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.