Search every subject world, from Preschool to Grade 12. The first five courses of every subject path are free.
190 courses
Mathematics · Preschool
Olly's laundry day and toy box teach the first big ideas of early mathematics: things can be the same, things can go together, and a group can be sorted by a rule. Children match pairs, sort pictures into two groups, say the rule, and find the one that does not belong, then sort real objects at home.
Mathematics · Preschool
With Olly's nest, garden and kitchen, children learn to see one, two and three at a glance, to say the matching number word, and to notice that two cats and two hats are both 'two'. They finish by making their own groups of one, two and three.
Mathematics · Preschool
Share the Picnic: Olly sets out one cup for each guest, and children learn to give one object to each person, to say one number for each thing they touch, and to tell a matched picnic from one where someone is missing out. A bedtime scene and a take-home table-setting job check that the idea works in new places.
Mathematics · Preschool
Who has more boats? Children compare groups of up to five by pairing things one to one and by counting each group, and learn the words more, fewer and the same. A final lesson shows that a longer line or bigger things do not mean more.
Mathematics · Preschool
Olly opens a shape box: circles, squares, triangles and rectangles. Children learn to name each shape whether it is big or small, turned or tilted, count its corners, and then go on a shape hunt to find circles and rectangles in clocks, coins, books and tents.
Mathematics · Preschool
Olly plays hide-and-seek and runs a treasure hunt. Children learn the position words in, on, under and beside, then in front of, behind, above and below, and use them to follow two-step directions in pictures and in a real obstacle path.
Mathematics · Preschool
Sun, moon, sun, moon: children find the part of a pattern that repeats, say what comes next, and build the next pieces themselves. They then copy a pattern with different pictures and spot mistakes, and make a pattern with blocks or body positions at home.
Mathematics · Preschool
Olly and friends share snacks fairly, ducks join each other on the pond, and birds fly away from a branch. Children deal out objects so everyone gets the same, put two small groups together and count them all, and find how many are left when some go away, all with objects and pictures and no symbols.
Mathematics · Pre-K
Olly's dot cards help children see groups of up to five without counting one by one: dice-like patterns, fingers and scattered groups. Children learn to see small groups inside bigger ones (four is two and two) and to match each group to its numeral from 1 to 5.
Mathematics · Pre-K
Children count up to ten things in lines, circles and scattered groups without losing track, count out exactly the number Olly asks for from a bigger pile, and connect the numerals 1 to 10 to groups and to their order on a number path.
Mathematics · Pre-K
An empty nest has zero eggs. Children learn that zero means none, compare groups up to ten by pairing and by counting, and find one more and one fewer by moving along a number path from 0 to 10.
Mathematics · Pre-K
Bunnies hop together and birds fly away. Children act out and solve put-together and take-away stories with totals up to ten, and learn that every story has a first, a then and a now, ending with more or fewer than it started. No plus or minus signs yet: just objects, pictures and words.
Mathematics · Pre-K
Olly builds with shape tiles. Children describe triangles, squares, rectangles, circles and hexagons by their sides and corners, put shapes together to make new shapes (two triangles make a square), and compare shapes by size, sides and corners. A first look at solid shapes sorts the ones that roll from the ones that stack.
Mathematics · Pre-K
Patterns grow up: apple, apple, banana; sun, moon, star; cat, dog, dog. Children find the part that repeats in longer patterns, extend them by several pieces, and rebuild the same pattern with new pictures and body positions, spotting and fixing mistakes along the way.
Mathematics · Pre-K
Which tower is taller? Which jar holds more? Children compare lengths and heights by lining up ends, put three things in order from shortest to tallest, and compare how much containers hold by pouring from one to another, discovering that taller does not always mean holds more.
Mathematics · Pre-K
Olly's class wants to know which fruit is the favourite. Children sort collections into groups, count each group, show the counts as a picture graph or bar graph, and read the graph to find the most, the fewest and how many are in a group.
Mathematics · Kindergarten
Kindergartners make counting exact: one number for each object, the last number tells how many, and moving the objects does not change the count. Ten strips show that each next number is one more, and zero shows a count of none. Children show and read numbers from 0 to 10.
