Today PJ and I had two classes. During the first class, we reviewed the steps for solving multi-step equations. PJ is doing a great job showing his work properly. Sometimes PJ will confuse the expression -3x to mean x minus 3. But he is getting better at recognizing their meaning. Our second class, we worked on word problems. PJ read a problem and then had to translate the math words into a math equation. These were a bit more difficult for PJ. We will continue to work on this concept next class.
Today Aiden and I continued to work with two step equations and word problems. This time we included decimals in our equations. I showed Aiden how to solve the equation the way we have been, using inverse operations. Then I showed Aiden what we could do to clear the problem of the decimals in the first place, so we never have to deal with them while we solve. We looked at decimals like 0.32 and considered what we would need to do to turn that into a whole number. We noticed if we multiplied by 10 we would get 3.2 which is still a decmial, however if we multiply by 100, we would get 32. For example, if we have a problem like 6.4x+0.32=20, we could solve it like we normally would (beginning with subtracting 0.32 on both sides). OR we could choose to clear the decimals right off the bat. If we multiply by 100 (on both sides of the equation), it could be turned into 640x+32=2000. Although these numbers are larger, they can be seen as "easier" numbers to work with. I explained to Aiden that it's not necessary to do this, but it's worth it to consider (and understand).
Finished reading Leben ohne Smartphone, discussed in German life without a smartphone. Finished reviewing essay question on Kapitel 12 test. Began watching short German video of Joshua's "Traumhaus" which is a hobbit house and how to build it.
Today Carson and I began a new chapter on 3-Dimensional Figures. We started by working on the white board. I had Carson draw a cube, rectangular prism and a cylinder. We labeled the sides. Then we came up with the formulas for the surface areas and volumes of each. Then we pulled up problems from his online savvas account. We proved the surface areas for cone and sphere. We used visual aids to SEE why the formulas are what they are. I showed Carson how to come up with the formulas on his own so he doesn't have to memorize them.
Today we started with ACT Prep. We covered problems that involved the Pythagorean Theorem, Linear Equations, and some basic Trig problems. Then we moved into our precalc content. We have been working on angles. Today we discussed how to go from degrees minutes seconds back into decimal degrees. I then showed Matthew how to use his calculator to do the conversions.
Today Joshua and I continued working with sine, cosine, and tangent. We discussed how we could use both their graphs, and the unit circle to determine if the functions are increasing, decreasing, concave up or concave down. We also discussed how to use proper notation to support this information. Next, we went into our AP Classroom and worked on Multiple Choice problems from 3.1. We are getting close to the end of the material, but we are actually behind in our pacing. I am trying to urge Joshua to put some pep in his step during class, because every minute counts at this stage in the game. He has 2 months until his exam and we need plenty of time to review.
We observed the ladybug habitat. We went outside on a nature walk and recorded our observations. We saw mushrooms, spiders, wet grass, a woodpecker, and squirrels. We came back to his room and drew a picture of a ladybug on his observation sheet.
