Grades K–2 — counting, place value, and the first operations
Six rooms, all open — counting, adding and subtracting, place value, the column with a trade, length, time and money, shapes and equal shares — and the daily lines for every grade.
6 units open · 0 in the workshop
The course
Course contentsMath, Grades K–2
5 units, 10 chapters, numbered lessons — each with a reading, key words, a source or the numbers, and three checks. Chapter reviews, unit tests, a word match and a writing task.
Adding and Subtracting
Operations
Putting Together and Taking Apart; Facts Within 20 and Good Strategies.
Place Value to 1,000
Number
Hundreds, Tens and Ones; Adding and Subtracting Bigger Numbers.
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Counting and how many
The counting words in order, one number for each thing, and the last number tells how many. Count on from any number, count by tens to 100, read a ten-frame, and compare two groups with more, fewer and the same. Study cards, hints, a three-level practice and four workshop activities.
Adding and subtracting within 20
Adding puts parts together; subtracting starts with the whole and finds the missing part. Count on and back, doubles, make a ten, fact families, a missing number in any place, and story problems that put together, take from and compare. Study cards, hints, a three-level practice and four workshop activities.
Tens and ones, then hundreds
A ten is ten ones and a hundred is ten tens. What each digit is worth, blocks, expanded form and number names, comparing with < = > by the left digit first, ten more and ten less, and skip-counting by 5s, 10s and 100s. Study cards, hints, a three-level practice and four workshop activities.
Adding and subtracting within 1,000
Ones, tens and hundreds; adding and subtracting in columns with a trade when a place gets too full or too empty; adding 10 or 100 in your head; estimating first so you can tell whether an answer makes sense. Study cards, hints, a three-level practice and four workshop activities.
Length, time and money
Measure with a ruler starting at zero, in inches and centimeters, and compare lengths; tell time to five minutes with a.m. and p.m.; count pennies, nickels, dimes, quarters and bills, biggest first. Study cards, hints, a three-level practice and four workshop activities.
Shapes and equal shares
Name circles, triangles, squares, rectangles, pentagons and hexagons by counting sides and corners; flat shapes and solid ones; build bigger shapes from smaller ones; halves, thirds and fourths of a circle and a rectangle, and why equal shares must be the same size. Study cards, hints, a three-level practice and four workshop activities.
Grades 3–5 — multiplication, fractions, and decimals
Eight rooms, all open — fractions from the ground up, the two column algorithms, multiplication and division, multi-digit multiplication, fractions, decimals, measurement, and geometry with the coordinate plane.
8 units open · 0 in the workshop
The course
Course contentsMath, Grades 3–5
6 units, 13 chapters, numbered lessons — each with a reading, key words, a source or the numbers, and three checks. Chapter reviews, unit tests, a word match and a writing task.
Multiplication and Division
Operations
What Multiplying Means; Division and Fact Families.
Place Value and Multi-Digit Arithmetic
Number
Place Value to the Millions; Multi-Digit Multiplication and Division.
Fractions
Number
What a Fraction Is; Adding, Subtracting and Multiplying Fractions; Dividing With Fractions.
Measurement and Data
Measurement
Area, Perimeter and Volume; Units, Time and Data Displays.
Geometry and the Coordinate Plane
Geometry
Angles, Lines and Shapes; The Coordinate Plane and Patterns.
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What a fraction is
Fair shares, top and bottom, more than a whole, close to what, which is bigger, same amount with a new name — six pages, circles and bars before symbols.
The operations that carry everything
Long division as four small moves, and column subtraction with regrouping — zeros included, up to five digits.
Multiplication and division: what they mean
Equal groups, arrays and area; division as sharing, grouping and a missing factor; fact families, the order, break-apart and grouping properties, and the strategies that make the facts to 100 easier. Study cards, hints, a three-level practice and four workshop activities.
