Decomposing Fractions


Our Decomposing Fractions lesson plan teaches students how fractions function by breaking them down into smaller parts. Students practice “decomposing” fractions with like denominators and learn lesson vocabulary.

Included with this lesson are some adjustments or additions that you can make if you’d like, found in the “Options for Lesson” section of the Classroom Procedure page. One of the optional additions to this lesson is to have your students color grids to show the various ways to decompose a single fraction.

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What our Decomposing Fractions lesson plan includes

Lesson Objectives and Overview: Decomposing Fractions helps students gain a deeper understanding of fractions and how they function. By breaking fractions down into smaller pieces – decomposing them – students will better understand how to work with these numbers as part of their math lessons. The lesson also reviews vocabulary like numerator and denominator, as well as mixed numbers and improper fractions. At the end of the lesson, students will be able to decompose fractions with like denominators. This lesson is for students in 4th grade and 5th grade.

Classroom Procedure

Every lesson plan provides you with a classroom procedure page that outlines a step-by-step guide to follow. You do not have to follow the guide exactly. The guide helps you organize the lesson and details when to hand out worksheets. It also lists information in the blue box that you might find useful. You will find the lesson objectives, state standards, and number of class sessions the lesson should take to complete in this area. In addition, it describes the supplies you will need as well as what and how you need to prepare beforehand. The supplies you will need for this lesson include dice and grid paper.

Options for Lesson

Included with this lesson is an “Options for Lesson” section that lists a number of suggestions for activities to add to the lesson or substitutions for the ones already in the lesson. One optional addition to the lesson activity is to have your students use three dice to create mixed numbers and improper fractions in order to create more advanced decomposition problems. You could also have your students play the activity with a partner instead of as a large group. To help reinforce their understanding of the lesson, you could have your students color grids to show the various ways to decompose a single fraction. Finally, you could have your students match visual images with algebraic representations as an activity.

Teacher Notes

The teacher notes page includes lines that you can use to add your own notes as you’re preparing for this lesson.


Decomposing Fractions

The Decomposing Fractions lesson plan includes two content pages. The word decompose means to break something into smaller pieces. Decomposing a fraction means breaking the fraction into smaller pieces. We call each of these pieces unit fractions. Unit fractions are fractions that have a numerator (the number on top of the fraction) of one. The denominator is the number on the bottom of the fraction.

To decompose the fraction 3/5, we need to break the fraction into a sum of unit fractions. We keep the denominator the same and only decompose the numerator. The lesson walks through this process using a model.

For the model, we take a rectangle and break it into five equal parts because the denominator is 5. Each of these pieces represents 1/5, or a single unit fraction. The numerator is 3, so we need three pieces of the rectangle. Decomposing 3/5 gives us three 1/5 parts (1/5 + 1/5 + 1/5 = 3/5).

We can only decompose a fraction using unit fractions. However, we can also decompose a fraction into parts using a combination of smaller fractions. For example, we can also decompose 3/5 into 1/5 + 2/5.

As another example, we can decompose the fraction 4/7 into its unit fractions: 1/7 + 1/7 + 1/7 + 1/7. We can also decompose it into other combinations: 1/7 + 1/7 + 2/7, 1/7 + 3/7, or 2/7 + 2/7, for example.

We can also decompose mixed numbers. If we wanted to decompose 3 1/2, we would first need to change it into an improper fraction. In this case, we change it to 7/2. We can then decompose 7/2 as we would any other fraction!


The Decomposing Fractions lesson plan includes three worksheets: an activity worksheet, a homework assignment, and a quiz. You can refer to the guide on the classroom procedure page to determine when to hand out each worksheet.


The class will work in teams to complete the lesson activity. The students on each team will take turns decomposing fractions into a sum of fractions with the same denominator. They will include a sketch on graph paper for each equation. They will keep going until they can make no more equations. The team with the final equation wins!

To generate the fractions for the game, the teacher or the students will roll two die. The teacher will write the fraction on the board with a t-chart to keep track of the decompositions as they are used.


For the practice worksheet, students will decompose fractions and shade the circle graphs.


This lesson also includes a quiz that you can use to test students’ understanding of the lesson material. For the quiz, students will first decide which of four expressions shows 4/9 as a sum of unit fractions. They will then write four different fractions as sums of fractions.

Worksheet Answer Keys

This lesson plan includes answer keys for the practice worksheet and the quiz. If you choose to administer the lesson pages to your students via PDF, you will need to save a new file that omits these pages. Otherwise, you can simply print out the applicable pages and keep these as reference for yourself when grading assignments.

Additional information


4th Grade, 5th Grade



State Educational Standards