Relate Fractions, Decimals, and Percents
I can write equivalent fractions, decimals, and percents for the same value.
How to Use This Deck
Click Present or press F11 for fullscreen. Use arrow keys to advance.
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Text boxes, polls, and drag-sort save automatically in the browser.
Press N or click 📝 in the toolbar for pacing tips and answers.
Launch the full HTML activity for independent practice.
File → Print or the print button for handout copies.
🎯 Content Objective / Objetivo de contenido
I can write equivalent fractions, decimals, and percents for the same value.
Today's Flow
Total pacing: ~45 min · Progress bar at top tracks your place
LAUNCH
⏱ ~10 min
⏱️ 3 MIN · THINK-PAIR-SHARE
A player scored 3/4 of the points. The leaderboard shows percents and the game engine uses decimals. What are three different ways to write the same score?
Check for Understanding #1
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Arcade Builder Challenge
You're designing the scoring system for a new arcade game. Players earn points as fractions of the total possible score. The leaderboard shows scores as percentages, but the game engine uses decimals. You need to convert between all three forms to build the display!
Concept Launch
💡 How can one value be written as a fraction, a decimal, AND a percent?
Equivalent forms name the same value in different ways. A fraction, a decimal, and a percent can all show the same amount.
To turn a fraction into a percent, divide the top by the bottom to get a decimal, then multiply by 100.
Check for Understanding #2
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Now it's your turn
VOCABULARY
⏱ ~8 min
| Term / Término | Meaning / Significado | Example / Ejemplo | Visual |
|---|---|---|---|
| Percent Porcentaje |
A way to compare a number to 100, shown with the % sign. Una manera de comparar un número con 100, con el signo %. |
25% means 25 out of 100 | |
| Decimal Decimal |
A number with a dot, like 0.5, that shows a part. Un número con un punto, como 0.5, que muestra una parte. |
0.75 means seventy-five hundredths | |
| Equivalent Equivalente |
Having the same value, just written a different way. Tener el mismo valor, escrito de otra forma. |
1/2 = 0.5 = 50% | |
| Benchmark Referencia |
A familiar number you use to guess, like 50% or 1/2. Un número conocido que usas para estimar, como 50% o 1/2. |
Common benchmarks: 25%, 50%, 75% | |
| Discount Descuento |
Money taken off the first price to make it cheaper. Dinero que se quita del precio original para que sea más barato. |
$40 shirt at 25% off: discount = $10 |
Vocabulary — True or False?
Which statements correctly use Equivalent?
Fix the False One
Which Word Fits?
A ratio that compares a number to 100, written with a % sign, is a ___.
Use It In a Sentence
Check for Understanding #3
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Turn & Talk — Launch
A player scored 3/4 of the points. The leaderboard shows percents and the game engine uses decimals. What are three different ways to write the same score?
👂 Listen For
Students give 3/4 = 0.75 = 75% and recognize these are three forms of one value, not three different scores.
Extend: Which form would be easiest to read on a leaderboard, and which is easiest for the game engine to calculate with? Justify your choices.
EXPLORE & PRACTICE
⏱ ~18 min
Visual Modeling Workspace
Use the drawing tray below to annotate the visual model. Teacher: say "Click to reveal" on key steps.
Explore Activity
Complete the conversion table. Each row shows the same value in three forms.
✍️ Explore Discourse
What pattern do you notice when converting between fractions, decimals, and percents?
Whiteboard Moment
Show your work clearly. Be ready to explain your thinking to a partner.
Turn & Talk — Explore
How did you convert a fraction like 3/5 into a decimal and a percent in the table?
👂 Listen For
Students describe dividing numerator by denominator (3 div 5 = 0.6) and multiplying by 100 to get 60%, and call the three forms equivalent.
Extend: Some fractions like 1/4 give a clean decimal, but others do not. How can a benchmark like 1/2 or 1/4 help you estimate before you divide?
Practice Check A
A game shows your score as 7/8 complete. What percent is that?
✍️ Show Your Work
Explain why your answer is correct using today's vocabulary.
Practice Check B
Convert 3/5 to a percent.
✍️ Show Your Work
Explain why your answer is correct using today's vocabulary.
Ratio Table Builder
Fill the ratio table. Each row must be equivalent.
| Factor | A | B |
|---|---|---|
| ×1 | ||
| ×2 | ||
| ×3 |
✍️ Justify Your Thinking
Order these values from least to greatest by sorting them into the correct position.
A classmate turned in the work below. One step has a mistake. Read every step, find it, name it, and fix it.
Choose ONE option to show what you know — then do it in the workspace below.
