Illustrative Mathematics Unit 6.7, Lesson 4: Ordering Rational Numbers

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Illustrative Math
Grade 6

Lesson 4: Ordering Rational Numbers

Let’s order rational numbers.

Illustrative Math Unit 6.7, Lesson 4 (printable worksheets)

Lesson 4 Summary

The following diagram shows how to compare and order rational numbers using a number line.

Lesson 4.1 How Do They Compare?

Use the symbols >, <, or = to compare each pair of numbers. Be prepared to explain your reasoning.
12 _____ 19
212 _____ 190
15 _____ 1.5
9.02 _____ 9.2
6.050 _____ 6.05
0.4 _____ 9/40
19/24 _____ 19/21
16/17 _____ 11/12

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Scroll down the page for the solutions to the “Are you ready for more?” section.

Lesson 4.2 Ordering Rational Number Cards

Your teacher will give you a set of number cards. Order them from least to greatest.
Your teacher will give you a second set of number cards. Add these to the correct places in the ordered set.

Lesson 4.3 Comparing Points on A Line

1. Use each of the following terms at least once to describe or compare the values of points M, N, P, R.

• greater than
• less than
• opposite of (or opposites)
• negative number

2. Tell what the value of each point would be if:
   a. P = 1/2
   b. N = -0.4
   c. R = 200
   d. M = -15
   
   

Are you ready for more?

1. Expand the list again to include fractions that have denominators of 5.
2. Expand the list you made to include fractions have denominators of 6.
3. When you add a new fraction to the list, you put it in between two “neighbors.” Go back and look at your work. Do you see a relationship between a new fraction and its two neighbors?

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Lesson 4 Practice Problems

1. Select all of the numbers that are greater than -5.
   A. 1.3
   B. -6
   C. -12
   D. 1/7
   E. -1
   F. -4
   
2. Order these numbers from least to greatest:
   1/2, 0, 1, -1 1/2, - 1/2, -1
   
3. Here are the boiling points of certain elements in degrees Celsius:
   

• Argon: -185.8
  
• Chlorine: -34
  
• Fluorine: -188.1
  
• Hydrogen: -252.87
  
• Krypton: -153.2
  List the elements from least to greatest boiling points.
  Put the states in order by their lowest elevation, from least to greatest.
  

4. Explain why zero is considered its own opposite.
   
5. Explain how to make these calculations mentally.
   A. 99 + 54
   B. 244 - 99
   C. 99 · 6
   D. 99 · 15
   
6. Find the quotients.
   a. 1/2 ÷ 2
   b. 2 ÷ 2
   c. 1/2 ÷ 1/2
   d. 38/79 ÷ 38/79
   

The Open Up Resources math curriculum is free to download from the Open Up Resources website and is also available from Illustrative Mathematics.

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