## Number and Proportion

## Properties and Calculations## Fractions, Decimals and PercentagesPercentages
Fractions, Decimals and Percentages
Define percentage as ‘number of parts per hundred’Interpret percentages as a fraction or a decimal (KS3) Translating between fractions, dcimals and percents (MAP)Full lesson plan and set of resources for a series of lessons on fractions, decimals and percentages. FSMA Fractions, decimals and percentages (Nuffield)Collection of worksheets with a variety of activities for converting between fractions, decimals and percentages. Fractions, decimals and percentages Cookie Monster (dannytheref via TES)Nice little odd one out activity, great for a starter/plenary or quick revision. KESH Maths Takeaway (Link / Answers)GCSE practice problems booklet (N.B. 1MA0 specification). Why compare fractions and percentages? (BBC Skillswise)Short clip looking at real-life examples of the importance of fraction and percentage conversions. Don Steward:**a to b as a percentage**: Problems to justify converting fractions to percentages.**Percentages to simplest fractions**: Some interesting visual representations of conversions.
FDP jigsaws (@surreallyno via Twitter)A cute little idea for creating FDP jigsaws. Percentage, fraction, decimal grid (Visnos)Well-animated tool for looking at equivalence of fractions, decimals and percentages. TES IBoard has a similar interactive which also asks questions.FDP card sort (Stacy Brookes)Simple match cards with fractions (unsimplified and simplified), decimals and percentages. Writing and Comparing Percentages
Express one quantity as a percentage of anotherCompare two quantities using percentages (KS3) Converting fractions to percentages using a ratio table (The Storeroom)Blog post about a quick method that my pupils have found very useful for writing percentages without a calculator. Why compare fractions and percentages? (BBC Skillswise)Short clip looking at real-life examples of the importance of fraction and percentage conversions. Percentages of Amounts
Interpret percentages as operators (KS3)From bar modelling to ratio tables - tidying up percentage calculation (The Storeroom)Blog post describing my ideas about progression from bar modelling to ratio tables for efficient calculations. Active Maths worksheets (Subscription needed)These are great for basic practice, with lots of options to choose which percentages appear on the worksheets. **Percentages of money (10%, 15%, 25%, 50% and 75%)****Percentages of money (multiples of 10 and whole number % less than 10%)****Percentages of money with a calculator**
Basic practice worksheets (Worksheet Math)Excellent customisable worksheet generator with answers: Worksheets from greatschools.org Percentage spider (Flash Maths)Quick starter finding a variety of percentages of amounts; infinite generator. Could also work very nicely for reverse percentages. Starter of the Day (Transum)- In Your Head
**One**/**Two**: A couple of percentage grids; find 50%, 25%, 10% and 15%. **Percentable**: Similar to above activity, but also includes 33 1/3%, 75% and 90%. There's also another one here.**Odd Percent Out**: Find the odd one out in percentage calculations.
Percentages of amounts (BBC Skillswise)Three percentage problems with step-by-step solutions; pupils have to order the solutions for each problem. Why learn about percentages? (BBC Skillwise)One-minute clip with real-life examples of percentage calculations. Percentages of amounts fantastic trail (whidds via TES)Comprehensive lesson on percentages of amounts, including a differentiated trail/treasure hunt. Percentage Bar (NZ Maths)Brilliant interactive percentage bar with problems to solve. See the Teacher's Notes for suggestions for use.Percentage Increase and Decrease
Interpret percentage changes as a fraction or a decimalWork with percentages greater than 100% Solve problems involving percentage increase and decrease (KS3) Basic practice worksheets (Worksheet Math)Excellent customisable worksheet generator with answers: Percentage increase and decrease treasure hunt (skimble38 via TES) Good treasure hunt activity, but does include some reverse percentages - probably best for revision at the end of a unit on percentages. 3 Act Maths Duelling discounts (Dan Meyer)Pupils solve a variety of problems choosing a percentage discount or fixed discount. Discount and sales tax (Fawn Nguyen)Shopping contest activity; pupils pick items from a superstore's online catalogue to get the closest to $500, including calculation of percentage discounts and tax. Needs a little adapting for a UK setting. One percentage increase followed by another (Don Steward)Pupils find a single percentage increase to represent a double change. Percentage Growth, Decay and Compound Interest
Solve problems involving percentage change, including simple interest in financial mathematics (KS3)Set up, solve and interpret the answers in growth and decay problems, including compound interest (KS4) Savings and interest resources (Nuffield FSMA)Worksheet-based lesson looking at developing use of percentage multipliers for compound interest calculations; pupils calculate the amount of money in an account after one year, then five years, which develops nicely into the "standard" formula. Three act maths - Fry's bank account (Dan Meyer)Activity based on a clip from Futurama; pupils calculate the amount of money in Fry's bank account after 1000 years. Simple and compound interest cards (jlcaseyuk via TES)A selection of bank account information cards; takes a little work to turn this into a proper lesson. ## Proportion, Ratio and Rates of ChangeProportion
Simple Direct Proportion
Solve problems involving direct proportion, including graphical and algebraic representations (KS3)Exploring proportional reasoning (The Storeroom)Blog post with lesson ideas for working with proportional reasoning using bar modelling and ratio tables. Simple Inverse Proportion
Solve problems involving inverse proportion, including graphical and algebraic representations (KS3)Coming soon! Interpreting Proportion Equations
Understand that X is inversely proportional to Y is equivalent to X is proportional to 1/YInterpret equations that describe direct and inverse proportion (KS4) Coming soon! Constructing Proportion Equations (H)
Construct equations that describe direct and inverse proportion (KS4 Higher only)Coming soon! Proportion Graphs
Interpret the gradient of a straight line graph as a rate of change (KS4)Recognise and interpret graphs that illustrate direct and inverse proportion (KS4) Instantaneous and Average Rates of Change (H)
Interpret the gradient at a point on a curve as the instantaneous rate of change; apply the concepts of instantaneous and average rate of change (gradients of tangents and chords) in numerical, algebraic and graphical contexts (KS4 Higher only)Ratio
Working with Ratio
Use ratio notation, including reduction to simplest formDivide a given quantity into two parts in a given part:part or part:whole ratio Express the division of a quantity into two parts as a ratio (KS3) Basic worksheets (Worksheet Math)Excellent worksheet generator with answers: Aunt Dotty (Transum) Quick starter using ratio to split money between two children. Mixing Paints (NRich)A lovely rich problems about mixing red and white paint to make different shades of pink. The follow-up, Mixing More Paints, is also worth a look for a bit of extra challenge. Ratio and proportion ITP (via TeachFind)Explore ratio and proportion by pouring different amounts and combining two coloured liquids. Ratios and Fractions
Understand that a multiplicative relationship between two quantities can be expressed as a ratio or a fraction Relate the language of ratios and the associated calculations to the arithmetic of fractions and to linear functions Identify and work with fractions in ratio problems (KS4) Coming soon! |
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