Wednesday, February 24, 2016

Day 107: compound interest for exponents & solving for x in vertex form

Today's estimation was the number of pages in Where the Sidewalk Ends. We then discussed the difference between the simple and compound interest data tables. Kids were able to describe the growth of the account balances, but I wanted them to really think about the question, "How was the INTEREST growing?" They realized simple interest had a constant interest based on the initial balance. Compound interest had a growing amount of interest because the interest was based on a percent of the previous year's balance.

Below was a common mistake on some students where they multiplied the total interest earned by 1.05 instead of the balance.
One of the mistakes I encountered.
Then students graphed the total interest earned and saw that it was slightly curved. They then analyzed the patterns they saw in the table. They saw that you multiply by 1.05 as many times as the years you've had the money in the bank. They articulated that (500*1.05) represented the year 1 balance and was equal to $525.

This lead to a need for an easier way to write the calculation without writing 1.05 so many times. They remembered that repeated multiplication can be written with an exponent. This was in anticipation of our Scientific Notation FAL tomorrow. We didn't have time to complete the pre-test, but I'm not worried, I'll use it as a post-assessment classwork assignment.

In accelerated we reviewed a set of 4 homework problems to start. Nicholas showed us how a factored equation can lead to writing 2 separate equations to solve for x. In part B Hailey described how to factor using a generic rectangle and a diamond. Then solve for x. Part C Davin showed the class how to complete the square before we got to that part of the chapter, and another student showed the factoring way. While completing the square is an important skill, students saw that it wasn't the most efficient method for this particular situation. Finally they factored 4x squared -1. It was a difference of squares problem, and one student actually added 1 to both sides, divided both sides by 4, and took the square root. I was impressed that Alex N showed this method because I hadn't thought of it that way and it was a great way to solve it, and get positive and negative 1/2 as the roots.

Homework review explained by students.
Students were at different points of the lesson, and I had different students come up and show the class how they interpreted certain problems. Tiffany showed us how to properly write an equation in vertex or graphing form in standard form. I graphed it in Desmos and asked how I knew it was correct. They said it was right because it overlapped the original graph.

In the second equation, Alex D correctly interpreted the vertex coordinates as (-3,2). He said it was the opposite of 3 and the y coordinate was positive 2. Robert demonstrated how to solve for the x intercepts when the equation was in vertex form, and finally Aaron showed us how to do the same procedure except showed what happens when you have a non-perfect square or irrational number as part of your answer.
Reviewing classwork.

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