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Ratio, Proportion and Rates of Change
Ratio and proportion compare quantities and describe how one amount changes with another. This topic also develops practical rates, compound measures and the idea of change per unit.
Work through the lessons in order or jump to the area you need. Foundation and Higher material is clearly signposted within each lesson.
Tier note: interpreting and using basic direct and inverse relationships is shared. AQA and Edexcel place formal construction of proportional equations in Higher content; OCR includes basic formal models at Foundation. Powers, roots and instantaneous rates on curves are Higher extensions. Areas Under Graphs and Accumulated Change is Higher.
Ratio and Scaling
1. Understanding and Simplifying Ratios Write, simplify and interpret ratios, link ratios to fractions, and compare quantities in consistent units.
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2. Sharing and Solving Ratio Problems Share quantities in two- and three-part ratios, find missing amounts, and solve multi-step ratio problems.
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3. Proportion in Practice: Recipes, Rates and Best Buys Use scaling and the unitary method for recipes, rates, prices, currency and practical comparisons.
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4. Units, Scale Drawings and Maps Convert related units, work with area and volume conversions, and use map scales and simple scale drawings.
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Proportional Relationships
5. Direct Proportion Use tables, equations and graphs for direct proportion, with Higher extensions involving powers and roots.
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6. Inverse Proportion Recognise inverse relationships, use constant products and reciprocal models, and extend to Higher power relationships.
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Rates and graph applications
7. Speed, Density and Pressure Calculate and rearrange compound measures, convert units and interpret average speed correctly.
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8. Rates of Change Interpret change per unit and gradients, then progress to Higher average and instantaneous rate estimates.
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9. Real-Life and Travel Graphs Read contextual and travel graphs, compare journeys and apply Higher tangents to curved motion.
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10. Areas Under Graphs and Accumulated Change Calculate and estimate accumulated change using areas, with distance, displacement, flow and money contexts.
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Related SumLogic lessons
Useful prerequisites and extensions include Fractions, Decimals & Percentages , Percentage Increase and Decrease , Rearranging Formulae , Linear Graphs and Functions .
Geometry now covers bearings , enlargements , similar-shape scale factors and trigonometric ratios . Number owns percentages, reverse percentages, simple interest and compound growth and decay . Numerical Methods and Iteration owns general iterative processes. Travel graphs are taught in Real-Life and Travel Graphs ; Higher accumulation is taught in Areas Under Graphs and Accumulated Change .
