Teach the whole lesson, not just hand out a worksheet
A teaching unit is the lesson itself: a fun real-world hook, a step-by-step teaching sequence, worked examples, the misconceptions to watch for, guided practice, differentiation and an exit ticket. Open one and teach the class from it, no textbook needed. 197 units across maths and English, free and printable.
Math
Counting to tell how many
The last number you say is the total, and it does not matter which object you start with
Making ten and the teen numbers
Breaking numbers apart within 10, finding the partner that makes 10, and seeing 11 to 19 as a ten and some more
Measuring, comparing and sorting
Naming what can be measured, comparing two objects directly, and sorting a group into counted categories
Naming and describing 2D and 3D shapes
Describing where a shape is, naming flat shapes correctly, and telling flat shapes apart from solid ones
Circles, triangles, squares and rectangles
Identifying, describing and comparing Virginia SOL K.10's four plane figures, no matter their size or orientation
Building and composing shapes
Comparing 2D and 3D shapes by their parts, building and drawing shapes, and joining shapes to make bigger ones
Growth and decay: compound interest
The multiplier method, compound interest and depreciation, and why compound interest overtakes simple interest
Vectors: translations and vector arithmetic
Describing a translation as a column vector, and adding, subtracting and scaling vectors
Direct and inverse proportion
Finding the constant k in y = kx or xy = k, and telling the two apart from a table of values
Prime factorisation, HCF and LCM
Writing a number as a product of prime factors in index notation, then using it to find the HCF and LCM
Bounds and error intervals
Writing the error interval for a rounded measurement, and finding upper and lower bounds in a calculation
Real-life graphs: distance-time and conversion graphs
Reading gradient as speed on a distance-time graph, and as a conversion rate on a conversion graph
Changing the subject of a formula
Rearranging a formula to make a different letter the subject, including when it is squared
Solving linear inequalities and number lines
Solving one- and two-step inequalities, and showing the solution set on a number line
Equation of a straight line, and parallel lines
Finding y = mx + c from a gradient and a point, from two points, and recognising parallel lines
Bearings
Three-figure bearing notation, back bearings, and the angle between two bearings
Circle sectors: arc length and area
Finding the arc length and area of a sector as a fraction of the full circle
Exact trigonometric values
Recalling sin, cos and tan for 0°, 30°, 45°, 60° and 90° without a calculator, and using them for exact answers
Quadratic graphs: roots, intercepts and turning points
Reading a parabola's key points off its graph, and deducing roots algebraically from factorised form
Plans and elevations
Interpreting the plan, front elevation and side elevation of a 3D solid, and counting cubes and view squares
Adding and subtracting within 10
Counting on, taking away, part-whole number bonds, and how adding and subtracting fit together
Counting to 100 by ones and tens
Counting on by ones, counting in tens, counting on from any number, and writing the numbers you count
Comparing numbers and groups
More, fewer and the same, comparing groups by matching and counting, and comparing written numbers
Addition and subtraction strategies
Reordering and grouping numbers to add more easily, linking subtraction to addition, and adding three numbers
The equal sign and finding the unknown
What the equal sign really means, deciding if an equation is true or false, and finding a missing number
Adding and subtracting with tens and ones
Adding within 100 using place value, finding ten more or ten less mentally, and subtracting multiples of ten
Length, time and data
Ordering and measuring length with same-size units, telling time to the hour and half hour, and reading a data table
Shapes: attributes, composing and partitioning
What actually defines a shape's name, joining shapes to build bigger ones, and splitting shapes into halves and quarters
Addition and subtraction within 20
Number bonds, counting on, counting back, making ten, and fact families
Tens and ones
Bundling into tens, partitioning two-digit numbers, and what each digit means
Comparing and ordering numbers to 100
Which is more, greater than and less than, and putting numbers in order using tens and ones
Counting and writing numbers to 120
Counting on from any number to 120, reading and writing numerals, and seeing every number as tens and ones
Adding several two-digit numbers, and jumping by tens and hundreds
Adding up to four two-digit numbers with place value, and mentally adding or subtracting ten or a hundred
Measuring and solving length problems
Measuring with a real ruler, solving length word problems, and using a number line to add and subtract
Telling time and displaying data
