Quesadilla Fractions

Our children are 12, 11, and 9, and they are able to use knives safely. We also use pizza cutters to cut our quesadillas. You can take turns making cuts and identifying the resulting fractions. In this picture, I cut the quesadilla into 2 equal parts. Each was 1/2 the whole quesadilla.

Then my son cut the halves in half, resulting in 4 equal pieces. Each was 1/4 the whole quesadilla.

You can get more ambitious about your cuts and make lots of other fractions! Don't worry about making them perfect, as long as children get the idea that they are basically equal in size. If they're sharing with siblings, they'll be motivated to make careful cuts!

While she was doing school work, I made my stepdaughter (11) a quesadilla. I surprised her by cutting it into lots of different fractional parts. Being silly and surprising kids is a great way to get their attention and get them engaged! Plus, it's more fun.

I asked her if she could tell what fraction of the whole quesadilla each piece was. She saw that on the left (where she is pointing in this picture), that half the quesadilla had been cut into 3 equal parts. Each of those parts would be 1/6 of the whole. That also shows that 1/3 of 1/2 is 1/6. We didn't write an equation about that, but we could have written 1/3 x 1/2 = 1/6.

Then, she imagined and used her hands to keep track of how many of the other pieces would be needed to cover or fill up the whole. She saw that 1/4 of a quesadilla had been cut into 2 equal parts, so she counted by 2's to determine it would take 8 of those parts (bottom right) to cover the whole. That means each is 1/8. She used a similar approach for the fourth that had been cut into 3 equal parts to determine that each part is 1/12 of the whole.

She understood that figuring out how many copies of a fractional part would be equal to 1 whole allowed her to determine the value of the part. This is a really important understanding about fractions and I was pleased to see her thinking this way!

I made half a quesadilla for myself for lunch, and I cut it into fractional parts of different sizes. I asked the kids what fraction of an entire quesadilla each part would be. Again, they visualized the whole and counted how many copies of each they would need to cover it. They saw that I had cut eighths and twelfths of a whole quesadilla.

You can also see in this picture that 1/4 of 1/2 quesadilla (top two parts) is equal to 1/8 of a whole quesadilla. And 1/6 of 1/2 quesadilla (bottom three parts) is equal to 1/12 of a whole quesadilla. These two equations show this idea symbolically.

1/4 x 1/2 = 1/8 and 1/6 x 1/2 = 1/12

Others might see two fourths of a whole quesadilla in this picture, each of which is cut into a different number of parts. 1/2 of 1/4 a quesadilla is equal to 1/8 of a whole quesadilla. 1/3 of 1/4 of a quesadilla is equal to 1/12 of a whole quesadilla. These two equations show this idea symbolically.

1/2 x 1/4 = 1/8 and 1/3 x 1/4 = 1/12

Don't worry too much about using equations or numbers to express your ideas about fractions (unless you want to). Instead, focus on sense making and talking a lot with your child about the fractions you make and see. Emphasize how you can use the relationship between the pieces and the whole to determine the value of the pieces.