Multi-digit multiplication
One problem, 23 × 14, worked four ways — breaking apart, the area model, partial products and the standard algorithm — with regrouping, the placeholder zero explained, and estimating to catch an answer with the wrong number of digits. Study cards, hints, a three-level practice and four workshop activities.
Fractions: add, subtract, multiply
Like denominators are just counting; unlike ones get renamed first, and the room shows why 1/2 + 1/3 is not 2/5. Mixed numbers with borrowing, a whole number times a fraction, a fraction of a fraction on a bar model, and why a product can be smaller than a factor. Study cards, hints, a three-level practice and four workshop activities.
Decimals
Tenths, hundredths and thousandths on a number line; comparing, ordering and rounding without falling for ‘longer is bigger’; adding, subtracting, multiplying and dividing with the points lined up, and money problems that use all of it. Study cards, hints, a three-level practice and four workshop activities.
Measurement: area, perimeter, volume
Perimeter as the distance around, area as the squares inside, volume as the cubes that fill a box — tile it, count it, then multiply; missing sides, L-shapes, which box holds more, and converting length, mass, capacity and time inside one system. Study cards, hints, a three-level practice and four workshop activities.
Geometry and the coordinate plane
Points, lines and rays; acute, right, obtuse and straight angles, and a protractor read on the right scale; parallel and perpendicular; triangles and the quadrilateral family, and why a square is a rectangle; lines of symmetry; the coordinate plane, ordered pairs, and shapes on a grid. Study cards, hints, a three-level practice and four workshop activities.
Grades 6–8 — the Interior, and the ground floor under it
Seventh grade follows the class’s own year, month by month, each month ending in its test prep. Under it, the ground floor: fractions, data and the two algorithms, pictures first. The rest of 6th, 7th and 8th grade follows, a room for each topic — ratios to the Pythagorean theorem — every one with study cards, hints, a three-level practice and four workshop activities.
20 units open · 0 in the workshop
The course
Course contentsMath, Grades 6–8
6 units, 16 chapters, numbered lessons — each with a reading, key words, a source or the numbers, and three checks. Chapter reviews, unit tests, a word match and a writing task.
Ratios, Rates and Proportions
Ratios and Proportional Relationships
Ratios and Unit Rates; Proportional Relationships and Percent.
The Number System
Number
Integers and Rational Numbers; Operations With Rational Numbers; Exponents, Roots and Scientific Notation.
Expressions, Equations and Inequalities
Algebra Begins
Expressions and Properties; Equations and Inequalities.
Functions and Linear Equations
Algebra
Linear Equations and Slope; Functions; Systems of Equations.
Geometry
Geometry
Area, Surface Area and Volume; Angles, Triangles and Scale; Transformations and the Pythagorean Theorem.
Statistics and Probability
Statistics and Probability
Describing Data; Probability and Sampling; Two-Variable Data.
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The 7th-grade year on one page
The long-term plan, September through December, with a door for every unit, every quiz in one room, how it runs, and the standards.
Review week · 6th-grade skills
Rounding, decimals, GCF and LCM, fractions — last year’s skills, asked before the new ones lean on them.
Integers
The number line walked, not memorized: where a number goes, how far from zero, adding and subtracting as steps, zero pairs, then the same walk on tenths and halves.
Multiply, divide, properties
Which sign, then how big; a fraction bar is a division sign; one rectangle read both ways; name the property; and which operation goes next.
Expressions
Combining like terms, and adding and subtracting linear expressions — flip every sign first, then gather.
Equations
From words to math, then a balance where every move is done to both pans — one step, then two, decimals and fractions included.
What a fraction is
Fair shares, top and bottom, more than a whole, close to what, which is bigger, same amount with a new name — six pages, circles and bars before symbols.
Numbers that tell a story
The mean as towers made even, the median and the range, the outlier that drags the mean, stem-and-leaf plots and line plots.
The operations that carry everything
Long division as four small moves, and column subtraction with regrouping — zeros included, up to five digits.