Reading a clock to the nearest five minutes, building a line plot from measurements, and reading picture and bar graphs
2D shapes and partitioning into equal shares
Recognising and drawing shapes from their attributes, partitioning a rectangle into rows and columns of squares, and naming equal shares
Addition and subtraction word problems within 100
Part-whole and comparison bar models for putting together, taking from, and comparing, with the unknown in any position
Arrays and repeated addition
Rectangular arrays up to 5 by 5, and writing the total as a sum of equal addends
Reading, writing and comparing numbers to 1000
Hundreds, tens and ones: numerals, number names and expanded form, then comparing three-digit numbers with the greater than, less than and equal to symbols
Two-digit addition with regrouping
Tens and ones, composing a ten, and the column algorithm for carrying
Two-digit subtraction with regrouping
Tens and ones, breaking a ten open, and the column algorithm for borrowing
Skip counting and number patterns
Counting in 2s, 5s and 10s, the pattern in the digits, and the runway to multiplication
Adding and subtracting within 100
Two-digit addition and subtraction with no regrouping, using tens and ones, the number line, and part-whole bars
Counting money and making change
Counting a mixed group of coins to a total, then working out the change from a purchase
Understanding fractions
Naming fractions, fractions on a number line, equivalence and comparing
Understanding multiplication
Equal groups, arrays, writing multiplication, and the commutative property
Understanding division
Sharing equally, making equal groups, and division as the inverse of multiplication
Rounding and place value
Reading three-digit numbers by place value and rounding to the nearest ten and hundred
Area and perimeter
Covering with unit squares, the length times width rule, distance around, and keeping the two ideas apart
Multiplication and division fact families
One array, four facts: how multiplication and division are two sides of the same rectangle
Properties of multiplication
The commutative, associative and distributive properties as strategies to multiply, seen on arrays
Two-step word problems
Solving problems that need two operations, using bar models and checking the answer is reasonable
Telling time to the minute, mass, and volume
Reading a clock to the minute, elapsed time, and measuring mass and liquid volume
Reading scaled graphs and line plots
Scaled picture graphs, scaled bar graphs, and line plots of fraction measurements
Shapes, partitioning, and area by counting squares
Classifying shapes by attributes, partitioning shapes into equal fractional areas, and measuring area by counting unit squares
Patterns in addition and multiplication tables
Spotting and explaining patterns in the addition and multiplication tables using properties of operations
Equivalent fractions and comparing
Building equivalent fractions, fractions on a number line, comparing unlike fractions, and simplest form
Multiplying by the area (box) method
Two-digit by one-digit multiplication using place value and partial products
Division with remainders
Sharing that does not come out even, writing the remainder, and reading what is left over
Place value to one million
Reading, writing, comparing and rounding whole numbers to 1,000,000
Mixed numbers on a number line
Counting past one whole, improper fractions and mixed numbers as one point, converting between them, and reading a measuring scale
Factors, multiples and prime numbers
Factor pairs as rectangles, multiples as skip counts, and telling primes from composites
Comparing and ordering fractions
Comparing with the benchmark 1/2, comparing with common denominators, and putting fractions in order
Multi-step word problems
Bar models for each step, choosing the operation, interpreting remainders, and checking with estimation
Number and shape patterns
Generating a pattern from a rule, and noticing features of the pattern beyond the rule itself
Measurement: units, formulas, and word problems
Converting measurement units, applying area and perimeter formulas, and solving multi-unit measurement word problems
Decimals: tenths, hundredths, and comparing
Adding fractions with denominators of ten and a hundred, and comparing decimals to the hundredths
Angles: turns, measuring, and adding parts
Understanding angles as turns measured in degrees, measuring and drawing angles with a protractor, and finding unknown angles by adding or subtracting parts
Lines, classifying shapes, and symmetry
Points, lines, rays, and angles; classifying two-dimensional figures by their properties; and identifying lines of symmetry
Adding and subtracting fractions
Unlike denominators, common denominators, and checking answers are reasonable
Decimals: tenths and hundredths
Reading, placing and comparing tenths and hundredths, and linking them to fractions
Multi-digit multiplication
The area model and the standard algorithm for multiplying two-digit numbers
Long division
Sharing by place value, the Divide-Multiply-Subtract-Bring down cycle, remainders, and a first two-digit divisor
