Introduction
Solving Percent Problems is an important Grade 7 math skill because students are moving from simple answers toward explaining how the math works.
In this lesson, students use models, real questions, worked examples, practice problems, and two online quizzes to build confidence with solving percent problems.
What Is Solving Percent Problems?
Solving Percent Problems means choosing a model, naming what each number means, and explaining the strategy.
The goal is not only to get the answer. Students should be able to show the idea, explain the strategy, and check whether the answer makes sense.
Understanding Solving Percent Problems
Before solving, students should slow down and decide what each number, shape, unit, or label represents.
- Read the question carefully and identify what is being asked.
- Choose a model, equation, table, or diagram that matches the situation.
- Solve one step at a time and keep units or labels attached.
- Use the answer explanation to check that the result makes sense.
Visual Models
Visual Model 1
Question: The grid above shows a percent model. What percent is shaded?
- A. \(40\%\)
- B. \(50\%\)
- C. \(60\%\)
- D. \(75\%\)
Why it works: The shaded region is \(\frac{60}{100} = 60\%\) of the grid.
Answer: \(60\%\)
Visual Model 2
Question: By how much did the video game price increase?
| Item | Original Price | Percent Increase |
|---|---|---|
| Video game | $40 | \(20%\) |
- A. \($4\)
- B. \($20\)
- C. \($12\)
- D. \($8\)
Why it works: A \(20\%\) increase of \($40\) is \(0.20 \times 40 = 8\) dollars.
Answer: \($8\)
Worked Examples
Example 1
Question: The bar model shows a number divided into equal parts. What is \(25\%\) of \(80\)?
- A. \(15\)
- B. \(30\)
- C. \(25\)
- D. \(20\)
- \(25\%\) of \(80\) is \(\frac{1}{4} \times 80 = 20\).
Answer: \(20\)
Example 2
Question: In a class vote, \(70\%\) of students voted Yes. If there are \(80\) students total, how many voted Yes?
| Category | Votes | Percent |
|---|---|---|
| Yes | 56 | \(70%\) |
| No | 24 | \(30%\) |
- A. \(48\)
- B. \(64\)
- C. \(60\)
- D. \(56\)
- \(70\%\) of \(80\) is \(0.70 \times 80 = 56\) students.
Answer: \(56\)
Example 3
Question: The double number line shows percents and values. What is \(50\%\) of \(200\)?
- A. \(50\)
- B. \(75\)
- C. \(100\)
- D. \(150\)
- \(50\%\) is half; half of \(200\) is \(100\).
Answer: \(100\)
Real-World Word Problems
Problem 1
Question: A store has a \(40\%\) off sale. If a jacket originally costs \($80\), what is the discount?
- A. \($16\)
- B. \($48\)
- C. \($40\)
- D. \($32\)
Why it works: The discount is \(40\%\) of \($80\): \(0.40 \times 80 = 32\) dollars.
Answer: \($32\)
Problem 2
Question: If a bicycle costs \($120\) and the sales tax is \(8\%\), what is the tax amount?
- A. \($8\)
- B. \($14.40\)
- C. \($12\)
- D. \($9.60\)
Why it works: The tax is \(8\%\) of \($120\): \(0.08 \times 120 = 9.60\) dollars.
Answer: \($9.60\)
Common Mistakes
- Rushing before identifying what the numbers represent.
- Choosing an operation that does not match the situation.
- Dropping labels, units, or context from the answer.
- Skipping the estimate or reasonableness check.
Strategy Tips
- Underline the question being asked.
- Use a model before jumping to computation.
- Write an equation that matches the story or picture.
- Explain the final answer in a sentence.
Practice Questions
Question 1
What is \(30\%\) of \(150\)?
- A. \(30\)
- B. \(180\)
- C. \(50\)
- D. \(45\)
Question 2
A soccer team won \(75\%\) of their \(20\) games. How many games did they win?
- A. \(5\)
- B. \(12\)
- C. \(15\)
- D. \(18\)
Question 3
What percent of \(80\) is \(20\)?
- A. \(20\%\)
- B. \(60\%\)
- C. \(40\%\)
- D. \(25\%\)
Question 4
If \(12\) is \(15\%\) of a number, what is the number?
- A. \(60\)
- B. \(72\)
- C. \(80\)
- D. \(100\)
Question 5
Maria scored \(85\%\) on a test with \(40\) questions. How many questions did she answer correctly?
- A. \(24\)
- B. \(30\)
- C. \(34\)
- D. \(36\)
Question 6
What is \(5\%\) of \(200\)?
- A. \(5\)
- B. \(20\)
- C. \(15\)
- D. \(10\)
Full Answer Explanations Click to show all answers and explanations
Question 1
Answer: \(45\)
\(30\%\) of \(150\) is \(0.30\times150=45\).
Question 2
Answer: \(15\)
\(75\%\) of \(20\) is \(0.75 \times 20 = 15\) games.
Question 3
Answer: \(25\%\)
\(\frac{20}{80} = \frac{1}{4} = 0.25 = 25\%\).
Question 4
Answer: \(80\)
If \(12 = 0.15 \times n\), then \(n = \frac{12}{0.15} = 80\).
Question 5
Answer: \(34\)
\(85\%\) of \(40\) is \(0.85 \times 40 = 34\) questions.
Question 6
Answer: \(10\)
\(5\%\) of \(200\) is \(0.05 \times 200 = 10\).
Connection to Standards
This lesson supports Grade 7 math expectations for reasoning, modeling, problem solving, and explaining answers clearly. It connects classroom skills to the kind of questions students see on state math assessments.
Summary
Solving Percent Problems becomes easier when students connect the question to a model, use clear steps, and explain why the answer fits.
GOLDEN RULE
Understand the model before choosing the operation.
