- 1. Introduction to Direct Proportion (Visualizing the Rules)
Verify if a relationship is directly proportional using the "Zero Test" and "Doubling Test", and fill in missing values on pre-drawn Double Number Lines using multiplicative jumps.
- 2. Direct Proportion in Ratio Tables (The Unitary Method)
Complete ratio tables with missing values using the unitary method (finding the value of 1) through multiplication and division.
- 3. Introduction to Decimal Multipliers (Percentage Increase)
Memorize and calculate decimal multipliers for percentage increases (e.g., +12% = \times 1.12) and apply them to baseline values in a single multiplicative step.
- 4. Direct Proportion Word Problems (Without Pre-Drawn Diagrams)
Extract data from real-world contexts and build Double Number Lines or Ratio Tables to solve direct proportion word problems.
- 5. Intuitive Inverse Proportion (The Halving Test)
Differentiate inverse proportion from direct proportion using the "Halving Test" and fill intuitive gaps in sharing and working contexts.
- 6. Decimal Multipliers (Percentage Decrease)
Calculate decimal multipliers for percentage decreases and apply them to baseline values using a single multiplication step.
- 7. Inverse Proportion in Ratio Tables
Use reciprocal operations (multiplying one side while dividing the other) to complete ratio tables for inverse proportion contexts.
- 8. Classifying Direct, Inverse, or Neither
Use the Zero, Doubling, and Halving tests to classify real-world contexts as direct proportion, inverse proportion, or neither.
- 9. Value for Money & Unit Pricing
Use the unitary method to find the cost per 1 item or cost per 100g to compare two options and determine Best Buy.
- 10. Scaling Recipes
Apply direct proportion using Double Number Lines and Ratio Tables to scale single ingredients and full recipe grids up and down.
- 11. Single-Step Exchange Rates
Students will convert currencies one-way and backwards using ratio tables with a fixed multiplier.
- 12. Finding the Actual Percentage Change
Determine the exact percentage increase or decrease between two values by finding the multiplier first.
- 13. Multi-Step Proportion & Cross-Contextual Problems
Students will track units carefully through 2- or 3-step ratio tables to make complex comparisons involving multi-currency chains and international best buys.
- 14. Non-Routine Mixed Consolidation
Students will solve rich, non-routine problems that mix direct, inverse, exchange rates, recipes, and reverse percentages, identifying the correct mathematical tools to use.