Ratios, rates and unit rates
Ratio language, equivalent ratios, tables, tape diagrams and double number lines; unit price and the better buy; speed; percent as a rate per 100. Study cards, hints, a three-level practice and four workshop activities.
Proportional relationships and percent
The constant of proportionality in a table, a graph and an equation; tax, tip, discount, percent change and simple interest. Study cards, hints, a three-level practice and four workshop activities.
Inequalities
Write one from words, graph it with an open or closed circle, solve it like an equation — and the one move that flips the sign, and why. Study cards, hints, a three-level practice and four workshop activities.
Area, surface area and volume
Every formula is a rectangle in disguise: parallelograms, triangles, trapezoids, composite figures, the circle around and inside, nets, surface area, and the volume of a prism. Study cards, hints, a three-level practice and four workshop activities.
Angles, triangles and scale drawings
Complementary, supplementary and vertical angles turned into equations; the triangle angle sum; which three lengths close into a triangle; one triangle, many or none; scale drawings and why area scales by the square. Study cards, hints, a three-level practice and four workshop activities.
Probability and sampling
Chance from 0 to 1, what should happen against what did, lists and tree diagrams for compound events, simulations, and what a fair sample lets you say about the whole. Study cards, hints, a three-level practice and four workshop activities.
Exponents, roots and scientific notation
An exponent counts factors, and every law is that counting: add, subtract, multiply. Zero and negative exponents, square and cube roots, numbers that never end, and scientific notation for the very large and the very small. Study cards, hints, a three-level practice and four workshop activities.
Linear equations and systems
Parentheses and the variable on both sides; one solution, none, or every number; two equations at once by graphing, substitution and elimination. Study cards, hints, a three-level practice and four workshop activities — draw both lines on a coordinate plane and watch them meet.
Functions and slope
One output for every input; linear and not; slope as the rate and the y-intercept as the start; y = mx + b from a table, a graph and a story; comparing two plans. Study cards, hints, a three-level practice and four workshop activities — one on a coordinate plane you plot with a fingertip.
Transformations, congruence and similarity
Slide, flip, turn, resize and their coordinate rules; rigid motions make congruent copies, a dilation makes a similar one; parallel lines, a transversal, and why a triangle makes 180°. Study cards, hints, a three-level practice and four workshop activities — flip a triangle corner by corner on a four-quadrant plane.
The Pythagorean theorem
Legs and hypotenuse however the triangle is turned; a² + b² = c² and a proof by rearrangement; missing sides; the converse that tests a corner; triples; ladders, screens and boxes; the distance between two points. Study cards, hints, a three-level practice and four workshop activities.
Grades 9–10 — Algebra I and Geometry
Eight rooms, all open — Algebra I from linear equations to quadratics, and Geometry from proof to circles — plus the daily lines, ten boxes a day.
8 units open · 0 in the workshop
The course
Course contentsMath, Grades 9–10
5 units, 13 chapters, numbered lessons — each with a reading, key words, a source or the numbers, and three checks. Chapter reviews, unit tests, a word match and a writing task.
Algebra I: Linear Equations, Functions and Systems
Algebra
Solving Linear Equations and Inequalities; Functions and Linear Models; Systems of Equations and Inequalities.
Algebra I: Exponents, Polynomials and Quadratics
Algebra
Exponents and Exponential Functions; Polynomials and Factoring; Quadratic Functions and Equations.
Geometry: Reasoning, Congruence and Triangles
Geometry
Reasoning and Proof; Congruence and Transformations; Triangles and Their Centers.
Geometry: Similarity, Trigonometry and Circles
Geometry
Similarity and Right-Triangle Trigonometry; Circles, Area and Volume.
Statistics in Algebra I
Statistics
Describing and Comparing Data; Lines of Fit and Correlation.