Multiplying a fraction by a whole number
Repeated addition of fractions, multiply the numerator, and mixed-number results
Finding a fraction of a quantity
Dividing by the denominator, multiplying by the numerator, and problems like 2/3 of 12
Adding and subtracting decimals
Lining up the point, regrouping across it, and checking with money and estimation
Rounding decimals
Rounding decimals to the nearest whole, tenth and hundredth using a number line and place value
Order of operations: parentheses, brackets and braces
Evaluating expressions with nested grouping symbols, and writing a numerical expression without computing it
The coordinate plane: plotting points and graphing patterns
Reading ordered pairs, plotting first-quadrant points, and graphing two related number patterns
Understanding and measuring volume
Volume as packed unit cubes, counting cubic units, and the length x width x height formula
Converting units of measurement
Converting between different-sized units within one measurement system, and using conversions in multi-step problems
Fractions as division, and multiplying fractions in real problems
Interpreting a fraction as division, sharing word problems, and multiplying fractions and mixed numbers in context
Powers of ten
Patterns when multiplying and dividing by 10, 100 and 1000, and writing powers of ten with exponents
Classifying two-dimensional shapes
Shared attributes within a category of shapes, and sorting quadrilaterals into a hierarchy
Understanding percentages
Percent as a rate per hundred, its fraction and decimal forms, finding a percent of a quantity, and the 10 percent building block
Ratios and rates
Ratio as a part-to-part comparison, equivalent ratios by scaling, unit rates, and sharing in a given ratio
Integers and negative numbers
Numbers below zero, opposites, and ordering integers on a number line
Dividing fractions
Dividing a fraction by a whole number and by a fraction, and why you multiply by the reciprocal
Greatest common factor and least common multiple
Common factors as shared rectangles, common multiples as shared skip counts, and choosing GCF or LCM
Dividing multidigit numbers and operating with decimals
The standard division algorithm with a multidigit divisor, and fluent add, subtract, multiply and divide with decimals
Exponents and algebraic expressions
Writing and evaluating exponents, writing algebraic expressions from words, and generating equivalent expressions
Understanding and solving one-step equations
What it means for a value to be a solution, and solving one-step equations from real-world problems
The coordinate plane in four quadrants, and relating two variables
Plotting and finding distances in all four quadrants, and using tables and graphs to relate a dependent and an independent variable
Area of triangles and quadrilaterals, and volume with fractional edges
Finding area by composing and decomposing shapes into rectangles and triangles, and extending the volume formula to fractional edge lengths
Statistical questions and summarizing data
Recognizing a question that expects varied answers, and summarizing a numerical data set with center, spread and shape
Operations with rational numbers
Adding, subtracting, multiplying and dividing positive and negative rational numbers, and solving real-world problems with them
Unit rates, proportional relationships and percent
Computing unit rates (including fractional ones), spotting proportional relationships, and solving multistep percent problems
Linear expressions and equations with rational numbers
Combining, expanding and factoring linear expressions, rewriting expressions to reveal structure, and solving multistep equations and inequalities
Circles, area, volume and surface area
Using the formulas for circumference and area of a circle, and finding the area, volume and surface area of 2D and 3D figures
Scale drawings and angle relationships
Finding actual lengths and areas from a scale drawing, reproducing a drawing at a new scale, and solving equations from angle facts
Probability models and experimental probability
Understanding probability as a number from 0 to 1, building probability models, and comparing them to observed results
Sampling and making inferences about a population
Understanding how a random sample can represent a whole population, and what makes a conclusion drawn from a sample valid
Linear functions and slope
Function rules, constant rate of change, slope, y-intercept and comparing representations
Rational numbers, exponents and roots
Classifying rational and irrational numbers, the laws of exponents, and square and cube roots
Scientific notation
Writing very large and very small numbers in scientific notation, and adding, multiplying and dividing them
Understanding, comparing and constructing functions
What makes a relationship a function, comparing functions across representations, linear vs nonlinear, and building your own
Slope, linear equations and systems
Graphing proportional relationships, finding slope and the equation of a line, solving linear equations, and solving systems of two equations
