40-minute lesson
Year 7 Mathematics: Integers
Lesson objective
- 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 criteria:
- 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.
Materials
- 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)
Introduction
4 minIntroduce today's 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.
Ask your child what they already know about integers.
Explanation
8 minIntegers 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
6 minOrdering integers
Write these numbers in order from smallest to largest: −3, 5, −8, 0, 2.
Step 1: Picture them on a number line. The negative numbers are on the left.
Step 2: −8 is further left than −3, so −8 is the smallest.
Step 3: 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?
Step 1: Start at −4 on the number line.
Step 2: A rise means moving to the right. 4 steps takes you to 0.
Step 3: 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?
Step 1: From −2 to 0 is 2 degrees.
Step 2: From 0 to 7 is 7 degrees.
Step 3: Add them: 2 + 7 = 9.
Answer: The difference is 9 degrees.
Guided practice (do together)
8 min1. Which of these numbers is the smallest?
(a) −2 (b) −7 (c) 0 (d) 3
2. Which statement is true?
(a) −5 > −1 (b) −3 > 2 (c) −1 > −5 (d) 0 < −4
3. The temperature is −3 °C and then falls by 4 degrees. What is the new temperature?
(a) 1 °C (b) −1 °C (c) −7 °C (d) 7 °C
4. 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?
(a) −3 (b) 3 (c) −7 (d) 7
Independent practice
10 min5. What number is 6 less than 2?
6. What is the difference in degrees between 8 °C and −3 °C?
7. Which integer is exactly halfway between −6 and 2 on a number line?
8. 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?
Questions to check understanding
- Can you place positive and negative numbers on a number line?
- Can you put a set of integers in order from smallest to largest?
- Can you work out a new temperature after it rises or falls?
- Can you find the difference between a positive and a negative number?
- What was the trickiest part today?
Answer guide
1. −7 — −7 is the furthest left on a number line, so it is the smallest.
2. −1 > −5 — −1 is to the right of −5 on the number line, so −1 is greater than −5.
3. −7 °C — Start at −3 and move 4 steps left: −4, −5, −6, −7. The new temperature is −7 °C.
4. −3 — Start at 2 and move 5 steps down: 1, 0, −1, −2, −3.
5. −4 — Start at 2 and move 6 steps left: 1, 0, −1, −2, −3, −4.
6. 11 — From −3 to 0 is 3 degrees, and from 0 to 8 is 8 degrees. 3 + 8 = 11.
7. −2 — The distance from −6 to 2 is 8. Half of 8 is 4, and 4 steps right from −6 is −2.
8. $25 — Start at −15 and move 40 to the right. 15 steps reach 0, and the remaining 25 steps reach 25.
Review
4 minRecap the success criteria together. Watch for these common misconceptions:
- 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.
Extension activities
- 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.
Suggested follow-up
- Revisit integers tomorrow with two or three quick questions from memory.
- Try the online practice check for this topic and look at any questions that need another go.
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.