Tuesday, February 23, 2016

Day 106: Compound Interest & Vertex->Standard Form

The estimation today was a Yellow Pages phone book. Most students underestimated it. They liked watching the video, and there's always comments about "How much time does he have?" I asked them if they had somewhere to be at the time. Haha. Also, I pointed out that if they were watching carefully, the pages don't start getting numbered until the beginning.

I passed back assessments and reviewed how they were graded. I pointed out common mistakes. A lot of students forgot the negative sign on the decreasing line. Then we went over a homework problem, y=-1/2x+6. I structured our discussion around what format the equation is in, what B meant. We originally learned it as Figure 0, but we now call it y-intercept. M used to be growth factor, and still is in y=mx+b, but we know it's synonym is slope. Students knew slope is the ratio of vertical change over horizontal change. The most concise explanation by students was to go down 1, and over to the right 2. I asked them if 1/-2 was the same as -1/2. They said it looked different, but was still the same because a positive divided by a negative is negative. I showed how slope can get you a point to the left of a point by going backwards and using rise of 1, and run to the left of -2.

Then students analyzed a simple interest and compound interest table. They noticed that simple interest had a constant rate of change, while compound interest had a growth that kept on increasing. They saw this when the graphed a compound interest situation. First they filled out a table, seeing that multiplying by 1.05 would get them 5% interest on the current account balance. It ended up being a curved graph.

Tomorrow we will analyze how this can be written as a function, and will be their reintroduction to what an exponent is used for.

Reviewing how to graph y=-1/2x+6. Also showing how to use the equation to solve for the x-intercept by substituting 0 for y.
Illustrating using slope to go down and up a line.
In accelerated we first reviewed how to find the vertex of a quadratic when the x-intercepts were given. I wanted to review the first step to prove what the x-intercepts were. Students are forgetting to factor out any common factors before they start the factoring process.

Then students worked on converting vertex form to standard form. Many students did not expand (x-2)^2 correctly. They said it was x^2-4. About 70% of the class made this mistake. So, during closure we discussed the mistake and a few students explained how instead of using a generic rectangle to multiply (x-2)(x-2) you can just square the first and last terms to get x squared and positive 4, and the middle terms are x times -2 then double it. That gets you x^2-4x+4.

A lot of students saw how the vertex form gave you the vertex. The number added or subtracted was the y coordinate of the vertex, and the number next to x was the opposite of the x coordinate.

Tomorrow students will practice this more, and also learn a new method for solving for the x intercepts when the equation is in vertex form.

Homework review. Zero product property.
Students saw that the vertex was (2,-5) when in this form. They also saw that in standard form it was the same graph as the vertex form.

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