Mathematics · Kindergarten
Children count to 100 by ones and by tens using a hundred chart, count forward from any number instead of starting at 1, and count groups of up to 20 objects and build the matching numeral, including the tricky teen numbers. Handwriting practice happens on paper with a grown-up watching.
Mathematics · Kindergarten
Is 7 greater than 5? Children compare groups of up to ten by pairing and counting, using the words greater than, less than and equal to, then compare written numbers on a number path and put three numbers in order from least to greatest.
Mathematics · Kindergarten
Putting groups together becomes addition. Children show joining stories with objects, fingers and drawings, learn the plus and equal signs, solve add-to and put-together story problems within 10, and become quick and confident with sums within 5.
Mathematics · Kindergarten
When some go away, we subtract. Children show take-away stories with objects, drawings and equations using the minus sign, solve take-away problems within 10 by counting back on a number path, decide whether a story needs adding or subtracting, and grow confident with subtraction within 5.
Mathematics · Kindergarten
Seven can be 5 and 2, or 4 and 3, or 6 and 1. Children break numbers up to 10 into two parts in different ways, record them with equations like 7 = 4 + 3, find every way to split a small number in an organised list, and find the partner that makes 10 for any number from 1 to 9 using a ten strip.
Mathematics · Kindergarten
Every teen number is a full ten and some more ones. Children build teen numbers with ten strips and blocks, write equations like 14 = 10 + 4, see why the 1 in a teen numeral stands for ten ones, and use 'ten and some more' to compare and order teen numbers.
Mathematics · Kindergarten
A pumpkin can be tall, heavy and wide all at once. Children learn the things we can measure about an object (length, height, weight, how much it holds), compare two objects directly by lining up ends, and compare weights with their hands and a balance scale, discovering that bigger is not always heavier.
Mathematics · Kindergarten
Children classify objects into given categories (animals with legs or without, things that travel on land, water or air), count how many are in each category, record the counts in a table and a bar graph, and put the categories in order from most to fewest to answer questions.
Mathematics · Kindergarten
Children name flat shapes and solid shapes in any size or position, tell flat from solid, describe shapes by their sides, corners (vertices) and faces, use position words to say where things are, and put small shapes together to build bigger ones.
Mathematics · Grade 1
First graders extend counting past 100 to 120 from any starting number, read and write numerals such as 104 and 117 correctly, count large collections by making tens, and compare numbers with the symbols >, < and =.
Mathematics · Grade 1
Ten ones bundled together make a ten. Learners build and write two-digit numbers as tens and ones, compare two-digit numbers by looking at the tens first, and find 10 more and 10 less than a number without counting, using base-ten blocks and the hundred chart.
Mathematics · Grade 1
Learners solve joining and putting-together stories within 20, including stories where the missing number is the part that was added. They add by counting on from the greater number, and use turn-around facts and smart grouping (make a ten first) to add two or three numbers.
Mathematics · Grade 1
Subtraction is more than taking away. Learners solve take-from stories, take-apart stories where one part is missing, and compare stories that ask how many more or fewer, all within 20. They learn to solve subtraction by thinking of a missing addend and choosing between counting back and counting up.
Mathematics · Grade 1
Learners build reliable strategies for facts within 20: making a ten to add (8 + 6 = 8 + 2 + 4), going back through ten to subtract (13 − 4 = 13 − 3 − 1), using doubles and near doubles, and using fact families so every addition fact also gives two subtraction facts. Facts within 10 are practised for accuracy, never against a clock.
Mathematics · Grade 1
The equal sign means 'is the same amount as', not 'the answer comes next'. Learners decide whether equations such as 7 = 8 − 1 and 4 + 1 = 5 + 2 are true or false, find unknown numbers in any position (5 = ☐ − 3), and balance equations with operations on both sides (4 + 5 = 3 + ☐).
Mathematics · Grade 1
Learners add within 100 using base-ten blocks, the hundred chart and number lines: adding tens to a two-digit number (34 + 20), adding ones with and without making a new ten (42 + 5 and 47 + 6), and explaining their steps in tens and ones while solving story problems.
