Maths lesson plans

A 40-minute Kindergarten lesson that fixes the two places rote counting breaks down: the decade bridge at 29 and counting by tens from anywhere other than ten.

A 30-minute Kindergarten lesson that breaks the habit of restarting at one, so a child asked to count from 47 says 48 rather than beginning the whole sequence again.

A 30-minute Kindergarten lesson connecting the numeral a child writes to the quantity it stands for, including the one numeral that stands for nothing at all.

A 30-minute Kindergarten lesson on cardinality: the last number said is the answer, and it stays the answer however the objects are moved.

A 30-minute Kindergarten lesson on counting up to twenty objects laid out in a line, an array, a circle or a scatter — where the arrangement changes the difficulty but never the answer.

A 30-minute Kindergarten lesson on deciding which of two groups has more by matching them one to one, so the answer does not depend on which group looks bigger.

A 30-minute Kindergarten lesson on comparing two numerals with no objects present, where the child has to think about what the numbers mean rather than what they can see.

A 30-minute Kindergarten lesson that gives adding and taking away their first representations — fingers, counters, drawings and acting out — before any equation is written.

A 30-minute Kindergarten lesson on solving word problems within 10, where the hard part is deciding what happened in the story rather than doing the arithmetic.

A 30-minute Kindergarten lesson on decomposing numbers to 10, where the discovery is that there is more than one right answer and the child gets to find them all.

A 40-minute Kindergarten lesson that builds the make-ten partners as a set of eight facts children can see on a ten frame, not eight facts they have to memorise.

A 30-minute Kindergarten lesson that moves adding and subtracting within 5 from counting every time to simply knowing, using the fact that five can be seen at a glance.

A 30-minute Kindergarten lesson that turns thirteen from a word into a structure — one full ten and three left over — which is the foundation the whole of place value stands on.

A 30-minute Kindergarten lesson on naming what can be measured about an object, and noticing that one object has several measurable attributes that can disagree.

A 30-minute Kindergarten lesson on comparing two objects by lining them up properly, where almost every wrong answer comes from starting them at different places.

A 30-minute Kindergarten lesson on sorting objects into given categories, counting each group, and then putting the groups in order by how many — the first data handling children ever do.

A 30-minute Kindergarten lesson pairing the names of flat and solid shapes with the words for where things sit — above, below, beside, in front of.

A 30-minute Kindergarten lesson on the fact that turning a shape does not change what it is — the single most common gap in early geometry, and the easiest to close.

A 30-minute Kindergarten lesson separating two-dimensional shapes from three-dimensional ones, using the one test a five-year-old can apply: can you pick it up?

A 30-minute Kindergarten lesson on describing how two shapes are alike and different by counting their sides and corners rather than by how they look.

A 30-minute Kindergarten lesson on joining shapes to make new ones — two triangles into a square — which is where fractions and area both begin.

A 40-minute Grade 1 lesson covering the four situations a word problem can describe — joining, taking from, putting together and comparing — and why the last of these is the one that catches everybody.

A 40-minute Grade 1 lesson on the properties that turn one known fact into several — turning the numbers round, adding three in a helpful order, and leaning on doubles.

A 40-minute Grade 1 lesson that reframes 13 − 8 as 'eight and what makes thirteen', which is both easier to work out and the reason fact families exist.

A 40-minute Grade 1 lesson connecting the count sequence to arithmetic — adding two means two steps forward, and the off-by-one error has a cause worth naming.

A 45-minute Grade 1 lesson that replaces counting on fingers with three strategies — make ten, near doubles, and count on from the larger number.

A 40-minute Grade 1 lesson on equations with a blank anywhere, which is also the lesson where the equals sign stops meaning 'here comes the answer'.

A 40-minute Grade 1 lesson taking the count past 100, where the sequence finally becomes regular and the hardest joins are the ones either side of a hundred.

A 40-minute Grade 1 lesson on two-digit place value, built around the one question that exposes whether a child understands it: what does the 4 in 47 actually mean?

A 40-minute Grade 1 lesson on comparing numbers by place value rather than by counting, and on the two symbols that record the comparison once it is made.

A 40-minute Grade 1 lesson on adding a one-digit number or a multiple of ten to a two-digit number, where the rule is that you add tens to tens and ones to ones.

A 40-minute Grade 1 lesson on ordering three objects by length and on comparing two things that cannot be moved next to each other, using a third object as a go-between.

A 40-minute Grade 1 lesson on reading o'clock and half past, where the whole difficulty is that the hour hand moves too, and at half past it is between two numbers.

A 40-minute Grade 1 lesson on collecting data into three categories and answering questions from the chart rather than from the objects it came from.

A 40-minute Grade 1 lesson separating the attributes that define a shape from the ones that merely describe it, so a thin red triangle is as much a triangle as a fat blue one.

A 40-minute Grade 1 lesson on splitting circles and rectangles into two and four equal shares, where the word doing all the work is 'equal'.

