Dewey Decimal system for ordering decimals

16 teachers like this lesson
Print Lesson


SWBAT to express decimal equivalents to compare and order decimals.

Big Idea

The Dewey Decimal System is used in libraries all around the world. The foundation of this system is based upon ordering decimals.


15 minutes

Read the story, Bob the Alien Discovers the Dewey Decimal System by Sandra DonovanMartin Haake (Illustrator). 

This is a nice easy read to introduce the students to the Dewey Decimal System.  As I read this story, I have the students predicting what each level of the system represents.  When the 500 level comes up, I always tell them that this is Bob’s favorite section.  What do you think it is? 

I chose this story because I’m using the DDS throughout this lesson as a real life example of comparing and ordering decimals. 

Discovering Equivalency

15 minutes

To start the lesson, I’m going to use decimal grids to prove equivalency.  Students have already used the grids to model.  Now they will model to prove equivalency.  As students are working through finding equivalent decimals, ask them what they notice about each decimal?  I’m expecting to hear that by adding a zero to the next place values makes decimals equivalent.  (SMP 8)  I explain to students that using decimal equivalents helps us to compare and order decimals.

Comparing Decimals

15 minutes

Students need to know that when we compare decimals, we use the <, >, = symbols (SMP 6) In order to compare decimals, we have to line up decimal points.  Ask the students why we line up decimal points?  Students should notice that when the decimal point is lined up, so are the place values.  Ask them why it is important to line up place values?  Students should respond that we can only compare equal parts, just like fractions.

Students that struggle can use their place value chart to help them line up the decimal place values.

Ordering Decimals

15 minutes

Students need to know that when they are asked to order decimals, they will be putting them in order from least to greatest or greatest to least (SMP 6)  Ordering decimals is similar to comparing, but there are more decimals to compare.  Again, we will use decimal equivalents to help us order decimals.

Common misconception:  Students will want to start comparing decimal places from the right and move left.  Remind students that they need to start with the largest place value (left) because this will eliminate the largest number right away. 

Before moving on, ask the students this:

Write down 5 decimals.  Put them in order from least to greatest. Have students do a HUSUPU to share their decimals and ordering with a partner.  Students can exchange papers with their partner and check each other’s work.  

This question allows students to work at their own level.  Watch to see that students are lining up decimal points and annexing zeros to create equal place values.  

A day at the library

20 minutes

Ask your librarian to compile some books for you to use in class.  Tell the students that they will need to put these books in order for the librarian.  In order for all students to be able to experience this, give each student choose 3 books.  They will need to put these three books in order according to the Dewey Decimal number and prove that their ordering is correct.  Students will be applying what they have learned about comparing and ordering decimals to this task.  As students are working on this task, walk around to make sure they are lining up decimal places, annexing zeros to create equal place values, and comparing the decimals starting with the largest place values.   The worksheet is set up so that the students can work at their own pace.  They can complete up to 3 investigations. (SMP 1,2,4,6)


5 minutes

Have student write down in their own words why it is important to line up decimal places when comparing and ordering?  Since students need to understand that the place value is what we are comparing they should say that by lining up the decimal points, lines up the place values.  Then we compare the decimal places values largest to smallest.