Fractions explained: add, multiply, divide and simplify
Learn how fractions work, with step-by-step examples for adding, multiplying, dividing and simplifying them. Ideal for KS3 and middle school.
KS3Middle SchoolUS · Grades 6–8
Middle school study guides (grades 6 to 8)
Get comfortable with fractions, ratios, percentages, the water cycle, cells and more. Short explanations, worked examples and practice questions help you understand the idea first, then check it.
StudyMorrow guides are independent study aids, not official course materials, so check your own syllabus or exam specification.
➗ Middle School Math
See all 19 →Solving linear equations step by step (with examples)
Learn the balance method for solving linear equations, including brackets and x on both sides, with worked examples for GCSE and Algebra 1.
KS3GCSEMiddle SchoolHigh SchoolPercentages: how to find, increase and decrease them
Work out a percentage of an amount, increase or decrease by a percentage and calculate percentage change, with worked examples for KS3 and GCSE.
KS3GCSEMiddle SchoolPythagoras' theorem: how to find a missing side
Use a² + b² = c² to find any side of a right-angled triangle. Worked examples for GCSE, and the Pythagorean theorem in US Geometry.
KS3GCSEMiddle SchoolHigh SchoolMean, median, mode and range: how to work them out
Find the mean, median, mode and range of a data set with clear worked examples, and learn which average to use when there is an outlier.
KS3GCSEMiddle SchoolHigh SchoolArea and circumference of a circle: formulas and examples
Learn the area and circumference formulas for circles, how to use radius and diameter, and how to work with semicircles, with worked examples.
KS3GCSEMiddle SchoolHigh SchoolProbability basics: how to calculate the chance of an event
Learn how to calculate probability, use 'not' events and find the probability of two events together, with worked examples for KS3 and GCSE.
KS3GCSEMiddle SchoolHigh SchoolBIDMAS and PEMDAS: the order of operations explained
Learn the correct order for working out a calculation, with worked examples and common traps. BIDMAS in the UK is the same as PEMDAS in the US.
KS3GCSEMiddle SchoolHigh SchoolNegative numbers: how to add, subtract, multiply and divide
Learn the rules for working with negative numbers, including subtracting a negative and multiplying signs, with number-line examples.
KS3GCSEMiddle SchoolHigh SchoolFactors, multiples and prime numbers explained
Learn what factors, multiples and prime numbers are, how to list them and how to test whether a number is prime, with worked examples.
KS3GCSEMiddle SchoolHigh SchoolHCF and LCM using prime factorisation (GCF and LCM)
Write numbers as products of primes, then find the highest common factor (greatest common factor in the US) and the lowest common multiple.
GCSEMiddle SchoolHigh SchoolMixed numbers and improper fractions: convert and calculate
Convert between mixed numbers and improper fractions, then multiply and compare them, with step-by-step examples and practice questions.
KS3GCSEMiddle SchoolFractions, decimals and percentages: how to convert them
Switch between fractions, decimals and percentages, including recurring decimals, with worked examples and practice questions to check your answers.
KS3GCSEMiddle SchoolHigh SchoolRatio and proportion: how to simplify, share and scale
Simplify ratios, share an amount in a ratio and solve scaling problems with the unit method, with worked examples for GCSE and middle school.
KS3GCSEMiddle SchoolHigh SchoolSimplifying algebraic expressions: collecting like terms
Collect like terms, multiply and divide algebraic terms and simplify expressions with brackets, with step-by-step examples and practice questions.
KS3GCSEMiddle SchoolHigh SchoolAngles in parallel lines and polygons: rules and reasons
Learn the angle rules for straight lines, triangles, parallel lines and polygons, and how to give a reason for each step, with worked examples.
KS3GCSEMiddle SchoolHigh SchoolArea of 2D shapes: rectangle, triangle, trapezium and more
Calculate the perimeter and area of rectangles, triangles, parallelograms, trapeziums (trapezoids) and compound shapes, with worked examples.
KS3GCSEMiddle SchoolHigh SchoolScatter graphs: correlation and the line of best fit
Plot scatter graphs, describe correlation, draw a line of best fit and make estimates, and learn why correlation does not mean causation.
KS3GCSEMiddle SchoolHigh SchoolVenn diagrams and set notation: how to read and use them
Use sets, Venn diagrams and the symbols for union, intersection and complement to solve problems and find probabilities, with examples.
KS3GCSEMiddle SchoolHigh School🧬 Middle School Biology
See all 3 →Photosynthesis explained: equation, process and limiting factors
Learn how plants make glucose and oxygen from light, water and carbon dioxide, with the equation, limiting factors and practice questions.
