Sugar-Free Fraction Fest

Today is a special day at Hero Academy. Everyone gets to bring in a sugar-free treat to share with friends. Our superheroes-in-training had to look up special recipes and bake a treat all by themselves.

There are so many delicious goodies to choose from! It is hard to believe they are sugar free! There is everything imaginable at the Sugar-Free Treat Fest. There are brownies, cookies, cupcakes, and fruit cakes. There are chocolate-dipped strawberries, fruit-filled donuts, and homemade ice cream. There are so many delightful, sugar-free items that they barely fit on the long buffet table. Everyone wants to taste a little bit of everything. All of the kids are gathered around the table with their plates and forks.

Everyone wants an equal piece. How are they ever going to split things evenly? Donte knows just want to do. Looking at same-sized wholes and the fractions for each would ensure that everyone gets the same amount of treats!

Joe suggests that they start with his famous, sugar-free brownies. He brought two big pans that are the same size because he knows everyone will love them. Joe cuts each pan of brownies into eight equal pieces. Each pan of brownies is the same whole because it is the same size. Joe cuts each pan into the same number of equal pieces

Since both pans are the same size, Joe can cut the brownies into 8 equal pieces, and everyone will get the same amount. The denominator for both pans is 8, since they are both cut into 8 equal pieces.

Joe begins to share his brownies. He shares all of the brownies from one pan and realizes there will not be enough for everyone to have a brownie. Donte says he made a pan of brownies too! He cut his pan into 8 pieces as well! Donte holds his brownie pan next to Joe’s. Everyone notices his pan is much smaller than Joe’s.

Oh, no! Since the two pans are not the same size, they cannot be the same whole! Even though Donte’s pan is cut into 8 equal pieces, the pieces are not the same size as the pieces in Joe’s pan! \({\frac{1}{8}}\) of Donte’s brownie pan is much smaller than \({\frac{1}{8}}\) of Joe’s brownie pan. Everyone can still have a brownie, but not everyone will get an equal amount.

Ian wants to share the giant, fruit-filled donuts he brought to share. He cuts the first donut into two pieces. He hands a piece to Alani. He cuts the second donut into two pieces also. He shares a piece of the second donut with Donte.

Alani and Donte look at each other. Something is not right. Each of them has one half of a donut, but the halves are not the same size. This means Alani and Donte did not get equal-size pieces, since the donuts were not the same whole size to start. That’s okay, though. The donuts still taste great. Ian can try again with the next donuts. He just needs to make sure that

he chooses donuts that are the same size AND that he cuts each donut into the same number of equal parts.

Now, all of the superheroes are making sure the treats are the same size when they start, and are cutting them into the same number of parts. They want everyone to get a fair share of sugar-free treats!

The Hero Academy Sugar-Free Treat Fest was a success. Fractions made sure that everyone got an equal piece of each treat. We should do this again every year!