01 · DISCOVER
Adding and Subtracting Rational Numbers: before you begin
Build your understanding of adding and subtracting rational numbers through examples and practice. Explain each step and check whether your answer makes sense. For related lessons, return to the math pathway collection. When your teacher allows it, use the Desmos graphing calculator to check coordinates, equations, or calculations.
Enter your name and school email to save your learning. You’ll explore adding and subtracting rational numbers and then practice 12 questions with feedback.
Success criteria
- I can explain the main math idea in my own words.
- I can use a model, calculation, or example to solve a related problem.
- I can check my answers and explain why a solution makes sense.
Essential question: How can we use adding & subtracting rational numbers to solve problems?
02 · LEARN & EXPLORE
Where this matters
Temperatures rise and fall, account balances change, and elevations may be above or below zero.
03 · LEARN & EXPLORE
Understand the mathematics
Start at -3 on a number line. Subtracting 5 means move five units left to -8. For subtracting a negative, add its opposite: -7 – (-3) = -4.
Trace each operation and verify the result by checking the original problem.
Visualize -3 – 5: begin at -3 and travel 5 units left to -8.
04 · LEARN & EXPLORE
Model the first situation
A temperature of −6°C rises by 9°C. Start at −6 on a number line and move nine units right. You land at 3°C.
Think: Which operation or representation best shows this situation?
05 · LEARN & EXPLORE
Why this concept matters
Temperatures rise and fall, account balances change, and elevations may be above or below zero.
Use diagrams, number lines, tables, or algebraic representations where appropriate to explain why a procedure works.
06 · LEARN & EXPLORE
Understand a second strategy
To calculate −4 − (−7), change subtraction to adding the opposite: −4 + 7 = 3. Subtracting a negative moves right.
Try it: Check the reasoning with your own numbers or a visual model.
07 · LEARN & EXPLORE
Apply your learning
A bank account at −$8 receives a $12 deposit and then has a $5 fee. Write −8 + 12 − 5 = −1. The final balance is −$1.
Strategy reminder: Draw a number line and label the start, movement, and end. Estimate the sign before you calculate.
08 · LEARN & EXPLORE
Connect the idea
Adding a positive moves right on a number line; adding a negative moves left. Subtracting a number is the same as adding its opposite.
Explain the idea in your own words and identify when you would use it.
INDEPENDENT PRACTICE · 1 OF 12
What is 4 + (-9)?
Choose the best answer, then study the feedback.
Start at 4 and move 9 units left.
INDEPENDENT PRACTICE · 2 OF 12
What is -7 – (-3)?
Work independently and check that your answer makes sense.
Subtracting -3 means adding 3.
INDEPENDENT PRACTICE · 3 OF 12
-6 + 4 = ?
Work out your answer before choosing. Compare with the explanation and revise your reasoning.
Review the worked example and apply the inverse operations or number relationships carefully.
INDEPENDENT PRACTICE · 4 OF 12
-8 – 3 = ?
Work out your answer before choosing. Compare with the explanation and revise your reasoning.
Review the worked example and apply the inverse operations or number relationships carefully.
INDEPENDENT PRACTICE · 5 OF 12
-5 – (-2) = ?
Work out your answer before choosing. Compare with the explanation and revise your reasoning.
Review the worked example and apply the inverse operations or number relationships carefully.
INDEPENDENT PRACTICE · 6 OF 12
3.5 + (-1.2) = ?
Work out your answer before choosing. Compare with the explanation and revise your reasoning.
Review the worked example and apply the inverse operations or number relationships carefully.
INDEPENDENT PRACTICE · 7 OF 12
-2.5 – 1.5 = ?
Work out your answer before choosing. Compare with the explanation and revise your reasoning.
Review the worked example and apply the inverse operations or number relationships carefully.
INDEPENDENT PRACTICE · 8 OF 12
1/2 + (-1/4) = ?
Work out your answer before choosing. Compare with the explanation and revise your reasoning.
Review the worked example and apply the inverse operations or number relationships carefully.
INDEPENDENT PRACTICE · 9 OF 12
-3/4 – 1/4 = ?
Work out your answer before choosing. Compare with the explanation and revise your reasoning.
Review the worked example and apply the inverse operations or number relationships carefully.
INDEPENDENT PRACTICE · 10 OF 12
Which expression equals -9?
Work out your answer before choosing. Compare with the explanation and revise your reasoning.
Review the worked example and apply the inverse operations or number relationships carefully.
INDEPENDENT PRACTICE · 11 OF 12
-1.8 + 0.6 = ?
Work out your answer before choosing. Compare with the explanation and revise your reasoning.
Review the worked example and apply the inverse operations or number relationships carefully.
INDEPENDENT PRACTICE · 12 OF 12
Temperature is -2°C and drops 7°C. New temperature?
Work out your answer before choosing. Compare with the explanation and revise your reasoning.
Review the worked example and apply the inverse operations or number relationships carefully.
RESULTS · REFLECT
Your Learning Pathway Results
Reflect on your learning: Which problem best shows what you learned? What strategy helped, and what would you still like to practice? Explain your answer to a partner or write it on paper before submitting.
Check your work and submit your first-attempt score to your teacher.