Calculate sale prices and savings.
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 percent as a proportional relationship to solve problems?
02 · LEARN & EXPLORE
Why learn this?
A jacket costs $80 and is marked 25% off.
Use the lesson to solve practical comparisons and make predictions.
Estimate and determine added costs.
Interpret survey results and change.
03 · LEARN & EXPLORE
The mathematical idea
Percent means per hundred. Convert a percent to a decimal before multiplying by a whole.
04 · LEARN & EXPLORE
Build the language of proportional reasoning.
Use these terms as you explain your thinking.
A ratio per 100.
The complete amount, represented by 100%.
A portion of the whole.
A base-ten representation of a number.
An amount subtracted from an original price.
An amount added to a cost.
05 · LEARN & EXPLORE
Explore matching values
Study the quantities and explain what stays constant.
| Input | Output |
|---|---|
| 100 | 80 |
| 25 | 20 |
| 75 | 60 |
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.
Write the percent as a decimal.
Decimal rate × whole = part.
Compare the result with familiar benchmarks.
06 · LEARN & EXPLORE
Convert
Write the percent as a decimal.
1Notice what quantities, values, or representations are given.
2Use Convert 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.
Write the percent as a decimal.
%07 · LEARN & EXPLORE
Multiply
Decimal rate × whole = part.
1Notice what quantities, values, or representations are given.
2Use Multiply 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.
Decimal rate × whole = part.
×08 · LEARN & EXPLORE
Estimate
Compare the result with familiar benchmarks.
1Notice what quantities, values, or representations are given.
2Use Estimate 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.
Compare the result with familiar benchmarks.
check09 · LEARN & EXPLORE
Step-by-step worked example
A jacket costs $80 and is marked 25% off.
- 25% = 25/100 = 0.25.
- Find the discount: 0.25 × $80 = $20.
- Subtract: $80 − $20 = $60.
- Check: one quarter of $80 is $20.
| Input | Output |
|---|---|
| 100 | 80 |
| 25 | 20 |
| 75 | 60 |
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
Reflect and submit
Explain the strategy in your own words. How could this mathematical idea help you outside school? Check your units and answer.
INDEPENDENT PRACTICE · 1 OF 12
What is 20% of 80?
Find the value and explain your reasoning.
Set up a rate, table, equation, or diagram before choosing.
INDEPENDENT PRACTICE · 2 OF 12
$50 shirt discounted 10%. New price?
Find the value and explain your reasoning.
Set up a rate, table, equation, or diagram before choosing.
INDEPENDENT PRACTICE · 3 OF 12
30 is what percent of 150?
Find the value and explain your reasoning.
Set up a rate, table, equation, or diagram before choosing.
INDEPENDENT PRACTICE · 4 OF 12
Increase $60 by 25%. New amount?
Find the value and explain your reasoning.
Set up a rate, table, equation, or diagram before choosing.
INDEPENDENT PRACTICE · 5 OF 12
What decimal represents 7%?
Find the value and explain your reasoning.
Set up a rate, table, equation, or diagram before choosing.
INDEPENDENT PRACTICE · 6 OF 12
A $120 bill has a 15% tip. How much tip?
Find the value and explain your reasoning.
Set up a rate, table, equation, or diagram before choosing.
INDEPENDENT PRACTICE · 7 OF 12
What is 30% of 70?
Work independently. Select the best answer, complete any needed calculation, and check that the result fits the situation.
Compute 0.30 × 70.
INDEPENDENT PRACTICE · 8 OF 12
18 is what percent of 60?
Work independently. Select the best answer, complete any needed calculation, and check that the result fits the situation.
Divide part by whole.
INDEPENDENT PRACTICE · 9 OF 12
A $50 item has 8% sales tax. What is the tax?
Work independently. Select the best answer, complete any needed calculation, and check that the result fits the situation.
Multiply 50 by 0.08.
INDEPENDENT PRACTICE · 10 OF 12
A student answers 36 of 45 questions correctly. What percent is correct?
Work independently. Select the best answer, complete any needed calculation, and check that the result fits the situation.
Compute 36 ÷ 45.
INDEPENDENT PRACTICE · 11 OF 12
Which equation finds 15% of x?
Work independently. Select the best answer, complete any needed calculation, and check that the result fits the situation.
Convert 15% to a decimal.
INDEPENDENT PRACTICE · 12 OF 12
What decimal is equivalent to 35%?
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.