Numera → Curriculum

The whole path, published in full.

268 lessons across 26 units — every title, in the order you'd meet them. It starts at counting on, which is genuinely where it starts, and it does not stop until integrals. Each lesson runs about three minutes.

Nothing here is gated behind a level you have to grind for, and nothing skips a step. If a unit looks easy, walk it anyway — it's four minutes and it makes the next one free.

268 lessons 26 units ~3 min each

Foundations

Getting the four operations back under your feet — plus the order they run in.

Addition

The Meadow · 12 lessons

  1. 01Counting on
    Start from a number, not from one.
  2. 02Making tens
    The friendliest trick in arithmetic.
  3. 03Doubles and near-doubles
    4+4 you know. So 4+5 is free.
  4. 04Adding nine, the easy way
    Round up, then step back.
  5. 05Two digits, no sweat
    Tens with tens, ones with ones.
  6. 06Crossing the ten
    Watch numbers regroup themselves.
  7. 07Carrying, made visible
    See exactly what 'carry the one' means.
  8. 08Adding in your head
    Break numbers into friendly parts.
  9. 09Three numbers at once
    Order doesn't matter — use it.
  10. 10Bigger numbers, same idea
    Hundreds behave like tens.
  11. 11Estimating sums
    Close enough, fast — a real-life superpower.
  12. 12Addition, mastered
    Put the whole meadow together.

Subtraction

The Shore · 12 lessons

  1. 01Taking away
    Subtraction you can see.
  2. 02Finding the distance
    Subtraction is also a gap.
  3. 03Counting up to subtract
    Sometimes adding is the fastest way.
  4. 04Subtracting nine and friends
    Round numbers make it easy.
  5. 05Two digits apart
    Tens and ones, separately.
  6. 06Crossing back over ten
    Regrouping in reverse.
  7. 07Borrowing, made visible
    See what 'borrow' really borrows.
  8. 08Subtracting in your head
    Friendly numbers, tiny adjustments.
  9. 09Differences that matter
    Change, discounts, and time.
  10. 10Bigger numbers, same idea
    Hundreds hold no surprises.
  11. 11Estimating differences
    Fast, close, confident.
  12. 12Subtraction, mastered
    Cross the shore in one run.

Multiplication

The Forest · 14 lessons

  1. 01Groups of things
    Multiplication is counting groups.
  2. 02Rows and columns
    See it as a grid — and it clicks.
  3. 03Twos, fives, tens
    The patterns you already know.
  4. 04Switching the order
    3×4 is 4×3. Use whichever is easier.
  5. 05Threes and fours
    Build on what you have.
  6. 06Sixes without fear
    Double the threes.
  7. 07Nines have a secret
    The pattern that never misses.
  8. 08Sevens and eights
    The last two — with tricks.
  9. 09Multiplying by ten and friends
    Zeros do the work.
  10. 10Two digits times one
    Split, multiply, add.
  11. 11Multiplying in your head
    Round, multiply, adjust.
  12. 12Estimating products
    Ballpark answers, instantly.
  13. 13The times table, yours
    The whole forest at a glance.
  14. 14Multiplication, mastered
    Prove it to yourself.

Division

The Canyon · 12 lessons

  1. 01Sharing fairly
    Division is dealing cards.
  2. 02Making groups
    The other way to divide.
  3. 03Multiplication in reverse
    Every division hides a multiplication.
  4. 04Dividing by twos and fives
    Halves and fifths, fast.
  5. 05The whole table, backwards
    If you know 6×7, you know 42÷7.
  6. 06When it doesn't fit
    Remainders are honest answers.
  7. 07Dividing by ten and friends
    Zeros come off the way they went on.
  8. 08Two digits divided
    Split big numbers into easy pieces.
  9. 09Dividing in your head
    Friendly chunks, one at a time.
  10. 10Remainders in real life
    Buses, pizzas, and leftover slices.
  11. 11Estimating quotients
    Close counts, fast.
  12. 12Division, mastered
    The canyon, crossed.

