Order Decimals, Fractions, and Mixed Numbers


Order Decimals, Fractions, and Mixed Numbers teaches students how to put numbers in mixed formats into sequential order, both ascending and descending. Students will practice converting decimals to fractions and fractions to decimals. They will also learn how to convert mixed numbers more easily.

You will find several additional ideas and activities to incorporate into the lesson in the “Options for Lesson” section of the classroom procedure page. One idea, for instance, is to give each student three index cards and allow them to create their own fraction, mixed number, and decimal within specific parameters for the activity.

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What our Order Decimals, Fractions, and Mixed Numbers lesson plan includes

Lesson Objectives and Overview: Order Decimals, Fractions, and Mixed Numbers teaches students how to place decimals, fractions, and mixed numbers in ascending and descending order. Students will also learn how to convert fractions to decimals or decimals to fractions. This lesson is for students in 5th grade and 6th 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 yellow 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. You will need cards, scissors, glue, and an extra sheet of paper per student for this lesson. Students may also use calculators, but that is optional.

Options for Lesson

In the “Options for Lesson” section of the classroom procedure page, you will see some suggestions for additional activities or ideas to add to the lesson if you want to. In the activity, instead of changing groups, students could come to the front of the class and draw a new card with a different number. Give each student three index cards and allow them to create their own fraction, mixed number, and decimal within specific parameters. Ask students to choose their cards for every round and mix up the groups.

Teacher Notes

The teacher notes page provides an extra paragraph of information to help guide the lesson. It mentions that this lesson can help reinforce long division as well. You can use the blank lines to write down any other ideas or thoughts you have about the topic as you prepare.


What Is Sequence?

The Order Decimals, Fractions, and Mixed Numbers lesson plan contains three pages of content. You have learned that math involves putting things in order, or in a sequence. The simplest representation of a sequence is number lines. Another typical example is a ruler.

From these two examples, it’s easy to conclude there are two ways to put numbers in order, greatest to least or least to greatest. When numbers are arranged in order from greatest to least, it is called descending order. When numbers are placed in order from least to greatest, it is called ascending order. An easy way to remember the two is to think about climbing stairs, a mountain, a rock wall, or walking up a hill. As you go up, you are ascending. And going down is descending!

Fractions and decimals can be confusing. Some people think that fractions and decimals are like speaking two different languages. They may be challenging, but there are ways to make understanding fractions and decimals easier.

The easiest way to put them in order is for all the numbers to speak the same language—in this case, making them all fractions or all decimals. Number lines can be a helpful tool. But first, we must understand how to change fractions to decimals and decimals to fractions before placing them in order.

Converting Decimals and Fractions

Changing a fraction to a decimal is a division problem. To change a fraction into a decimal, divide the numerator by the denominator. You can either use long division or a calculator. Students can look at a few examples on this page to see how to make the conversion. Even easier, to change a decimal to a fraction, convert the decimal to a fraction. Then reduce. The lesson shows 0.25 as an example. First, it becomes 25/100 and then reduces to 1/4.

Mixed numbers are slightly more complicated. Recall that a mixed number is a whole number and a fraction. The easiest way to turn a mixed number into a decimal is to begin with the fraction. Divide the numerator by the denominator, then add the whole number. You can either use long division or a calculator. The lesson gives three more examples.

Finally, it’s time to sequence. Once you have changed all the fractions to decimals, you can use place value to put them in order. Another way to think of placing decimals in order is to change them to money. You know that $0.25 is way less than $2.70! Would you rather have $0.33 or $2.50? When there are only two places to the right of the decimal sign, changing decimals to money can help you place decimals in sequential order.

The lesson also offers one more way to keep track of the numbers to put them in order. Use the columns of lined paper to put the numbers in so you can compare them. To make it easier to compare, we insert zeros (0s) to hold the place where there is no number. Using the columns on lined paper can help you see the numbers and order them in a sequence of least to greatest or greatest to least.


The Order Decimals, Fractions, and Mixed Numbers lesson plan includes three worksheets: an activity worksheet, a practice worksheet, and a homework assignment. Each one will help students solidify their grasp of the material they learned throughout the lesson. You can refer to the classroom procedure guidelines to know when to hand out each worksheet.


Students will work with a partner for the activity. You will provide index cards with fractions or decimals on them. Students must shuffle the cards and then pick five to place in order for each round in the boxes on the worksheet. The worksheet describes whether students should sequence the numbers in ascending or descending order. There are five rounds total. Partners will check each other’s work at the end of each round.


Similar to the activity, students will have to place numbers in order. First, they will cut out the four numbers in each row. Then they will place them in order according to what the prompt says.


For the homework assignment, students will sequence several rows of numbers in ascending order and then several more in descending order. Then they will define what both ascending and descending order mean.

Worksheet Answer Keys

There are answer keys for both the practice and homework worksheets at the end of the lesson plan document. Correct answers are in red to make it easier to compare them to students’ responses. 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


5th Grade, 6th Grade



State Educational Standards


Lessons are aligned to meet the education objectives and goals of most states. For more information on your state objectives, contact your local Board of Education or Department of Education in your state.