Increasing and Decreasing by Percentages Worksheets
Percentage Decrease - Using a Bar Model
Year groups: 8, 9
Percentage Increase - Using a Bar Model
Year groups: 8, 9
Percentage Increase and Decrease
Year groups: 8, 9
Repeated Percentage Increase and Decrease (A)
Year groups: 8, 9
Repeated Percentage Increase and Decrease (B)
Year groups: 8, 9
Simple Interest
Year groups: 8, 9
Percentage Increase and Decrease with Multipliers
Year groups: 9, 10
What's the difference between a percentage increase and decrease worksheet and other percentage resources?
A worksheet on percentage increase and decrease focuses specifically on changing an amount by a given percentage, rather than just finding a percentage of a quantity. This distinction matters because students at KS3 and KS4 need to understand that increasing £80 by 15% requires finding 115% of the original, not 15% and then adding. The National Curriculum expects students to solve percentage problems multiplicatively, which builds the foundation for growth and decay calculations at GCSE.
These worksheets emphasise the multiplier method (using 1.15 for a 15% increase or 0.85 for a 15% decrease), which many students find more efficient than calculating the percentage separately. Teachers often observe that students who rely solely on finding the percentage and adjusting struggle with reverse percentage problems, where they need to work backwards from a final amount. Exam mark schemes consistently reward the multiplier approach, particularly in non-calculator papers where showing 1.24 × 50 is clearer than multiple steps.
Which year groups study increasing and decreasing by percentages?
These worksheets cover Years 8, 9, and 10, spanning both Key Stage 3 and Key Stage 4. The topic first appears properly in Year 8 once students have developed confidence with finding percentages of amounts. By Year 9, most students encounter reverse percentages (finding the original value before an increase or decrease), and Year 10 includes compound percentage changes where amounts increase or decrease repeatedly, which connects to exponential growth in later study.
The progression across these year groups moves from straightforward single-step problems using common percentages to more demanding multi-step calculations. Year 8 work typically involves increasing prices by VAT or decreasing in sales, Year 9 introduces problems where the final amount is given and students must find the original, and Year 10 includes contextual problems with repeated percentage changes. Teachers notice that students need regular revisiting of this topic because the conceptual leap from 'finding' to 'increasing by' often doesn't stick after one teaching block.
Why do students struggle with reverse percentage problems?
Reverse percentage problems require students to work backwards from an increased or decreased amount to find the original value. Many students instinctively try to reverse their method by subtracting the percentage if it was added, which produces incorrect answers. For example, if a price increased by 20% to £144, students might calculate 20% of £144 and subtract it, rather than recognising that £144 represents 120% of the original. The correct method involves dividing by the multiplier: £144 ÷ 1.2 = £120.
This skill connects directly to real-world financial contexts, particularly salary negotiations, tax calculations, and retail pricing. Estate agents calculate original house prices before percentage increases, retailers work backwards from sale prices to set original pricing, and economists analyse inflation by reversing percentage changes. Understanding that the same multiplier works in both directions (multiply to increase, divide to decrease) prepares students for exponential functions at A-level, where they manipulate growth and decay factors algebraically.
How do these worksheets help students master percentage increases and decreases?
The worksheets scaffold learning by starting with visual representations or structured steps that help students see the connection between the percentage change and the multiplier. Early questions might show 'find 105% of £60' alongside 'increase £60 by 5%' to reinforce that these are identical calculations. As students progress through each sheet, the scaffolding reduces and problems become more contextual, requiring them to identify what type of percentage change is needed from a written scenario rather than explicit instructions.
Teachers use these resources flexibly depending on student needs. They work well for intervention groups who missed the original teaching, as the answer sheets allow students to self-check and identify where their method breaks down. In mixed-ability classrooms, they provide differentiated practice while covering the same core concept. Many teachers set them for homework after initial teaching, then use common errors from the attempts to address misconceptions in the following lesson. The progression across the seven worksheets means they're also valuable for revision in Year 11, where percentage calculations appear in functional contexts across Foundation and Higher papers.