Order of operations

The Summit · 8 lessons

  1. 01Why order matters
    One expression, two answers? Not allowed.
  2. 02Parentheses go first
    Grouping decides everything.
  3. 03Multiply and divide before add and subtract
    The rule behind the rule.
  4. 04Left to right, when tied
    Break the tie the fair way.
  5. 05Reading long expressions
    Take them apart calmly.
  6. 06Building expressions
    Now you write the rules.
  7. 07Expressions in real life
    Receipts, recipes, and totals.
  8. 08The summit
    Everything, together, beautifully.

Numbers in every shape

Below zero, split into parts, written with a point, and compared as ratios.

Negative numbers

The Caves · 10 lessons

  1. 01Below zero
    Numbers don't stop at zero.
  2. 02The line goes both ways
    Meet the minus side.
  3. 03Which is smaller?
    −7 sits deeper than −2.
  4. 04Climbing up from below
    Adding when you start underground.
  5. 05Falling past zero
    5 − 8 has an answer. See it.
  6. 06Adding a negative
    Adding cold air still cools the room.
  7. 07Subtracting a negative
    Two minuses make a climb.
  8. 08Signs and multiplication
    The sign rules, finally visible.
  9. 09Floors, degrees, and debt
    Negatives run the real world.
  10. 10The Caves, crossed
    Below zero holds no fear now.

Fractions

The River · 12 lessons

  1. 01Breaking things fairly
    A fraction is a fair share.
  2. 02Halves, thirds, quarters
    The three you'll use forever.
  3. 03Top and bottom
    The bottom cuts; the top takes.
  4. 04A fraction of a number
    1/2 of 12 — with dots, not rules.
  5. 05Taking more than one part
    3/4 of 20, step by step.
  6. 06Same amount, different name
    1/2 and 4/8 are twins.
  7. 07Which fraction is bigger?
    Compare without a calculator.
  8. 08Adding matching pieces
    Same bottoms add like apples.
  9. 09Whole numbers in disguise
    8/4 was 2 all along.
  10. 10Fractions you already use
    Half past, quarter off, third full.
  11. 11Reading recipes and rulers
    Fractions at work in your kitchen.
  12. 12The River, crossed
    Split anything. Fear nothing.

Decimals

The Delta · 10 lessons

  1. 01The point of the point
    That dot means: smaller pieces ahead.
  2. 02Tenths, on the line
    Between 0 and 1, a whole world.
  3. 03Money knew it first
    You've been doing decimals for years.
  4. 04Hundredths, zoomed in
    Each tenth splits into ten again.
  5. 05Which decimal is bigger?
    0.8 beats 0.35 — see why.
  6. 06Decimals are fractions
    0.5 and 1/2 — same person, new coat.
  7. 07Adding with the point
    Line up the dots. That's the trick.
  8. 08The point that hops
    ×10 just slides the point over.
  9. 09Rounding, gently
    3.7 lives closer to 4.
  10. 10The Delta, crossed
    Tenths and hundredths, tamed.

Ratios & proportion

The Confluence · 10 lessons

  1. 01Parts against parts
    2 to 1 is a recipe, not a total.
  2. 02Recipes are ratios
    2 flour to 1 sugar — at any size.
  3. 03Scaling up
    Double every part, the taste stays.
  4. 04Scaling down
    Half the guests, half of each part.
  5. 05The unit trick
    Find the price of one — unlock any amount.
  6. 06Same ratio, new numbers
    2:3 and 8:12 are the same recipe.
  7. 07Sharing in a ratio
    Split 12 in 2:1 — see who gets what.
  8. 08Speed, price, and dose
    Proportions run your daily life.
  9. 09Maps and models
    1 cm to 1 km — the world, scaled.
  10. 10The Confluence, crossed
    Two streams, one balance. Yours.

Percentages

The Fields · 10 lessons

  1. 01Out of one hundred
    Percent literally means per hundred.
  2. 02The hundred-square field
    See every percent at once.
  3. 03The friendly three
    50%, 25%, 10% — instant.
  4. 04Ten percent is the key
    Find 10%, unlock everything.
  5. 05Percent of a number
    30% of 60, without panic.
  6. 06Building hard from easy
    35% is just 25% + 10%.
  7. 07Discounts, decoded
    What 40% off actually costs.
  8. 08Tips without a phone
    18% in your head, politely.
  9. 09Percents are fractions
    Same idea, different coat.
  10. 10The Fields, crossed
    One hundred squares, all yours.