KS3GCSEMiddle SchoolHigh School+1Plant and animal cells: parts, functions and magnification
Learn the parts of plant and animal cells, what each one does and how to calculate magnification, with worked examples and practice questions.
KS3GCSEMiddle SchoolHigh School+1Food chains and food webs: producers, consumers and energy
Read food chains and food webs, name trophic levels and calculate how much energy passes between them, with worked examples.
KS3GCSEMiddle SchoolHigh School⚗️ Middle School Chemistry
See all 3 →Atoms and the periodic table: protons, neutrons, electrons
Learn atomic structure, atomic and mass number, isotopes and how the periodic table is organised, with worked examples.
KS3GCSEMiddle SchoolHigh SchoolStates of matter: solids, liquids, gases and changes of state
Use the particle model to explain melting, boiling and condensing, and why temperature stays constant during a change of state.
KS3GCSEMiddle SchoolHigh SchoolChromatography and separation techniques: Rf values explained
Choose between filtration, crystallisation and distillation, and calculate Rf values in chromatography, with worked examples.
KS3GCSEMiddle SchoolHigh School⚡ Middle School Physics
See all 6 →Newton's laws of motion explained with worked examples
Learn Newton's three laws, use F = ma and understand inertia and action-reaction pairs, with worked examples and practice questions.
KS3GCSEMiddle SchoolHigh SchoolSpeed, velocity and acceleration: formulas and examples
Calculate speed and acceleration, read distance-time and velocity-time graphs and use v² = u² + 2as, with worked examples.
KS3GCSEMiddle SchoolHigh SchoolResultant forces and free body diagrams (net force)
Add forces to find the resultant (net) force, draw free body diagrams and calculate weight, with worked examples and practice questions.
KS3GCSEMiddle SchoolHigh SchoolDensity: formula, units and how to measure it
Use density = mass ÷ volume, convert units and measure the density of regular and irregular objects, with worked examples.
KS3GCSEMiddle SchoolHigh SchoolRefraction and reflection of light: rules and ray diagrams
Learn the law of reflection and how light bends when it changes medium, with ray diagram examples and practice questions.
KS3GCSEMiddle SchoolHigh SchoolWork done and power: formulas and worked examples
Calculate the work done by a force and the power of a machine or appliance, with step-by-step examples and practice questions.
KS3GCSEMiddle SchoolHigh School📖 Middle School English
See all 14 →Parts of speech: noun, verb, adjective, adverb and more
Learn the eight parts of speech with examples, and see how the same word can change class depending on how it is used.
KS3Middle SchoolApostrophes and commas: its vs it's and comma splices fixed
Fix the most common punctuation mistakes: its and it's, possession with apostrophes and comma splices, with examples and practice.
KS3GCSEMiddle SchoolHigh SchoolPEEL and CER paragraphs: how to structure analysis
Build clear paragraphs with PEEL (UK) or Claim-Evidence-Reasoning (US), with worked examples for English and science answers.
KS3GCSEA-LevelMiddle School+2Persuasive writing techniques: rhetorical devices explained
Use ethos, pathos, logos and devices such as the rule of three and rhetorical questions in speeches and articles, with examples.
KS3GCSEMiddle SchoolHigh School+1Simile, metaphor and personification: techniques explained
Spot and explain similes, metaphors, personification, alliteration and onomatopoeia, and learn how to describe their effect.
KS3GCSEMiddle SchoolHigh SchoolSimple, compound and complex sentences explained
Identify clauses and build simple, compound and complex sentences for clearer, more varied writing, with examples.
KS3GCSEMiddle SchoolHigh SchoolSubject-verb agreement: rules and tricky cases
Make verbs agree with their subjects, including collective nouns, either/or and phrases that sit between the subject and the verb.
KS3GCSEMiddle SchoolHigh SchoolCommonly confused words: their, there, affect and effect
Choose between their, there and they're, affect and effect, your and you're, and other mixed-up words, with a quick test for each pair.
KS3GCSEMiddle SchoolHigh SchoolSpelling rules and patterns that help you spell more words
Learn the most useful spelling rules for endings, plurals and prefixes, with common exceptions and UK and US spelling differences.
KS3GCSEMiddle SchoolHigh SchoolConnectives and transition words: link your ideas smoothly
Use linking words to connect ideas within and between paragraphs so your writing flows, with examples for each type.
KS3GCSEMiddle SchoolHigh SchoolMaking inferences and retrieving information from a text
Find information stated directly in a text and read between the lines to infer what is not said, with examples.