Mathematics · Grade 1
Seventy take away thirty is like seven take away three, but with tens. Learners subtract multiples of ten from 10 to 90 using ten-sticks and number-line jumps, use addition to subtract by counting up in tens, and solve story problems with tens, including differences of zero.
Mathematics · Grade 1
How long is it? Learners order objects by length, compare two lengths that cannot be put side by side by using a string as a go-between, and measure lengths by laying same-size units such as cubes end to end with no gaps or overlaps. They learn to spot measuring mistakes and explain why they change the answer.
Mathematics · Grade 1
Learners tell and write time to the hour and half hour on analog and digital clocks: the short hand shows the hour, the long hand shows the minutes, and half past means the long hand has gone halfway around. They then put the events of a day in time order and find one hour later.
Mathematics · Grade 1
A class asks a question, collects answers and turns them into a table, a picture graph and a bar graph. Learners organize data into up to three categories, show it in a graph, and answer questions about how many are in each category, how many in all, and how many more or fewer one category has than another.
Mathematics · Grade 1
What makes a triangle a triangle? Learners separate defining attributes (three straight sides, closed) from attributes that do not matter (colour, size, direction), build new shapes from flat and solid shapes, and split circles and rectangles into two and four equal shares called halves and fourths, discovering that more equal shares means smaller shares.
Mathematics · Grade 2
Ten tens make a hundred. Learners build three-digit numbers with base-ten blocks, read and write them as numerals, number names and expanded form (406 = 400 + 6), find the value of each digit, and show the same number in more than one way, such as 254 as 25 tens and 4 ones.
Mathematics · Grade 2
Learners skip-count by 5s, 10s and 100s within 1,000 (including across a new hundred), compare three-digit numbers by looking at hundreds, then tens, then ones, and add or subtract 10 and 100 in their heads, explaining which digit changes and why.
Mathematics · Grade 2
Learners become accurate and flexible with addition and subtraction facts within 20: they use make ten, doubles, near doubles and think-addition, choose the strategy that fits each fact, and explain it. They also find out whether a group up to 20 is odd or even by pairing, and write even numbers as doubles. Fluency means accurate and flexible, never timed.
Mathematics · Grade 2
Learners add within 100 and then within 1,000 by adding hundreds to hundreds, tens to tens and ones to ones, making a new ten or a new hundred when a place gets full. They add up to four two-digit numbers by looking for friendly pairs, explain why their strategies work, and check answers by estimating.
Mathematics · Grade 2
When there are not enough ones to take away, trade a ten for ten ones. Learners subtract within 100 and then within 1,000 with base-ten models, including tricky numbers with zeros such as 403 − 158, use counting up as a second strategy, and check every subtraction with addition.
Mathematics · Grade 2
Learners solve story problems within 100 by drawing bar (tape) diagrams and writing equations with a symbol for the unknown, wherever the unknown is, including tricky compare stories. They plan and solve two-step problems, then check that their answers make sense in the story.
Mathematics · Grade 2
Four plates with 3 cookies each: learners make and recognise equal groups, find totals by skip counting and repeated addition, and organise objects into arrays of rows and columns (up to 5 by 5). They write repeated-addition equations by rows and by columns and discover that both give the same total, the foundation for multiplication in Grade 3.
Mathematics · Grade 2
Learners measure with rulers in inches and centimeters (starting at 0, or finding the length when an object starts elsewhere), choose tools such as yardsticks, meter sticks and measuring tapes, estimate lengths with benchmarks, explain why smaller units give bigger numbers, and find how much longer one object is than another.
Mathematics · Grade 2
A number is a distance from 0. Learners place numbers on number lines with equally spaced points (counting by 1s, 5s and 10s), show addition and subtraction within 100 as jumps, and solve length story problems with number-line drawings and equations with an unknown.
Mathematics · Grade 2
Learners tell and write time to the nearest five minutes by skip counting around the clock, use a.m. and p.m., find the value of groups of pennies, nickels, dimes, quarters and dollar bills, write amounts with ¢ and $, and solve shopping problems.
Mathematics · Grade 2
Learners measure several objects and show the lengths on a line plot, read picture graphs and bar graphs with up to four categories, and use bar graphs to solve put-together, take-apart and compare problems.
