Today Ben and I worked on exponents. This is a review for Ben. When I showed him the problems he did not recall what to do. We reviewed the properties of multiplying like bases. I explained to him WHY we add the powers. Then we applied these skills to a problem. Ben struggled a bit, but he got through it. We tried multiple problems to make sure he understood what to do.
9-1 Solving Quadratic Equations Using Graphs and Tables – We reviewed how to use a graph to identify the x-intercepts as solutions of a quadratic equation. If the graph of the function has no x-intercepts then the equation has no real solutions. If the graph touches the x-axis but does not cross it then there is only one x-intercept and one real solution. Next we practiced finding the vertex of the parabola by putting the equation in the form ax2 + bx + c and calculating the x-coordinate by the formula –b/2a and
we found the y-coordinate by using the formula –b/2a. Next we plugged the x-coordinate of the vertex into the original quadratic equation to find the y-coordinate of the vertex.
Assignment: Complete the assigned problems for homework.
9-2 Solving Quadratic Equations by Factoring – We learned that in the standard form of a quadratic equation the factors of the equation determine the solutions. Then we learned the Zero-Product Property and factoring to find the solutions of a quadratic equation. Next we learned to apply factoring to solve real-world problems. Then we used the zeros of a quadratic equation to sketch a graph. Next we learned to write the factored form of a quadratic function from the graph.
Assignment: Complete the assigned problems for homework.
Today Ben was quite tardy for class, so we didn't have enough time to dive into a formal lesson. Instead we talked informally about computer storage and how the prefixes (mega, tera, giga) are related. We looked up what they mean and saw that megabits are tiny and megabytes are large. We learned that there are 1 million megabytes in 1 terabyte. We compared that to the storage of a photo in a cellphone. I looked up a photo to see it was the size of 1.6 megabytes. We learned there are 1,000 megabytes in a gigabyte and 1,000 gigabytes in a terabyte.
Ben resumed his MAPs testing today. He worked hard on the problems. One of them he read and did not understand and I took a look at it. I am confident there was an error in the problem (I took a photo of it to ask a colleague). He worked hard the whole period. The problems got into complex numbers and solving quadratic equations which is Algebra 2 content. He did his best. He did not finish but is close to it.
When I arrived to Ben's classroom he shut the door on me. He told me NO. I opened the door and told him how rude that is, and it's not up to him whether we have class or not. He told me he just arrived and wasn't ready for class. I told him I was going to retrieve the computers and he had a few minutes to get ready, but when I returned we were going to finish the MAPS test. When he saw that I was upset from him shutting the door on me, he became very friendly, in almost an apologetic way. I think he realized that wasn't appropriate to do.
We began testing. He again worked hard on the problems, articulating his way through each. The problems are starting to get challenging for him and he was seeming to become defeated. I let him know it's ok not to know everything, that I appreciated his efforts, and that if he needed to take a guess to move on, that is ok. He did not finish the test, so we will resume next period.
8-5 Linear, Exponential, and Quadratic Models – Linear, quadratic, and exponential functions are differentiated by their average rates of change over different intervals. A linear function models a relationship between x and y in which the differences between successive y-values are constant. A quadratic function models a relationship in which the second differences, or the difference between the first differences, are constant. An exponential function models a relationship where the ratios of consecutive y-values are constant.