KS3GCSEMiddle SchoolHigh SchoolDescriptive writing: techniques and examples that work
Use the senses, 'show, don't tell', figurative language and varied sentences to paint a picture with words.
KS3GCSEMiddle SchoolHigh SchoolNarrative writing: plot structure and how to start a story
Plan a story with a five-part plot structure, write a strong opening and punctuate dialogue correctly.
KS3GCSEMiddle SchoolHigh SchoolFormal letter and email writing: layout, tone and sign-off
Lay out a formal letter or email, choose the right sign-off and match your tone to your audience, with examples.
KS3GCSEMiddle SchoolHigh School🏛️ Middle School History
See all 4 →The Industrial Revolution: causes, inventions and effects
Find out why the Industrial Revolution began in Britain, how factories and steam power changed life and what reforms followed.
KS3GCSEMiddle SchoolHigh School+1World War Two: causes, key events and timeline
Get a clear overview of why World War Two began, who fought, the key events and how the war ended in Europe and Asia.
KS3GCSEMiddle SchoolHigh School+1The US Constitution and Bill of Rights explained
Understand how the Constitution was written, the three branches of government, checks and balances and the first ten amendments.
Middle SchoolHigh SchoolAPThe Civil Rights Movement: key events, laws and leaders
Follow the struggle against segregation in the United States, from Brown v. Board of Education to the Civil Rights Act and Voting Rights Act.
Middle SchoolHigh SchoolAP🌍 Middle School Geography
See all 3 →The water cycle: evaporation, condensation and precipitation
Follow water from sea to sky to land, learn each stage of the water cycle and see how people affect it.
KS3Middle SchoolPlate tectonics: boundaries, earthquakes and volcanoes
Learn how Earth's plates move, the three types of plate boundary and why earthquakes and volcanoes happen, with real examples.
KS3GCSEMiddle SchoolHigh SchoolRivers: erosion, transport, deposition and river landforms
Learn how rivers shape the land from source to mouth, and how V-shaped valleys, meanders and oxbow lakes form.
KS3GCSEMiddle SchoolHigh School💻 Middle School Computing
See all 5 →How AI works: machine learning and chatbots for students
Understand machine learning, training data and large language models, plus the limits of AI and how to use it responsibly.
KS3GCSEMiddle SchoolHigh SchoolStaying safe online: strong passwords, 2FA and phishing
Build strong passwords, turn on two-factor authentication and spot phishing messages, and know what to do if you click a bad link.
KS3GCSEMiddle SchoolHigh SchoolHow the internet works: IP addresses, DNS and packets
Learn what happens when you open a website, from DNS lookups to packets and HTTPS, in plain English.
KS3GCSEMiddle SchoolHigh SchoolBinary numbers: convert binary to decimal and back
Learn how computers store data as bits and bytes, convert between binary and decimal and add binary numbers, with worked examples.
KS3GCSEMiddle SchoolHigh SchoolProgramming basics: variables, if statements and loops
Understand variables, data types, selection and loops, with pseudocode examples you can trace by hand.
KS3GCSEMiddle SchoolHigh School🧠 Middle School Study skills
See all 8 →Active recall: the best way to revise (with examples)
Learn why testing yourself beats rereading, and four simple ways to use active recall: flashcards, blank-page recall and practice questions.
KS3GCSEA-LevelMiddle School+3Spaced repetition: how to remember what you revise
Review material at increasing gaps to remember it long term, with an example schedule and the Leitner box system.
KS3GCSEA-LevelMiddle School+3How to make a revision timetable you can stick to
Plan backwards from your exam dates and use focused study blocks with breaks, with a simple way to share your time between subjects.
KS3GCSEA-LevelMiddle School+3Cornell notes: how to take notes you can revise from
Set up Cornell notes with cue, notes and summary sections, and turn them into a self-test for revision.
KS3GCSEA-LevelMiddle School+2Mind maps for revision: how to make them work
Use mind maps to organise a topic, then turn them into a memory test so they actually help you remember.
KS3GCSEA-LevelMiddle School+2Mnemonics and the memory palace: remember lists and facts
Use acronyms, acrostics and the method of loci to remember lists and ordered facts, and learn when mnemonics help most.
KS3GCSEA-LevelMiddle School+2The Feynman technique: study by explaining it simply
Check your understanding by explaining a topic in plain language, spotting the gaps and fixing them.
KS3GCSEA-LevelMiddle School+2How to stay focused when studying (and avoid your phone)
Set up your space, plan sessions and manage your phone so your study time is actually productive.
KS3GCSEA-LevelMiddle School+2