Understanding and Using Percentages — Ascentis Entry Level Foundations for Learning Revision

    This subtopic focuses on understanding percentages as a way to express parts of a whole, and on performing essential calculations including percentage part

    Topic Synopsis

    This subtopic focuses on understanding percentages as a way to express parts of a whole, and on performing essential calculations including percentage parts, increases, and decreases. Learners will develop practical skills for real-world applications such as discounts, interest rates, and data interpretation, and will gain confidence in using a calculator to solve percentage problems efficiently.

    Key Concepts & Core Principles

    Exam Tips & Revision Strategies

    Common Misconceptions & Mistakes to Avoid

    Examiner Marking Points

    Understanding and Using Percentages

    ASCENTIS
    vocational

    This subtopic focuses on understanding percentages as a way to express parts of a whole, and on performing essential calculations including percentage parts, increases, and decreases. Learners will develop practical skills for real-world applications such as discounts, interest rates, and data interpretation, and will gain confidence in using a calculator to solve percentage problems efficiently.

    7
    Learning Outcomes
    28
    Assessment Guidance
    31
    Key Skills
    7
    Key Terms
    34
    Assessment Criteria

    Assessment criteria

    Ascentis Level 1 Award in Mathematics (Stepping Stones to Functional Skills) - Understanding and Using Percentages
    Ascentis Level 2 Certificate in Mathematical Skills
    Ascentis Level 1 Certificate in Mathematical Skills
    Ascentis Level 1 Extended Award in Mathematical Skills
    Ascentis Level 1 Extended Award in Mathematics (Stepping Stones to Functional Skills)
    Ascentis Level 1 Certificate in Mathematics (Stepping Stones to Functional Skills)
    Ascentis Level 1 Award in Mathematics (Stepping Stones to Functional Skills)

    Topic Overview

    Percentages are a way of expressing a number as a fraction of 100. In the Ascentis Level 1 Award in Mathematics, this topic builds on your understanding of fractions and decimals, showing how they all connect. You'll learn to find percentages of quantities, convert between percentages, fractions, and decimals, and solve real-life problems like calculating discounts, interest, and VAT. Mastering percentages is essential for everyday tasks such as budgeting, shopping, and interpreting data in news reports.

    This topic is a stepping stone to functional skills because percentages are everywhere—from sale signs in shops to statistics in the media. By the end of this unit, you should be able to calculate percentages without a calculator for simple cases (like 10%, 25%, 50%) and use a calculator for more complex ones. You'll also understand percentage increase and decrease, which is crucial for understanding pay rises, price changes, and population growth.

    In the wider context of the Ascentis qualification, percentages link directly to fractions and decimals, and they appear in other topics like ratio and proportion. A solid grasp of percentages will help you in later modules on data handling and financial mathematics. The Level 1 award is designed to build confidence, so you'll start with simple calculations and progress to multi-step problems.

    Key Concepts

    Core ideas you must understand for this topic

    • →Percentage as 'out of 100': e.g., 45% means 45 out of 100, or 45/100 = 0.45.
    • →Finding a percentage of a quantity: multiply the quantity by the percentage (as a decimal or fraction). For example, 15% of 200 = 0.15 × 200 = 30.
    • →Converting between percentages, fractions, and decimals: e.g., 60% = 60/100 = 3/5 = 0.6.
    • →Percentage increase and decrease: increase by 10% means multiply by 1.10; decrease by 10% means multiply by 0.90.
    • →Using percentages in real-life contexts: discounts (e.g., 20% off), interest rates, and statistics.

    Learning Objectives

    What you need to know and understand

    • Understand whole number percentages., Be able to calculate percentage parts of whole number quantities., Understand how to calculate percentage increase., Understand how to calculate percentage decrease., Be able to use a calculator to calculate percentages.
    • Be able to order and compare percentages, Be able to calculate percentage increase, Be able to calculate percentage decrease, Be able to find percentage parts of quantities and measurements, Be able to evaluate one number as a percenatge of another
    • Understand whole number percentages., Be able to calculate percentage parts of whole number quantities., Understand how to calculate percentage increase., Understand how to calculate percentage decrease., Be able to use a calculator to calculate percentages.
    • Understand whole number percentages., Be able to calculate percentage parts of whole number quantities., Understand how to calculate percentage increase., Understand how to calculate percentage decrease., Be able to use a calculator to calculate percentages.
    • Understand whole number percentages., Be able to calculate percentage parts of whole number quantities., Understand how to calculate percentage increase., Understand how to calculate percentage decrease., Be able to use a calculator to calculate percentages.
    • Understand whole number percentages., Be able to calculate percentage parts of whole number quantities., Understand how to calculate percentage increase., Understand how to calculate percentage decrease., Be able to use a calculator to calculate percentages.
    • Understand whole number percentages., Be able to calculate percentage parts of whole number quantities., Understand how to calculate percentage increase., Understand how to calculate percentage decrease., Be able to use a calculator to calculate percentages.

