Finding the original amount after a decrease
Lesson details
Learning outcome
I can calculate the original value, given the final value after a stated percentage decrease.
Key learning points
- A bar model can be used to find the original amount after a percentage decrease.
- A double number line can be used to find the original amount after a percentage decrease.
- A ratio table can be used to find the original amount after a percentage decrease.
- In all of these representations a single multiplier can be used to find the original amount after a percentage decrease.
Keywords
Reciprocal - The reciprocal is the multiplicative inverse of any non-zero number. Any non-zero number multiplied by its reciprocal is equal to 1.
Common misconception
A single digit percentage is incorrectly worked out by dividing by 10 and not 100 e.g 3% = 0.3. This error continues when increasing amounts e.g increase 40 by 3% has a multiplier of 1.3
Remind pupils that to covert a percentage into a decimal we divide by 100. This applies with increase too e.g 120% has a multiplier of 1.2
Teacher tip
Before starting on the second learning cycle assess their understanding of multipliers using MWBs. Ask them questions such as, '0.7 is my multiplier what percentages could I be finding?'. Here you could be finding 70% or a decrease of 30%.
Licence
Lesson video
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Prior knowledge starter quiz
6 Questions
Q1.Which of the following is the correct calculation for finding 20% of 300?
Q2.A number is increased by 25%. 1 part is equal to 25%. What will be the total number of parts representing the new number?
Q3.The cost of a TV increases by 20%. The new price is £420. What was the cost of the TV before the price increase? Without calculating the answer, decide whose answers cannot possibly be correct?
Q4.Jun thinks of a number and increases it by 20%. Jun's new number is 720. What was his original number?
Q5.The cost of a TV increases by 20%. The new price is £420. The cost of the TV before the price increase is £ .
Q6.The cost of a concert ticket is £80. This is an increase of 25% on last year. The cost of the ticket last year was £ .
Assessment exit quiz
6 Questions
Q1.Which of the following words indicate an increase?
Q2.Which of the following is the correct calculation for finding 3% of 300?
Q3.Match each percentage question to the correct multiplier.
Q4.A t-shirt costs £12 in a sale offering a 25% discount. The cost of the t-shirt before the discount was £ .
Q5.The value of a motorbike depreciates by 14% each year. It is now worth £5590. Last year the motorbike was worth £ .
Q6.Mr. Oak sells a vase is sold for £102. This gives him a profit of 20%. Mr. Oak originally purchased the vase for £ .
To help you plan your 8 maths lesson on: Finding the original amount after a decrease, download all teaching resources for free and adapt to suit your pupils' needs...
To help you plan your 8 maths lesson on: Finding the original amount after a decrease, download all teaching resources for free and adapt to suit your pupils' needs.
The starter quiz will activate and check your pupils' prior knowledge, with versions available both with and without answers in PDF format.
We use learning cycles to break down learning into key concepts or ideas linked to the learning outcome. Each learning cycle features explanations with checks for understanding and practice tasks with feedback. All of this is found in our slide decks, ready for you to download and edit. The practice tasks are also available as printable worksheets and some lessons have additional materials with extra material you might need for teaching the lesson.
The assessment exit quiz will test your pupils' understanding of the key learning points.
Our video is a tool for planning, showing how other teachers might teach the lesson, offering helpful tips, modelled explanations and inspiration for your own delivery in the classroom. Plus, you can set it as homework or revision for pupils and keep their learning on track by sharing an online pupil version of this lesson.
Explore more key stage 3 maths lessons from the Understanding multiplicative relationships: percentages and proportionality unit, dive into the full secondary maths curriculum, or learn more about lesson planning.