Which Is Bigger 2/3 Or 1/2 - T-Tees - Your Answers Await, Life's Questions Unraveled

Real-World Fractions Lesson

Every math teacher must occasionally contend with the question, “why does this matter?” There are plenty of places where a deep understanding of comparing fractions can help you in the real world.

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Fractions are found when precise measurements are needed, for example when measuring medicine or baking pastries.
Combining the correct fractions of ingredients is critical to making all sorts of materials such as slime, cement, and paint.
Chemists must be extraordinarily precise with their fractions in order to create chemical reactions like testing for a virus.

Not only is fraction arithmetic important in the real world, but so is what a fraction means in the first place. The fraction (frac{2}{3}) is greater than (frac{1}{2}) when they are fractions of the same thing, but it is important to also understand what the fraction is measuring or how is it is being presented. If a news report claims that (frac{2}{3}) of Americans support something, which Americans? How was the poll created? Or consider the claim that one theater is at (frac{2}{3}) capacity whereas another is at (frac{1}{2}) capacity. Are the theaters the same size?

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Let’s get to a lesson for Grades 4-5 that you can implement in your classroom to teach this concept. Begin by having students hunt for fractions in the real world. You can lead them towards particular fractions if you want to connect it to something topical, for example the U.S. Senate needing a supermajority for a vote.

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Step 1: Assign students a place to look for a fraction. This can be done in just a few minutes online with direction like “everyone, search for a news article containing the word ‘supermajority.’” This can also be done as a longer assignment, for example, “your homework is to find a fraction in a book or webpage that’s not about math.”

Step 2: Have students independently write down their responses to the following questions. Note that these questions may have multiple correct responses.

How is the fraction being used in the book or webpage? (for example, “describe a supermajority”)
Is it being compared to another fraction? If so, what fraction(s)? (for example, “yes, a typical majority”)
What is the numerator? What is the denominator?
What is the part? (for example, “senators voting yes”)
What is the whole? (for example, “all U.S. senators”)

Step 3: Compare students’ responses. Begin by identifying similarities and differences among responses and having students explain their responses. Facilitate a discussion specifically around what assumptions the source makes about the fraction. Some sample questions are provided below.

Does the fraction represent a large or small number? The magnitude of a fraction is relative. Two-thirds of all senators is a lot when only half the senators are expected to vote yes, but two-thirds is not much when every single senator is expected to vote yes.
Does the fraction represent an increase, decrease, or neither? The direction of a fraction is also relative—an idea you can connect to negative numbers if students are ready. Comparing a fractional gain to a fractional loss can be different from comparing a whole number gain to a whole number loss. For example, if a sum of money increased by a factor of two-thirds then decreased by a factor of two-thirds, it would not be back where it started. (It would be five-ninths of where it started.)

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