Below there are 93 Ratio, Proportion & Rates of Change Topics
Ratio is a comparision of two quantities, Proportion is an equality of two ratios and
Rate of Change is the speed at which a variable changes over a specific period of time.
Candidates often get these mixed up in their GCSE Maths Exam.
Step 01
Ratio, Proportion &
Rates of Change
Key Stage 2 - GCSE Basics
- Convert a percentage to a number of hundredths or tenths.
- This is the only topic at Step 01
Step 02
Ratio, Proportion &
Rates of Change
Key Stage 2 - GCSE Basics
- Read and construct scale drawings
- This is the only topic at Step 02
Step 03
Ratio, Proportion &
Rates of Change
Key Stage 2 - GCSE Basics
- Use fraction notation to describe parts of shapes
- Recognise the equivalence of percentages, fractions and decimals
- Define percentages as number of parts per hundred
- Draw lines and shapes to scale
- Use and interpret maps and scale drawings, using a variety of scales and units
- Estimate length using a scale diagram
- These are the only topics at Step 03
Step 04
Ratio, Proportion &
Rates of Change
Key Stage 3 - Pre GCSE
- Divide a quantity into two parts in a given ratio, where ratio given in ratio notation
- Convert a larger whole number metric unit to a smaller unit (e.g. 3 kilograms to 3000 grams)
- Convert between simple metric units.
- Convert a smaller whole number metric unit to a larger unit (e.g. 3000 grams to 3 kilograms)
- Express one number as a fraction of another
- Express the division of a quantity into a number of parts as a ratio
- Use percentages to compare simple proportions
- Recall equivalent fractions, decimals and percentages including for fractions that are greater than 1. Match across all 3 types, and need to be simple fractions (1/2, 1/4, 1/5, 1/10)
- Express one given number as a percentage of another
- Find a percentage of a quantity using a multiplier
- Interpet percentages and percentage change as a fraction or a decimal
- Use ratio notation
- Reduce a ratio to its simplest form
Step 05
Ratio, Proportion &
Rates of Change
Key Stage 3 - Pre GCSE
- Use the unitary method to solve simple word problems involving ratio and direct proportion
- Divide a quantity into more than two parts in a given ratio
- Divide a quantity into more than two parts in a given ratio
- Convert one metric unit to another, including decimals (e.g. 3250 grams to 3.25 kilograms, or 3.25kg to 3250g)
- Use fraction notation to express a smaller whole number as a fraction of a larger one
- Use a ratio to find one quantity when the other is known
- Use proportional reasoning to solve a problem
- Use strategies for finding equivalent fractions, decimals and percentages involving decimal percentages and decimals greater than 0
- Find the outcome of a given percentage increase
- Find the outcome of a given percentage decrease
- Use a multiplier to increase or decrease by a percentage
- Use percentages greater than 100%
- Express one quantity as a percentage of another
- Simplify a ratio expressed in different units
- Reduce ratios in the simplest form, including three-part ratios
Step 06
Ratio, Proportion &
Rates of Change
Key Stage 3 - Pre GCSE
- Compare ratios by changing them to the form 1 : m or m : 1
- Solve a ratio problem in context
- Divide a given quantity into two parts in a given part:part or part: whole ratio
- Write as ratio as a fraction
- Know rough metric equivalents of imperial measures in daily use (feet, miles, pounds, pints, gallons)
- Convert between area measures (e.g. mm² to cm², cm² to m², and vice versa)
- Convert between metric measures of volume and capacity eg 1 cm³ = 1 ml
- Set up equations to show direct proportion
- Use expressions of the form y α x
- Identify direct proportion from a graph
- Recognise graphs showing constant rates of change, average rates of change and variable rates of change
- Use a unitary method, e.g. if £40 is 60%, find 1% by dividing by 60 and then 100% by multiplying by 100. Give them the scaffolding to answer the question
- Compare two quantities using percentages, including a range of calculations and contexts
- Use percentages in real-life situations: VAT, value of profit or loss, simple interest, income tax calculations
- Use and interpret maps, using proper map scales (1 : 25 000)
- Simplify a ratio expressed in fractions or decimals
- Write ratios in the form 1: m or m: 1
Step 07
Ratio, Proportion &
Rates of Change
KS4 - Foundation GCSE
- Interpret and write ratios to describe a situation
- Understand and use compound measures (density, speed, pressure)
- Solve problems using constant rates and related formulae
- Solve problems involving compound measures
- Write lengths, areas and volumes of two shapes as ratios in simplest form
- Estimate conversions
- Use algebraic methods to solve problems involving variables in direct proportion
- Use expressions of the form y α 1/x
- Interpret the gradient of a straight line graph as a rate of change
- Use calculators to explore exponential growth and decay
- Use compound interest
- Represent repeated proportional change using a multiplier raised to a power
Understand direct proportion as equality of ratios
- Understand direct proportion as equality of ratios
- Use measures in ratio and proportion problems ( currency conversion, rates of pay, best value)
- Express a multiplicative relationship between two quantities as a ratio or a fraction
- Use the unitary method for an inverse operation, e.g. If I know an item was 80% of the original cost in a sale, find the original price
- Use and interpret scale drawings, where scales use mixed units, and drawings aren't done on squared paper, but have measurements marked on them.
- Know that enlargements of 2D shapes produce similar shapes
Step 08
Ratio, Proportion &
Rates of Change
KS4 - Foundation GCSE
- Write a ratio as a linear function
- Extend to simple conversions of compound measures (e.g. convert 2 m/s to km/hr)
- Convert imperial units to imperial units
- Convert between metric and imperial measures
- Use graphs to calculate measures including unit price, average speed, distance, time, acceleration
- Use percentages in real-life situations: compound interest, depreciation, percentage profit and loss
- Calculate repeated proportional change
- Find the original amount given the final amount after a percentage change ( reverse percentages)
- Use calculators for reverse percentage calculations by doing an appropriate division
- Understand that the ratio of any two sides is constant in similar right-angled triangles
- Understand the implications of enlargement for perimeter
- Identify the scale factor of an enlargement as the ratio of the lengths of any two corresponding line segments
- Enlarge 2-D shapes and recognise the similarity of resulting shapes
Step 09
Ratio, Proportion &
Rates of Change
KS4 - Foundation GCSE
- Use expressions of the form y α x²
- Identify direct proportion from a table of values by comparing ratios of values
Step 10
Ratio, Proportion &
Rates of Change
Key Stage 4 - Higher GCSE
- Solve problems involving inverse proportion using graphs by plotting and reading values from graphs
- Solve problems involving inverse proportionality, including problems where y is inversely proportional to the square of x
- Calculate an unknown quantity from quantities that vary in direct or inverse proportion
- Set up and use equations to solve word and other problems involving direct or inverse proportion
- Calculate the new area of a shape after enlargement
Step 11
Ratio, Proportion &
Rates of Change
Key Stage 4 - Higher GCSE
- Recognise sketch and interpret graphs of exponential functions y = kx for positive values of k and integer values of x
- Find points that divide a line in a given ratio, using the properties of similar triangles
Step 12
Ratio, Proportion &
Rates of Change
Key Stage 4 - Higher GCSE
- Calculate the new volume of a shape after enlargement
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