Shapes & space

The Gardens · 10 lessons

  1. 01Around the edge
    Perimeter is a walk around the fence.
  2. 02Covering the ground
    Area is counting the tiles.
  3. 03Rectangles, measured
    Length × width — the whole rule.
  4. 04Squares are honest
    Same side, squared.
  5. 05Fences and floors
    Around vs. covering — know which you need.
  6. 06Odd shapes, split up
    Cut tricky floors into easy rectangles.
  7. 07Filling the box
    Volume is stacking the layers.
  8. 08Litres, boxes, and trunks
    How much fits — measured.
  9. 09Paint, tiles, and fences
    Which number does the job need?
  10. 10The Gardens, crossed
    You measure the world now.

Coordinates

The Atlas · 8 lessons

  1. 01The address of a point
    Over, then up. Every point has an address.
  2. 02Plotting the point
    You drop the pin this time.
  3. 03The map below zero
    The grid keeps going — in every direction.
  4. 04How far apart?
    Two points, one subtraction.
  5. 05Shapes on the grid
    The Gardens, now with addresses.
  6. 06Charts are grids
    Every chart you've ever seen is this map.
  7. 07Two points, one climb
    Across, then up — the climb, measured.
  8. 08The Atlas, mapped
    You can read any map now.

Unknowns

The Mist · 10 lessons

  1. 01The hidden number
    x is just a box with a number inside.
  2. 02Solving by undoing
    x + 5 = 12. Undo the +5.
  3. 03Undoing a subtraction
    x − 4 = 9 works the same way.
  4. 04Undoing a multiplication
    3x = 12. Share it back out.
  5. 05Undoing a division
    x ÷ 2 = 8. Double back.
  6. 06Two steps back
    2x + 1 = 9, one undo at a time.
  7. 07Checking your answer
    Put it back in. Does it hold?
  8. 08Words into symbols
    'Five more than a number' is x + 5.
  9. 09Unknowns all around you
    Budgets, recipes, and road trips.
  10. 10The Mist, cleared
    Nothing hidden scares you now.

The language of algebra

Unknowns, machines, and two conditions at once. This is where math starts talking.

Functions

The Observatory · 10 lessons

  1. 01The machine
    In goes a number. Out comes another.
  2. 02Guess the rule
    Watch the machine. Catch its secret.
  3. 03Naming the machine
    f(x) is just the machine's name.
  4. 04Feeding the machine
    f(x) = x + 3. What's f(5)?
  5. 05Two-step machines
    Multiply, then add. In order.
  6. 06Tables of ins and outs
    Every machine leaves footprints.
  7. 07The rule from the table
    Read the footprints backwards.
  8. 08Machines feeding machines
    One's output is the next one's input.
  9. 09Functions everywhere
    Fares, forecasts, and phone plans.
  10. 10The Observatory, reached
    You've reached the stars.

Systems & inequalities

The Junction · 10 lessons

  1. 01Where two roads meet
    One pair fits both rules. Just one.
  2. 02Swapping one for the other
    Trade equals for equals, and two becomes one.
  3. 03Adding the equations away
    Opposites cancel. Watch them go.
  4. 04Roads that never meet
    What 0 = 5 is quietly telling you.
  5. 05Two unknowns in the wild
    Tickets, receipts, and two prices at once.
  6. 06Answers with room in them
    Not one number — a whole stretch of them.
  7. 07Solving with room
    Same undo move. Wider answer.
  8. 08The move that flips it
    Times a negative turns the line around.
  9. 09Inside the lines
    A line splits the plane. Pick your side.
  10. 10The Junction, crossed
    Points, ranges, regions — all yours.

Reading the world

Averages, chance and spread — the math you meet in the news every single day.

