume the puppy grows at a constant rate. The purpose is for students to understand the puppy was not 14 ounces after 10 days, but 14 ounces at birth, or at day 0. Then it was 28 ounces after 10 days.
Correct rate of change interpreted.
Students were quite successful with the above estimation of a tissue paper bundle. I illustrated how they saw the 12 kleenex boxes. I also asked students what it meant to find the mean average of data. I asked them to write it down if they had forgotten. We also reviewed a missing width of a rectangle with length and area known. It also gave me an opportunity for tips on long division.
Below that you can see the way I set up the CPM Red Light Green Light strategy. It empowers students to work as a group, and send a member up to check the answer. If they are wrong, it's a red light and they need to discuss and fix it. If they get it right, they have the green light to go to the next problem. Sounds simple, but it motivates students to know they can check their work without me there.
Correct start to the graph, but had doubling which wouldn't create a constant rate.
I had students compare and contrast the last 2 tables.