G8

Copyright © Swun Math Grade 8 Unit 1 Lesson 8 P TE

Input/Model

(Teacher Presents)

Directions: Place the numbers on a number line. Then compare using an inequality.

1. √ 7 , 3, 2, 2.5

Solution:

• *If needed, provide students the numbers to write below the notches on the number line.


• Step 1 - Analyze the irrational number to narrow down answer between two consecutive integers on a
  number line:
  Since I know that 22 = 4 and 32 = 9,√ 7 must be between these two numbers.


• Step 2 - Continue narrowing it down more precisely if necessary:
  Since 2.5^2 = 6. 25 , and √ 7 is more than that, √ 7 will be between 2.5 and 3.


• Step 3 - Compare the numbers: conclude that the inequality will be 2 < 2.5 < √ 7 < 3.
  Answer: 2 < 2.5 < √ 7 < 3

2. √ 23 , 4 , √ 19 , 5

Solution:

• Step 1 - Analyze the irrational number to narrow down answer between two consecutive integers on a
  number line:

Since I know that 42 = 16 and 52 =25,√ 19 and (^) √ 23 must be between these two numbers.

• Step 2 - Continue narrowing it down more precisely if necessary:
  Since 4.5^2 =20. 25 , and √ 19 is less than 4.5, and √ 23 will be between 4.5 and 5.


• Step 3 - Compare the numbers: conclude that the inequality will be 4 < √ 19 < √ 23 < 5
  Answer: 4 < √ 19 < √ 23 < 5

4 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5 5. 1

√ 19 √^23

2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3 3. 1

√^7