Today we will be working on writing subtraction situations. This lesson is designed to help students contextualize situations in which fractions are taken away from fractions. Students have been practicing the computations needed to make equivalent fraction common denominators in order to add and subtract fractions. *We have not moved into mixed numbers, so for these situations, no regrouping is needed.
To ensure that the numbers we work with do not pose regrouping situations, I provide students with the equations they will work will today, rather than have them make their own.
To get started on this lesson, I ask the students to generate a list of topics for fraction story problems. This helps the students generate ideas more easily when they are working in groups.
Some items that students listed include:
After students share their list of topics, I write 2/3 - 1/2 on the board. Students are given time to think about this equation and try to "write" a story problem that is related. They don't have to actually write the problem down, just collaborate with a friend, or think to themselves.
At first, I give the students time to think on their own, I try to hold back from providing any support until they have had time to try on their own. If I see groups are struggling, I probe with open-ended questions such as "what are you thinking about?", "what would that look like if you made a drawing"?
I call on one group of students to share their story problem.
Maddison has 2/3 of a candy bar. She eats 1/2 of that. What fraction of her candy bar is left?
Today we are going to take our understanding of working with unlike denominators to the next level. Rather than simply solving a problem using computations, we are also going to use fraction tiles or number lines to model our thinking. The real challenge will be making sure the equation, models, and math computations all match up. We are going to work through this one together.
Story problems that are generated by the students can be tricky to work with because they are not entirely clear in their writing. This lesson helps them realize the need for precision in the wording of the problem (MP6). In the example problem, because the problem says 1/2 of that, there is room for interpretation. Does Maddison eat 1/2 of the candy bar? Or 1/2 of what she has left? When subtracting fractions, it is essential for the students to understand that they are taking a 1/2 of the whole away from 2/3 of the whole.
I use this story problem to help students stretch their thinking. I present them with a picture that doesn't match the math.
Often times I think modeling is thought of as a way to help students who are struggling. Sometimes when the students seem to "get it", we focus more on the abstract components of math and less on the concrete and modeling.
This lesson is an example of how using models increases the rigor of a lesson. At this point, my students are able to convert two fractions to equivalent fraction with like denominators. The computations become almost automatic.
Pushing students to represent their problem using models requires them to think about each fraction in relation to the whole, then comparing them using subtraction.
Building a strong foundation here will help students have more clarity when multiplying fractions later.
Students work in pairs to create story problems about 3 more subtraction equations.
5/6 - 2/3
11/18 - 1/3
6/8 - 2/4
I provide the students with the equations, so when we share at the end, they share from common ground. I allow students to choose the topic they wish to write about and the approach they want to use for modeling. Students choose between number line, fraction tiles, or drawing "brownies"
The focus of the problem creation is using clear language in writing the story and making sure the math, models, and story align (MP3, MP4, MP6).
To wrap up class, students share their story problems out loud. As a group, we listen for clear language that emphasizes that it is a part of whole taken away from a part of a whole. Moving forward, students will continue to work with this skill, both in class and for homework.