Step 1
Equivalent ratios keep the same relationship
If you multiply both parts of a ratio by the same number, the relationship stays the same.
👀 2:3 × 2 = 4:6
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Grade 6 · Maths · Lesson 1.2
Equivalent Ratios and Scaling
Build equivalent ratios by multiplying or dividing both quantities by the same factor.
CCSS.MATH.CONTENT.6.RP.A.3
Lesson Mission
How can we create new ratios that show the same relationship?
⚖️ MATH-G6-RP01 · Ratios, Unit Rates, and Proportional Relationships
✅ I can identify equivalent ratios.
✅ I can use multiplication to scale a ratio up.
✅ I can use division to simplify a ratio.
AI Learning Helper
Grade 6 Teacher
Helping with: Equivalent Ratios and Scaling
MATH-G6-RP01 · The Ratio Balance Lab
Teacher Welcome
Hi, I am your Grade 6 Math Coach. Today we are working inside MATH-G6-RP01: Ratios, Unit Rates, and Proportional Relationships. I will help you understand Equivalent Ratios and Scaling by focusing on creating equivalent ratios using scale factors.
Teacher Response
Guided Hint
What is the original ratio?
Ask for a Specific Hint
Teacher Tip
Read the problem, identify the quantities, choose a model, and explain each step. This skill matters because Equivalent ratios help scale recipes, maps, classroom supplies, game levels, and digital designs.
Common Mistake Alert
Do not multiply only one side of a ratio. Both quantities must change by the same factor.
Student Question Box
Helper Suggestion
Type a question above. The helper will guide the student toward the first step without giving away the answer immediately.
Challenge Prompt
Create a ratio table with at least five equivalent ratios for 3:5.
Warm-Up
Think First
A paint mix uses 2 cups of blue paint for every 3 cups of white paint. What would the mix be if doubled?
Show expected answer
Doubling both quantities gives 4 cups of blue paint and 6 cups of white paint.
Vocabulary
Key Words
Ratio
A comparison of two quantities by division, written as a:b, a to b, or a/b.
Equivalent ratios
Ratios that compare quantities in the same relationship, even if the numbers are different.
Unit rate
A rate that compares a quantity to exactly 1 unit of another quantity.
Proportional relationship
A relationship where two quantities increase or decrease by the same constant factor.
Tape diagram
A visual model that uses equal-sized parts to show ratio relationships.
Real-World Connection
Why This Matters
Equivalent ratios help scale recipes, maps, classroom supplies, game levels, and digital designs.
Mini Lesson
Learn the Concept
Step 2
Scaling up uses multiplication
When you need more of something, multiply both ratio parts by the same scale factor.
👀 2:3, 4:6, 6:9, 8:12
Step 3
Simplifying uses division
When both quantities share a common factor, divide both by the same number.
👀 8:12 ÷ 4 = 2:3
Interactive Practice
Practice, Build, Simulate, Explain
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Activity 1 · ratio-table
Paint Mix Ratio Table
Complete the ratio table for blue paint to white paint.
15 ptsNot checked
💡 Look for the multiplier that keeps both sides of the ratio equivalent.
| Blue Paint | White Paint |
|---|---|
| 2 | 3 |
| 4 | 6 |
| 6 | 9 |
| 8 | ? |
Show explanation
The ratio 2:3 is scaled by 2, 3, and 4 to create 4:6, 6:9, and 8:12.
Activity 2 · numeric-input
Smoothie Scaling
A smoothie recipe uses 3 bananas for every 5 cups of berries. If the recipe uses 15 cups of berries, how many bananas are needed?
10 ptsNot checked
💡 Type the number only unless the question asks for a unit.
Unit: bananas
Activity 3 · multiple-choice
Equivalent Ratio Check
Which ratio is equivalent to 4:7?
10 ptsNot checked
💡 Choose the answer that correctly represents the ratio relationship.