Ratio and Proportion

Ratios compare quantities. 2:3 tells us 'for every 2 of this, we have 3 of that.' Scaling a recipe, reading a map, mixing paint — all are ratio work. The answer is checked by the original ratio relationship.

• Framework: Montessori
• Unit: Mathematics
• Learning area: Algebra
• Level: Ages 8-9

Objectives

• Express ratios in simplest form
• Solve proportions using cross-multiplication
• Apply ratios to scaling and measurement
• Prepare for percentages and rates

Materials

• Ratio cards with real-world problems
• Simple scale models (map with scale indicated, recipe to scale up)
• Paper and pencil
• Measuring cups (for kitchen ratios)

Instructions

1. Introduce ratio notation: 2:3 or 2/3. 2. Simplify 6:9 by dividing both by 3 → 2:3. 3. Show that 2:3 = 4:6 = 6:9 — equivalent ratios. 4. Solve a proportion: 2:3 = x:12. 5. Cross-multiply: 2 × 12 = 3 × x, so x = 8. 6. Apply to a map: if 1 cm = 10 km, how far is 5 cm? → 50 km. 7. Apply to a recipe: if 2 cups flour makes 12 muffins, how much for 18? → 3 cups. 8. Write the solution as a complete sentence. 9. Progress to percent (per hundred) as a special ratio.

Educator tip

Cook with children and scale recipes by ratio. The kitchen is a ratio laboratory.

Assessment

Note ratio simplification, correct cross-multiplication, and applied solutions.

More from Mathematics

• Volume — Measuring Three Dimensions
• Factor Trees and Prime Factorization
• Addition Snake Game
• Subtraction Snake Game
• Multiplication Snake Game
• Decanomial Bead Bar Layout (Short Form)
• Introduction to Negative Numbers
• Area of a Rectangle — Formula from Counting