Find an ingredient amount for a new serving size.
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 solving missing values in proportions to solve problems?
02 · LEARN & EXPLORE
A real-world missing-value problem
Three shirts cost $27. How much do five shirts cost at the same price?
Equivalent ratios help solve a missing value by finding a unit rate.
Predict distance, time, or fuel.
Scale dimensions accurately.
03 · LEARN & EXPLORE
A powerful idea built over time.
Proportion-solving methods grew from practical problems in trade, surveying, astronomy, and construction. Modern algebra explains why scaling and cross products work.
04 · LEARN & EXPLORE
Build the language of proportional reasoning.
Use these terms as you explain your thinking.
An equation stating that two ratios are equal.
A value to be determined.
The product of a numerator and the opposite denominator.
A multiplier connecting equivalent ratios.
An operation that reverses another.
Whether an answer makes sense in context.
05 · LEARN & EXPLORE
Master three connected ideas.
You will learn each idea separately, practice with support, and then combine them independently.
Explore the math visually
1input units
2input units
3input units
4input units
Compare one unit with multiple units. Identify the multiplier and explain what remains constant.
Use when one ratio is an obvious multiple.
Divide first, then multiply.
Use equivalent fraction structure.
06 · LEARN & EXPLORE
Scale
Use when one ratio is an obvious multiple.
1Notice what quantities, values, or representations are given.
2Use Scale 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.
Use when one ratio is an obvious multiple.
× factor07 · LEARN & EXPLORE
Unit rate
Divide first, then multiply.
1Notice what quantities, values, or representations are given.
2Use Unit rate 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.
Divide first, then multiply.
per 108 · LEARN & EXPLORE
Cross products
Use equivalent fraction structure.
1Notice what quantities, values, or representations are given.
2Use Cross products 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.
Use equivalent fraction structure.
ad=bc09 · LEARN & EXPLORE
Solve with a unit rate
- Write 3 shirts : $27.
- Divide $27 by 3 to find $9 per shirt.
- Multiply 5 by $9 to get $45.
- Check: 27/3 = 45/5 = 9.
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.
Interactive practice tip: Use a quick sketch, table, or graph to test each answer. After selecting an answer, read the explanation and revisit your model if necessary.
12 · LEARN & EXPLORE
You connected all three ideas.
Before finishing, make sure you can explain each idea in your own words and show how it supports proportional reasoning.
01.Scale
Use when one ratio is an obvious multiple.
02.Unit rate
Divide first, then multiply.
03.Cross products
Use equivalent fraction structure.
INDEPENDENT PRACTICE · 1 OF 12
If 3 pencils cost $6, what do 8 cost?
Find the value and explain your reasoning.
Set up a rate, table, equation, or diagram before choosing.
INDEPENDENT PRACTICE · 2 OF 12
Solve 4/7=x/21.
Find the value and explain your reasoning.
Set up a rate, table, equation, or diagram before choosing.
INDEPENDENT PRACTICE · 3 OF 12
If 5 tickets cost $45, what do 2 cost?
Find the value and explain your reasoning.
Set up a rate, table, equation, or diagram before choosing.
INDEPENDENT PRACTICE · 4 OF 12
Solve 6/10=9/x.
Find the value and explain your reasoning.
Set up a rate, table, equation, or diagram before choosing.
INDEPENDENT PRACTICE · 5 OF 12
A car travels 120 miles in 3 hours. Distance in 5 hours?
Find the value and explain your reasoning.
Set up a rate, table, equation, or diagram before choosing.
INDEPENDENT PRACTICE · 6 OF 12
Which value makes x/8=3/4?
Find the value and explain your reasoning.
Set up a rate, table, equation, or diagram before choosing.
INDEPENDENT PRACTICE · 7 OF 12
Solve 2/3 = n/18.
Work independently. Select the best answer, complete any needed calculation, and check that the result fits the situation.
Multiply both 2 and 3 by 6.
INDEPENDENT PRACTICE · 8 OF 12
Five meters of fabric cost $42.50. What do 8 meters cost?
Work independently. Select the best answer, complete any needed calculation, and check that the result fits the situation.
Find cost per meter first.
INDEPENDENT PRACTICE · 9 OF 12
Solve 7/12 = 21/n.
Work independently. Select the best answer, complete any needed calculation, and check that the result fits the situation.
7 was multiplied by 3.
INDEPENDENT PRACTICE · 10 OF 12
A car uses 6 gallons for 162 miles. How far on 10 gallons?
Work independently. Select the best answer, complete any needed calculation, and check that the result fits the situation.
Find miles per gallon.
INDEPENDENT PRACTICE · 11 OF 12
Which equation correctly models 9 pencils for $5.40 and x pencils for $12?
Work independently. Select the best answer, complete any needed calculation, and check that the result fits the situation.
Keep pencils over dollars in both ratios.
INDEPENDENT PRACTICE · 12 OF 12
In 3/5 = n/20, what scale factor connects 5 to 20?
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.