Minds On
Hot and cold
06.01
One of the coldest temperatures recorded in Canada was in Eureka, Nunavut one morning at −34 degrees Celsius.
One of the hottest days on record in Canada was in Yellow Grass, Saskatchewan when the thermometer read +45 degrees Celsius.
- How can you show these values visually?
- How can you determine the change in temperature between the hottest and coldest degrees? Describe the strategy you used in a recording or to a partner.
Action
Exploring integers
Integers
Integers are the set of whole numbers and their opposites.
Explore the following images and descriptions to learn more about integers and some of the different ways they can be represented.
Positive numbers are numbers that are greater than zero. Negative numbers are numbers that are less than zero. Zero is neither positive nor negative as it has no value, it’s zero!
A list of the numbers: -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5. A blue label indicates the negative numbers from -5 to -1. A red label indicates the positive numbers from 1 to 5. A black label indicates that zero is neither positive nor negative.
Integers can be represented using two different types of counters or items. Two different colours, or even two different shaped counters, can be used to represent the positive and negative values.
3 different representations of counters used to show positive and negative integers. A red positive circle and blue negative circle. A positive circle shape and a negative square shape. A yellow positive circle and a red negative circle. 3 yellow positive circles equal positive 3. Four negative squares equal negative 4.
Integers can also be represented on a number line. As we move from left to right
on a number line, the values get bigger. As we move from right to left on a
number line, the values get smaller.
Note: even though the negative digits get larger they are “more negative”,
so the value is smaller the further away they are from the zero!
A number line from -10 to +10. An arrow from right to left shows that values are increasing. An arrow from left to right show that values are decreasing.
The opposite of a positive integer is its negative equivalent. So, the opposite of the integer +5 is −5. This is because they are the same distance away from zero, but in opposite directions. We call these pairings opposite integers!
A number line highlighting the values of -5 and +5 and indicating that they are opposite integers.
A zero pair is a set of positive and negative numbers that equal zero when added together. In other words, they cancel each other out! For example, +2 and −2 are a zero pair because these opposite integers add up to zero.
A yellow positive counter and a red negative counter come together to from a “Zero Pair” which equals zero in value when they are added together. In other words, they “cancel” each other out!
Student Success
Think-Pair-Share
Consider where you might find integers in everyday situations.
Create a list of positive and negative integers that could be displayed using counters, tiles or number lines.
Why do you think integer pairs are considered opposites?
Note to teachers: See your teacher guide for collaboration tools, ideas and suggestions.
Task A: Adding integers
- What sum does each set of tiles model? How do you know you are correct?
- 3 round counters and 2 square counters
- 3 round counters and 4 square counters
- 2 square counters and 2 round counters
- Represent each sentence with integers, then find each sum. Use counters or a number line to
show your work.
- The temperature drops 3°C and rises 4°C.
- Mario earned $7 and spent $4.
- A stock rises 13¢, then falls 5¢.
- Jeremy moves his game piece 7 squares backward, then 4 squares forward.
- Demitrie deposits $12, then withdraws $5.
- Compare adding on a number line to adding with shaped counters. Which method do you prefer? When might you need to use a different method?
If you would like, you can complete this activity using TVO Mathify. You can also use your notebook or the following fillable and printable document.
Press the ‘TVO Mathify' button to access this interactive whiteboard and the ‘Activity’ button for your note-taking document. You will need a TVO Mathify login to access this resource.
TVO Mathify (Opens in new window) Activity (Open PDF in a new window)Task B: Subtracting integers
- Use integers. Write a subtraction question that would answer each question.
- Find two integers with a sum of and a difference of
- Create and solve a similar integer question.
Consolidation
Preferred city
The following are average temperatures in the top 3 major cities of Canada at different times of the year:
| City/Season | Winter | Summer | Fall | Spring |
|---|---|---|---|---|
|
Montreal |
−13 °C to −2 °C |
12 °C to 26 °C |
−1 °C to 20 °C |
−6 °C to 19 °C |
|
Toronto |
−10 °C to 0 °C |
11 °C to 27 °C |
0 °C to 21 °C |
−3 °C to 18 °C |
|
Vancouver |
0 °C to 7 °C |
11 °C to 22 °C |
3 °C to 18 °C |
5 °C to 16 °C |
Choose one of the 3 cities to work with. Answer the following questions:
- What is the difference between the highest and lowest temperature for that city in each season?
