Today PJ and I worked on comparing ratios. We discussed a scenario where Athlete 1 got 3 hits out of every 4 times at bat and Athlete 2 got 4 hits out of every 5 times at bat. I asked PJ to consider who had a better ratio, Athlete 1 or 2. He said Athlete 2 but wasn't sure why. I told him he was right, and showed him two ways to compare. First, I asked PJ what the Least Common Multiple between 4 and 5 is. He came up with 20. So we compared the fractions 3/4 and 4/5 by changing them both to have a denominator of 20. PJ successfully changed 3/4=15/20 and 4/5=16/20. Doing this we could compare the 15 and 16. Which indicated that 4/5 is larger than 3/4. Then I showed PJ an easier way to compare. We can use this technique where we multiply from the bottom diagonally across. It's much quicker and just as efficent. We moved onto another problem where we needed to compare the ratios 7:8 with 10:11. PJ turned them into fractions, multiplied up and diagonally to compare 77 with 80. He then was able to confidently say 10:11 is larger than 7:8. We practiced with a few more ratios, finding equivalent fraction forms and using them to predict future values.
Richard took his spelling test and practiced words with sub un and pre prefixes. He read books with words he can read. We watched some of the movie, The Boy Who Harnessed the Wind.
Matthew and I continued practicing the unit circle today. I had had Matthew draw it out himself. We started with the quadrants and labeling them in degrees and radians. Then we practiced "slicing" each quadrant into fourths and considering how that would affect the degrees/radians there. Matthew did well with this. It got tricky when we shifted to multiples of 30 degrees (or pi/6). But after we practiced, Matthew started to see the patterns on his own. Once we completed the circle, we related it back to the trig functions sine, cosine, and tangent. We will need to practice more again tomorrow.
After going through Sasha's weekly folder, I noticed that her math homework was reading intensive (many geometry word problems). I helped her read the problems and translate the information into a math problem. She seemed to gain confidence with each program. To conclude, she read a short story on RazKids and answered the comprehension questions. Sasha demonstrates good recall for details and test-taking strategies.
We began to create a Native American craft this afternoon. Luke colored and cut out various designs and assembled a totem pole using a glue stick with which to assemble the pieces to make a replica of a totem pole. Luke followed directions well, and we reviewed facts about totem poles as we worked. e hope to finish the craft tomorrow.
