5.1 & 5.2 Review and 5.4 Solving Radical Equations
Lesson Outline
We began by working a 5.1 & 5.2 Mixed Review online. JPaul practiced converting fraction exponents to roots and evaluating them. He also practiced rationalizing roots that have radicals in the denominator. He completed the assignment at 100%. We then did another mock-quiz. Of the 10 questions, he got 7 correct, 1 partially correct, 2 incorrect. I assigned him practice problems to reiterate the concepts he has the most trouble with.
We then moved on to 5.4 Solving Radical Equations. (We are skipping 5.3 for now). JPaul found this to be an easy lesson. A challenge for him comes when it’s time to check his solutions. Sometimes there are extraneous solutions which need to be eliminated. So he will continued to be reminded to check his solutions once he is done with a computation.
Assignment
5.2 30,39,46 & 5.4 #6-14 even
Session Minutes
120
Minutes Student Attended
120
Lesson Comments
JPaul was on his game today! He even brought donuts for the staff. How nice!!
We began today by viewing the Algebra 2 Savvas website. JPaul worked through 2 examples that were from yesterday’s lesson. He had difficulty with the problems. We rediscussed the concepts using a different approach. I had him slow down and think about WHY he was doing the operations and articulate that to me outloud while he worked. I’ve learned JPaul’s mind works faster than his hands, so he’s balancing multiple steps at once rather than doing one step, writing it down, then moving on to the next step, writing that down, etc. He’s getting lost in the computations. I told him this is a “good” problem to have, because we can easily work on it. I am encouraging him to show his work so that his thought process can be seen. We reviewed his home learning, he showed about 70% mastery. Then we completed 5.2 Notes on Properties of Exponents. The last portion of 5.2 JPaul seemed to enjoy because it was easier for him. We ended the class by having JPaul take a 15 minute mock-quiz. When time was up he asked for 5 extra minutes which I allowed. Of the 5 problems, he got 2 correct, 2 partially correct, and 1 incorrect. Tonight’s home learning will allow him to continue practicing the problems he finds challenging.
Assignment
5.2 Pg. 290 #11-29 odd
Session Minutes
120
Minutes Student Attended
120
Lesson Comments
The first thing JPaul said to me this morning was, “I’m so tired today and I don’t know why.” He did seem a little slower than usual, but he pushed through it!
Today we continued with 5.2. We discussed how it is considered “improper math” to leave a radical in the denominator, when simplifying. We used the “I do- we do - you do” method to practice simplifying radicals with variables. We started out with simple numbers to ensure understanding, then we increased to higher-order thinking questions. Today focused on multiplication and division operations. Tomorrow’s lesson will discuss addition and subtraction.
5.1 Roots, Radicals, Rational Exponents & 5.2 Properties of Exponents and Radicals
Lesson Outline
We began by reviewing the Home Learning that was assigned for while JPaul was away. Although he completed it, it was apparent we will need to continue to review old skills as we gain new skills. JPaul said when he is with me he knows how to do it, by when he is by himself he freezes. I explained that he should use his notes and the text book to review similar problems to see if it helps.
Today we took notes on both 5.1 and 5.2. Together, we did computational and application problems. JPaul is picking up on these concepts quickly. His errors lie in doing computations too quickly and not articulating his thought process on paper. We will work on that.
Also today, Megan worked with us to get both of our online accounts setup.
We began today reviewing last night’s home learning. J.Paul did very well on the assignment. We then moved to the Smart Board to do a Quadratic activity that incorporated finding the key features of a quadratics function (intercepts, vertex, axis of symmetry) and use them to complete the graph. This was all review, but designed to strengthen his confidence so he knows exactly what to do when he see those problem types. We then transitioned into finishing our review of exponents and radicals. Next week J.Paul will be in Oregon, so we finished today by introducing what our first content will be on the New Material.
J.Paul said he will commit 10 minutes/day while he’s on vacation to continue to review so that his skills do not slip while he’s gone. On Monday July 24 we will begin brand new Semester 2 Algebra 2 material.
Today we began by reviewing HW. J.Paul showed that he had difficulty with the assignment. We decided that we would continue to move onto exponents, while continuing to review factoring/solving quadratics. We will do this by starting the day with “warmups” and assigning 1-2 problems daily so he can continue to review. We tried to get J.Paul set up on his online account, however we had some difficulty. I will be reaching out to Megan regarding that.
J.Paul and I took review notes on properties of exponents and did practice together. We also reviewed the relationship between fraction exponents and radicals (roots). We will continue with this concept tomorrow. This is a great topic to transition into the new material which we will begin when he returns from his trip to Oregon.
J.Paul likes exponents more than factoring! He has a quick brain, he reaches calculations in his head extremely fast. We are working on “showing his work” more, so I can see his thought process. I’ve explained if he just writes an answer and it’s wrong, I can’t give him partial credit because I don’t know what he did. But if he shows his work step by step, it’s easier to see where the error occurred.
We began the lesson by reviewing HW. J.Paul made simple calculation errors, but showed understanding of the fundamentals we reviewed. Today we focused on the application of Factoring - what is the purpose, and how can we apply it to real world scenarios? We tied in J.Paul's likeness for golf with problems such as "If a golfer hits a ball modeled by this function ________, how long will it take for the ball to hit the ground?" We used the Smart Board (Desmos graphing calculator) to show on a graph what Factoring a function can do for us (it shows us where the graph intersects the x-axis). We also reviewed the Quadratic formula and confirmed it will NOT be given to him on the ACT formula sheet - he will need to have it memorized. Lastly - J.Paul earned 1% Bonus on his first Test because I made a calculation error, he caught it, questioned it, and explained to me why I was wrong. I loved that! It showed me he was really paying attention (instead of just following along with what I was saying but truly not understanding).
J.Paul and I discussed a future schedule and determined 7:30-9:30am would work best for us both moving forward.
We began the lesson by taking notes on the 5 types of Factoring Polynomials:
1) Greatest Common Factor
2) Trinomials (a=1)
3) Difference of Squares
4) Grouping
5) Trinomials (a>1)
J.Paul had decent recollection, but today's lesson seemed to be of great benefit for review. I explained to J.Paul that although Factoring is an Algebra 1 topic, it resurfaces again in Algebra II, PreCalculus, and Calculus, so having a solid foundation is important.
After notes, we moved to the Smart Board where we practiced a mixed review of factoring. J.Paul asked great questions when he was confused.
For homework, I assigned 10 problems (of mixed styles). We will review it tomorrow.
We began the session by playing some getting-to-know-you games. I learned he has triplet sisters and he learned I would never go sky-diving. We then discussed his previous Alg 2 semester to see how much material was covered. We discussed future plans: He has an ACT coming up and he aims to study Business in college. After building some rapport, we began to review problems together. We reviewed Algebra 1 skills such as: factoring, graphing linear equations, operations with exponents, and solving multi-step equations. It is apparent that J.Paul has a basic understanding of these skills, but is in need of remedial review before moving on. We will continue working this week reviewing necessary skills and then dive into the 2nd half of the content next week
Assignment
J.Paul is to bring his calendar/notebook to class tomorrow.