    Assessment Criteria

    Key criteria assessors look for in your portfolio

    • Award credit for correctly converting a whole number percentage to its decimal or fraction equivalent (e.g., 25% = 0.25 or 1/4).
    • Award credit for accurately calculating a percentage of a quantity using multiplication (e.g., 15% of £80 = 0.15 × 80 = £12).
    • Award credit for demonstrating the correct method for percentage increase: finding the increase amount and adding it to the original value.
    • Award credit for demonstrating the correct method for percentage decrease: finding the decrease amount and subtracting it from the original value, or using the multiplier method (multiplying by (100% – decrease%)).
    • Award credit for using a calculator efficiently to perform percentage calculations, including using the percentage button where available, and correctly interpreting the result.
    • Award credit for correctly converting percentages to decimals or fractions when performing calculations, showing all steps clearly.
    • Look for accurate application of the formula for percentage change: ((new value - original value) / original value) × 100.
    • Assess the ability to interpret word problems correctly, identifying the base value and the part to calculate percentage parts or evaluate one number as a percentage of another.
    • Credit should be given for using appropriate methods to order and compare percentages, including converting to a common representation (decimals or fractions) and ranking them accurately.
    • Award credit for correctly expressing a whole number percentage as a fraction out of 100 (e.g. 25% = 25/100).
    • Credit given for accurately calculating a percentage of a whole number quantity, demonstrating multiplication by the percentage divided by 100.
    • Learners should show ability to compute percentage increase by adding the calculated increase to the original amount.
    • Marks allocated for demonstrating percentage decrease by subtracting the calculated decrease from the original quantity.
    • Award marks for efficient and correct use of a calculator’s percentage key to verify manual calculations.
    • Evidence of checking results using an alternative method (e.g. reverse percentage) should be rewarded.
    • Award credit for correctly explaining that a percentage is a fraction with denominator 100, e.g., stating that 25% means 25 out of 100.
    • Award credit for demonstrating accurate computation of a given percentage of a quantity, such as finding 15% of £80 = £12, showing the multiplication method (quantity × percentage ÷ 100).
    • Award credit for correctly applying the multiplier method or two-step method to calculate an increased amount, e.g., a 20% increase on £50 yields £60.
    • Award credit for accurately computing a decreased amount, e.g., a 30% decrease on £200 yields £140.
    • Award credit for proficient use of the percentage key or equivalent operations on a calculator to solve percentage problems, with checks for reasonableness.
    • Award credit for correctly converting a percentage to a fraction or decimal to find a percentage part of a quantity, showing clear working or calculator steps.
    • For percentage increase, credit is given for correctly calculating the increase amount and adding it to the original, or using a multiplier method.
    • For percentage decrease, credit is given for correctly subtracting the decrease from the original amount, demonstrating understanding of the final value being less than 100%.
    • When using a calculator, look for correct use of the percentage key or equivalent decimal multiplication, with answers rounded appropriately to two decimal places in money contexts.
    • Award credit for correctly converting a whole number percentage into a fraction or decimal (e.g., 25% = 0.25).
    • Award credit for accurately finding a percentage of a quantity without a calculator by using benchmark percentages (e.g., 10%, 5%).
    • Award credit for demonstrating the correct method for percentage increase by adding the percentage amount to the original.
    • Award credit for correctly calculating percentage decrease by multiplying by (100% - decrease%) and showing working.
    • Award credit for using a calculator efficiently, including the percentage key or equivalent decimal multiplication.
    • Award credit for correctly identifying the percentage as a fraction out of 100 and converting it to a decimal for calculations.
    • Award credit for accurately calculating a given percentage of a whole number quantity using a chosen method, such as finding 10% first or multiplying by the decimal equivalent.
    • Award credit for demonstrating the correct procedure for calculating percentage increase, including adding the increase to the original amount.
    • Award credit for demonstrating the correct procedure for calculating percentage decrease, including subtracting the decrease from the original amount.
    • Award credit for correctly using a calculator to determine percentages, including inputting sequences like 'amount × percentage ÷ 100' or using the % key appropriately, and showing working.