Transformations, congruence, similarity and angle relationships
Reflections, rotations, translations and dilations on the coordinate plane, what makes shapes congruent or similar, and angle facts from parallel lines
The Pythagorean theorem and volume of round solids
Finding a missing side of a right triangle, and the volume of cylinders, cones and spheres
Scatter plots and lines of best fit
Building and interpreting scatter plots for bivariate data, and fitting and using a line of best fit
Mean, median, mode and range
Four ways to summarise a data set: the average, the middle, the most common, and the spread
Ratio and proportion
Ratio notation and simplifying, sharing a quantity in a given ratio, ratio as a fraction, and scale factors, maps and direct proportion
Boxplots and the five-number summary
Comparing the centre, spread and shape of numerical data with the minimum, quartiles, median and maximum
Quadratics: expand, factorise and solve
Expanding binomial products, factorising monic quadratics, and solving quadratic equations by factorising
Linear equations and expressions
Building algebraic expressions from words, substituting into formulas, and solving one-variable equations
Pythagoras' theorem and trigonometry
Finding a missing side with Pythagoras' theorem, and the sine, cosine and tangent ratios
Compound probability
Complementary events, independent 'AND' events, two-way tables, and comparing simulated results with theory
The quadratic formula and completing the square
Solving any quadratic exactly, reading the discriminant, and finding a turning point from completed-square form
Circle theorems
Angle at the centre, angle in a semicircle, same segment, cyclic quadrilaterals, and the tangent-radius right angle
Square numbers and square roots
Squaring a whole number, finding the square root of a perfect square, and estimating roots that aren't whole numbers
Transformations on the Cartesian plane
Translating, reflecting and rotating a point, and describing each move with coordinates
Two-way tables and scatterplots
Reading and constructing two-way frequency tables, describing association from a scatterplot, and telling association apart from causation
Financial mathematics: percentages, GST and simple interest
Percentage mark-ups and discounts, adding and removing 15% GST, and calculating simple interest
Algebraic expressions and equations: expanding, solving and rearranging
Collecting like terms, expanding a bracket, factorising, forming and solving linear equations, and substituting into and rearranging formulae
Perimeter, circumference and area: shapes that relate back to a rectangle
Perimeter of 2D shapes, circumference of circles and the perimeter of half and quarter circles, and the area of parallelograms, trapeziums and kites
Theoretical and experimental probability
Systematically listing outcomes for a sample space, finding theoretical probability, and comparing it to experimental probability from real trial data
Powers, roots and standard form
Evaluating integer powers, finding exact and approximate roots, and writing very large or very small numbers in standard form
Transformations: translations, reflections and rotations
Describing and performing translations, reflections and rotations of points and shapes on a coordinate grid
Trigonometric ratios in right-angled triangles
Using sine, cosine and tangent to find a missing side or a missing angle in a right-angled triangle
Number sequences
Generating terms from a rule, finding the nth term of an arithmetic sequence, and using it to solve problems
Pythagoras' theorem
Finding the hypotenuse, finding a missing leg, and solving real-world right-triangle problems
Averages and spread: mean, median, mode and range
Calculating and comparing measures of central tendency and spread, and understanding the effect of an outlier
Negative numbers
Ordering positive and negative numbers on the number line, and the 4 operations with directed numbers
Algebraic notation and simplifying expressions
Writing and interpreting algebraic notation, substituting values, collecting like terms, and expanding or factorising a single bracket
Solving linear equations
Solving one-step and 2-step equations, and equations with a bracket or the unknown on both sides
Function tables and reading real-data graphs
Evaluating a linear rule, finding the rule from a table of values, plotting the pattern, and reading a rate from a real-world graph
Position in three dimensions and time zones
Locating a point with three coordinates, and solving duration and clock problems across time zones
Scientific notation, measurement error and logarithmic scales
Writing and calculating with very large and very small numbers, quantifying measurement error, and reading logarithmic scales like Richter and pH
Place value, rounding and estimation with large numbers
Writing large numbers in expanded form using powers of 10, rounding decimals to a given accuracy, and estimating to check an answer is reasonable