Mathematics · Grade 2
Learners name triangles, quadrilaterals, pentagons and hexagons by counting sides and angles and describe cubes by their faces. They split rectangles into rows and columns of same-size squares and count them, and split circles and rectangles into halves, thirds and fourths, discovering that equal shares of the same whole do not have to be the same shape.
Mathematics · Grade 3
Learners revisit place value to 1,000 and then learn to round numbers to the nearest ten and the nearest hundred by deciding which multiple a number is closer to on a number line. They use the halfway rule, avoid the 'round twice' trap, and use rounding to make sensible estimates in real situations.
Mathematics · Grade 3
Learners become fluent with addition and subtraction within 1,000: they connect base-ten models to the written column method (regrouping in each place), subtract across zeros, choose smart strategies such as adjusting 398 to 400 or counting up, check with the inverse operation, and use rounding to judge whether an answer is reasonable.
Mathematics · Grade 3
Multiplication is a fast way to count equal groups. Learners read 5 × 7 as '5 groups of 7', represent products with equal groups, arrays and equal jumps on a number line, and solve story problems about bags, rows and lengths, explaining what each number in the equation means.
Mathematics · Grade 3
Division answers two different questions: how many in each share, and how many groups. Learners share objects equally, make groups of a given size, connect both meanings to the division sign, solve divisions by thinking of the missing factor in a multiplication, and decide which meaning fits each story problem.
Mathematics · Grade 3
Learners use the properties of multiplication as tools: turn-around facts and the rules for 0 and 1, grouping three factors in a helpful order, and breaking a hard fact into two easier facts with an array (8 × 7 = 8 × 5 + 8 × 2). They then build efficient strategies such as doubling and 'ten groups minus one group' for nines.
Mathematics · Grade 3
Learners become fluent with multiplication and division facts within 100 by using known facts and strategies, find unknown numbers in any position of a multiplication or division equation, and multiply one-digit numbers by multiples of ten (4 × 70 = 280) by thinking in tens. Fluency means accurate and strategic, never timed.
Mathematics · Grade 3
Learners plan and solve two-step word problems with any of the four operations, write equations with a letter for the unknown, and check that answers are reasonable by estimating. They then hunt for patterns in the addition and multiplication tables and explain why patterns such as 'four times any number is even' must always be true.
Mathematics · Grade 3
Learners discover that a fraction names equal parts of one whole, build non-unit fractions from unit fractions, and then see that every fraction is also a number with its own place on the number line. A garden-trail scene checks that the idea transfers to a new kind of whole.
Mathematics · Grade 3
Building on fractions as numbers on a line, learners discover that different fractions can name the same amount (1/2 = 2/4 = 4/8), write whole numbers as fractions (4/4 = 1, 3 = 3/1), and compare fractions that share a numerator or a denominator by reasoning about the size of the parts. A pizza puzzle shows why comparisons only make sense for the same whole.
Mathematics · Grade 3
Area is the number of unit squares that cover a shape; perimeter is the distance around it. Learners tile rectangles and connect tiling to multiplying side lengths, split rectangles and L-shapes into parts, find perimeters (including a missing side), and discover that shapes with the same perimeter can have different areas.
Mathematics · Grade 3
Learners tell time to the minute and find elapsed time on a number line, estimate and solve problems with grams, kilograms and liters, read scaled picture graphs and bar graphs where one symbol stands for several, and show lengths measured to the nearest half or quarter inch on a line plot.
Mathematics · Grade 3
Learners sort quadrilaterals into categories by their attributes (rhombuses, rectangles, squares and others), discover that one shape can belong to several categories (every square is a rectangle and a rhombus), split shapes into parts of equal area named by unit fractions, and practise writing mathematical explanations with a claim, a reason and an example or counterexample.
Mathematics · Grade 4
Learners extend place value to one million. They see that a digit is worth ten times as much as the same digit one place to its right, read and write large numbers in standard, word and expanded form, compare them digit by digit with >, = and <, and round them to any place using number lines and place-value reasoning.
