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Unit 7: Percentage changePlanning guidanceUnit objectivesWithin this unit, students will learn to:convert between fractions, decimals and percentagesuse percentages greater than 100%express one quantity as a percentage of anothercompare two quantities by percentageincrease or decrease a quantity by a given percentageunderstand how to compare quantities using percentagesfind the original quantity given its part and a percentagefind the original quantity using its final amount and percentage changesolve problems involving percentage change and reverse percentagesStudents worked on converting between fractions, decimals and percentages at the end of Year 7. It is important that they recognise not only that fractions, decimals and percentages are not distinct types of number, but rather different representations of number. They should know the difference between the use of fractions, decimals and percentages as operators (such as finding a fraction of an amount) or simply as a number. Students can use this prior knowledge to progress onto solving problems involving percentage change and reverse percentages. Bar models provide an excellent representation of percentage change and equivalence between amounts and hence should be used throughout the unit to deepen student understanding.This unit should take two weeks. ?There are three sections of work provided and it is left to individual teachers and departments to determine how much time is spent on each section. ?Within each overview page there are a number of tasks that departments should complete together and which should support the planning process. ?Then, using the additional resources under the documents tab, teachers can plan lessons to suit their individual classes. ?All resources are provided in Smart, ActivInspire and PowerPoint formats.Suggested StructureThe actual number of lessons spent on each section will depend on the individual class and the number of lessons available to teachers. We suggest the following based on a total of 6, 8 or 10 lessons over the fortnight:Section6 lessons8 lessons10 lessonsUsing percentages, fractions and decimals234Percentage change: increase and decrease233Calculating reverse percentages223Using percentages, fractions and decimalsObjectivesAppreciate the equivalence of fractions, percentages and decimalsUse bar models to represent quantitiesConvert between fractions, percentages and decimalsCompare and order quantities given as percentages, fractions and decimalsWork with percentages over 100%During this section, students will consolidate the work done in year 7 whilst meeting more complex concepts such as percentages over 100. Pictorial representations should be used to reinforce these ideas.Students will work on comparing and ordering fractions, decimals and percentages as numbers during this unit. It is important to use lots of concrete and pictorial representations such as 100 grids and bar models. In addition, students should reflect on the difference between this and using fractions, decimals and percentages as operators by considering questions such as how can 10% be more than 20%? (When they are percentages of different amounts).Sufficient time should be spent on this section to support students’ depth of understanding and to develop their fluency when working with and changing between the three quantities.For further guidance, including the Department Tasks for this section, click Using percentages, fractions and decimals under Planning resources on the main page for this unit.Percentage change: increase and decreaseObjectives:Express one quantity as a percentage of anotherFind a percentage of a quantity with and without a calculatorUse the decimal equivalent of a percentage in calculationsIncrease or decrease a quantity by a given percentageUnderstand how to compare quantities using percentagesSolve problems involving percentage changeAppreciate the more complex properties of percentages:Percentages are not additiveX% decrease does not ‘undo’ a X% increaseDuring this section students will explore calculations involving percentages through a variety of investigative tasks. Throughout the section, bar models are used as a pictorial representation to support students in deepening their conceptual understanding.There is a real emphasis on developing problem solving strategies in this section and as such students are encouraged to solve problems in different ways, to compare and contrast methods and to begin to determine the most efficient strategy for a given problem. In addition, there is plenty of opportunity for students to develop their reasoning skills by looking at common misconceptions, such as a 20% decrease followed by a 20% increase will result in no change from the original amount. Again, pictorial and concrete representations can be used to consolidate these ideas and to support students’ reasoning skills.For further guidance, including the Department Tasks for this section, click Percentage change: increase and decrease under Planning resources on the main page for this unit.Calculating reverse percentagesObjectives:find the original quantity given its part and a percentagefind the original quantity using its final amount and percentage changesolve problems involving percentage change and reverse percentagesApply both calculator and non-calculator methods to a variety of problemsDuring this unit there is a huge emphasis placed on using pictorial representation (especially bar models) to support problem solving and to develop conceptual understanding so that students do not rely on rote learn methods.It is in this section that students often have the most difficulties as misconceptions can be rife. It is vital to demonstrate clearly why, in order to find the price before a 10% increase, we don’t find 10% of the current amount. Working with concrete manipulatives to demonstrate this (for example with the pebble tasks) will help to clarify this for students.For further guidance, including the Department Tasks for this section, click Calculating reverse percentages under Planning resources on the main page for this unit. ................
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