Ratios: Unpacking How They Work
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Ratios: Unpacking How They Work
Year 8 Mathematics Understanding relationships between quantities Connecting ratios to real-world applications
WALT - We Are Learning To
Understand what ratios represent and how they show relationships Express ratios in different forms and simplify them Connect ratios to fractions, decimals, and percentages Apply ratio knowledge to solve real-world problems Use ratios to make predictions and comparisons
Success Criteria
I can identify ratios in everyday situations I can write ratios in simplest form I can convert between ratios, fractions, and percentages I can use ratios to solve problems involving scaling and proportion I can explain what a ratio tells us about the relationship between quantities
What do you already know about ratios?
Think about recipes, sports, or mixing drinks Have you heard ratios mentioned in everyday life? What might a ratio of 2:1 mean?
What is a Ratio?
A ratio compares two or more quantities It shows the relationship between amounts Written as 'a:b' or 'a to b' Example: In a class of 15 boys and 10 girls, the ratio of boys to girls is 15:10 The order matters! Boys:Girls is different from Girls:Boys
Ratios vs. Fractions
{"left":"Ratios compare parts to parts\nShow relationships between different quantities\nCan compare more than two things (a:b:c)\nOrder is important","right":"Fractions show parts of a whole\nAlways have a numerator and denominator\nRepresent a portion of something complete\nCan be converted to decimals and percentages"}
Ratio Detective Activity
Look around the classroom and identify 3 ratios Examples: Windows to doors, desks to chairs, boys to girls Write each ratio in the form a:b Share your findings with a partner Discuss what each ratio tells us
Simplifying Ratios
Like fractions, ratios can be simplified Find the highest common factor (HCF) of both numbers Divide both parts by the HCF Example: 15:10 → HCF is 5 → 15÷5:10÷5 = 3:2 Simplified ratios are easier to understand and work with
Simplification Practice
Simplify these ratios: 20:15 24:18 35:14 Work in pairs and show your working Check your answers with another pair
Connecting Ratios to Fractions
Every ratio can be written as a fraction Ratio 3:2 means 3 parts to 2 parts (total 5 parts) First quantity = 3/5 of the total Second quantity = 2/5 of the total This helps us find actual amounts when we know totals
Ratios in Different Forms
{"left":"Ratio form: 3:4\nFraction form: 3/4\nDecimal form: 0.75\nPercentage form: 75%","right":"Word form: 3 to 4\nAll represent the same relationship\nDifferent forms useful in different contexts\nConverting between forms is a key skill"}
Real-World Ratio Challenge
A recipe calls for 2 cups of flour to 3 cups of sugar What's the ratio of flour to sugar? If you want to make a smaller batch with only 1 cup of flour, how much sugar do you need? Discuss your thinking with your table group