Teaching Advanced Fractions

Teacher Guide by Anna Warfield

Find this Common Core aligned Teacher Guide and more like it in our Elementary School Category!

Advanced Fractions Lesson Plans

Once students have mastered the basics of fractions, more complex concepts can be introduced. Adding and subtracting fractions, as well as recognizing and manipulating improper fractions, are topics that are crucial during the elementary grades and into middle school.

These math lessons and activities on more advanced fractions provides examples of questions to ask students, classroom activities to promote learning, and visuals to create using Storyboard That! If you are just starting fractions, check out our Introduction to Fractions!

Advanced Fractions Lesson Plans, Student Activities and Graphic Organizers

Parts of Wholes or Sets

The most important concept for beginning fraction masters is that of parts of wholes or parts of sets. Students see and hear parts and wholes in use daily, but representing those values numerically can be challenging. Begin first with shapes that have been divided up into equal shares (circles, squares, hexagons, etc.), and then once students have grasped the concept, move on to fractions of sets. Fractions of a set is a far more useful concept for world problems and real-world application.

One example might be:

1/4 of the class is 6 students, how many students are in the class?

In this activity, students will create different examples of fraction sets by creating equal groups of simple shapes or objects and color coding the groups. There are many ways to modify "Fraction of Sets Starter" storyboard in order to meet the needs of your students. The starter template is intended to be used for students who need a lot of guidance. Make it more challenging by adding rows and/or columns, providing less guiding information in the description boxes, or having students choose the number and types of objects.

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Add and Subtract with a Common Denominator

Revisit what “numerator” and “denominator” mean, stressing that the denominator gives the name to the fraction. When adding fractions, you are adding parts; as long as you are adding the same kind of parts (common denominator), you only need to worry about how many parts in all.

Give students examples of when you might add parts together, but be careful of how you word your questions!

“Dennis ate 2 pieces of pizza and Larry ate 2 pieces of pizza. How much pizza did they eat?”

Is the answer four pieces? Four-eighths? All of the pizza?

Be explicit in the question or example. Identify how many pieces make up the whole. Use precise language when asking the question, such as “what fraction” or “how many pieces”, so students know what they are looking for.

By rewording the story, you can use the same example for subtraction. You can change the question to “what fraction of the pizza is left” or “how many pieces are left?”

Just as in subtraction with whole numbers, be sure students are writing the numbers in the correct order. Typically, students have not yet encountered improper fractions, and certainly not negative numbers. The larger fraction goes first in the number sentence: 3/4 - 1/4 = 2/4.

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Improper Fractions and Mixed Numbers

Fractions with a numerator that is less than the denominator, such as 1/2 or 3/8, are called proper fractions. When the numerator is greater than the denominator, such as 4/3 or 15/2, we call these fractions improper fractions.

Have students write a fraction story that shows an example of improper fractions. The story may or may not include instructional or explanatory cells.

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Adding and Subtracting Mixed Numbers

Operating on mixed numbers combines students’ knowledge of addition and subtraction, converting wholes to fractions, converting mixed numbers to improper fractions, and regrouping.

Adding mixed numbers may look a little daunting at first, but if you break down the mixed numbers into wholes and fractions, into pictures, or into improper fractions, everything starts to come together.

Be careful with subtraction! Students may rewrite the order of the number sentence or regroup incorrectly. Start with pictures, like the fraction circles available on Storyboard That. An interesting exercise would be to have an open discussion about subtracting mixed numbers before teaching it, but use your best judgment with your group of students. It may be better to teach mixed number subtraction explicitly before any misconceptions or bad habits start forming.

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•   (English) Advanced Fractions   •   (Español) Fracciones Avanzadas   •   (Français) Fractions Avancées   •   (Deutsch) Erweiterte Fraktionen   •   (Italiana) Frazioni Avanzate   •   (Nederlands) Geavanceerde Fracties   •   (Português) Frações Avançadas   •   (עברית) שברים מתקדמים   •   (العَرَبِيَّة) الكسور المتقدم   •   (हिन्दी) उन्नत फ़ेक्शंस   •   (ру́сский язы́к) Продвинутые Фракции   •   (Dansk) Avancerede Brøker   •   (Svenska) Avancerade Fraktioner   •   (Suomi) Advanced Murtoluvut   •   (Norsk) Avanserte Brøk   •   (Türkçe) İleri Kesirler   •   (Polski) Frakcje Zaawansowane   •   (Româna) Fracțiile Avansate   •   (Ceština) Pokročilé Frakce   •   (Slovenský) Pokročilé Zlomky   •   (Magyar) Részletes Frakciókat   •   (Hrvatski) Napredne Frakcije   •   (български) Разширени Фракции   •   (Lietuvos) Išplėstinė Frakcijos   •   (Slovenščina) Napredno Frakcije   •   (Latvijas) Advanced Frakcijas   •   (eesti) Täpsem Fraktsioonid