Ben had a great class today. He was in the bathroom for a long time, but when he came back he was ready to work. He had a sense of humor and he was in a great mood. We worked on classifying polynomials by degree and number of terms. Today, he did not protest writing the words out. He willingly answered the questions, even seeming motivated to get it done. He did a great job.
7-7 Factoring Special Cases – We practiced identifying and factoring a trinomial that is a perfect square or a binomial that is a difference of two squares. Then we factored special cases of polynomials within the context of real-world problems.
Assignment: Complete the assigned problems for homework.
Review and Test on Topic 7 Polynomials and Factoring.
Today Ben and I continued with learning about the classification of polynomials. I gave Ben a sheet that had graphic organizers of polynomials categorized by number of terms and degree. I asked Ben to write in the box the answers: "monomial", "cubic", etc. He protested. He did not want to do any writing. I asked why, and he did not answer. I said, "I know that you dislike writing, but I also know that you are capable of doing it." He for monomial, he wrote "Mon." I said, "I do understand what you mean, but adding a few more letters to what you wrote is within your ability." I erased it, wrote "Monomial" and moved on to the next one. I asked him to write, "binomial". He did, but he took about 2 minutes to write it out, slowly writing B....then I....then erasing it, then rewriting it. I couldn't tell if it was a stall tactic or he was processing it. I didn't pay attention to his attempt to escape, I continue to push him. He eventually started to write faster. I asked him questions along the way to make sure he understood, like, "what's the difference between a variable and a constant." He mostly answered, "I don't know". So I explained it to him. With 10 minutes left in class, he asked if he could go to the bathroom. He was in the bathroom when the bell rang.
We prepared for a test on Lessons 10-1 to 10-4. The Product Property of Square Roots says that for any numbers greater than or equal to zero the square root of their product is equal to the product of each number’s square root. I had Hudson work on putting that to use in solving radical expressions. The Quotient Property of Square Roots says that when there is a radical expression in the denominator, the expression is not in simplest form. So, we performed a process called rationalizing the denominator which eliminates radicals from a denominator. I had Hudson practice this, too.
Today Ben and I started by reviewing the vocab that we learned yesterday. Then we discussed what it means for a polynomial to be in standard form, the degree/power must be highest first, then decrease from there. I gave Ben polynomial expressions and asked him if they were in standard form. If they were not, I asked him to tell me how to rewrite them so that they are in standard form. After that, we practiced classifying them. I wrote all of the classification types on the board so he could refer to them. I told him eventually, he will need to have them memorized. For more practice, I wrote problems on the board, had Ben change them into standard form, then classify them by degree and number of terms. He did well with this lesson.
Ben and I began a new chapter today. We discussed the idea of a polynomial. We discussed the difference between a variable and a constant. Then we discussed what the degrees are. Then we talked about classification. I wrote on the board a graphic organizer with the classifications of polynomials by number of terms: monomial, binomial, trinomial, and polynomial. I gave Ben examples of each so he could differentiate them. Next we discussed their classification by degree: constant, linear, quadratic, cubic, quartic, quintic. Next I gave Ben the activity of classifying polynomials by both degree and number of terms. It was a good vocab lesson but Ben needs more practice tomorrow.
7-6 Factoring ax2 + bx + c – We learned how to factor a trinomial algebraic expression in the form ax2 + bx + c when the coefficient a is not equal to one.
We discovered that factoring out a GCF before finding the factor pairs made the numbers smaller and easier to work with.
7-7 Factoring Special Cases – We learned that when a trinomial has the pattern a2 + 2ab + b2, then it can be factored as (a + b)2 or (a - b)2 if a2 - 2ab + b2. If a binomial has a pattern a2 - b2, then it can be factored as (a + b)(a - b) where the middle term equals 0.
Assignment: Complete the assigned problems for homework.
Lesson 10-3 Operations with a Radical Expressions – We completed the homework problems for Lesson 10-3 Operations with Radical Expressions. Hudson had difficulty with most of these problems. I sent him a few problems to do which reviewed the concepts from Lesson 10-2 Simplifying Radical Expressions – We reviewed the Product Property of Square Roots and the Quotient Property of Square Roots. We will work on a practice test on Wednesday.
Ben was supposed to complete a quiz with a substitute on Friday but the note said that Ben was not feeling well so he did not complete the quiz. So today we started with doing a review of the problems he would see. When he was ready I gave him the Quiz. Ben did excellently. There was one problem that Ben did not understand because the font was printed differently. I showed him what the font was intending it to look like (the way I previously showed him) and he was able to apply it correctly. He got a 100% on his quiz, way to go Ben.
