01 · DISCOVER
Before you begin
Enter your name and school email to save your learning. You’ll explore Proportional Relationships in Tables and then practice 12 questions with feedback.
- 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 rational number problem solving to solve problems?
02 · LEARN & EXPLORE
Where this matters
Budgeting, temperature, elevation, and shared expenses combine rational operations.
03 · LEARN & EXPLORE
Understand the mathematics
A diver starts 2 meters below the surface, descends 5 meters, then rises 3 meters. Model the changes: -2 – 5 + 3 = -4. The final depth is 4 meters below the surface.
Trace each operation and verify the result by checking the original problem.
Start at -2 meters, descend 5, then rise 3. Finish at -4.
04 · LEARN & EXPLORE
Model the first situation
A hiker starts 2 meters below sea level, climbs 7 meters, then descends 4 meters. Model −2 + 7 − 4 = 1 meter above sea level.
Think: Which operation or representation best shows this situation?
05 · LEARN & EXPLORE
Why this concept matters
Budgeting, temperature, elevation, and shared expenses combine rational operations.
Use diagrams, number lines, tables, or algebraic representations where appropriate to explain why a procedure works.
06 · LEARN & EXPLORE
Understand a second strategy
A purchase of $12.50 from a $10 balance gives 10 − 12.50 = −2.50. Negative represents a debt.
Try it: Check the reasoning with your own numbers or a visual model.
07 · LEARN & EXPLORE
Apply your learning
Calculate the combined change (−2.5) × 3 + 4 = −3.5. Follow multiplication before addition.
Strategy reminder: Write each quantity with a sign and unit, then combine operations in order.
08 · LEARN & EXPLORE
Connect the idea
Choose operations from the situation, compute with signed rational numbers, and estimate first so you can judge whether the final answer is reasonable.
Explain the idea in your own words and identify when you would use it.
INDEPENDENT PRACTICE · 1 OF 12
A bank balance is $12.50 and a $20 charge posts. What is the new balance?
Choose the best answer, then study the feedback.
A charge decreases the balance.
INDEPENDENT PRACTICE · 2 OF 12
A temperature changes from -4.5°C to 3°C. How much did it increase?
Work independently and check that your answer makes sense.
Compute final minus initial.
INDEPENDENT PRACTICE · 3 OF 12
Balance $15, purchase $23. New balance?
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
Temperature -4°C rises 9°C. Result?
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
A diver at -6 m rises 2 m. Position?
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
Three -$2 charges total?
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
Share -$20 equally among 4 accounts. Change each?
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
(-3.5)+2.25 = ?
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
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 · 10 OF 12
(-4)(-3)+(-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 · 11 OF 12
-12 ÷ 3 + 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 · 12 OF 12
An elevator at floor -2 goes up 7 then down 3. Floor?
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
Check your work and submit your first-attempt score to your teacher.