## Friday, January 22, 2016

### Day 87: similar shapes & exponential decay

Today's estimation was a followup to yesterdays. It was how heavy is the money chair. Unfortunately, students were a bit all over the place. I like that some students used their own weight as a reference. I also referenced a bag of cement, which some students knew was around 50 pounds and pretty hard to carry.

Today's lesson is one of my favorite hands on lessons CPM has for similar figures. Basically, students need to compare the lettered shapes to the original shape and justify which are similar and which are not and why. They are prompted to look at the angles and side lengths. They come to the conclusion that there are two requirements for shapes to be similar: congruent corresponding angles and parallel corresponding sides. They also are starting to see and will recall that their side lengths are also proportional to each other by a scale factor. A few thought a scale factor that would make the shape smaller would be a negative figure, while others said it had to be a fraction between 0 and 1 to make it smaller. Here are the card sets:

 Students compare by putting the shapes on top or under the original shape to get a closer look comparing.
 Some estimation reasoning.
In accelerated we reviewed the lesson from yesterday. I made a T chart on the board and asked volunteers to tell me differences between simple and compound interest along with the equations from yesterday. Here's what they came up with:

 I like how this student compared the weight of the chair to their luggage on an airplane trip.
Then students completed trials in the penny lab. They put 100 pennies on their table, spread them out, and then removed the ones with tails side up. They recorded how many were left, shook those ones up, and then removed again.

On Monday we will finish up discussing it's discrete graph and the equation. Then students will work on half-life problems.
 Students in action.