Ordering Rational Numbers

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SWBAT compare and order rational numbers.

Big Idea

Students order numbers using a number line.

Do Now

10 minutes

Students have previously worked on identifying integers.  The Do Now is a review of this concept.  

Do Now

Identify the integers in the list of numbers.

-3/4, 2, 1/2, -8, 704, 0, -1, 2.4, -8.6

Students will have about 5 minutes to complete the Do Now in their notebooks.  I will encourage students to use refer back to the definition of integers.  

As a class, we will discuss which numbers are integers and why. 


Comparing Integers Game

10 minutes

In a previous lesson, students learned how to identify integers and how they are placed on a number line.  Before continuing on with comparing rational numbers, I want to ensure that students have a firm grasp of integers.

Integer Game Rules (see Integer Game)

Students will play the integer game.  Students can either play in pairs or groups (recommended maximum of 4).  Groups will receive a standard deck of cards.  They should be told that the black cards represent positive integers and the red cards represent negative integers.  The Aces represent 1, the Jacks represent 11, the Queens represent 12, and the Kings represent 13.

It may help to compare the game to the card game, "War", which many students are familiar with. For this game, the deck of cards should be divided equally among the group.  Each student should have their cards in a stack face down.  At the same time, the students should place their top card face up for everyone to see.  They should determine which student has the largest number and he then will keep all of the cards.  Students should continue playing into one student has all of the cards.

As students play, I will monitor their games to ensure that they are comparing integers properly.

Mini Lesson

15 minutes

This lesson will cover how to order and compare rational numbers.  Students may have different strategies.

We  will discuss three examples together as a class.

Ex. 1 - Order from least to greatest    0.5 ,  -1.0 ,  1.5 ,  0 ,  -1/4  

Are all of these numbers integers? 

Students should recognize that not all of the numbers are integers.

What are rational numbers?  What word do you see in rational?  What is a ratio?

Students should develop a definition of rational numbers.

Rational number - a number that can be written as a fraction

It may be difficult to compare fractions to decimals, so how can we approach this problem?

Most students will suggest changing the fraction to a decimal, but there may be some students who prefer to work with fractions. 

Students have difficulty with ordering negative numbers, so we will plot them on a number line.This is helpful to visual learners. See Number Line.

Where does 1/4 fall on the number line?  Where does -1/4 fall on the number line?

Students should make the connection that if 1/4 is between 0 and 1, but closer to 0; then -1/4 is between 0 and -1, but closer to 0.

After determining where the numbers lie on the number line, we will order them.

Ex. 2 - Order from least to greatest    2.5 ,  -1.4 ,  -0.3 ,  1/5 ,  -11/4

What would make it easier to compare these fractions and decimals?

Again, most students will suggest changing the fractions to decimals.  I will encourage those students who prefer to change the decimals to fractions to use their strategy and decide if we arrive at the same answer.

Before ordering the numbers, we will plot them on a number line to help students visualize their location.

Ex. 3 -   Order from least to greatest     -1/4,  20%,  1,  -18/36,  0.6,  5/4


We will approach this example as we did the others, but now students need to consider how to compare percents, fractions, and decimals.

Independent Practice

10 minutes

For the independent practice, students' understanding of the lesson will be assessed.  Although it is independent practice, students will be encouraged to ask one another questions as they work.


Independent Practice

Compare  < , > , =

1)  -0.1   and -1/10

2)  -3/8  and   -0.5

3)    60%  and   1/5

Order from least to greatest

4)-2/5, 30%, -1/2, 1/2, -0.4

5)15%, -4/6, -1, -1/8

 After about 5 minutes, I will review the problems with the class.  

Lesson Review

5 minutes

To review the lesson as a class, I will present the students with one more problem.  We will discuss the following problem.

Jason ordered the numbers, −119, -118, and -118.77, from least to greatest by writing the following statement:  -118<-118.77<-119.  Is this a true statement?

Students should be able to determine that -118.77 is between -118 and -119.  However, they should realize that the inequality is incorrect.