# ﻿Comparing Numbers and Distance from Zero

Warmup

Activity #1

Using symbols to compare numbers.

Here are some numbers. Use inequality symbols (<, =, >) to write true comparison statements. To use the applet to access inequality symbols, here are the steps below;

• For Question (1), after selecting the numbers you want to use, go to ABC​.
• Type the first number.
• Enter the inequality sign using your keyboard.
• Type the second number and click OK.
• You can use the return button to delete or undo the last action. To clear and start all over, use the reset button, .

(1.) Select two numbers and one comparison symbol and use them to write a true statement.

(2.) Write a sentence in words with the same meaning, using the following phrases: For example, you could write 4 < 8 and also write, “4 is less than 8.”

(i.) is equal to​

(ii.) is the absolute value of​

(iii.) is greater than​

(iv.) is less than

Activity #2

Plot Rational Numbers on a Number Line.

a” is a rational number.

• Choose a value for a.
• Plot the value of a on the number line below.

(1.) Based on where you plotted a, plot -a on the same number line. What is the value of -a that you plotted?

(2.) Noah said, “If a  is a rational number, -a will always be a negative number.” Do you agree with Noah? Explain your reasoning.

A submarine is at an elevation of -100 feet (100 feet below sea level). Let’s compare the elevations of these four people to that of the submarine:

• Clare’s elevation is greater than the elevation of the submarine. Clare is farther from sea level than the submarine.
• Andre’s elevation is less than the elevation of the submarine. Andre is farther away from sea level than the submarine.
• Han’s elevation is greater than the elevation of the submarine. Han is closer to sea level than is the submarine.
• Lin’s elevation is the same distance away from sea level as the submarine’s

Complete the table as follows.

• Write a possible elevation for each person.
• Use <,  >, or = to compare the elevation of that person to that of the submarine.
• Use absolute value to tell how far away the person is from sea level (elevation 0).

As an example, the first row has been filled with a possible elevation for Clare.

Priya says her elevation is less than the submarine’s and she is closer to sea level. Is this possible? Explain your reasoning.

Activity #3

Make Truth Statements by Comparing Numbers.

• Answer the following absolute value inequality problems below.

For each question, choose a value for each variable to make the whole statement true. (When the word “and” is used in math, both parts have to be true for the whole statement to be true.)

(1.) Is the statement true if one variable is negative and one is positive?

(2.) Is the statement true if both values are negative?

(3.) Is the statement true if one variable is negative and one is positive?

(4.) Is the statement true if both values are negative?

(5.) Is the statement true if one variable is negative and one is positive?

(6.) Is the statement true if both values are negative?

(7.) Is the statement true if one variable is negative and one is positive?

(8.) Is the statement true if both values are negative?

Challenge #1

Challenge #2

Mai received and spent money in the following ways last month. For each example, write a signed number to represent the change in money from her perspective.

(1.) Her grandmother gave her $25 in a birthday card. (2.) She earned$14 dollars babysitting.

(3.) She spent $10 on a ticket to the concert. (4.) She donated$3 to a local charity.

(5.) She got \$2 interest on money that was in her savings account.

Challenge #3

Match the the statements written in English with the mathematical statements.

Quiz Time