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Year 8 Autumn 1 Lesson 13: Using multipliers to find percentage decreaseObjectiveTo use and compare the use of both multipliers and ratio tables for finding percentage increase.AimThis moves onto percentage increase from last lesson. The students need to look at what type of multiplier they would need to increase an amount by a given percent.However, students will also encounter percentage increase and decrease on non-calculator papers. In these situations a ratio table can be useful.This lesson uses both approaches and moves between the two. This is intentional so that they don’t just always follow a given ‘method’, but can think about the problemResourcesPowerpointWorksheetLoop CardsActivity 1: Craig goes to the wholesalers. As this follows on from the multipliers lesson, the box and arrow template is still used for the decrease. The percentage decrease is more difficult, and so time might need to be taken to ensure they have the correct multiplier.This moves onto the same question, but to be done without a calculator with a ratio table. It is important that students understand they cannot use their calculator for this part of the lesson. It may be worth saying that they must turn their calculator over at this point.Questions for progressionIf you take 12 ? % off, what percentage remains?What is that as a decimal?What would 88% be as a decimal? 87%?So how can this help you find 87.5%?Activity 2: What would the multiplier be?Students answer the next question on their whiteboards, filling in the ratio table for a 12% increase. The ratio table is then linked to finding the multiplier.Students complete the sentences for the multiplier. This slide can be printed off for those who struggle to copy down.Questions for progressionIf you add on 15%, what percentage do you have now?What is that as a decimal?Why can’t it be 0.15?What does 150% increase mean?What percentage would you have if you added 150% to your original amount?Activity 3: Students answer the percentage increase and decrease questions on their whiteboards. Some are multipliers, some are with ratio tables.Questions for progressionFor the multiplier qustionsIf you add on 7%, what percentage do you have now?What is that as a decimal?Why isn’t it 1.7%What increase would 1.7 be?For the ratio table questionsIf you want to increase by 15%, what percentage do you want to end up with?How can you make up 15%?How does this relate back to the multiplier?Activity 4: Silent independent work.Students answer the three questions on the sheet – once with a ratio table and once with a multiplier. The questions are intended to be straight forward, although the final question may bring out some problems.If they finish, they should write and answer their own questions. Questions for progressionIf you add 8% what percentage should you have now?Why is that not 1.8 as a multiplier?(In the ratio table) How can you many 8%?What would be a good percentage to start with? (10%?)Can you make 2% from that?Can you now make 8%?When making their own question:Can you write a simple question? A difficult question?What makes a question difficult?Activity 5: Consolidation pair workStudent complete the loop activity in pairs. The instructions are on the Powerpoint. These could be cut out as loop cards, or just one set printed off and put up around the room for students to move about and collect (depending on the class).These should be done with a calculator, as the aim of this activity is to consolidate the finding of multiplers.Questions for progressionIf they can’t find the answer on a different cardShow me your box and arrow diagram?Is the question an increase or a decrease?Are you adding or subtracting form 100?What should your multiplier be?Acknowledgements:NCETM Multiplicative reasoning project for Craig’s problemMathsbox for loop cards. ................
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