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Algebra I: linear equations and inequalities
Solve linear equations and name the property behind every step; tell one solution from none or all; solve inequalities without losing the sign flip; turn a phone plan or a formula into algebra and say what the solution means. Study cards, hints, a three-level practice and four workshop activities.
Algebra I: functions and linear models
Decide what is a function and read f(x); find domain, range, intercepts and rate of change from a formula, table or graph; build a linear model from data and say what its slope and intercept mean in units. Study cards, hints, a three-level practice and four workshop activities.
Algebra I: systems
Solve a system of two linear equations by graphing, substitution and elimination, know why elimination is legal, and tell one solution from none or infinitely many; turn tickets, coins and mixtures into a system; graph a linear inequality and a system of inequalities as a region. Study cards, hints, a three-level practice and four workshop activities.
Algebra I: exponents, polynomials, factoring
Exponent laws as counting factors; polynomials added, subtracted and multiplied with the area model; then factoring as multiplication run backwards — GCF, difference of squares, perfect-square trinomial and the ac method. Study cards, hints, a three-level practice and four workshop activities.
Algebra I: quadratics
The parabola and its vertex, axis, intercepts and zeros; standard, factored and vertex form; solving by square roots, factoring, completing the square and the quadratic formula, with the discriminant to predict the roots — and a thrown ball that turns every feature into a sentence. Study cards, hints, a three-level practice and four workshop activities.
Geometry: proof, congruence and triangles
Definitions built on the undefined terms; vertical angles and linear pairs; the four angle pairs of a transversal and their converses; the angle-sum and exterior-angle theorems; congruence as a rigid motion, SSS, SAS, ASA, AAS and HL, and the numbers that sink SSA; two-column proofs ending in CPCTC. Study cards, hints, a three-level practice and four workshop activities.
Geometry: similarity and right-triangle trigonometry
Scale factor and dilations; AA, SSS and SAS similarity; proportions for a missing side and why area scales by k²; opposite, adjacent and hypotenuse from the angle; sine, cosine and tangent as ratios; solving for a side or an angle; elevation and depression; the 45-45-90 and 30-60-90 triangles; a tree measured with a tangent. Study cards, hints, a three-level practice and four workshop activities.
Geometry: circles, area and volume
Radius, diameter, chord, tangent, arc and the angles at the center and on the circle; circumference and area, arc length and sector area as a fraction of the whole, radians and the equation of a circle; cylinders, cones and where the ⅓ comes from, spheres, surface area, Cavalieri, density, and which container really holds more. Study cards, hints, a three-level practice and four workshop activities.
Grades 11–12 — Algebra II, statistics, and the math of adult life
Seven rooms, all open — Algebra II, trigonometry, sequences, statistics, financial math and a modeling capstone — plus the daily lines.
7 units open · 0 in the workshop
The course
Course contentsMath, Grades 11–12
5 units, 10 chapters, numbered lessons — each with a reading, key words, a source or the numbers, and three checks. Chapter reviews, unit tests, a word match and a writing task.
Algebra II: Polynomial, Rational and Radical Functions
Algebra
Polynomial Functions; Rational and Radical Functions.
Algebra II: Exponential, Logarithmic and Trigonometric Functions
Algebra
Exponentials and Logarithms; Trigonometric Functions.
Sequences, Series and Modeling
Algebra and Modeling
Sequences and Series; Modeling With Functions.
Statistics: From a Sample to a Claim
Statistics and Probability
Distributions and the Normal Curve; Sampling, Inference and Claims.
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Algebra II: polynomial and rational functions
Degree and leading coefficient fix the ends; zeros and their multiplicity cross or bounce; division, the Remainder Theorem and complex numbers finish the picture. Rational functions bring asymptotes, holes and extraneous solutions. Study cards, hints, a three-level practice and four workshop activities.
Algebra II: exponential and logarithmic functions
Growth and decay as a factor multiplied every step, linear versus exponential in a table and a story, doubling time and half-life, compound interest. Then the logarithm as the inverse question, its rules, and the routine that solves 500 = 100·2ᵗ for t. Study cards, hints, a three-level practice and four workshop activities.
