Fractions Day 14: To Be or Not to Be (Equal to 1/2)…

Good morning! This is the last lesson of this series of 15-20 min initial fraction explorations. I would have gone on for the duration of distance learning, but we have some measuring to do!

1. We warmed up with some comparing of fractions. Using index cards, I just wrote a bunch of fractions (that he could check with the fraction strips). We flipped the cards face down and mixed them up. He would flip a card face up; I would do the same. We would compare our fractions, and whoever had the largest fraction got to keep the cards. Which one is bigger? How do you know? (Example: I know 1/2 is bigger than 3/8 because 4/8 is a half.) He often had to show me with his fraction strips to explain (See here? This one is bigger.). Note that some of the fractions are equivalent, which gave us some nice places to pause and discuss who won. I let him choose how to deal with the equivalent ones (He chose to put them back upside down and reshuffle.). See below for fraction cards for the game.
2. I gave him the problems below. Each one compares 1/2 to other fractions. 1/2 is considered a “benchmark fraction”. It is a great one to use for estimation and relating to the size of other fractions. We looked at each pair individually. Is the fraction greater than, less than, or equal to half? How do you know? Notice the first 6 pairs start with the equivalent relationship, to push Chris into using half to reason about the very next pair of fractions with the same denominator. The last three pairs were to see if he would apply the “comparing to half” strategy. Below is a video of his thinking.

If I had another day, I would continue with this idea of comparing to half. It caused Chris to really consider how the numerator and denominator related to each other and to the fraction 1/2.