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.
Today I had PJ complete some review problems. He overall got 75% of the problems correct. I was really proud of what he did remember. He made some errors on the exponent evaluations (forgot that anything to the 0 power is 1). But after a few reminders on the rule, PJ remembered what to do. We also practiced translating math sentences into mathematical sentences. PJ translated "22 less than the product of 4 and k" to 4k-22. He did great!
Today we practiced changing the decimal form of degrees into degrees minutes seconds. This was a review, so JPaul knew what to do. Next, I showed him how to use his calculator to do the conversions easily. Then we started the concept of sectors, their area, and rotation. We will need to continue this tomorrow.
Today Carson and I reviewed all of the formulas for 3-Dimensional Figures, their surface area, and their volume. Then we decided to make a reference sheet instead of looking them up each time. I looked up in the standards that in 8th grade students are not required to memorize the formulas, however they need to be able to apply them and understand their use. We got a poster and markers and started to create a formula sheet we can hang in his room. We will finish this tomorrow.
Today we practiced converting Degrees Minutes and Seconds back into their decimal form. JPaul worked to take the decimal part of the degree and divide it by 60 and then 3600 to convert them into their degrees minutes seconds form. Then I showed JPaul how to use the calculator functions to do that. Next, we started an introduction on Areas of sectors. We considered the vobabulary and formula. We will need to continue with this tomorrow.
Today we reviewed the theorems we were discussing before spring break. Specifically, the pythagorean theorem. Andrew recalled the theorem as a^2+b^2=c^2. He recalled that c must be the hypotenuse and a and b could be either side. I asked him to find the missing side. Then, Andrew spent a LONG time in the bathroom. When he returned I had 3D figures on the board, to which I asked Andrew to find the longest diagonal segment. This was challenging. Andrew had to use the pythagorean theorem to find the missing side of one triangle, then use that side to determine the diagonal length. We had to do that twice so then we could compare which figure was the longest.
Right now Aiden and I have been working on solving two step equations. I noticed the book has mixed in fractions and decimals into the equations - which can make the problems seem more difficult. To simplify this, I wanted to show Aiden some techniques on how to clear fractions and decimals from the equation. We've already discussed decimals. Today I wanted to discuss fractions, however in order to do that we first needed to recall how to find the Greatest Common Factor (GCF) and how to cross cancel to reduce fractions. Today we started by practicing finding the GCF between 12 and 18. I showed Aiden how to write out all of the factors to ensure all of them are considered. Next, we practiced simplifying fractions. I explained to Aiden that terms could be simplified top/bottom since it is implying division. We practiced these skills today so that tomorrow I can show them how we will apply them when solving two-step equations with fractions inside.
