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# Topic 6 Year 8 Mathematics

 Mathematics Topic Direct and inverse Proportion No of lessons 12 When is it happening Term 2 Year 8 What will students learn This unit begins by looking at proportional relationships in familiar contexts building on their understanding of ratio from the previous unit. Students look at the meaning of direct proportion and make links to linear graphs from the last unit. Students will develop their proportional reasoning skills by solving a variety of problems. Students are encouraged to compare different approaches to solving problems involving direct proportion. In the second week of this unit, students will meet the concept of inverse proportion. Students will encounter different contexts where one variable increases, the other decreases, but their product remains constant. As a way into this, students are invited to make different rectangles with a constant area. The graphing of the side lengths will reveal an inversely proportional relationship. Students will use this understanding to solve problems involving inverse proportion. Key Knowledge that students should know at the end of 'Topic' This is the knowledge that students will meet for the first time in this topic relationships algebraically This is knowledge that students may have met before but will need to deepen their understanding Proportional reasoning, different ways of defining ratio and proportion. multiplication, division, fractions, decimals and percentages, as well as a unit introducing the formal notation for ratio. Key Skills that students should be able to demonstrate at the end of 'Topic' This is the skills  that students will meet for the first time in this topic Simplify, understand : means ratio This is skills that students may have met before but will need to develop Using a scientific calculator Key vocabulary that students should know and understand Proportion, Proportional The Big Question It takes 4 friends 6 hours to clean a garden, how long will it take 2? Key questions that students should be able to answer at the end of the 'Topic' What is direct proportion? What is the unitary method? If 4 pens cost 1.60 how much do 12 pens cost? How do you solve proportion problems? How do you solve money problems? How do you use a proportion graph? How do you solve a direct proportion problems? If four tickets cost £42 how much does 9 cost? What is inverse proportion? If it takes 2 people 3 hours to clean a house how long does it take 4? What does an inverse proportion graph look like? What is the difference between direct and inverse proportion?