Primary 6 · Mathematics · Number
Integers
Locate, order and compare positive and negative whole numbers on a number line, and use them to describe changes in contexts such as temperature.
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These lessons were written around Australian Curriculum strands and matched to Singapore levels by age (Primary 1 is the first year of primary school). They are not aligned to MOE syllabuses or the PSLE, so check them against the syllabus your child is working towards.
This lesson uses some Australian examples (places, animals or contexts). Swap in local examples from Singapore as you teach.
Learning goals
Learners will
- Understand what negative numbers are and where they appear in everyday life.
- Locate, compare and order integers using a number line.
- Use a number line to work out changes in temperature and similar situations.
Success looks like
- I can place positive and negative numbers on a number line.
- I can put a set of integers in order from smallest to largest.
- I can work out a new temperature after it rises or falls.
- I can find the difference between a positive and a negative number.
The big idea
Integers are whole numbers that can be positive, negative or zero. Negative numbers are numbers less than zero. We write them with a minus sign in front, like −5, which we read as “negative five”.
Negative numbers appear in real life. On a frosty winter morning in Canberra the temperature can drop below 0 °C. Places below sea level, basement floors in a car park and amounts of money owed can all be described with negative numbers.
On a number line, zero sits in the middle. Positive numbers go to the right and negative numbers go to the left. The further right a number is, the greater it is. So −2 is greater than −7, because −2 is further right. A useful way to think about it: −2 °C is warmer than −7 °C.
We use the symbols < (less than) and > (greater than) to compare. For example, −6 < −1 and 3 > −10.
To work out a change, start at the first number and move along the number line. A rise means moving right and a fall means moving left. If it is −4 °C and the temperature rises 9 degrees, start at −4 and count 9 steps to the right to reach 5 °C.
To find the difference between a positive and a negative number, count the steps from one to zero and then from zero to the other number, and add them. From −2 to 7 is 2 steps to zero, then 7 more steps, so the difference is 9.
Worked examples
Ordering integers
Write these numbers in order from smallest to largest: −3, 5, −8, 0, 2.
- Picture them on a number line. The negative numbers are on the left.
- −8 is further left than −3, so −8 is the smallest.
- Then comes −3, then 0, then the positive numbers 2 and 5.
Answer: −8, −3, 0, 2, 5
A temperature rise
At 6 am the temperature at Thredbo is −4 °C. By midday it has risen by 9 degrees. What is the temperature at midday?
- Start at −4 on the number line.
- A rise means moving to the right. 4 steps takes you to 0.
- 9 − 4 = 5 steps are left, which takes you to 5.
Answer: The midday temperature is 5 °C.
Finding a difference
The temperature in Hobart is 7 °C and in Perisher it is −2 °C. What is the difference between the two temperatures?
- From −2 to 0 is 2 degrees.
- From 0 to 7 is 7 degrees.
- Add them: 2 + 7 = 9.
Answer: The difference is 9 degrees.
Practice check
Have a go, then check your answers. Each answer comes with an explanation.
Answer guide for parents
Which of these numbers is the smallest?
−7 — −7 is the furthest left on a number line, so it is the smallest.
Which statement is true?
−1 > −5 — −1 is to the right of −5 on the number line, so −1 is greater than −5.
The temperature is −3 °C and then falls by 4 degrees. What is the new temperature?
−7 °C — Start at −3 and move 4 steps left: −4, −5, −6, −7. The new temperature is −7 °C.
In a building, the ground floor is 0 and basement floors are negative. A lift starts on floor 2 and goes down 5 floors. Which floor does it stop on?
−3 — Start at 2 and move 5 steps down: 1, 0, −1, −2, −3.
What number is 6 less than 2?
−4 — Start at 2 and move 6 steps left: 1, 0, −1, −2, −3, −4.
What is the difference in degrees between 8 °C and −3 °C?
11 — From −3 to 0 is 3 degrees, and from 0 to 8 is 8 degrees. 3 + 8 = 11.
Which integer is exactly halfway between −6 and 2 on a number line?
−2 — The distance from −6 to 2 is 8. Half of 8 is 4, and 4 steps right from −6 is −2.
Ella's savings tracker shows −$15 because she owes her brother $15. She then earns $40 and adds it to her tracker. How many dollars will the tracker show now?
$25 — Start at −15 and move 40 to the right. 15 steps reach 0, and the remaining 25 steps reach 25.
Watch out for
- Thinking −8 is greater than −3 because 8 is greater than 3. Use a thermometer or number line: −8 °C is colder, so it is less.
- Forgetting to count zero as a step when crossing it, or counting it twice. Practise by stepping along a floor number line out loud.
- Ignoring the minus sign when ordering, for example placing −5 between 4 and 6. Always check which side of zero a number sits.
Tips for parents
- Make a large number line from −10 to 10 on the floor with masking tape and let the learner physically walk the rises and falls.
- Look at the weather forecast for alpine towns or Antarctica together and compare minimum and maximum temperatures.
- Encourage the learner to say “negative” rather than “minus” when reading a number such as −5, to separate the number from the operation.
Go further
- Record the overnight minimum and daytime maximum temperatures for a cold location for a week, then find the daily differences.
- Research the lowest and highest places in Australia relative to sea level and show them on a vertical number line.
- Create a board game on a number line from −20 to 20 where cards tell players to move up or down by different amounts.
About 40 minutes
You'll need
- A long strip of paper or masking tape on the floor to make a number line
- Textas or a pencil
- A thermometer (optional)
- Weather pages or a weather app showing minimum temperatures (optional)
Key words
- Integer
- A whole number that can be positive, negative or zero, such as −3, 0 or 5.
- Negative number
- A number less than zero, written with a minus sign, such as −4.
- Positive number
- A number greater than zero.
- Number line
- A line with evenly spaced numbers, with negative numbers to the left of zero and positive numbers to the right.
- Difference
- How far apart two numbers are on the number line.
Still tricky?
For parents
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