Ratio and Proportion

Ratio compares; proportion equates two ratios. 3:4 = 6:8 (both = 3/4). Maps use ratio: 1 cm represents 10 km. Indirect aim: algebraic equation solving, preparation for trigonometric ratios and similar triangles.

• Framework: Montessori
• Unit: Mathematics
• Learning area: Algebra
• Level: Ages 9-11

Objectives

• Express ratios in a:b form and as fractions
• Simplify ratios
• Solve proportions by cross-multiplication
• Apply to scaling and real problems

Materials

• Ratio cards
• Problem slips
• Map with scale
• Recording paper

Instructions

1. Write ratio of girls to boys in class (e.g., 7:8). 2. Simplify if possible. 3. Equivalent ratios: 3:4 = 6:8 = 9:12. 4. Write as proportion: 3/4 = 9/12. Cross-multiply: 3×12 = 4×9 = 36. 5. Solve for x: 3/4 = x/20. Cross: 4x = 60. x = 15. 6. Apply: if a map is 1:100,000, how far is 5 cm? Answer: 5 km. 7. Scale a recipe. 8. Record.

Educator tip

Cross-multiplication is algebra's workhorse for proportions. Introduce it as a derived shortcut from the rule 'same ratio means same quotient'.

Assessment

Observe ratio simplification, proportion solving, and real-world application.

More from Mathematics

• Integer Operations — Signed Number Arithmetic
• Word Problems — Distance, Rate, Time
• Geometry Chart 1 — Basic Figures
• Congruence and Similarity
• Geometric Symmetry — Reflection, Rotation, Translation
• Measurement — Length in Metric
• Measurement — Weight and Mass
• Measurement — Capacity and Volume