- Which season would appeal to you the most in this city? Why?
- What is the biggest difference you found? What is the smallest difference you found?
- Why did you choose this city?
Reflection
As you read the following descriptions, select the one that best describes your current understanding of the learning in this activity. Press the corresponding button once you have made your choice.
I feel...
Now, expand on your ideas by recording your thoughts using a voice recorder, speech-to-text, or writing tool.
When you review your notes on this learning activity later, reflect on whether you would select a different description based on your further review of the material in this learning activity.
Press ‘Discover More’ to extend your skills.
Discover MoreTime Zones
By exploring the map of Canada we know there are 6 different time zones. These six time zones cover Canada from east to west and correspond to Newfoundland Time, Atlantic Time, Eastern Time, Central Time, Mountain Time, and Pacific Time. Time zones in some provinces and territories may span two time zones.
For example, if the time in Ottawa, Ontario is 5pm, what time is it in Vancouver, British Columbia? If you notice the time zone map, Ottawa is in the Eastern Time Zone which is -5 and Vancouver is in the Pacific Time Zone which is -8. To go from -5 to -8 on a number line you would move 3 spots in the negative direction. Therefore, British Columbia is 3 hours behind Ottawa: 5pm - 3 hours = 2pm. Therefore, it is 2pm in Vancouver.
As integers we can show it as an addition statement:
Or we can use a subtraction statement to express it as well.
Use the map and integers to solve the following scenarios. Express your work using number lines and integers equations:
- Jana sends an email from Toronto, Ontario at 9pm. When you would expect this message to arrive in Charlottetown, P.E.I?
- If it were 10am in Toronto, Ontario, what time would it be in Saskatoon, Saskatchewan?
- If it was 6pm in Winnipeg, Manitoba what time would it be in Quebec City, Quebec?
- Farah sends an email from Toronto at 10pm. When would you expect this message to
arrive in each of these cities?
- Ottawa, Ontario
- Calgary, Alberta
- Victoria, British Columbia
- St. John’s, Newfoundland and Labrador
- Kimesha lives in Jasper, Alberta and wants to call Stephanie at 7pm in Whitehorse, Yukon. What time should Kimesha make her call?
- What 2 time zones include parts of Ontario? Locate 2 cities in different time zones and create your own integer problem.
- The Winter Olympics was broadcasted live from Whistler, British Columbia in 2010. If
the final event of men’s hockey started at 6pm, at what time do sports fans need to
tune in at each of these cities to also enjoy it live?
- Toronto, Ontario
- Halifax, Nova Scotia
- Montreal, Quebec
- Regina, Saskatchewan
- Yellowknife, Northwest Territories
Global time zones
Time zones go across the globe. The imaginary dividing lines begin at Greenwich, a suburb of London England. This primary dividing line of longitude is called the Prime Meridian. It is the “zero of the number line of time zones.” To the right, or East, of this line, time zones increase in hours (clocks are ahead). To the left, or west, of this line, time zones decrease in hours (clocks are behind). Canada is hours behind London.
A travel agent prepares travel options for their customers. Pick three cities anywhere in the world they could travel to by plane.
Research direct plane travel times and time zones in these three cities. Suppose departure times from the airport where you live are at 7pm. Calculate arrival times to each of these cities using integer addition or subtraction.
Explain and show your work using visuals (number lines, counters). Include temperature
changes between cities so travelers know what to pack.
Connect with a TVO Mathify tutor
Think of TVO Mathify as your own personalized math coach, here to support your learning at home. Press ‘TVO Mathify’ to connect with an Ontario Certified Teacher math tutor of your choice. You will need a TVO Mathify login to access this resource.
TVO Mathify (Opens in new window)