More on negative numbers
🎯 In this topic you will
- Read and write numbers that are less than zero, using correct mathematical language (for example, −6 is read as negative six).
- Explain how negative numbers are used to describe real-world situations, such as very cold temperatures or positions below sea level.
🧠 Key Words
- temperature
- zero
Show Definitions
- temperature: A measure of how hot or cold something is, usually measured in degrees such as degrees Celsius (°C).
- zero: The value that represents no amount of a quantity; on a number line it separates positive numbers from negative numbers.
Using Negative Numbers in Real Life
I n this section, you will use negative numbers in real-life contexts such as temperature or being above or below sea level.
Icebergs and Sea Level
A n iceberg is ice that has broken off a glacier and is now floating. There is much more ice below sea level than there is above sea level.
❓ EXERCISES
1. Look at the number line. Write where you would land on the number line after these moves.
a. start $-5$, count on $1$
b. start $-2$, count back $4$
c. start $-3$, count on $3$
d. start $6$, count back $9$
👀 Show answer
a. $-4$
b. $-6$
c. $0$
d. $-3$
2. Here is a number line.
a. Which numbers do the arrows A, B, C and D point to?
b. Which letter shows the position of a number greater than $-4$ and less than $0$?
👀 Show answer
a. $A=-5$, $B=-2$, $C=3$, $D=5$
b. $B$
3. Look at this thermometer. What numbers are the arrows pointing to at a, b and c?
👀 Show answer
$a=-8^\circ\text{C}$, $b=-2^\circ\text{C}$, $c=12^\circ\text{C}$
4. Which temperature is the coldest? $-6^\circ\text{C}$, $0^\circ\text{C}$, $1^\circ\text{C}$, $-2^\circ\text{C}$
👀 Show answer
$-6^\circ\text{C}$
5. The temperature in a town one day was $5^\circ\text{C}$. The temperature dropped by $9^\circ\text{C}$ overnight. What was the lowest night-time temperature?
👀 Show answer
$-4^\circ\text{C}$
6. The letters on the number line are in the place of numbers. Copy and complete the table to solve the puzzle and find out where emperor penguins live.
👀 Show answer
ANTARCTICA
7. What mistake has Marcus made? How can you help him correct this mistake?
👀 Show answer
He compared the digits without considering their position on the number line. $-5^\circ\text{C}$ is colder than $-4^\circ\text{C}$ because it is further to the left.
8.
a. What temperature is $6$ degrees warmer than $-4^\circ\text{C}$?
b. What temperature is $5$ degrees less than $1^\circ\text{C}$?
c. What temperature is $3$ degrees warmer than $-2^\circ\text{C}$?
d. What temperature is $3$ degrees cooler than $0^\circ\text{C}$?
e. What temperature is $5$ degrees higher than $-1^\circ\text{C}$?
👀 Show answer
a. $2^\circ\text{C}$
b. $-4^\circ\text{C}$
c. $1^\circ\text{C}$
d. $-3^\circ\text{C}$
e. $4^\circ\text{C}$
🧠 Think like a Mathematician
The coldest place where people live is Oymyakon in Siberia. In 1933 the temperature fell to −67 °C. It was so cold that people’s eyelashes froze.
Task: Use real temperature data to compare places and organise your findings from coldest to warmest.
Equipment: Internet access (or books/magazines), paper or a digital document for your poster, calculator (optional), graph paper or a spreadsheet (optional).
Method:
- Collect data: Choose at least 6 places (include Oymyakon if you can). For each place, find a typical winter temperature and a typical summer temperature (record the units in °C).
- Record clearly: Make a small table with columns: Place, Winter (°C), Summer (°C), and Source.
- Order from coldest: Decide what “coldest” means for your list (e.g., lowest winter temperature). Sort your places starting with the coldest.
- Show your findings: Create a poster (paper or digital). Include your ordered list and at least one visual (e.g., bar chart of winter temperatures, or a simple map with labels).
- Extend: Find extra temperature examples (magazines or the internet) and add them to your poster. You may include maps, pictures, and graphs.
Follow-up Questions:
👀 show answer
a) Example outcome (your data may differ):
| Place | Winter (°C) | Summer (°C) | Note |
|---|---|---|---|
| Oymyakon, Russia | −67 | 15 | Record low mentioned in the text |
| Place B | −45 | 20 | Replace with real data |
| Place C | −25 | 30 | Replace with real data |
| Place D | −5 | 25 | Replace with real data |
Ordering rule: Sort by the lowest winter temperature (most negative first). If two places tie, use the next coldest value or note that they are equal.
b) What a strong poster includes:
- A clear title (e.g., “Comparing Winter and Summer Temperatures”).
- Your ordered list from coldest to warmest (state the rule you used).
- A neat table with temperatures in °C and a source for each place.
- At least one visual: bar chart, line chart (winter vs summer), or a labeled map.
c) Extra examples you can add:
- A weather-map screenshot showing a cold snap or heatwave (with date and location).
- A graph of temperatures across a week for one city.
- A comparison of how far $-67$°C is below $0$°C (e.g., “$67$ degrees below freezing”).
Check: Always confirm whether a value is an average or a record temperature, and keep your comparison consistent.