After yesterday's lesson I wanted to scaffold the content a bit. I provided Ben with a graphic of all the Nth roots from 1-15. It showed Ben how 1^2=1, 2^2=4, 3^2=9 and so on. We discussed how it goes from squaring to square rooting and how these operations are inverses of each other. As we were working, he began to get distracted and bring up random topics. In a teasing way I said to Ben, "The function of your behavior is escape, Come back to meeee!" He asked me WTH I was talking about. I explained to him that we as humans have 4 behavior functions: escape, access to tangibles, attention, and sensory/automatic. It opened up a dialogue of his behavior, his diagnoses, and learning about how his mind works. He said he wondered if he was a bad attention seeking kid or if his brain just worked differently. I told him that he absolutely isn't bad, but he learns, processes, and experiences the world differently than others. He explained to me how he has a cylinder of emotions and when communicating with someone with a lot of emotions it pulls from his cylinder more and more until it has no emotion left and it takes time for it to refill. He explained it to me as one of the ways his autism affects him. I could completely relate.
6-2 Exponential Functions – We learned to sketch graphs showing key features of exponential functions. Then we wrote exponential functions using tables and graphs. Next we compared linear and exponential functions.
We have been working on exponents for quite some time now, so I wanted to give Ben the opportunity to expand. I introduced the topic of fraction powers and how to change them into radicals/roots. Ben was hesitant to stop his video and legos to do work, but he complied when I asked him to. I asked him questions like, "What would that reduce to?" and he answered, "I don't know." I asked him what about it did he not understand and he shrugged his shoulders. I continued to try to get him to respond (to questions that I know he knows), but he was not interested in participating. He closed his eyes and put his head down and fell asleep.
6-2 Exponential Functions – We learned that an exponential function models the relationship between two quantities that differ by a constant ratio. Exponential functions are modeled using f(x) = abx where a - is the initial amount and b is the constant ratio. We became familiar with the terms asymptote, constant ratio, and exponential function.
Today Ben was in a new room and seemed in a good mood because of it. He said he was slow moving to get back into the swing of things. I told him I felt similarly lol. We discussed what we have covered so far this year and what we still need to cover. Then he listened as I reviewed exponent properties. We discussed the square root and the idea of it being a fraction power. I realized Ben and I need to review radical properties.
6-1 Rational Exponents and Properties of Exponents – We solved equations with rational exponents using the properties of exponents. We reviewed the Power of a Power, Power of the Product, Product of Powers, and Quotient of Powers Properties.
Assignment: For homework complete assigned problems.
Lesson 11-8 Rational Equations – We practiced solving rational equations and simplifying rational expressions to prepare for a quiz tomorrow. We practiced adding and subtracting rational expressions with unlike denominators. Then we solved rational algebraic equations and determined the extraneous solutions.
Lesson 11-8 Rational Equations – We practiced solving rational equations. We completed homework where we used the cross product to solve rational expressions when both sides of the equation are single fractions. Then we practiced solving rational equations by multiplying each side of the equation by the LCD to eliminate fractions. Next, we practiced determining which solutions make the denominator of a rational expression zero.
Lesson 11-8 Rational Equations – We learned how to solve rational equations. We practiced using the cross product to solve rational expressions when both sides of the equation are single fractions. Then we learned how to solve rational equations by multiplying each side of the equation by the LCD to eliminate fractions. Next, we learned how to determine which solutions are extraneous solutions. We reviewed the fact that any value of a variable that makes the denominator of a rational expression zero must be excluded from the domain. In the same way, when a solution of a rational equation results in a zero in the denominator, that solution must be excluded. These solutions are called extraneous solutions.
Today I met Ben on Teams. We first did a few review problems with simplifying exponents. He is getting good at remembering the rules/properties. Next we discussed the concept of Pi. Today's date is 3/14 so it's "Pi Day". We discussed the digits of pi. It has an infinite number of digits and has no pattern to it, so it's considered an irrational number. We discussed that Pi is found by taking the perimeter of a circle, also known as circumference, and dividing by the diameter.
