Ratios, rates and proportional reasoning

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عدد المتطلبات السابقة الإلزامية (حتى الأساس): 5

ستتعلّم

• Solve ratio and rate problems using tables, double number lines and unit rates.
• Recognise proportional relationships y = kx in tables, graphs and situations, and identify the constant k.
• Compute percentages and percentage changes, and explain why a 10% rise followed by a 10% fall does not return to the start.

تعريف

• A ratio a : b compares two quantities; it is equivalent to ka : kb for every k > 0.
• A unit rate is the amount of one quantity per one unit of another.
• Quantities x and y are proportional if y = kx for a fixed constant k.

مبرهنة

• The graph of a proportional relationship is a straight line through the origin.
• p% of x is (p/100) · x.
• Successive percentage changes multiply: a 10% increase and then a 10% decrease give an overall factor of 1.1 × 0.9 = 0.99.

مفاهيم خاطئة شائعة

• Using additive reasoning ('3 more') where multiplicative reasoning ('3 times as many') is needed.
• Thinking every linear relationship is proportional; y = 2x + 1 is not.
• Adding successive percentage changes.

يقود إلى

اكتشافات اختيارية

• Probability When outcomes are equally likely, a probability is the ratio of favourable outcomes to all outcomes.

مسارات التعلّم

• Adult beginner pathway