The All The Same to Me Game reinforces students' understanding of the equivalence between improper fractions and mixed numbers. It's quite challenging to come up with four versions of the same improper fraction in different forms and especially when the denominators are not the same. To make matters even more challenging, there's a lot of strategy needed to come up with the best interpretation of the roll of the dice. Students will have to choose the best possible way to build their fractions as quickly as they can. Most kids will need some scratch paper as they work out fractional equivalencies when the denominators of the fractions don't end up being the same.
Pay close attention as students are forming their answers and you can test their knowledge. Do they really understand that 8/7 is exactly the same as 1-1/7? Is it clear to them that 5/3 and 10/6 represent the same exact fraction? Can they also see that the mixed number forms of these numbers 1-2/3 and 1-4/6 are also the same?
If you feel that students are still having too much trouble with fractions there's another classroom strategy you can use with this game. Give each student a game board with just one fraction already filled in for him or her. Make sure all four gameboards have completely different fractions that are not equivalent to each other. Then write all the different answers for four All the Same to Me gameboards on the board in advance but make sure they are all mixed up. Students will then need to find and fill in their answers from those that exist on the board.
With larger classes you can break students into teams and have one team member responsible for going to the board and circling a fraction they've taken. It doesn't mean that another opposing team member can't circle the fraction as well, but someone is going to be incorrect! In the meantime, it gives you time to circulate in class so you can get a handle on the difficulties they're having.
Common Core Mathematical Standard
3.NF Develop understanding of fractions as numbers.
4.NF Extend understanding of fraction equivalence and ordering.
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