Adding & Subtracting Integers
Positive, Negative or Zero?
Sort each integer into the correct column.
Match to the Number Line
Draw a line to match each description to its integer.
Adding Integers
Circle the correct answer.
3 + (−5)
-4 + 7
-6 + (−3)
−10 + 10
-2 + (−8)
Subtracting Integers
Circle the correct answer.
5 − 8
-3 − 4
6 − (−2)
-5 − (−3)
Integer Sequences
Fill in the missing integers.
Match Temperature Changes
Match each situation to the correct result.
Integer Word Problems
Solve each problem and show your working.
The temperature in Canberra was −6°C at night. By midday it had risen 14°C. What was the midday temperature?
A submarine is at −80 m. It rises 35 m. What is its new depth?
Sam owes $25 and earns $40. How much does Sam have now?
Multiplying Integers
Same signs → positive. Different signs → negative. Circle the correct answer.
3 × (−4)
(−5) × (−2)
(−6) × 3
(−4) × (−4)
Dividing Integers
Apply the same sign rules. Circle the correct answer.
−20 ÷ 4
(−18) ÷ (−3)
15 ÷ (−5)
(−24) ÷ (−8)
BODMAS with Negative Numbers
Use order of operations. Circle the correct answer.
3 + 2 × (−4)
(−3)² − 10
−2 × (5 − 8)
4 − (−3) × 2
Distance Between Integers
The distance between two integers equals |a − b|. Match each pair to their distance apart.
Real-World Integer Problems
Write a calculation and solve each problem.
A diver is at −12 m. She descends a further 8 m. She then ascends 5 m. What is her final depth?
A bank account starts with $50. Five equal withdrawals of $18 are made. What is the balance? Is this an overdraft?
Integer Puzzles
Find the missing integer.
? + (−5) = −2. Find ?
? × (−3) = 12. Find ?
(−4) − ? = 1. Find ?
Integer Expressions — Positive or Negative Result?
Sort each expression by the sign of its result.
Integer Sequences — Multiplying
Fill in the missing terms.
Altitude Word Problems
Write integer calculations and solve.
A plane is at altitude 8000 m. It descends at 200 m per minute. Write an expression for its altitude after t minutes. What is its altitude after 30 minutes?
A lift starts at level −3 (basement). It goes up 8 levels, then down 5 levels. What level does it end at?
Comparing Negative Values
Circle the correct comparison.
−5 ○ −10
|−8| ○ |5|
−3² ○ (−3)²
Investigate Integer Patterns
Complete the pattern and explain the rule.
Calculate: (−1)¹, (−1)², (−1)³, (−1)⁴, (−1)⁵. Describe the pattern.
Calculate: (−2)¹, (−2)², (−2)³, (−2)⁴. What is the pattern of signs?
Integer Grid — Sums
In the 3×3 grid, fill in integers so that every row, column, and diagonal sums to the given value.
Fill a 3×3 grid using integers from -4 to 4 (each used once) so every row, column and diagonal sums to 0. Write your grid here.
How many different solutions can you find?
Absolute Value — Order
Sort these integers in order from smallest absolute value to largest.
Integer Algebra — Substitution
Substitute the given integer value and evaluate.
If a = −3, find: (a) a² (b) 2a + 5 (c) a² − a
If x = −4 and y = 2, find: (a) xy (b) x − y (c) x² + y²
Integer Coordinates
Plot and describe points on a coordinate plane with negative values.
Plot these points on a coordinate plane: A(−3, 2), B(4, −1), C(−2, −4), D(0, 3). Label each quadrant.
In which quadrant does the point (−5, −2) lie? Explain.
What is the distance from (−3, 0) to (5, 0)?
Quadrants
Match each point to its quadrant.
Integer Properties
Circle the correct value.
(−8) + 8 =
Any integer × 0 =
−(−(−5)) =
|−12| − |8| =
Interpreting Negative Numbers in Graphs
A graph shows a diver's depth over time.
At t = 0, the diver is at −10 m. At t = 2, she is at −25 m. At t = 5, she is at −10 m. Describe what happened. Draw a sketch of the graph.
What is the change in depth from t = 0 to t = 2?
What is the change in depth from t = 2 to t = 5?
Integer Magic Square
Create a magic square using nine consecutive integers.
Using integers −4, −3, −2, −1, 0, 1, 2, 3, 4, arrange them in a 3×3 grid so all rows, columns and diagonals sum to 0. Show your solution.
If you added 5 to every integer in the grid, what would the new magic number be?
Integer Expressions — Sort by Value
Sort these expressions from smallest to largest value.
Solving Integer Puzzles with Algebra
Use algebra and integer operations.
The sum of three consecutive integers is −12. Find the integers.
When a number is multiplied by −3 and then 7 is added, the result is −5. Find the number.
Integers in Science — Subzero Temperatures
Use integer arithmetic to solve these science-based problems.
On Mars the temperature ranges from −125°C to 20°C. What is the range (difference)?
If it is −40°C outside and the windchill makes it feel 15°C colder, what is the apparent temperature?
The thermosphere reaches 2000°C. The stratosphere reaches −56°C. What is the difference?
Integer Sequences — Design Your Own
Create three different integer sequences and describe the rule for each.
Sequence 1 (arithmetic): Write the first 5 terms and state the rule.
Sequence 2 (geometric): Write the first 5 terms and state the rule.
Sequence 3 (your own pattern): Write the first 5 terms and state the rule.
Integers and Binary Numbers
Computers represent negative numbers using a concept called two's complement.
In 4-bit binary, 0000 = 0, 0001 = 1, 0010 = 2, …, 0111 = 7. What does it mean if we use 1000 = −8, 1001 = −7, 1110 = −2, 1111 = −1? Write the values for 1010 and 1100.
Why would representing negative numbers be useful for a computer?
Create Your Own Integer Problem Set
Design a problem set for a younger student learning about integers.
Write two addition of integers problems with real-world context.
Write two multiplication of integers problems with answers.
Write one challenge word problem that requires multiple integer operations.
Reflection: What I Know About Integers
Summarise your learning in your own words.
Explain in your own words why subtracting a negative number gives the same result as adding a positive number. Give an example.
Give three real-world contexts where negative integers naturally occur.
What is the most interesting thing you learned about integers? Why?
Integers at Home
Practise integers in real-world situations.
- 1Track the daily temperature minimum and maximum for one week. Calculate daily ranges using subtraction.
- 2Create a budget using integers: income as positive, expenses as negative. What is the net balance?
- 3Play the game 24: use operations with four integers (some negative) to reach 24.
- 4Watch the weather forecast and record temperatures. Identify which city had the coldest (most negative) temperature.