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Investigation: Integers everywhere

Lesson

Previously, we looked at how integers can be used to describe events in everyday life. We will now investigate how we can use positive and negative integers to describe everyday events and show our work on number lines.

 

Bank on it

There are many technical terms used in financial math. Here are some key terms used in money math. In small groups, discuss the terms and answer the questions.

  • A balance is the amount of money in a person's bank account at any one time.
  • A deposit is money a person puts in to a bank account. If a person deposited money into their account, would there balance increase or decrease? What mathematical operation (+, -, x or ÷) would show this?
  • A withdrawal is money a person takes out of a bank account. If a person withdrew money from their account, would there balance increase or decrease? What mathematical operation (+, -, x or ÷) would show this?

 

Activity

Write each event about what happens in Jack's bank account as an integer. Model the integer on the number line using an appropriate scale and mathematical symbols.

Jack opened a bank account when he got his first job and then the following happened:

  • His wage of $\$200$$200 was deposited.
  • He withdrew $\$105$$105 to buy a new skateboard.
  • He then withdrew another $\$7$$7 to buy lunch.
  • His grandma deposited $\$30$$30 into his account for his birthday.

 

Complete the table with the information.

Event Integer in Event Number line model
Opened bank account & $\$200$$200 deposited $200$200
Withdrew $\$105$$105 $-105$105

 

 

 

   

 

 

 

   

 

Discussion questions

  1. How could the table above help to track his account balance?
  2. What other scenarios can you think of where integers could be helpful?
  3. What would happen if he withdrew another $\$170$$170 for a new gaming system? Do you think the bank would allow that? Why or why not?

 

What's the weather like?

Temperature is another common example of where we use integers everyday. There are two common scales for measuring temperature - Celsius and Fahrenheit. In the US, we use Farenheit day to day, but Celsius in science and other classes. There is a formula to convert between these two scales, but we'll learn about that later.

Activity

1. Look at the thermometer on the left. Record the temperature in Celsius and Fahrenheit. Are the scales equivalent (ie. Do the numbers mean the same thing on both sides)?

2. What integer is approximately equivalent (equal) to $14$14 $^\circ$°F?

3. Find out and record today's temperature as an integer in Celsius and Fahrenheit.

4. Investigate the temperature at which water freezes in Celsius and Fahrenheit.

5. Investigate the temperature at which water boils in Celsius and Fahrenheit.

6. How would you write "$17$17 degrees Celsius below zero" as an integer?

7. If someone told you it was $90^\circ$90° outside, what measurement scale do you think they would be using? Justify your answer.

 

 

Outcomes

MGSE6.NS.5

Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, debits/credits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.

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