Comparing and Ordering Fractions and Decimals Task

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SWBAT use place value to determine the order of fractions and decimals, then justify their answers with models.

Big Idea

Models can help students compare and order fractions and decimals.


5 minutes

Rationale for teaching with a task:

After I have worked directly with the students on a skill, I like to use a task.  A task gives the students more practice on the skill while working in groups.  Allowing the students to work in groups gives the students different perspectives from their classmates.  Students can learn from each other.  As the students work on a task, I am the facilitator, walking around monitoring and questioning the students to lead them to the solution.


I let the students know that today we will do a task.  I remind the students of the structure and routine of a task.  First, the students will have private work time to think about and plan how to solve the task.  Next, the students will work in groups to explore the concept of the lesson.  Finally, the students will share/analyze/and discuss the task as a whole class.  Each student should have a copy of the task at their desk, as well as a decimal place value chart to help solve the task.   

In today's lesson, the students use their understanding of place value to solve this task without direct instruction.  They have to find the answers by comparing place value (4.NF.C7).


5 minutes

Comparing and Ordering Fractions and Decimals Task.docx


Thomas, Tim, and Terry are brothers.  Thomas said that 9 3/100 is larger than .93 and 9.3.  Terry disagreed with his brother.  He said that .93 is the highest number.  Therefore, it is the largest number.  Tim disagreed with both of his brothers.  Tim said that 9.3 is the largest number.  Who is correct?



1.  Place each number on the decimal place value chart

2. Compare the numbers using >, <, and =

3. Put the numbers in order from least to greatest


Give the students about 5 minutes of independent time to read and plan to solve this task (MP1).  The students should have a decimal place value chart at their desk.  The students can use the decimal place value chart at this time to plan how to solve the task (MP5).   The decimal place value chart will help the students understand that they must consider the value of each number in order to compare and order the numbers.  After the 5 minutes of independent planning, the lesson will go to the next phase of group exploration.

Skill Building/Exploration

20 minutes

During the group exploration/discovery phase, the students work in groups of 3.  Each group has a copy of the task and a Decimals Place Value Chart.docx.  The students must work together to complete all requirements of the task.  The students reason abstractly and quantitatively by decontextualizing the information and representing it symbolically.    During this phase, the students do not receive direct instruction.  In this lesson, they should apply skills previously learned.   The students are guided to the conceptual understanding through questioning by their classmates, as well as by me.

The students are required to compare and order fractions and decimals by looking at the value of each number (4.NF.C7).  The students must communicate with each other and agree upon the equation.  This takes discussion, critiquing, and justifying of answers by all 3 students (MP3).  Each group has a decimal place value chart.  During this part of the lesson, the students should use the chart to determine the value of the numbers (MP5)

During the phase, I will monitor and assess the students' progression of understanding through questioning.  Possible questions to help lead to the solution are as follows:

1. How do you say the word name of the number?

2. How many pieces was the whole divided into?

3.  Where do you place the number on the place value chart?

4.  Will it be a mixed number or a fraction?  How do you know?

5.  Which number is greater?  How do you know?

As I walk around the classroom, I am questioning the students and looking for common misconceptions among the students.  Any misconceptions are addressed at the point, as well as whole class at the end of the activity.

 Any student that finishes the assignment early, can go to the computer to practice fractions and decimals at the following site until we are ready for the whole group sharing:



15 minutes

To close the lesson, I bring the students back together as a whole class.  I feel that it is very important to let the students share their answers as a whole class.  This gives those students who still do not understand another opportunity to learn it.  I like to use my document camera to show the students' work during this time.  Some students do not understand what is being said, but understand clearly when the work is put up for them to see.

I feel that by closing each of my lessons by having students share their work is very important to the success of the lesson.  Students need to see good work samples (Student Work - Comparing and Ordering Decimals.jpg), as well as work that may have incorrect information.  More than one student may have had the same misconception.  In the Video - Comparing and Ordering Fractions and Decimals, a student shares his work. During the closing of the lesson, all misconceptions that were spotted during the activity will be addressed whole class. 

I collect all papers from the students.  All struggling students identified as I monitored during their activity will receive further instruction in small group.