Rational numbers: the number line, the four operations, and signed numbers
Converting and ordering rational numbers on a number line, combining fractions, decimals and percentages with the four operations, then extending to signed integers, fractions and decimals
Reading data displays and sampling methods
Reading and interpreting numerical data displays, then choosing and evaluating sampling methods for collecting data fairly
Surface area of prisms and triangle congruence
Finding the surface area of rectangular and triangular prisms by adding face areas, then testing whether two triangles are congruent
Solving quadratics: completing the square and the quadratic formula
Two exact methods that work even when a quadratic will not factor
Adding, subtracting and multiplying polynomials
Polynomials behave like a number system: combine like terms to add and subtract, distribute to multiply
Exponential functions: growth, decay and geometric sequences
Telling linear and exponential change apart, then constructing both kinds of function from input-output pairs
Radicals and rational exponents
What x^(1/2) really means, and applying the exponent rules when exponents are fractions
Writing formal proofs: lines, angles and triangles
The two-column proof format, and four foundational Congruence theorems
Fractions and decimals: equivalence, ordering and the 4 operations
Converting exactly between fractions and terminating decimals, ordering a mixed set, and adding, subtracting, multiplying and dividing fractions and mixed numbers
Percentages: of an amount, increase, decrease, reverse and simple interest
Finding a percentage of an amount, expressing 1 quantity as a percentage of another, percentage change, working backward to an original amount, and simple interest
Factors, multiples and prime factorisation
Prime numbers, writing a number as a product of its prime factors, and finding the highest common factor and lowest common multiple of 2 numbers
Angle facts: points, lines, parallel lines, triangles and polygons
Angles at a point and on a straight line, vertically opposite angles, corresponding/alternate/co-interior angles in parallel lines, and the angle sum of triangles and polygons
Linear graphs and simultaneous equations
Reading gradient and intercept from y = mx + c, plotting and reading coordinates, and solving 2 linear equations together
Algebraic manipulation: expanding double brackets and rearranging formulae
Expanding the product of 2 binomials, and rearranging a standard formula to make a different letter the subject
Geometric sequences
Recognising, continuing and finding the nth term of a sequence that grows or shrinks by a constant ratio
Standard units, compound measures and inverse proportion
Converting between related standard units, solving speed/density/best-value problems, and inverse proportion word problems
Rounding: decimal places, significant figures and error intervals
Rounding numbers to an appropriate degree of accuracy, and writing the error interval for a rounded measurement
Congruence, similarity and 3D solids
Congruence criteria (SSS, SAS, ASA, RHS), similar shapes and enlargement, classifying triangles and quadrilaterals, and 3D solid properties
Statistical charts: pie charts and scatter graphs
Calculating pie chart sector angles and percentages from a frequency table, and describing correlation on a scatter graph
Area and perimeter: triangles, parallelograms, trapezia, circles and composite shapes
Deriving and applying the right formula for each 2D shape, including circles in terms of pi, and composite shapes built from rectangles
Volume of prisms: cuboids, triangular prisms and cylinders
Finding volume as cross-sectional area times length, for cuboids, triangular prisms and cylinders
Probability: the 0-1 scale, sample spaces and enumerating sets
Simple and combined events, theoretical probability from a sample space, and reading a 2-set Venn diagram
Reading and writing Roman numerals
The seven symbols, the addition rule, subtractive notation, and reading Roman numerals in the real world
Equal groups and sharing
Solving one-step multiplication and division problems with objects, pictures and arrays
Comparing, measuring, time and UK money
A Year 1 measurement sequence for length, mass, capacity, chronology, dates, clocks and denominations
Position, patterns and turns
Whole and fractional turns in Year 1, then sequences, straight-line movement and right-angle turns in Year 2
Coordinates, translations and polygons
Reading first-quadrant coordinates, describing translations and plotting points to complete polygons
Line graphs, tables and timetables
Comparison, sum and difference problems from line graphs, then completing and interpreting tables
Financial mathematics: simple interest, discounts and GST
Using mathematical modelling to solve real money problems: simple interest on savings and loans, percentage discounts, and adding or removing GST
Area of triangles, parallelograms and composite shapes
Deriving the triangle and parallelogram area formulas from a rectangle, then combining them to find the area of L-shaped and composite figures