Mathematics · Grade 4
Learners add and subtract multi-digit whole numbers with the standard algorithm, regrouping across several places and across zeros. They use rounding to estimate whether an answer is reasonable, check results with the inverse operation, and analyse common mistakes in worked calculations.
Mathematics · Grade 4
Learners use multiplication to compare amounts ('5 times as many'), multiply numbers up to four digits by a one-digit number, and multiply two two-digit numbers. Area models and partial products built on place value show why each method works, and estimates help learners judge whether a product is reasonable.
Mathematics · Grade 4
Learners divide numbers up to four digits by a one-digit number using place value, partial quotients and area models, check quotients with multiplication, find remainders, and decide what a remainder means in a word problem: round up, use only full groups, or answer with the remainder itself.
Mathematics · Grade 4
Learners find all factor pairs of numbers up to 100, see that a number is a multiple of each of its factors, sort numbers into prime and composite, and build number and shape patterns from a rule, noticing features of the pattern that the rule does not state.
Mathematics · Grade 4
Learners use fraction bars and number lines to see why multiplying the numerator and denominator by the same number gives an equivalent fraction, generate equivalent fractions, and compare fractions with different numerators and denominators using common denominators, common numerators and the benchmarks 1/2 and 1, always for the same whole.
Mathematics · Grade 4
Learners add and subtract fractions with the same denominator as joining and separating parts of the same whole, decompose fractions into sums in more than one way, add and subtract mixed numbers (regrouping a whole when needed), and solve word problems with fraction bars and number lines.
Mathematics · Grade 4
Learners see every fraction as a multiple of a unit fraction (5/4 = 5 × 1/4), multiply a whole number by a fraction as repeated groups of that fraction (3 × 2/5 = 6/5), solve word problems with bars, number lines and equations, and reason about which two whole numbers a product lies between.
Mathematics · Grade 4
Learners connect tenths and hundredths: they rename tenths as hundredths to add them (3/10 + 4/100 = 34/100), write fractions with denominators 10 and 100 as decimals, place decimals on number lines, and compare decimals to hundredths with >, = and <, always for the same whole.
Mathematics · Grade 4
Learners learn the relative sizes of metric and customary units (km, m, cm; kg, g; lb, oz; L, mL; hours, minutes, seconds), convert from larger to smaller units with two-column tables, solve measurement and money word problems, and make and use line plots with measurements in halves, fourths and eighths.
Mathematics · Grade 4
Learners name points, lines, segments, rays and angles, understand an angle as a turn measured in degrees (one degree is 1/360 of a full turn), find unknown angles by adding and subtracting parts, classify triangles and quadrilaterals by their angles and by parallel and perpendicular sides, and find lines of symmetry.
Mathematics · Grade 4
Learners plan and solve multi-step word problems with all four operations, write equations with a letter for the unknown, decide what remainders mean, check answers with estimates, use area and perimeter formulas for rectangles (including finding a missing side), and write and critique mathematical justifications.
Mathematics · Grade 5
Learners discover that each place is worth ten times the place to its right, use exponents to write powers of ten, and explain why digits shift when a number is multiplied or divided by 10, 100 or 1,000. They then read, write, compare and round decimals to thousandths, and carry the same reasoning into metric measurement.
Mathematics · Grade 5
Learners estimate with rounding and powers of ten, multiply multi-digit whole numbers by connecting area models and partial products to the standard algorithm, and divide four-digit numbers by two-digit divisors with partial quotients. The course ends with real situations where the remainder must be interpreted.
Mathematics · Grade 5
Learners model decimal sums and differences on hundredths grids and number lines, then add and subtract decimals to hundredths by lining up place values and regrouping across the decimal point. Estimation and inverse operations are used to check every answer, and the course closes with money and measurement problems.
Mathematics · Grade 5
Learners multiply decimals by whole numbers with jumps on a number line, multiply two decimals with area models, and place the decimal point by estimating. They then divide decimals by sharing and by asking how many groups fit, and apply both operations to prices, recipes and lengths.
Mathematics · Grade 5
Learners see why fractions must be cut into same-size pieces before they can be added or subtracted, then use equivalent fractions to add and subtract unlike fractions and mixed numbers, including regrouping. Benchmark estimates (0, 1/2 and 1) are used to catch unreasonable answers in recipes, hikes and building projects.
