I begin today with two sheets of green construction paper. One is 8 1/2 x 11 and the other is 12 x 18. I ask students if I cut them both in half, will the halves be the same size. I have them shut their eyes and vote yes or no. (By closing eyes, they are less likely to copy their friends). I tell them to open their eyes and we will check because some people said yes and some said no.
I cut the first piece in half and hold up the halves. I now cut the second piece in half. Are they the same? (No). So if that is true, what would happen if I cut them into quarters. Would the quarters be the same? (no). I ask students what we have learned about fractions and their sizes? (It depends on the size of the whole that you start with.)
I then introduce that when we are working with fractions it is important that we know what whole the fraction refers to. Can you think of places where the fraction one quarter is used? (quarters of a dollar, quarters of an hour, etc.). So, the fraction 1/4 means different things depending on what the whole is. If the whole is a dollar, one quarter means 25 cents. If the whole is one hour, 1/4 means 15 minutes.
Another place we work with one quarter, and other fractions, is in cooking. Has anyone ever seen a recipe? Have you ever seen fractions in a recipe? What sorts of things do we use to measure when we cook? (Cup, teaspoon, Tablespoon). So, what does it mean when we see 1/4 in a recipe? (It depends on the whole).
I show the class a one cup measuring cup and a teaspoon, as well as a quarter cup and quarter teaspoon to illustrate this point.
Today, we will be working with one cup as our whole.
I put up a list of ingredients on the board, each with a fractional part. I have purchased a variety of dry ingredients that can be measured and put into a trail mix. I purchased jelly beans, popcorn, Chex cereal, raisins and mini marshmallows.
I tell students that they will be working in 2 groups. They need to measure each ingredient according to the recipe and then divide it evenly among all of the cooks in the group. I ask them what they will do if the recipe calls for 2/4 of a cup? (use the 1/4 twice, or use the 1/2). Students have been introduced to having more than one name for a fraction. We have looked at how 1/4 of a shape and 1/4 of a shape then means we have 2/4, and that this is also one half of the whole thing. We review the idea of equivalent fractions briefly here as needed. I check for a few other equivalents that might come up with the measuring cups.
I divide students into 2 groups. Students take turns reading an ingredient and amount, finding the correct measuring cup, and measuring that ingredient into the large bowl. When all the ingredients are in, they mix the trail mix.
Now I ask how many students in their group? (9). How will we make sure we each get the same part of the whole mix? Remember that we are no longer talking about the whole measuring cup, now we are talking about the whole amount of trail mix that we made. What fraction would each person get? 1/9. I help students decide which measuring tool might work best and then we divide the mix into 9 cups. When the mixture is divided students are asked what fraction in standard measure did they get?
I ask the second group the same question and then I have students think about why both groups ended up with the same amount of trail mix? (We used standard measures and we followed the same recipe.)
I hand out the trail mix to each student. While they eat their fractions, we review why in something like cooking it is important to be clear what the whole is. When we are talking about a half or third or quarter of something, the size of the fraction depends on the size of the whole that it refers to.