    Assessment Guidance

    Guidance for achieving higher grades

    • 💡Always write down the multiplier or the full method even when using a calculator, as examiners can award marks for correct working even if the final answer is wrong.
    • 💡Check your answer by estimating – for example, 10% is easy to calculate mentally, so use it to gauge if your answer is reasonable.
    • 💡When calculating percentage change, remember that a percentage increase results in a value greater than the original, and a decrease results in a smaller value; a quick reality check can prevent silly mistakes.
    • 💡If you use the calculator's percentage button, verify the result using a manual method (e.g., converting to a decimal) to ensure you have entered the problem correctly.
    • 💡Always write down the formula you are using before substituting values; this demonstrates understanding even if the final answer is incorrect.
    • 💡In word problems, highlight or underline key information (original value, new value, percentage) to avoid misreading the question.
    • 💡Double-check your calculations by reverse-checking: if you found 20% of 50 is 10, check if 10 is 20% of 50 using a different method.
    • 💡When ordering percentages, convert them all to decimals or fractions with a common denominator to ensure accurate comparison.
    • 💡Always write the percentage as a fraction over 100 before multiplying to find a part – this helps avoid decimal errors.
    • 💡For increase and decrease problems, clearly show the step where you add or subtract the change to reinforce understanding.
    • 💡When using a calculator, check your answer by doing the calculation in reverse (e.g. if you found 20% of 50 is 10, confirm 10/50 = 0.2).
    • 💡Read questions carefully to distinguish between ‘find the percentage increase’ and ‘increase by a percentage’ – the required method differs.
    • 💡In coursework, present calculations in a logical sequence and label each step to demonstrate your process to the assessor.
    • 💡Always show your method step by step, even when using a calculator, as marks are awarded for the process, not just the final answer.
    • 💡Before solving, ask yourself what kind of percentage calculation is required (part, increase, decrease) and choose the appropriate strategy.
    • 💡Estimate a rough answer first to check that your final result is sensible—this can catch common mistakes like decimal errors.
    • 💡Practice using different calculator models if possible, so you are comfortable both with the percentage button and manual calculation (e.g., multiply by percentage ÷ 100).
    • 💡Always write down the calculation you intend to perform in words or symbols before using a calculator – this demonstrates understanding and can earn marks even if the final answer is wrong.
    • 💡In functional skills assessments, relate your answer back to the context (e.g. money, savings, population) and check if it makes sense – does a discount make the price lower?
    • 💡For increase and decrease problems, you can use the multiplier method: multiply by 1.15 for a 15% increase or 0.85 for a 15% decrease – this is quicker and less error-prone.
    • 💡Always show your working clearly, even when using a calculator, to demonstrate understanding and earn method marks.
    • 💡Double-check whether the question asks for the percentage amount, the increased total, or the decreased total, to avoid misreading.
    • 💡Use quick mental estimates (like 10%) to verify your calculator answer is reasonable.
    • 💡In written tasks, label your final answer with appropriate units (e.g., £, %) to ensure clarity.
    • 💡Always show your working: even if using a calculator, write down the steps to demonstrate understanding and to gain partial credit if the final answer is incorrect.
    • 💡For percentage increase, add the percentage to 100% first; for decrease, subtract from 100%; then multiply the original amount by this new percentage as a decimal.
    • 💡When using a calculator, double-check your answer by estimating mentally (e.g., 20% of 50 must be 10) to catch input errors.
    • 💡Understand that 'percent' means 'out of 100' – this fundamental concept helps you set up problems correctly every time.
    • 💡Always show your working out, even if you use a calculator. This helps you get method marks if you make a small arithmetic error.
    • 💡Check if the question asks for a percentage increase or decrease. Look for keywords like 'increase', 'decrease', 'discount', 'rise', 'fall'. Underline them to avoid mistakes.
    • 💡For non-calculator questions, use simple percentages like 10%, 25%, 50% as building blocks. For example, to find 15%, find 10% then half of 10% (5%) and add them together.