Data & averages

The Overlook · 10 lessons

  1. 01What's typical?
    One number can speak for many.
  2. 02The average, by hand
    Share the total out evenly — that's the mean.
  3. 03Averages you already use
    Star ratings, split bills, race paces.
  4. 04Reading a bar chart
    Height is the whole story.
  5. 05Reading a line chart
    Up, down, and what it means.
  6. 06The middle number
    The median doesn't care about show-offs.
  7. 07When the average lies
    One huge number can drag it around.
  8. 08Range: how spread out?
    Biggest minus smallest. That's it.
  9. 09Charts in the wild
    News, bills, forecasts — readable now.
  10. 10The Overlook, reached
    You read data like a landscape.

Probability

The Crossroads · 10 lessons

  1. 01Will it happen?
    Chance is a fraction of the ways.
  2. 02Coins and dice
    Count the ways, divide by all of them.
  3. 03From never to certain
    Chance lives on a line from 0 to 1.
  4. 04More ways, more likely
    Why some outcomes keep showing up.
  5. 05The percent chance
    A 30% rain forecast, decoded.
  6. 06This or that
    Chances add when paths split.
  7. 07This and that
    Chances shrink when both must happen.
  8. 08What to expect
    Play it a hundred times in your head.
  9. 09Chance in the wild
    Forecasts, games, and fine print.
  10. 10The Crossroads, crossed
    You read chance like a local.

Statistics

The Commons · 10 lessons

  1. 01Same middle, different crowds
    One average, two completely different stories.
  2. 02The middle fifty
    Fold the crowd in four.
  3. 03How far from the middle, on average
    One number for how spread out it is.
  4. 04The shape of a crowd
    Watch the mean chase the tail.
  5. 05The one that drags everything
    Which summaries even noticed?
  6. 06You can't ask everyone
    Grab more, and the guess stops jumping.
  7. 07Who did you ask?
    More people from the same corner is still that corner.
  8. 08Two things at once
    One dot is one thing, measured twice.
  9. 09Together, but not because
    What else changes at the same time?
  10. 10The Commons, crossed
    A summary is never one number.

The high country

Growth, its inverse, curves, and triangles. Everything calculus is about to need.

Exponents

The Cliffs · 10 lessons

  1. 01Multiplication, stacked
    A power is repetition with a shorthand.
  2. 02Squares are squares
    3² is a literal square. See it.
  3. 03Powers of ten
    Zeros, counted for you.
  4. 04Doubling runs away
    Why powers climb so fast.
  5. 05The quiet rules
    x¹ and x⁰ — simpler than they look.
  6. 06Un-squaring
    Square roots undo the square.
  7. 07Roots of bigger numbers
    √144 without a calculator.
  8. 08Growth in real life
    Bytes, bacteria, interest.
  9. 09Big and small, fast
    Powers shrink as fast as they grow.
  10. 10The Cliffs, climbed
    Nothing steep about them now.

Logarithms

The Ladder · 10 lessons

  1. 01How many times did it double?
    Not how big — how many climbs.
  2. 02The question, written down
    log just asks: how many?
  3. 03Any ladder, any base
    Steps of 3, of 5, of 10.
  4. 04Two climbs, one ladder
    Multiply the numbers, add the climbs.
  5. 05Running the ladder down
    Divide takes rungs away.
  6. 06Solving for the exponent
    x is stranded up high. Bring it down.
  7. 07When the ruler is a ladder
    Why some charts breathe and others crush.
  8. 08The base that turns up everywhere
    Watch a number settle on e.
  9. 09Logs in the wild
    How long until this doubles?
  10. 10The Ladder, climbed
    Powers and logs — one relationship, both ends.

Quadratics

The Arch · 10 lessons

  1. 01The curve that comes back
    Every graph so far was straight. Not this one.
  2. 02Every arch has a turning point
    One moment where it stops climbing.
  3. 03Where it crosses zero
    An arch lands twice. Usually.
  4. 04Two numbers, one rectangle
    Factoring is just re-laying the tiles.
  5. 05When something times something is nothing
    A zero product gives up its secret.
  6. 06Completing the square, literally
    Buy the last tile. Finish the square.
  7. 07The formula, earned
    Your tiles, written down once and for all.
  8. 08How many times it lands
    Read one number, know the shape.
  9. 09Arches in the wild
    Thrown balls, bridges, and the best you can do.
  10. 10The Arch, crossed
    Curves hold no fear now.

