## Monday, September 14, 2015

### Day 10: Proportional Situations & Cubic Functions

In CC 8 we reviewed the post it notes from part A of the problem, which said Parvin washed 17 dishes in 10 minutes. Write down various times and dishes cleaned. The post its allowed students to critique each others work and remind them what they did on Friday. Then I let them finish parts b and c, then went over the students results. Then I told them to write down the requirements for a relationship to be proportional. I told them that they were going to tell me what to write. Students told me that when graphed it passes through the origin, is a straight line, grows at a constant rate, and if you double one number you can double the other.

Here in part c, a student deposits \$20 in a bank account that doubles every year. I asked students to notice the differences and which one was correct. They noticed the left one had year 0 at \$20, while the second post it had year 1 at \$20. They thought the one on the left was right because when you deposit the money a year hasn't passed by yet. I also made sure to point out that both graphs showed the fact that the lines were not straight. Students observed they were curved. I asked if it's growing at a constant rate and they said no.

This was part b. Basically, a puppy is born with a weight of 14 ounces. In 10 days it doubles it's weight. It continues growing at a constant rate. The one on the right was a common misconception of a weight of 14 ounces in 10 days. Then they erased and changed it to 0 days. Also, students noticed that 20 days should be 42 days, and not 56. Some students took it literally that it would keep doubling. That was just a coincidence.

A student in another class also said that if it went from 14 to 28 ounces in 10 days, then it grew 7 ounces every 5 days, because that was half the growth. I thought that was a great observation.

Students also analyzed a table that was not a proportional relationship and had to explain why. Students observed that if you found the unit rate for \$17.50 for 5 pounds of ferret food, then that's \$3.50. But when you multiply \$3.50 by 30 you don't get the entry of 30 pounds for \$89. They also saw 5 pounds times 6 equals 30 pounds, but \$17.50 times 6 doesn't equal \$89. Two great explanations. Also, some students graphed it and saw it wasn't a straight line.

In the accelerated class students finished up their square root of x posters, then I gave explicit instructions on how to give positive constructive feedback. They need to work on this. They also worked on graphing the cube root of x. The class didn't combine their ideas in their groups and did too much independent work which left students at all different points. Tomorrow they'll graph the absolute value of x for the first time.