 Integers Everywhere (Investigation)

Lesson

In Is it Positive or Negative, we looked at how maths is like a special language that we can use to describe events in everyday life. In this exercise, you are going to investigate how we can use positive and negative integers (whole numbers) to describe everyday events and show your working on number lines.

Bank on it There is groups of technical terms used in consumer arithmetic (that's just maths that involves money). Here are some key terms used in money maths. 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 his wage of $\$200$$200 is deposited. He withdrew \105$$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$$200 deposited 200200 Withdrew \105$$105 $-105$105 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. Only the United States uses the Fahrenheit scale as their primary measure of temperature. All other countries use the Celsius scale. 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^\circ$14°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.