Using Grid Models to Solve Percentage Problems
A \(\color{blue}{10 \times 10}\) grid is a powerful visual tool for understanding percentage problems. Because the grid has exactly 100 squares, each square represents 1%. You can use it to find the part, the percent, or the whole — the three quantities in every percentage problem.
What Is a Grid Model for Percentages?
A grid model is a square divided into 100 equal cells. Shading a certain number of cells represents that percentage of the whole. The relationship can be written as:
\(\color{blue}{\text{ Part } = \text{ Percent } \times \text{ Whole }}\)
Every percentage problem asks you to find one of these three values when the other two are known.
How to Use Grid Models to Solve Percentage Problems
Finding the Part
Shade (percent) cells out of 100 to represent the percent. The shaded cells correspond to the part of the whole.
Example: 30% of 50. The grid shows 30 shaded cells out of 100. Scale: \(\color{blue}{0.30 \times 50 = 15}\).
Finding the Percent
Count the shaded cells (or equivalent cells out of 100). That count is the percent.
Example: 24 out of 80. Scale down: \(\color{blue}{\frac{24}{80} = \frac{30}{100} = 30\%}\).
Finding the Whole
The percent \(\color{blue}{\text{ shaded } = \text{ part }}\) ÷ \(\color{blue}{\text{ whole } \times 100}\). Rearrange: \(\color{blue}{\text{ whole } = \text{ part }}\) ÷ (\(\color{blue}{\frac{\text{ percent }}{100}}\)).
Example: 60% of what number is 18? \(\color{blue}{18 &\text{ div }; 0.60 = 30}\).
Step-by-Step Summary
- Identify which value is missing: part, percent, or whole.
- Write the formula: \(\color{blue}{\text{ Part } = \text{ Percent } \times \text{ Whole }}\).
- Substitute the two known values and solve for the third.
- On a grid: count or shade cells to visualize and verify.
Watch: Finding a Percent of a Number (Video Lesson)
Math Antics explains the step-by-step approach to finding a percent of a number using visual methods:
Worked Examples
Example 1: What is 30% of 50?
Formula: \(\color{blue}{\text{ Part } = 0.30 \times 50 = 15}\).
Answer: 15
Example 2: 24 is what percent of 80?
Formula: \(\color{blue}{\text{ Percent } = \frac{24}{80} \times 100 = 30\%}\).
Answer: 30%
Example 3: 60% of a number is 18. What is the number?
Formula: \(\color{blue}{\text{ Whole } = 18 &\text{ div }; 0.60 = 30}\).
Answer: 30
Example 4: A grid has 45 cells shaded. The full grid represents 200 items. How many items does the shaded portion represent?
Percent shaded: \(\color{blue}{45\%}\). Part: \(\color{blue}{0.45 \times 200 = 90}\).
Answer: 90 items
More Practice: Percent Word Problems
Math with Mr. J applies these exact three-part percentage strategies to word problems:
Exercises
- What is 25% of 80?
- 36 is what percent of 90?
- 75% of a number is 60. What is the number?
- A grid has 55 shaded squares. The whole represents 300 people. How many people does the shaded part represent?
- What is 40% of 125?
- 18 is 45% of what number?
Answers
- \(\color{blue}{20}\)
- \(\color{blue}{40\%}\)
- \(\color{blue}{80}\)
- \(\color{blue}{165 \text{ people }}\)
- \(\color{blue}{50}\)
- \(\color{blue}{40}\)
Frequently Asked Questions
Can I use a grid model when the whole is not 100?
Yes. The grid still represents 100%, but each cell represents (whole ÷ 100) units. Shade the number of cells equal to the percent, then multiply by (whole ÷ 100) to get the part.
What formula should I memorize?
Remember: \(\color{blue}{\text{ Part } = \text{ Percent } \times \text{ Whole }}\). All three forms follow from this: \(\color{blue}{\text{ Percent } = \text{ Part }}\) ÷ Whole; \(\color{blue}{\text{ Whole } = \text{ Part }}\) ÷ Percent. Convert the percent to a decimal before calculating.
What is the most common mistake with grid models?
Forgetting to divide the percent by 100 before multiplying. Always convert percent to decimal first: \(\color{blue}{30\% = 0.30}\), not 30.
Related Topics
Related to This Article
More math articles
- 10 Most Common 7th Grade MCAS Math Questions
- 3rd Grade OSTP Math Worksheets: FREE & Printable
- Descriptive Statistics Calculator — Mean, SD, Quartiles (Free)
- Free Grade 3 English Worksheets for Nevada Students
- The 5 BEST Online Math Tutoring Tools
- FREE 7th Grade ACT Aspire Math Practice Test
- Overcoming Mental Blocks in Algebra: A Student’s Guide
- Free Grade 8 English Worksheets for Colorado Students
- GED Test: Everything You Need to Know
- Beating Baccarat: What a Million-Hand Simulation Actually Shows
What people say about "Using Grid Models to Solve Percentage Problems - Effortless Math: We Help Students Learn to LOVE Mathematics"?
No one replied yet.