📐 Proportional Reasoning
Master Ratios & Rates with Visual Models
Learn with tape diagrams, double number lines, and interactive tools.
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UNIT 1: Proportional Reasoning with Ratios and Rates
PART 1: INTRO TO RATIOS
1. Basic Ratios
Description:
A ratio compares two quantities. It tells us how much of one thing there is compared to another. Ratios can compare part to part or part to whole.
Explanation (TEKS 6.4C & 6.4D):
Write ratios in three ways:
- Using "to" → 3 to 5
- Using a colon → 3:5
- As a fraction → 3/5
Critical rule: Keep the order exactly as the problem asks.
- "Ratio of boys to girls" is different from "ratio of girls to boys"
Example 1:
A class has 8 boys and 12 girls.
Ratio of boys to girls = 8 to 12 = 8:12 = 8/12 (simplifies to 2/3)
Ratio of girls to boys = 12 to 8 = 12:8 = 12/8 (simplifies to 3/2)
Ratio of boys to total students (part to whole) = 8 to 20 = 8:20 = 8/20
⚙️ Interactive Ratio Builder
Adjust the sliders to see how the ratio changes:
Simplified Ratio = 2 : 3
✅ QUIZ 1: Basic Ratios + Ratios as Fractions/Decimals
Question 1: A zoo has 24 lions, 18 tigers, and 30 bears. Write the ratio of tigers to total animals in simplest form.
Question 2: Convert the ratio 5:8 to a decimal.
Question 3: In a box, the ratio of pens to pencils is 9:15. Simplify and write as a fraction.
PART 2: VISUALIZE EQUIVALENT RATIOS
3. Ratios with Tape Diagrams
Description:
A tape diagram is a visual tool that uses rectangular strips (tapes) to represent quantities. Each "tape" represents an equal part. This helps see the relationship between quantities.
Tape Diagram: Red : Blue = 3 : 2
🔴 15 red marbles → each tape = 5 → 🔵 10 blue marbles
📊 Interactive Tape Diagram Generator
Enter a ratio and see the tape diagram:
🧩 Tape Diagram Solver
Find missing quantities using tape diagrams:
5. Create Double Number Lines
Description:
A double number line has two parallel lines with matching tick marks. The top line shows one quantity, the bottom line shows the related quantity. It helps visualize scaling ratios.
📏 Interactive Double Number Line Generator
Create your own proportional number lines:
📐 Double Number Line Solver
Enter a proportional relationship to generate a complete number line:
✅ QUIZ 2: Equivalent Ratios
Question 4: Are 7:11 and 21:33 equivalent?
Question 5: A factory produces 300 widgets in 5 hours. How many in 8 hours?
PART 3: EQUIVALENT RATIOS
8. Ratio Tables
Description:
A ratio table is an organized way to list equivalent ratios. Each column (or row) shows a pair of numbers that keep the same multiplicative relationship.
📊 Interactive Ratio Table Generator
Generate a ratio table for any ratio:
🔍 Missing Ratio Solver
Find the missing value in a proportion:
✅ QUIZ 3: Unit Rates
Question 6: What is the unit rate for 300 miles in 6 hours?
Question 7: Which is the better buy? 10 pencils for $2.50 or 16 pencils for $3.68?
Enter the number of pencils in the better deal.
📚 Practice Questions
Test your skills with these practice questions. Questions change each time you refresh!
🎓 Generate Your Certificate
Enter your name to receive a certificate of completion:
🏆 Certificate of Completion
Awarded to Student
For successfully completing the Proportional Reasoning unit!
✅ All learning goals completed
✅ All 7 quiz questions answered correctly
Date:
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Key Concepts
- Ratio: a:b or a/b
- Proportion: a:b = c:d
- Condition: a × d = b × c
- Rule of Three: Known × Required ÷ Corresponding
- Unit Rate: Quantity per 1 (e.g., 60 miles/hour)
- Tape Diagram: Visual representation using equal parts
- Double Number Line: Two parallel lines showing related quantities
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