This document contains notes from lessons on positive and negative numbers. It includes examples of using positive and negative numbers to represent bank account balances, temperatures, and elevations. The lessons cover locating positive and negative numbers on horizontal and vertical number lines, and understanding that opposites are the same distance from zero. Homework is assigned for several days during the upcoming week.

1. Module 3 Lesson 1 & 2 Merged.notebook
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January 20, 2015
Oct 8­8:53 AM
Monday No School
Tuesday
Problem Set Lesson 1 # 1,5,6,7
Problem Set Lesson 2 all
Wednesday Problem Set Lesson 3 & 4
Thursday
Problem Set Lesson 5 & 6
Due Monday
Friday Complete Thursday's hw

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Aug 26­5:45 PM
MODULE 3 Rational Numbers
Topic A: Understanding Positive and Negative Numbers on the
Number Line
Lesson 1: Positive and Negative Numbers on the Number Line—
Opposite Direction and Value
Lesson 2: Real­World Positive and Negative Numbers and Zero
Student Outcomes
§ Students extend their understanding of the number line, which includes zero and numbers to the right, that are above zero, and numbers to the left, that are below zero.
§ Students use positive integers to locate negative integers, moving in the opposite direction from zero.
§ Students understand that the set of integers includes the set of positive whole numbers and their opposites, as well as zero. They also understand that zero is its own opposite.
Student Outcomes
§ Students use positive and negative numbers to indicate a change (gain or loss) in elevation with a fixed reference point, temperature, and the balance in a bank account.
§ Students use vocabulary precisely when describing and representing situations involving integers; e.g., an elevation of ‐10 feet is the same as 10 feet below the fixed reference point.
§ Students choose an appropriate scale for the number line when given a set of positive and negative numbers to graph.

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Jan 28­9:01 AM
The set of whole numbers and their opposites, including zero, are
called integers.
A number line diagram shows integers listed in increasing order
from left to right using equal spaces.
Starting at 0, as I move further to the left of zero on a horizontal number
line, the values get smaller. These numbers are called negative numbers
because they are less than zero. Notice the curved arrow is pointing to
the left to show a negative direction. The position of the point is now,
negative 3, written as ‐3.

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This is also true for a vertical number line. On a
vertical number line, positive numbers are located
above zero. As we look upward on a vertical
number line, the values of the numbers increase.
On a vertical number line, negative numbers are
located below zero. As we look further down on a
vertical number line, the values of the numbers
decrease.

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What is the relationship between 3 and ‐3 on the number line?
Opposites are the same distance from
zero but on opposite sides.
Zero is its own opposite.

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Explain how you would show 150 on a number line.

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Nov 17­2:29 PM
Example 1: Take it to the Bank
For Tim’s 13th birthday, he received $150 in cash from his mom. His dad took him to the bank to open a
savings account. Tim gave the cash to the banker to deposit into the account. The banker credited Tim’s
new account $150 and gave Tim a receipt. One week later, Tim deposited another $25 he had earned as
allowance. The next month, Tim asked his dad for permission to withdraw $35 to buy a new video
game. Tim’s dad explained that the bank would charge $5 for each withdrawal from the savings account
and that each withdrawal and charge results in a debit to the account.

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Example 2: How Hot, How Cold?
Temperature is commonly measured using one of two scales, Celsius or Fahrenheit. In the
United States the Fahrenheit system continues to be the accepted standard for non‐scientific
use. All other countries have adopted Celsius as the primary scale in use. The thermometer
shows how both scales are related.
a. The boiling point of water is 100°C. Where is 100 degrees Celsius located on the
thermometer to the right?
b. On a vertical number line, describe the position of the integer that represents 100°C.
c. Write each temperature as an integer.
i. The temperature shown to the right in °F:
ii. The temperature shown to the right in °C:
iii. Freezing point of water in Celsius:
d. If someone tells you your body temperature is 98.6° what scale are they using? How do you
know?
e. Does the temperature 0 degrees mean the same thing on both scales?

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Exercises 3–5
3. Write each word under the appropriate column, “Positive Number” or “Negative Number”.
Receive
Gain
Loss Deposit
Credit
Debit
Charge
Below Zero
Withdraw
Owe

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Closing
§ How did we represent debit and credit on a number line?
ú A debit is represented as a negative number, located to the left of zero. A credit is
represented as a positive number, located to the right of zero.
§ Can a temperature of ‐9 degrees be described as “Negative nine degrees below zero?”
Why or why not?
ú No, because “below zero” already means that the temperature is negative.
Please take out your exit ticket for Lesson 2, close your
binder, and complete the exit ticket. This will be collected.

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Closing

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Jan 28­10:51 AM