Mathematics · Grade 5
Learners find fractions of whole numbers with tape diagrams, multiply fractions with area models, and find areas of rectangles with fractional sides. They then reason about scaling, predicting whether a product is bigger or smaller than a factor without computing, and solve recipe, garden and map problems with mixed numbers.
Mathematics · Grade 5
Learners discover that a fraction is a division (3 ÷ 4 = 3/4) by sharing pizzas and granola bars, then divide a unit fraction by a whole number and a whole number by a unit fraction with bars and number lines. Every quotient is checked with multiplication, and the final lesson asks learners to decide which division a story describes.
Mathematics · Grade 5
Learners evaluate expressions with parentheses, brackets and braces, translate words into expressions and reason about expressions without calculating them. They then build two numerical patterns from two rules, line up corresponding terms as ordered pairs and explain the relationship between them, before modelling costs and savings with expressions.
Mathematics · Grade 5
Learners meet the coordinate plane (axes, origin and ordered pairs) and plot and read points in the first quadrant. They graph the ordered pairs made by two numerical patterns, interpret points in real situations, find horizontal and vertical distances, and use a graph to compare two savings plans.
Mathematics · Grade 5
Learners measure volume by packing unit cubes in layers, connect layers to the formulas V = l × w × h and V = B × h, and find the volume of solids made of two rectangular prisms. The course ends with boxes, sandboxes and aquariums, including finding a missing dimension and converting cubic centimeters to liters.
Mathematics · Grade 5
Learners convert between metric units with powers of ten and between customary units with the relationships 12, 3, 16, 4 and 2, then use conversions in multi-step problems. They read and build line plots of measurements in halves, fourths and eighths, and use fraction operations to answer questions about the data, including sharing a total out equally.
Mathematics · Grade 5
Learners classify triangles and quadrilaterals by their properties and organise them in a hierarchy, explaining why every square is also a rectangle and a rhombus. The second half of the course pulls the whole year together: learners plan, solve and check multi-step problems that combine fractions, decimals, volume and unit conversion, and critique flawed solutions.
Mathematics · Grade 6
Learners describe relationships with ratio language, build equivalent ratios in tables and on double number lines, and solve part-part-whole problems with tape diagrams. They then graph ratio pairs, see that they fall on a line through the origin, and compare mixtures such as paint and lemonade.
Mathematics · Grade 6
Learners find unit rates such as price per item and speed, use them to predict and to choose the better buy, and then treat percent as a rate per 100. They find percents of quantities, find a whole from a part and a percent, and convert measurement units with ratio reasoning.
Mathematics · Grade 6
Learners interpret fraction division as 'how many groups?' and 'how much in one group?', model quotients with number lines and tape diagrams, and then connect the models to the common-denominator and multiply-by-the-reciprocal methods. Story problems about servings, ribbons, trails and areas close the course, with every quotient checked by multiplication.
Mathematics · Grade 6
Learners build fluency with the standard algorithms: long division of multi-digit whole numbers (including decimal quotients), and adding, subtracting, multiplying and dividing multi-digit decimals. Each algorithm is connected to place value, every answer is checked with an estimate, and the course ends with shopping, fabric and fencing problems.
Mathematics · Grade 6
Learners find factors, multiples and prime factorizations, then use them to find greatest common factors and least common multiples. They rewrite sums such as 36 + 8 as 4(9 + 2) with the distributive property, and decide whether real problems about kits, tiles and schedules call for a GCF or an LCM.
Mathematics · Grade 6
Learners use positive and negative numbers for temperatures, elevations and money, place and order rational numbers on a number line, and interpret absolute value as distance from zero. They then extend the coordinate plane to four quadrants, reflect points across the axes and find distances between points that share a coordinate.
Mathematics · Grade 6
Learners write and evaluate numerical expressions with whole-number exponents, then move to expressions with variables: writing them from words, naming their parts and evaluating formulas such as the area of a square and the volume of a cube. The course ends with equivalent expressions made with the distributive property and like terms, tested by substitution.