Planning a statistical investigation and critiquing statistical claims
Using the Problem-Plan-Data-Analysis-Conclusion cycle to run a fair investigation, and spotting the flaws in misleading survey reports and graphs
Simultaneous equations: substitution and elimination
Solving two linear equations in two variables at once, by substitution and by elimination, and reading the solution as the point where two lines cross
Coordinate geometry: gradient, midpoint and distance
Finding the gradient of a line segment, the midpoint of an interval, and the distance between two points on the Cartesian plane
Algorithms and networks: computational thinking in geometry
Designing, testing and refining step-by-step algorithms for geometric problems, and interpreting networks with Euler's formula
Reading
Rhyming and beginning sounds
Hearing rhymes and identifying the first sound in a spoken word, the foundation phonological awareness skills before letters and spelling
Retelling a story and key details
Tell a story back in your own words: who, what, where and when, with the beginning, the middle and the end in the right order
Finding the main idea and details
The one big point a paragraph is about, the smaller details that hold it up, and how to check by summarising in one sentence
Making inferences
Reading between the lines: using text clues and what you already know to work out what the author does not say outright
Story structure and sequencing
Beginning, middle and end, the problem and its solution, and how each part of a story builds on the one before
Working out word meaning from context
Be a word detective: use the clues in the surrounding words to work out what an unfamiliar word means, then check your guess
Prefixes and suffixes
Build and unlock words like Lego: add a prefix or a suffix to a base word, and use the parts to work out what a new word means
Summarising a text and finding the theme
Shrink a whole text into a few sentences, then work out the big idea the author wants you to carry away
Reading comprehension strategies
Using summarising, predicting, connecting and questioning together to find theme and central idea in fiction and non-fiction
Citing several pieces of evidence and tracing theme development
Backing up an analysis with more than one piece of text evidence, and following how a theme or central idea grows across a whole text rather than stating it once
Citing the strongest evidence and theme across plot and character
Choosing the single most convincing piece of text evidence from several candidates, and tracing a theme or central idea as it develops through both what happens and who characters become
Phonics
Consonant digraphs: sh, ch, th, wh
Two letters that team up to make one new sound, and how to blend, read and spell the words that use them
Consonant blends: bl, cl, st, tr, sp
Two consonants side by side where you still hear each sound, and how to blend, read and spell the words that use them
Long vowels with silent e: a_e, i_e, o_e, u_e
The magic e on the end that jumps back and makes the vowel say its own name, and how to read and spell the words that use it
Grammar
Nouns, verbs and building a sentence
Naming words and doing words, and how to join them into a complete sentence with a capital letter and a full stop
Adjectives and adverbs
Describing words that add colour: adjectives that describe nouns, adverbs that describe verbs, and where each one goes
Pronoun case, vague references, and keeping shifts in check
Using I, me, we, us and other pronouns correctly, fixing pronouns that could point to more than one person or thing, stopping a sentence from switching tense or person partway through, and setting off extra information with commas, parentheses or dashes
Phrases, clauses, and writing with sentence variety
Telling a phrase apart from a clause, explaining what job each one does in a sentence, using them to build simple, compound, and complex sentences, and combining coordinate adjectives with commas
Verbals, active and passive voice, and verb mood
Recognizing a gerund, participle, or infinitive doing a noun-like, adjective-like, or adverb-like job, choosing active or passive voice on purpose, and forming and using the indicative, imperative, interrogative, conditional, and subjunctive verb moods
Writing
Writing a narrative (a short story)
Be the author of your own story: a strong start, events in order, feelings and details, and an ending that wraps it up
Building a paragraph
A topic sentence, supporting details and a closing sentence, and how to put them together into one clear paragraph
Writing an opinion piece
State an opinion, back it with reasons and evidence, join your ideas with linking words, and finish with a strong conclusion
Writing to inform or explain
Introducing a topic clearly, organizing facts and definitions into logical, well developed sections with strong transitions, and writing a conclusion that follows from the information presented
History
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