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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.
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 real-world rates & comparisons to solve problems?
02 · LEARN & EXPLORE
Real-world challenge
Store A sells 6 oranges for $3. Store B sells 8 oranges for $3.60. Which is cheaper per orange?
First make a prediction, then learn a mathematical strategy for checking it.
Compare speed and fuel efficiency.
Compare pay or production rates.
03 · LEARN & EXPLORE
Build the core concept
Unit rates let us compare options even when quantities differ, using a shared measure of one item.
Think about which quantity is input, which is output, and what their units mean.
04 · LEARN & EXPLORE
Build the language of proportional reasoning.
Use these terms as you explain your thinking.
Cost for one unit of an item.
Distance traveled per unit of time.
Useful output compared with input.
An examination of similarities or differences.
The level of detail in a measurement.
The option that best meets stated criteria.
05 · LEARN & EXPLORE
Explore the structure
Store A sells 6 oranges for $3. Store B sells 8 oranges for $3.60. Which is cheaper per orange?
Represent the known quantities in a table, equation, number line, or graph. Identify what remains constant.
Notice how the bars scale. Determine whether the real problem keeps a constant ratio, and explain your reasoning.
Find a rate per one common unit.
Convert quantities to the same units.
Choose based on the goal, not only the total.
06 · LEARN & EXPLORE
Normalize
Find a rate per one common unit.
1Notice what quantities, values, or representations are given.
2Use Normalize to describe the multiplicative relationship—not only what changed.
3Check that the reasoning works for every value and that the units make sense.
Start with this foundation.
Find a rate per one common unit.
÷07 · LEARN & EXPLORE
Match
Convert quantities to the same units.
1Notice what quantities, values, or representations are given.
2Use Match to describe the multiplicative relationship—not only what changed.
3Check that the reasoning works for every value and that the units make sense.
Build on the first idea.
Convert quantities to the same units.
units08 · LEARN & EXPLORE
Interpret
Choose based on the goal, not only the total.
1Notice what quantities, values, or representations are given.
2Use Interpret to describe the multiplicative relationship—not only what changed.
3Check that the reasoning works for every value and that the units make sense.
Connect everything with the final idea.
Choose based on the goal, not only the total.
decide09 · LEARN & EXPLORE
Worked solution with reasoning
- Store A: $3 ÷ 6 = $0.50 per orange.
- Store B: $3.60 ÷ 8 = $0.45 per orange.
- Compare $0.45 and $0.50.
- Store B has the lower unit price by five cents per orange.
10 · LEARN & EXPLORE
Choose the steps; use a hint if needed.
The next three problems remove some of the support. Identify what is known, select the right strategy, calculate carefully, and check the units or representation.
11 · LEARN & EXPLORE
Now complete the work independently.
Complete six questions without following a worked model. Hints remain available when you truly need them, and feedback will explain every answer.
12 · LEARN & EXPLORE
Explain and apply
Explain the mathematical strategy used in this lesson and describe how it would help in a different everyday situation. Give a reasonableness check.
INDEPENDENT PRACTICE · 1 OF 12
Six oranges cost $3. Unit price?
Find the value and explain your reasoning.
Set up a rate, table, equation, or diagram before choosing.
INDEPENDENT PRACTICE · 2 OF 12
A 12 oz snack costs $3 and a 20 oz costs $4. Which has lower unit price?
Find the value and explain your reasoning.
Set up a rate, table, equation, or diagram before choosing.
INDEPENDENT PRACTICE · 3 OF 12
Drive 180 miles in 3 h. Speed?
Find the value and explain your reasoning.
Set up a rate, table, equation, or diagram before choosing.
INDEPENDENT PRACTICE · 4 OF 12
Which is faster, 30 mi in 0.5 h or 100 mi in 2 h?
Find the value and explain your reasoning.
Set up a rate, table, equation, or diagram before choosing.
INDEPENDENT PRACTICE · 5 OF 12
Rice costs $8 for 4 pounds. Price per pound?
Find the value and explain your reasoning.
Set up a rate, table, equation, or diagram before choosing.
INDEPENDENT PRACTICE · 6 OF 12
A worker earns $72 for 6 h. Pay for 9 h?
Find the value and explain your reasoning.
Set up a rate, table, equation, or diagram before choosing.
INDEPENDENT PRACTICE · 7 OF 12
Which is the lower unit price: 12 oz for $3.60 or 18 oz for $5.22?
Work independently. Select the best answer, complete any needed calculation, and check that the result fits the situation.
Divide each price by ounces.
INDEPENDENT PRACTICE · 8 OF 12
Runner A travels 5 miles in 40 minutes. Runner B travels 6 miles in 45 minutes. Who is faster?
Work independently. Select the best answer, complete any needed calculation, and check that the result fits the situation.
Find miles per minute for each.
INDEPENDENT PRACTICE · 9 OF 12
Job A pays $72 for 6 hours. Job B pays $91 for 7 hours. Which hourly rate is greater?
Work independently. Select the best answer, complete any needed calculation, and check that the result fits the situation.
Divide pay by hours.
INDEPENDENT PRACTICE · 10 OF 12
Before comparing 3 feet per second with 48 inches per second, what should you do?
Work independently. Select the best answer, complete any needed calculation, and check that the result fits the situation.
Feet and inches are different units.
INDEPENDENT PRACTICE · 11 OF 12
A vehicle travels 315 miles on 9 gallons. Its efficiency is—
Work independently. Select the best answer, complete any needed calculation, and check that the result fits the situation.
Divide miles by gallons.
INDEPENDENT PRACTICE · 12 OF 12
Which measure makes differently sized packages easiest to compare?
Work independently. Select the best answer, complete any needed calculation, and check that the result fits the situation.
Return to the vocabulary and three main ideas if needed.
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.