Trigonometry

The Ridge · 10 lessons

  1. 01The angle that fixes the shape
    Grow the triangle. The ratio refuses to move.
  2. 02Naming the three sides
    Two of the three names depend on where you stand.
  3. 03Three ratios, three names
    Sine was always just a fraction.
  4. 04Measuring what you can't reach
    A tree's height, from the ground.
  5. 05Working backwards to the angle
    That little −1 asks a question.
  6. 06The triangle on a circle
    Your triangle, relocated. Radius 1 changes everything.
  7. 07Past the corner
    Angles don't stop at 90°.
  8. 08Unrolling the circle
    That's not a new shape. That's the circle, unrolled.
  9. 09Waves in the wild
    Tides, daylight, heartbeats.
  10. 10The Ridge, crossed
    Triangle, circle, wave — one idea.

The calculus arc

Change, closeness, slope and area — arrived at gently, after everything that earns it.

Rates of change

The Slopes · 10 lessons

  1. 01How fast is fast?
    Distance over time — that's a rate.
  2. 02Rise over run
    Steepness, finally measured.
  3. 03The slope of a line
    One number tells the whole climb.
  4. 04Slope from two points
    Two dots are all you need.
  5. 05Downhill is honest too
    Negative slope, no drama.
  6. 06Slope inside equations
    y = 2x + 1 climbs 2. Always.
  7. 07Rates everywhere
    Price per kilo, words per minute.
  8. 08Average rate of change
    The overall climb, start to end.
  9. 09Steeper or flatter?
    Compare slopes at a glance.
  10. 10The Slopes, crossed
    You read steepness like a map now.

Limits

The Edge · 10 lessons

  1. 01Halfway there, forever
    Walk half the distance. Repeat. Forever.
  2. 02Sequences that settle
    2.9, 2.99, 2.999… you can feel it.
  3. 03The destination number
    A limit is where you're heading.
  4. 04Knowing without arriving
    You never land — and still know where.
  5. 05From both sides
    Approach from the left, from the right.
  6. 06When paths don't settle
    Some sequences run away. That's an answer too.
  7. 07Fractions fading out
    1/n heads to zero, calmly.
  8. 08Limits from tables
    Read the destination off the numbers.
  9. 09Why limits matter
    They make the impossible precise.
  10. 10The Edge, reached
    You can stand here comfortably now.

Derivatives

The Peak · 10 lessons

  1. 01Zoom until straight
    Every smooth curve hides a line.
  2. 02Slope at a single point
    Not the average — the right-now.
  3. 03The derivative is a slope
    That's it. That's the secret.
  4. 04Straight lines first
    f(x) = 3x climbs 3. Everywhere.
  5. 05The square curve's secret
    x² climbs 2x. Watch it happen.
  6. 06The power rule
    Bring it down, step it down.
  7. 07Where curves flatten
    Slope zero: tops and bottoms.
  8. 08Speed is a derivative
    Your speedometer does calculus.
  9. 09Derivatives in the wild
    Growth, cooling, profit, dosage.
  10. 10The Peak, reached
    The scariest word in math, yours.

Integrals

The Valley · 10 lessons

  1. 01Adding tiny pieces
    Big totals from small slices.
  2. 02Area under a line
    The space beneath tells a story.
  3. 03Bars that hug the curve
    Thinner bars, truer area.
  4. 04Accumulation
    Rain filling a barrel, slowly.
  5. 05The triangle shortcut
    Area under f(x) = x, instantly.
  6. 06Total from rate
    Distance from speed — integrated.
  7. 07Undoing the derivative
    Integrals climb back up.
  8. 08Areas in real life
    Doses, downloads, distance.
  9. 09The two great ideas
    Slope and area are twins.
  10. 10The Valley, crossed
    From counting dots to calculus. You.

Walk it from the start.

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