Mathematics · Grade 6
Learners treat an equation as a balance, test values by substitution, and solve one-step equations of the forms x + p = q and px = q with whole numbers, fractions and decimals. They write equations for real situations and finish with inequalities such as x > c, which have infinitely many solutions shown on a number line.
Mathematics · Grade 6
Learners study two quantities that change together: they decide which variable depends on which, write equations such as d = 65t from tables, and graph the relationships in the first quadrant. The course ends by using tables, graphs and equations together to answer questions and compare two plans.
Mathematics · Grade 6
Learners find the areas of parallelograms, triangles and trapezoids by rearranging and decomposing them into rectangles, and extend this to composite polygons, including polygons drawn on the coordinate plane. They then unfold prisms and pyramids into nets to find surface area, and find volumes of boxes with fractional edge lengths by packing small cubes and with V = lwh.
Mathematics · Grade 6
Learners tell statistical questions, whose answers vary, from questions with one answer. They describe distributions in dot plots by center, spread and shape, build and read histograms with equal intervals, and summarize data with a five-number summary and a box plot.
Mathematics · Grade 6
Learners describe data sets, find the mean as a fair share and balance point, and measure spread with the mean absolute deviation. They compare the mean and MAD with the median and IQR and choose the measures that fit the shape of the data. The course closes with a modeling lesson that combines ratios, rates, percents, fractions and data summaries from the whole year.
Mathematics · Grade 7
Learners compute unit rates from ratios of fractions (half a mile in a quarter hour is 2 miles per hour), test whether two quantities are proportional using tables and graphs, find the constant of proportionality in every representation and write equations of the form y = kx. The course ends by interpreting points on a proportional graph, especially (0, 0) and the unit-rate point (1, r).
Mathematics · Grade 7
Learners treat every percent change as a multiplier: an 8% tax multiplies by 1.08 and a 25% discount multiplies by 0.75. They solve tax, tip, markup, discount, commission and simple-interest problems, chain several changes together, compute percent increase, decrease and error relative to the original amount, and work backward from a final price to the original.
Mathematics · Grade 7
Learners see that opposite quantities combine to make zero, add positive and negative integers, decimals and fractions as moves on a number line, and discover from patterns why subtracting a number is the same as adding its opposite. They finish by finding distances between rational numbers as the absolute value of their difference and by solving multi-step problems about temperatures, elevations and money.
Mathematics · Grade 7
Learners discover the sign rules for multiplication from patterns and prove (−1)(−1) = 1 with the distributive property, then divide signed numbers, see why division by zero is undefined and why −(3/4) = (−3)/4 = 3/(−4). They use long division to show that every fraction becomes a terminating or a repeating decimal, and finish by solving multi-step problems with all four operations.
Mathematics · Grade 7
Learners combine like terms and subtract expressions with rational coefficients, expand products such as −3(2x − 5) and (1/2)(4x + 6), and factor expressions by taking out a common factor, including negative and fractional factors. They then rewrite expressions to reveal what they mean in context, for example seeing that a + 0.05a = 1.05a describes a 5% increase.
Mathematics · Grade 7
Learners solve two-step equations of the forms px + q = r and p(x + q) = r with positive and negative rational numbers, compare arithmetic and algebraic solutions, and write equations for word problems, using estimation to check that answers are reasonable. They then solve inequalities such as −2x + 7 ≥ 15, reversing the inequality when multiplying or dividing by a negative number, and interpret the solution set in context.
Mathematics · Grade 7
Learners treat a scale as a proportional relationship: they find actual lengths and areas from maps, plans and models, explain why areas grow by the square of the scale factor, and redraw a figure at a new scale. They then reason about constructing triangles: which three lengths can meet, why the angles always add to 180°, and which sets of measurements give exactly one triangle, more than one, or none.
Mathematics · Grade 7
Learners discover π as the constant ratio of circumference to diameter, use C = πd and A = πr² with exact answers in terms of π and approximations with π ≈ 3.14, and see why the area formula works by rearranging wedges. They then write and solve equations for unknown angles using complementary, supplementary, vertical and adjacent angles, and find areas of composite figures made of polygons and parts of circles.