A 45-minute Grade 2 lesson on word problems that need two calculations, where the difficulty is not the arithmetic but noticing that the first answer is not the answer.

A 40-minute Grade 2 lesson that builds recall of addition and subtraction facts through strategy sorting, with a defensible position on where timed drills do and do not belong.

A 45-minute Grade 2 lesson defining even as 'pairs up with none left over' rather than as a list of digits to memorise, so the rule can be tested on any number.

A 45-minute Grade 2 lesson on finding the total in a rectangular array by adding equal rows — the last step before multiplication, and the one that makes multiplication make sense.

A 45-minute Grade 2 lesson on three-digit place value, including the zero-as-placeholder problem that causes most written errors in this standard.

A 45-minute Grade 2 lesson on counting within 1000 and skip counting by fives, tens and hundreds, where the hard part is every boundary the count crosses.

A 45-minute Grade 2 lesson on comparing three-digit numbers by working left to right, stopping at the first place where the digits differ.

A 45-minute Grade 2 lesson on fluent two-digit addition and subtraction, where regrouping is taught as a trade between columns rather than as a digit that jumps.

A 45-minute Grade 2 lesson extending the trade to a third column, including the case everybody dreads: subtracting from a number full of zeros.

A 45-minute Grade 2 lesson on measuring length with a ruler, where nearly every error comes from starting at the end of the ruler instead of at zero.

A 45-minute Grade 2 lesson on reading a clock to the nearest five minutes, where the twelve numbers on the face have to mean two different things at once.

A 45-minute Grade 2 lesson on counting mixed coins, where the rule that makes it work is to sort by value and start with the largest.

A 45-minute Grade 2 lesson on building a graph from data with up to four categories, then answering put-together, take-apart and compare questions from it.

A 45-minute Grade 2 lesson on naming and drawing shapes by their number of sides, angles and faces, including the quadrilaterals that have no everyday name.

A 45-minute Grade 2 lesson on splitting shapes into halves, thirds and fourths, and on the fact that equal parts of the same whole need not be the same shape.

A 45-minute Grade 3 introduction to multiplication that establishes what 5 × 7 means before any fact is memorised — and why the order of the two numbers is a convention, not a rule.

A 45-minute Grade 3 introduction to division that separates the two questions it answers — how many in each group, and how many groups — before any fact is practised.

A 45-minute Grade 3 lesson on word problems where the pupil must decide between multiplying and dividing, using what is known and what is missing rather than a keyword.

A 45-minute Grade 3 lesson on equations with a missing number in a multiplication or division, where the fix is to work out which of the three roles is empty.

A 45-minute Grade 3 lesson on the three properties that turn a handful of known facts into all of them — turning round, regrouping three factors, and breaking one factor apart.

A 45-minute Grade 3 lesson that turns every division into a multiplication with a gap, so a pupil who knows their tables already knows their division facts.

A 45-minute Grade 3 lesson on fluency to 10 × 10, which starts by showing pupils how few facts are actually left once the easy ones and the turnarounds are taken out.

A 45-minute Grade 3 lesson on two-step problems where the two steps use different operations, and on estimating first so an unreasonable answer gets noticed.

A 45-minute Grade 3 lesson on spotting arithmetic patterns and, more importantly, on saying why they happen — because a pattern nobody can explain is a coincidence.

A 45-minute Grade 3 lesson that teaches rounding as finding the nearer of two landmarks on a number line, rather than as a rule about the digit after the one you want.

A 45-minute Grade 3 lesson on choosing between the standard algorithm and a mental strategy, because 502 − 498 does not deserve a written method.

A 45-minute Grade 3 lesson on multiplying a one-digit number by a multiple of ten, taught as a known fact plus a unit change rather than as a rule about adding a zero.

A 45-minute Grade 3 lesson on what the two numbers in a fraction mean, built on the requirement that the parts be equal — the condition most fraction errors quietly drop.

A 45-minute Grade 3 lesson that moves fractions off the pizza and onto the number line, where a fraction stops being a piece of something and becomes a number with a position.

A 45-minute Grade 3 lesson on comparing fractions by reasoning about their size, and on the rule that makes the whole thing work: you can only compare parts of the same whole.

A 45-minute Grade 3 lesson on reading a clock to the minute and finding elapsed time, where the trap is that time does not carry in tens.

A 45-minute Grade 3 lesson establishing what area is before any formula appears — the amount of surface covered, measured in squares that must not overlap or leave gaps.

A 45-minute Grade 3 lesson on counting unit squares to find area, and on the moment a pupil notices they are counting the same number over and over.

A 45-minute Grade 3 lesson connecting area to multiplication, where the formula is derived from the rows of an array rather than handed over as a rule.

A 45-minute Grade 3 lesson on the distance around a shape, taught alongside area so that the two are told apart deliberately rather than confused later.

A 45-minute Grade 3 lesson on shape categories that contain other categories, where the sentence to survive is that a square is a rectangle and a rectangle is not a square.

