Fraction Equivalence and Ordering

Would you rather have $${{4\over9}}$$, $${{2\over3}}$$, $${{5\over7}}$$, or $${{3\over4}}$$ of your favorite pie? Show or explain your reasoning.

Play the following game with a partner using a set of Fraction Cards. The goal is to compare the two fractions appearing on each card, determining if they are equivalent and, if not, which is larger. The rules for the game are as follows:

1. Deal out the cards evenly so that each player has half of the deck. Each player should place their stack face down in front of them. 
2. Each player turns up a card at the same time.
   1. The player with the greater fraction takes both cards and puts them on the bottom of their stack of cards. Students can use any method to compare them. If they disagree, they should discuss until reaching a consensus, drawing a model if necessary. 
   2. If the fractions are equivalent, then each player deals three cards facedown and turns the fourth one face up to compare. The player with the larger second fraction takes all of the cards that have been dealt out. If the fractions are again equivalent, then another three are dealt facedown and the fourth face up to be compared. (This can continue as long as it needs to.) 
3. The game is over when one player has all of the cards.

Order the following fractions from smallest to largest:

$${{2\over3},{4\over5},{3\over7},{5\over6}}$$

Explain your reasoning.