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 multi-step real-world problems to solve problems?
02 · LEARN & EXPLORE
Where this matters
Multi-step problems require choosing information, representing relationships, and checking units.
03 · LEARN & EXPLORE
Understand the mathematics
A museum charges $7 per student plus a one-time $25 booking fee. For 12 students, total cost = 7(12) + 25 = $109. The fee means the relationship is not proportional.
Trace each operation and verify the result by checking the original problem.
For 12 museum tickets at $7 each plus a $25 booking fee, total is $109.
04 · LEARN & EXPLORE
Model the first situation
Eight museum tickets cost $7 each, plus a $15 booking fee: 8 × 7 + 15 = $71.
Think: Which operation or representation best shows this situation?
05 · LEARN & EXPLORE
Why this concept matters
Multi-step problems require choosing information, representing relationships, and checking units.
Use diagrams, number lines, tables, or algebraic representations where appropriate to explain why a procedure works.
06 · LEARN & EXPLORE
Understand a second strategy
For $100 available, calculate how much remains after spending $71: 100 − 71 = $29.
Try it: Check the reasoning with your own numbers or a visual model.
07 · LEARN & EXPLORE
Apply your learning
For 12 tickets, update only the variable part: 12 × 7 + 15 = $99. The flat fee stays $15.
Strategy reminder: Underline the amounts, distinguish one-time costs from per-item rates, then check units.
08 · LEARN & EXPLORE
Connect the idea
Translate the situation into a sequence of operations, keep track of units, and use estimation to check your result.
Explain the idea in your own words and identify when you would use it.
INDEPENDENT PRACTICE · 1 OF 12
A $60 item is discounted 10%. What is the sale price?
Choose the best answer, then study the feedback.
Find 10% of 60, then subtract it.
INDEPENDENT PRACTICE · 2 OF 12
A 12.5-mile trip is driven twice. How many miles total?
Work independently and check that your answer makes sense.
Two trips means multiply by 2.
INDEPENDENT PRACTICE · 3 OF 12
4 notebooks cost $3 each plus $2 tax. 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 · 4 OF 12
5 tickets at $8 minus a $6 coupon. Pay?
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 60-mile trip has 15 miles left. Fraction completed?
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
2.5 kg costs $4 per kg. 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
Start with $50; spend $12 and $19. Remain?
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 hours at $15/h with $5 supplies fee. 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 · 9 OF 12
$80 item discounted 25%. Sale price?
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
A 12-mile path: hike 1/3 then 1/4 of total. Miles left?
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
5 students share a $35 bill plus $10 tip equally. 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 · 12 OF 12
Buy 6 pens at $1.50 and 2 folders at $3. 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.
RESULTS · REFLECT
Your Learning Pathway Results
Check your work and submit your first-attempt score to your teacher.