A 45-minute Grade 3 lesson joining geometry to fractions: split a shape into equal areas, and each part is a unit fraction of the whole.

A 50-minute Grade 4 lesson on the second meaning of multiplication — times as many rather than groups of — and on telling it apart from 'more than', which is addition.

A 50-minute Grade 4 lesson on multi-step problems that teaches students to find the unstated middle question, and to judge whether a remainder should be rounded up, down, or reported.

A 50-minute Grade 4 lesson on finding all the factor pairs of a number, which is also how you find out whether it is prime without guessing.

A 50-minute Grade 4 lesson on generating a pattern from a rule and then noticing the features that the rule never mentioned but produced anyway.

A 50-minute Grade 4 lesson on the rule that generates the whole place value system: each place is worth ten of the place beside it, which is why digits move rather than change.

A 50-minute Grade 4 lesson on reading six-digit numbers aloud and comparing them, where grouping the digits in threes does most of the work.

A 50-minute Grade 4 lesson on rounding to any place, where naming the two neighbouring multiples first removes almost every error the digit rule produces.

A 50-minute Grade 4 lesson on the standard algorithm for multi-digit addition and subtraction, taught as a compressed record of place value trades rather than a set of moves.

A 50-minute Grade 4 lesson on multiplying multi-digit numbers using an area model first, so that every partial product in the written method has somewhere it came from.

A 50-minute Grade 4 lesson on dividing larger numbers by a one-digit divisor, and on the question that has no arithmetic answer: what to do with what is left over.

A 45-minute Grade 4 lesson that gets students to justify equivalence with a visual model before the multiply-top-and-bottom rule is handed to them.

A 50-minute Grade 4 lesson on comparing fractions with nothing in common, using benchmarks and common denominators — and knowing which to reach for.

A 50-minute Grade 4 lesson on adding and subtracting fractions that share a denominator, built on the idea that 3/5 is simply three of the thing called a fifth.

A 50-minute Grade 4 lesson on multiplying a fraction by a whole number, treated as repeated addition of the same unit fraction rather than as a new rule.

A 50-minute Grade 4 lesson on decimal notation for tenths and hundredths, where the decimal point is introduced as the marker that says where the whole numbers stop.

A 50-minute Grade 4 lesson on word problems involving distance, time, mass, volume and money, where the first step is always to get everything into the same unit.

A 50-minute Grade 4 lesson applying the rectangle formulas in both directions, including the problems that give you the answer and ask for a side.

A 50-minute Grade 4 lesson establishing that an angle measures turn, not the length of its arms — which is the single fact that makes protractor work possible.

A 50-minute Grade 4 lesson on the vocabulary of geometry — point, line, segment, ray, parallel, perpendicular — and on finding these inside ordinary shapes.

A 50-minute Grade 4 lesson on finding lines of symmetry by folding, which settles the arguments that looking at a shape never quite does.

A 50-minute Grade 5 lesson on evaluating expressions with brackets, where the point is that the order is a convention agreed so everyone gets the same answer.

A 50-minute Grade 5 lesson on generating two sequences from two rules and finding the relationship between corresponding terms — the first step towards graphing a function.

A 45-minute Grade 5 lesson on decimal place value that targets the longer-is-bigger error directly, using place-value alignment rather than the trailing-zeros trick.

A 50-minute Grade 5 lesson on rounding decimals to any place, using the same two-neighbours method that works for whole numbers, because it is the same idea.

A 50-minute Grade 5 lesson on the standard multiplication algorithm, where every line of the working is tied back to the partial product it represents.

A 50-minute Grade 5 lesson on dividing by a two-digit divisor, where the real skill is estimating each digit of the quotient rather than knowing a fact.

A 50-minute Grade 5 lesson on all four operations with decimals, where lining up the place values matters more than lining up the decimal points.

A 50-minute Grade 5 lesson that makes the common denominator necessary before it is taught, so students stop adding denominators and start asking what the pieces are.

A 50-minute Grade 5 lesson on multiplying fractions, where the fact to confront head-on is that multiplying by a fraction less than one makes things smaller.

A 50-minute Grade 5 lesson on dividing a whole number by a unit fraction and the reverse, where the answer to 'how many halves in 4' surprises everyone the first time.

A 50-minute Grade 5 lesson on converting within a measurement system, where the check that prevents every error is asking whether the number should get bigger or smaller.

A 50-minute Grade 5 lesson establishing volume as the number of unit cubes that fill a solid, and separating it from the surface area it is so often confused with.

A 50-minute Grade 5 lesson deriving the volume formula from layers of cubes, so that length times width times height is a conclusion rather than a rule to remember.

A 50-minute Grade 5 lesson on the coordinate plane, where the whole lesson turns on the fact that the order of the two numbers is a convention that has to be obeyed.

A 50-minute Grade 5 lesson on attributes being inherited by subcategories, so that everything true of all rectangles is automatically true of every square.