Ratio And Proportion
Overview
Mix white paint and blue paint in the ratio 3 to 2, then work out what 20 litres of the mixture costs. Buy a 400 gram jar for $3.20 or a 650 gram jar for $5.07 and say which is better value. Work out how many cards you can cut from a thousand centimetres of ribbon. These three questions look like three different subjects and they are all the same idea: quantities that keep a fixed relationship to one another as they change.
You will write ratios and reduce them to their simplest form, see how a ratio connects to a fraction, divide a quantity in a given ratio, and apply ratio to problems that do not announce themselves as ratio problems. You will use common measures of rate, including rates of pay and best-buy comparisons, and solve problems involving direct and inverse proportion, including repeated proportional change. On the Extension Tier you will meet exponential growth and decay, where the multiplier itself is the model.
Objectives
- [Core] use ratio notation, including reduction to simplest form and links to fraction notation
- [Core] divide a quantity in a given ratio
- [Core] apply ratio to solve problems
- [Core] use common measures of rate, including calculating rates of pay and best-buy problems
- [Core] solve problems involving direct and inverse proportion including repeated proportional change
- [Extension] exponential growth and decay
Mind map
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Lesson Note
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Lesson Evaluation
Congratulations on completing the lesson on Ratio And Proportion. Now that youve explored the key concepts and ideas, its time to put your knowledge to the test. This section offers a variety of practice questions designed to reinforce your understanding and help you gauge your grasp of the material.
You will encounter a mix of question types, including multiple-choice questions, short answer questions, and essay questions. Each question is thoughtfully crafted to assess different aspects of your knowledge and critical thinking skills.
Use this evaluation section as an opportunity to reinforce your understanding of the topic and to identify any areas where you may need additional study. Don't be discouraged by any challenges you encounter; instead, view them as opportunities for growth and improvement.
- White paint and blue paint are mixed in the ratio 3 : 2. What fraction of the mixture is blue? A. 2/3 B. 3/2 C. 2/5 D. 3/5 Answer: C
- 6 workers build a wall in 10 days. How long would 4 workers take, working at the same rate? A. 6.7 days B. 8 days C. 15 days D. 24 days Answer: C
- The mass of 40 cubic centimetres of copper is 354 grams. What is the mass of 100 cubic centimetres? A. 141.6 g B. 414 g C. 885 g D. 1416 g Answer: C
- In the model N = 12 000 a^t with a = 0.8, what is the value of N when t = 0? A. 0 B. 0.8 C. 9600 D. 12 000 Answer: D
- Coffee costs $3.20 for 100 g, $7.75 for 250 g or $22.80 for 750 g. Which is the best value? A. the 100 g jar B. the 250 g jar C. the 750 g jar D. they are all the same value Answer: C
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