    Common Mistakes

    Common errors to avoid in your coursework

    • Mistaking the percentage symbol as a unit rather than a proportion, leading to errors like treating 50% as 50 rather than 0.5 in calculations.
    • Incorrectly placing the decimal point when converting percentages to decimals, especially for single-digit percentages (e.g., writing 7% as 0.7 instead of 0.07).
    • Forgetting to add the increase to the original amount or subtract the decrease, only calculating the change itself.
    • Misapplying the percentage button on a calculator, such as trying to calculate a percentage increase directly without understanding the underlying arithmetic, leading to misinterpretation of the displayed number.
    • Confusing percentage increase with the new total: learners often calculate the increase only but forget to add it to the original amount.
    • Misidentifying the original value in percentage change calculations, e.g., using the wrong base when evaluating one number as a percentage of another.
    • Adding or subtracting percentages incorrectly in multi-step problems, such as applying a discount and then VAT without considering the compounding effect.
    • Failing to convert percentages to decimals correctly when using a calculator, e.g., treating 5% as 0.5 instead of 0.05.
    • Confusing a percentage point change with a percentage change (e.g. thinking a rise from 10% to 15% is a 5% increase rather than 50%).
    • Forgetting to convert the percentage to a decimal or fraction before multiplying (e.g. calculating 15% of 80 as 15 × 80 = 1200).
    • Adding or subtracting the percentage value directly rather than the calculated amount (e.g. increasing £50 by 10% to £60 instead of £55).
    • Using the percentage increase formula incorrectly by dividing by the new amount instead of the original.
    • Misinterpreting ‘percent’ as a fixed quantity rather than a proportion, leading to errors with larger or smaller wholes.
    • Confusing percentage with decimal, such as treating 50% as 0.5 but then misplacing the decimal point during multiplication (e.g., 0.5 × 60 = 3 instead of 30).
    • Misinterpreting percentage points versus percentages in increase/decrease scenarios, leading to incorrect addition or subtraction.
    • Forgetting to convert the percentage to a decimal before multiplying on a calculator when not using the % key, resulting in errors like entering 25 × 200 instead of 0.25 × 200.
    • Over-relying on the calculator without estimating the answer first, making it harder to spot keying errors or unreasonable results.
    • Confusing percentage points with percentage – e.g. treating an increase from 10% to 20% as a 10% increase rather than a 10 percentage point increase.
    • Incorrectly applying the percentage increase formula: adding the percentage number directly instead of adding the calculated increase amount.
    • Misplacing the decimal point when converting percentages to decimals, e.g. 5% as 0.5 instead of 0.05.
    • When using a calculator, misinterpreting the result of the percentage function, such as pressing 50 + 10% and not realising the calculator adds 10% of 50 automatically.
    • Confusing percentage increase with finding a percentage of the original amount (e.g., adding the percentage directly instead of adding the increase).
    • Incorrectly applying the percentage when decreasing, such as subtracting the percentage number from the original without converting to decimal.
    • Misinterpreting 'percent off' as the sale price rather than the discount amount.
    • Forgetting to divide by 100 when converting a percentage to a decimal for calculator use.
    • When using a calculator, pressing the percentage key without understanding the order of operations, leading to wrong results.
    • Confusing percentage points with percentages, e.g., thinking an increase from 10% to 20% is a 10% increase rather than a 100% increase.
    • In percentage change calculations, dividing by the new amount instead of the original amount when finding the percentage increase or decrease.
    • Misapplying the calculator % key: not understanding that it may perform a different function depending on the calculator model, leading to incorrect results if not checked with manual methods.
    • Forgetting to convert the decimal back to a percentage when finding a percentage increase or decrease from a multiplier, e.g., interpreting a multiplier of 1.2 as 20% increase but then writing it as 120% instead of 20%.
    • Calculating the percentage part of a quantity incorrectly by multiplying by the percentage without dividing by 100 (e.g., 25% of 40 = 25×40 = 1000 instead of 10).
    • Thinking that a percentage can be greater than 100% only in special cases (like a 200% increase means tripling). In everyday contexts, percentages over 100% are possible, e.g., a 150% increase means the new value is 2.5 times the original.
    • Confusing percentage increase with percentage of. For example, if a price rises from £50 to £60, the increase is £10, which is 20% of the original price, not 20% of the new price.
    • Forgetting to convert the percentage to a decimal or fraction before multiplying. For instance, to find 30% of 80, you must multiply 80 by 0.30, not by 30.

    Frequently Asked Questions

    Common questions students ask about this topic

    Before You Start

    Prior knowledge that will help with this topic

    • •Basic multiplication and division skills (e.g., multiplying by 0.5 or dividing by 2).
    • •Understanding of fractions (e.g., knowing that 1/4 = 25%).
    • •Ability to work with decimals (e.g., converting 0.75 to 75%).

    Key Terminology

    Essential terms to know

    • Understand whole number percentages., Be able to calculate percentage parts of whole number quantities., Understand how to calculate percentage increase., Understand how to calculate percentage decrease., Be able to use a calculator to calculate percentages.
    • Be able to order and compare percentages, Be able to calculate percentage increase, Be able to calculate percentage decrease, Be able to find percentage parts of quantities and measurements, Be able to evaluate one number as a percenatge of another
    • Understand whole number percentages., Be able to calculate percentage parts of whole number quantities., Understand how to calculate percentage increase., Understand how to calculate percentage decrease., Be able to use a calculator to calculate percentages.
    • Understand whole number percentages., Be able to calculate percentage parts of whole number quantities., Understand how to calculate percentage increase., Understand how to calculate percentage decrease., Be able to use a calculator to calculate percentages.
    • Understand whole number percentages., Be able to calculate percentage parts of whole number quantities., Understand how to calculate percentage increase., Understand how to calculate percentage decrease., Be able to use a calculator to calculate percentages.
    • Understand whole number percentages., Be able to calculate percentage parts of whole number quantities., Understand how to calculate percentage increase., Understand how to calculate percentage decrease., Be able to use a calculator to calculate percentages.
    • Understand whole number percentages., Be able to calculate percentage parts of whole number quantities., Understand how to calculate percentage increase., Understand how to calculate percentage decrease., Be able to use a calculator to calculate percentages.

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