Building Fraction Sense

For many students in late elementary school, the return from winter break will kick off a different kind of season: Fraction Season! Fractions are mission critical for success in late elementary, middle and high school math but are often a source of frustration and confusion for students, parents and teachers alike. One way to reduce at least some of the frustration is to help students build a stronger fraction sense. 

What is Fraction Sense?

Fraction Sense is essentially having a foundational understanding of what a fraction represents. Simple enough, right? The challenge is that a true foundational understanding of fractions needs to be flexible, and not depend on just one way of representing or modeling a fraction. One of the main reasons fractions are so intimidating is we tend to only associate them with mental images of shapes that have been divided into equal parts with some of them shaded (ok either that, or PIZZA!).  To demonstrate mastery of fractional standards however, students must be able to apply their knowledge of what a fraction is to real world situations and examples that can’t always be represented with a circle divided into 8 equal parts. This is why you'll see fractions taught using number lines and set models, along with those shaded shapes.

Why is Fraction Sense Important?

In addition to helping them succeed with those fractions lessons & units, developing a strong fraction sense can help students in other areas of math, different academic subjects like science, as well as in life. Fractions really are everywhere! Students will see fractions:

• In other areas of math right now, as they solve problems related to distance, rate, time, measurement and more. 
• Throughout middle school and high school, where almost every new math skill they will be confronted with will contain a fractional element as they explore concepts like ratios and proportions, percents, statistics and probability, expressions, equations and functions.
• In real life: cooking, shopping, measuring, managing time, managing money and more all include the use of fractions.
• In the professional world - look closely and you'll see fractions in almost every in-demand profession like medicine, construction, engineering and computer science.

Why Do Students Struggle with Fraction Sense?

As critical as these skills are, fractions do present a difficult hurdle for many students. Sometimes this comes from a general lack of fraction sense. After all, if they don't spend enough time exploring different ways that fractions can be represented then their understanding of fractions is likely to be limited. However, there are a couple of specific challenges that frequently crop up around fraction sense:

1. Confusing Number Sense and Fraction Sense
   When learning about whole numbers, students concretely learn to associate numbers with quantities. However, while fractions are numbers, and also represent a quantity, the quantity a fraction represents can only be determined by understanding the part to whole relationship of the numbers that make up a fraction. Additionally, when working with fractions, students continue to rely on their knowledge of rules that apply to whole numbers. These rules sometimes, but not always apply to fractions, which can be very confusing.
2. Not All Wholes are Created Equal
   In the beginning students mainly solve problems involving fractional quantities that do not provide context and they can always assume that the size of the corresponding wholes are the same. However, students will progress to solving problems that do include context in which each fraction's whole may be different. For example, if Holly and Natalie read 1/2 of the same book, then they both read an equal amount. On the other hand, if Holly read 1/2 of a book with 200 pages and Natalie read 1/2 of a book with 400 pages, then they definitely didn't read equal amounts. It is important for this concept to be established early to make sure to consider the size of the wholes when they are given in a problem.

How Can You Help Students Build a Stronger Fraction Sense?

As with most areas of math, repeated practice and exposure to different ways to model fractions can go a long way towards helping them succeed. One easy way to help your student build a strong foundation with fractions is by showing them all the ways we use fractions in everyday life.  Here are some examples to get you started:

• Gas tank gauges: Most cars have gas gauges that are divided into fourths.  Point out the 4 equal sections of the gauge to your student and have them try to catch it when the tank is ¼, 2/4, and ¾ full.  Also have them try to name the fraction 4/4 after you fill your tank up and talk about how when the tank is full you could say it is 4/4 full or 1 whole tank of gas. But don’t stop there!  Go on to show them the halves and even sixteenths if your gauge has the additional tick marks.
• Measuring Cups:  Whether in the kitchen preparing a home cooked meal from scratch or mixing up a snack mix in the classroom, things need to be measured!  So again, point out the different equal sections of the measuring cups: the lines that separate the whole cup into thirds, fourths, etc. Let your student measure the correct amount and help out!  Challenge them with measuring cups that only represent one fractional amount such as ⅓ cup and ask them, if this amount is ⅓ of the whole, how many of these would we need to make 1 whole cup?
• Money: In a world of debit cards, pull out some cash and coins every now and then and explore ALL of the many possibilities to build fraction sense and also brush up on counting money!  Start small for example with a dime and ten pennies and talk about how one penny is 1/10 of a dime, 2 pennies is 2/10, etc.  Next, change your whole to a quarter and show how since it takes five nickels to make a quarter, 1 nickel is ⅕ of 25 cents! Then, investigate all the many fractional amounts of 1 dollar. 
• Sets of Objects and Equally Packaged Items: Students should learn early that fractions can also represent a part of a group of objects, commonly referred to as a set.  In everyday life, many items, food and drinks that we purchase can represent a set.  For example, before eating that pack of skittles, dump them out and identify what fraction of each color skittle there is. If you buy a variety pack of individual bags of chips, you can discuss what fraction of the bags are spicy nacho flavored or what fractions of the bags are cool ranch flavored?

Once kids begin seeing the world through a fractional filter, they will find even MORE fractions in daily life. Encourage them to think of and point out other examples they see. The possibilities really are endless, so challenge them to keep going!

Another way to help students strengthen their fraction sense is to incorporate the use of manipulatives to provide them with a visual and concrete representation of a fraction. Fraction strips, sometimes called fraction tiles or fraction bars, can be used to represent and model different fractions from halves to twelfths. You can purchase plastic or wooden sets, make your own with paper, or grab your free fraction strips printable to get started!

For more help with fractions, check out our Grade Level Fractions Guides, available for 3rd, 4th, 5th and 6th grades. You can also find in-depth lessons in our digital course series, Fractions Unlocked 1 and Fractions Unlocked 2 where we help students solidify a knowledge of fractions by exploring the part-whole relationship fractions represent across many different contexts & models and practicing multiple ways of representing fractions to help them accurately work through and solve problems involving fractions.