Trigonometric functions
The unit circle in degrees and radians with its special points and quadrant signs, then sine and cosine as waves — amplitude, period, midline and phase shift — with a tide and a Ferris wheel modeled and checked, the Pythagorean identity, inverse trig and equations on [0, 2π). Study cards, hints, a three-level practice and four workshop activities.
Sequences and series
Arithmetic and geometric sequences named by one subtraction or one division; recursive and explicit rules and how to turn one into the other; sigma notation, Gauss’s pairing, the finite geometric sum and the subtraction that proves it, and infinite series that settle on a number. Study cards, hints, a three-level practice and four workshop activities.
Statistics: from a sample to a claim
Population and sample, mean and standard deviation by hand, the normal curve with its seven landmarks and z-scores; surveys, observational studies and experiments and what each may conclude; margin of error and why 52% ± 3 is not a lead; a simulation that puts a claim to the test. Study cards, hints, a three-level practice and four workshop activities.
Financial math
A pay stub read line by line, simple interest as a line and compound interest as an exponential, APR turned into a monthly rate, a loan amortized month by month and two loans compared by total cost with the fee included; credit cards, inflation, tax brackets and a 50/30/20 budget, all with invented example numbers. Study cards, hints, a three-level practice and four workshop activities.
Capstone: model it
The modeling cycle worked on one invented case — a club’s T-shirt fundraiser: a measurable question, assumptions written down, cost and profit functions, break-even and the goal, a trend fitted to a week of sales, validation against last year, a price chosen with a quadratic, and a report that says how far the model can be trusted. Study cards, hints, a three-level practice and four workshop activities.
The engines
Every activity here is one of these kinds, and all six work now.
Move it with your hands
Open · the m- and c-pagesA number line you walk, a balance you load on both pans, an area rectangle read both ways, towers made even. Every page opens three ways: watch one first, work the set, or take one more.
Test prep that names the mistake
Open · Test prep, by monthStudy cards you tap to reveal, a hints sheet, and a quiz at three levels where every wrong option is a specific misconception with its own feedback.
Ten daily lines, with room to work
Open · the grade buttonsDaily Drafts: column algorithms worked from the ones place, long division as a staircase, fractions read across the line, and the error named when it is certain.
Label, graph, sort, order, argue
Open · the Lab tabThe Lab every science and social studies unit carries — table to graph, put the steps in order, claim-evidence-reasoning — ready for the math rooms as they are built.
The coordinate plane
Open · Functions and slopeTap a point card, then tap the grid: plot a table, watch the line draw itself, read its slope and where it starts. Two lines that draw themselves to their crossing, a triangle flipped corner by corner, and the fourth corner of a garden found on a first-quadrant grid run on it too.
The shape bench
Open · the geometry roomsTap two opposite corners and a rectangle is laid on the figure. Cut a garden, or a building plot, into rectangles you choose — every cut that covers it with no gap and no overlap is accepted, because that is what cutting a shape into rectangles means. Then read the drawing back: the lengths nobody printed, the area, the fence around it, and what the area becomes when every length is doubled. On the angles room it is a protractor instead of a grid, with two scales printed the way a real one has them: the reading counts as right when it is close, and every angle deduced from it has to be exact.
For the teacher
<b>This page is a map.</b> It saves nothing about a student and sends nothing anywhere. Each door opens an activity page; a finished activity sends its one summary row to your Sheet, under the name the student typed, and nothing else leaves the device.
<b>Hand out one band.</b> Add the band to the address and the page opens there: <b>/math#6-8</b>. Every door has a short address too — <b>Show on the board</b> prints it large enough for the back row.
<b>Nothing on this door is in the workshop.</b> Every unit and every engine named here is built, and every one of them opens. The mark is kept for units named later: one carrying it has no page behind it and no link, on purpose, until it does.