Use evidence from today's lesson to complete each frame.
Today's key idea is: "To turn a fraction into a percent, divide the top by the bottom to get a decimal, then multiply by 100." — and it works because ___.
Because Percent means ___, but a tricky part is ___, so I have to ___.
A common mistake with Percent is ___. It happens because ___, and the fix is ___.
I can prove my answer is correct by ___, using Decimal to check my work.
✍️ TWR · WRITE 3 SENTENCES · 7 MIN
To turn a fraction into a percent, divide the top by the bottom to get a decimal, then multiply by 100. because ___
To turn a fraction into a percent, divide the top by the bottom to get a decimal, then multiply by 100. but ___
To turn a fraction into a percent, divide the top by the bottom to get a decimal, then multiply by 100. so ___
🌱 TWR · GROW THE KERNEL · 6 MIN
Answer these to add detail
Sentence starters (tap to use)
Student Workspace
Complete the conversion table. Each row shows the same value in three forms.
| Fraction | Decimal | Percent |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/4 | ||
| 0.75 | ||
| 20% | ||
| 3/5 | ||
| 0.1 |
✏️ Sketch Your Strategy
Differentiation Paths
Step-by-step with a worked model and sentence frames.
Scaffolded practice with visual supports.
Core practice aligned to the standard.
Extension with error analysis or multi-step reasoning.
Partner Activity
Work with your partner on the practice problems at your differentiation path level. Explain each step using math vocabulary.
Check for Understanding #4
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Real-World Connection
🌍 Math in the Wild
A store has a clearance sale: 'Everything 3/5 off!' Your friend says that means 35% off. Another friend says it's 60% off. The original price of a game is $40.
✍️ Connection Reasoning
Who is correct, and how much would the game cost on sale?
The friend who said ___% is correct because 3/5 = ___ = ___%. The sale price is $___.
Turn & Talk — Connect
Two arcade games show their loading bars differently: Game A is 0.7 loaded and Game B is 3/4 loaded. Which game is closer to fully loaded, and how do you know without a calculator?
👂 Listen For
Students convert both to the same form (0.7 = 70%, 3/4 = 0.75 = 75%) and use 75% > 70% to conclude Game B is closer to fully loaded.
Extend: Use the benchmark 3/4 to estimate before converting: how can knowing 3/4 = 75% help you judge a loading bar at a glance?
CLOSURE & REFLECT
⏱ ~8 min
Today I learned that ___ because ___.
One thing I am still not sure about is ___.
Which shows 0.45 as a fraction and a percent?
Bonus Exit Check
Convert 7/20 to a percent.
✍️ Show Your Work
Explain why your answer is correct using today's vocabulary.
Reflection & Self-Assessment
Continue Learning
Launch the Full Interactive Activity
Students continue practice in the HTML lesson engine with auto-check, hints, and differentiation.
Family Connection
Share tonight's family homework and discuss one vocabulary word at home.
Open Family Homework ↗Teacher Notes
⏱️ Pacing Guide
- Launch & vocab: 12 min
- I Do / We Do / You Do: 15 min
- Explore & practice: 15 min
- Connect & closure: 8 min
Total: ~45 min
🎯 Listen For · Common Errors
• Students give 3/4 = 0.75 = 75% and recognize these are three forms of one value, not three different scores.
• Students describe dividing numerator by denominator (3 div 5 = 0.6) and multiplying by 100 to get 60%, and call the three forms equivalent.
• Students convert both to the same form (0.7 = 70%, 3/4 = 0.75 = 75%) and use 75% > 70% to conclude Game B is closer to fully loaded.
• Listen for students naming a specific strategy tied to 6.RP.3c — not just "I multiplied." They should connect steps to the key idea.
Common mistake: A common mistake in Relate Fractions, Decimals, and Percents is skipping the key idea: "To turn a fraction into a percent, divide the top by the bottom to get a decimal, then multiply by 100." — always check your work against this rule before you submit.
Answer Key (Teacher Appendix)
Hide this slide during presentation or move to the end of your copy.
✓ Practice 1: 87.5% — 7 ÷ 8 = 0.875, and 0.875 × 100 = 87.5%.
✓ Practice 2: 60% — 3 ÷ 5 = 0.6 = 60%.
✓ Practice 3: 35% — 7 ÷ 20 = 0.35 = 35%.
✓ Practice 4: 0.45 — To convert a percent to a decimal, divide by 100: 45 ÷ 100 = 0.45.
✓ Exit ticket: 9/20 and 45% — 0.45 = 45/100 = 9/20 (simplified). 0.45 × 100 = 45%.