Teacher Guide: Introduction to Percentages
Learn what percentages are and how they relate to fractions and decimals.
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Class quiz
10 questions on Percentages. Students join with a name, you see everyone's score.
For Teachers
- Define percent as a ratio out of 100
- Convert between percents, fractions, and decimals
- Calculate a percent of a given number
- Apply percentages to real-world contexts like discounts and test scores
- • Understanding of fractions and equivalent fractions
- • Ability to convert between fractions and decimals
- • Basic multiplication and division skills
- 1. Where have you seen percentages used in your daily life this week?
- 2. Why do you think stores advertise '50% off' instead of 'half off'?
- 3. If you scored 90% on a test with 10 questions versus 90% on a test with 100 questions, did you get the same number correct?
- 4. Can something be more than 100%? When might that happen?
Thinking larger percent always means larger amount
Confusing the direction of decimal conversion
For Struggling Students:
- • Focus on benchmark percents: 10%, 25%, 50%, 75%, 100%
- • Use visual models like hundred grids
- • Connect to money: 25% = 25 cents per dollar
For On-Level Students:
- • Convert between all three forms: fractions, decimals, percents
- • Solve percent problems involving discounts and tips
- • Compare percentages in different contexts
For Advanced Students:
- • Calculate percent increase and decrease
- • Work with percents greater than 100%
- • Solve multi-step percent problems (tax + tip)
- 6.RP.A.3c (CCSS.MATH.CONTENT.6.RP.A.3.C)
Find a percent of a quantity as a rate per 100; solve problems involving finding the whole, given a part and the percent
- 7.RP.A.3 (CCSS.MATH.CONTENT.7.RP.A.3)
Use proportional relationships to solve multistep ratio and percent problems
- visualInteractive Percent Bar
Students drag to see percent as parts of 100
- activityDiscount Calculator Game
Calculate sale prices in a virtual shopping scenario
- worksheetPercent Conversions Practice
Convert between fractions, decimals, and percents
Lesson Content
Everything students see: definition, examples, common mistakes, applications. Tap to open.
Lesson Content
Everything students see: definition, examples, common mistakes, applications. Tap to open.
Definition
- (the whole thing)
Worked Examples
Write as a fraction in lowest terms.
Write as a fraction over 100
→
Find the GCD of 75 and 100
Factors of 75: 1, 3, 5, 15, 25, 75\nFactors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100\nGCD = 25 → GCD = 25
Divide both by GCD
→
Answer:
Common Mistakes
Confusing with
Why it's wrong: When converting, students sometimes forget to multiply by 100. , not .
Correct: To convert decimal to percent, multiply by 100:
Forgetting that means the whole thing
Why it's wrong: Students sometimes think percentages can't reach 100 or go beyond.
Correct: (all of it). You can even have more than : means 1.5 times the original.
Moving the decimal the wrong direction
Why it's wrong: Confusion about which way to move when converting between decimals and percents.
Correct: Percent to decimal: divide by 100 (move left 2 places). Decimal to percent: multiply by 100 (move right 2 places).
Why It Matters
- Shopping: Sales and discounts ("25% off")
- School: Test scores ("85% correct")
- Sports: Statistics ("Made 70% of free throws")
- News: Statistics and polls ("60% of voters agree")
- Health: Nutrition labels ("15% of daily calcium")
Real World Applications
Shopping Discounts
Stores use percentages to advertise sales and help customers calculate savings.
Example:
A 25% discount on a 40 dollar item saves you 10 dollars.
You're buying a video game that normally costs 80 dollars. The store has a 15% off sale.
How much will you pay after the discount?
Step 1: Write the mathematical expression
First find 15% of 80, then subtract:
Test Scores
Teachers use percentages to show how well you performed on tests and assignments.
Example:
Getting 17 out of 20 questions correct means you scored .
You answered 42 questions correctly out of 50 on a math test.
What is your percentage score?
Step 1: Write the mathematical expression
Divide correct by total, then multiply by 100:
Nutrition Labels
Food packages show the percent of daily nutrients in each serving.
Example:
If a snack provides 20% of your daily fiber, eating 5 servings would give you 100% of your daily fiber needs.
A glass of milk provides 30% of your daily calcium. You drink 2 glasses.
What percentage of your daily calcium did you get?
Step 1: Write the mathematical expression
Multiply the percent by the number of servings:
Key Takeaways
- 1Percent means "per hundred" - the symbol % represents this relationship
- 2To convert percent to decimal: divide by 100 ()
- 3To convert decimal to percent: multiply by 100 ()
- 4To convert percent to fraction: write over 100 and simplify ()
- 5To find a percent of a number: convert to decimal and multiply ( of )
Frequently Asked Questions
Can a percentage be more than 100%?
What's the difference between percent and percentage point?
Why do we use percentages instead of fractions?
Glossary
- Percent
- A ratio expressed as a fraction of 100, using the symbol %
- Percentage
- Another word for percent; a proportion expressed out of 100
- Percent of a number
- A fraction of a quantity found by converting the percent to a decimal and multiplying
- Discount
- A reduction in price, often expressed as a percentage off the original price
Formula Card
Percent to Decimal
Divide the percent by 100 to convert it to a decimal
Decimal to Percent
Multiply the decimal by 100 to convert it to a percent
Percent of a Number
Convert the percent to a decimal, then multiply by the whole