Mathematics · Grade 7
Learners slice right rectangular prisms and pyramids in their minds and describe the cross-sections, then use the idea that every slice of a prism parallel to its base is the same to justify V = Bh for rectangular, triangular and composite prisms. They find surface areas from faces and nets, and finish by deciding whether a real problem is about filling (volume) or covering (surface area), including missing dimensions and rounding up when buying materials.
Mathematics · Grade 7
Learners separate populations from samples, tell random samples from biased ones, and use random samples to estimate percents and means, seeing in a simulation that larger samples vary less. They then compare two groups by their centers and their mean absolute deviations, express the gap between means as a number of MADs, and use that measure to make careful informal inferences about two populations from random samples.
Mathematics · Grade 7
Learners place probabilities on a 0-to-1 scale, compute them for equally likely outcomes, and compare theoretical probabilities with the long-run relative frequencies of experiments, including results that show a model is wrong. They build uniform and non-uniform probability models, then find probabilities of compound events with organized lists, tables and tree diagrams, and design simulations for events that are hard to compute.
Mathematics · Grade 7
The grade 7 capstone. Learners model multi-step percent and rate situations with multipliers, write and solve equations and inequalities for real constraints, and act as checkers who find, name and fix the first error in flawed solutions. They finish by comparing two correct methods and by transferring the year's tools (scale, area, volume, probability and data) to unfamiliar situations, with cumulative retrieval throughout.
Mathematics · Grade 8
Learners use long division to see why every fraction becomes a decimal that stops or repeats, and then run the process backwards to turn repeating decimals into fractions. They solve x^2^ = p and x^3^ = p with square and cube roots, meet numbers such as √2 and π that are not fractions at all, and squeeze those irrational numbers between rational ones to place and compare them on the number line.
Mathematics · Grade 8
Learners explain the properties of integer exponents by counting factors, extend them to zero and negative exponents with patterns and the quotient rule, and then use powers of ten to write very large and very small quantities in scientific notation. They compare magnitudes by asking how many times as much, and multiply, divide, add and subtract in scientific notation, including calculator E-notation and sensible units.
Mathematics · Grade 8
Learners connect the unit rate of a proportional relationship to the slope of its graph and compare proportional relationships given as equations, tables, graphs and descriptions. They use slope triangles and similar triangles to explain why a line has one constant slope, compute slopes from two points, and derive and graph y = mx and y = mx + b.
Mathematics · Grade 8
Learners solve linear equations with the variable on both sides, naming the property of equality behind every step. They distribute and combine like terms, clear fractions and decimals, and use the structure of an equation to decide whether it has exactly one solution, no solution or infinitely many solutions.
Mathematics · Grade 8
Learners see the solution of a system of two linear equations as the point that lies on both lines, check ordered pairs in both equations and solve systems by graphing. They use slopes and intercepts to recognise systems with no solution or infinitely many solutions, solve by substitution, elimination and inspection, and model real situations with systems whose solutions they interpret in context.
Mathematics · Grade 8
Learners define a function as a rule that gives each input exactly one output and test relations given as pairs, tables, graphs and descriptions. They find and interpret the rate of change and initial value of linear functions, compare functions shown in different representations, tell linear from nonlinear functions, and read and describe qualitative graphs.
Mathematics · Grade 8
Learners study the three rigid motions (translations, reflections and rotations), verify that they keep lengths, angle measures and parallel lines, and describe them with coordinate rules, including reflections across the axes and 90° and 180° rotations about the origin. The course ends by defining congruence as a sequence of rigid motions and by finding and checking such sequences.
Mathematics · Grade 8
Learners describe dilations with coordinates and scale factors, define similarity as rigid motions plus dilations, and use scale factors to find missing lengths. They then find angles formed when parallel lines are cut by a transversal, explain why a triangle's angles add to 180° and why an exterior angle equals the sum of the two remote interior angles, and use the angle-angle criterion to prove triangles similar and solve measurement problems.
Mathematics · Grade 8
Learners see why a^2^ + b^2^ = c^2^ through an area argument with squares, and use the converse to test whether a triangle has a right angle. They then find missing sides of right triangles in real situations, extend the theorem to the space diagonal of a box, and compute distances between points on the coordinate plane, giving exact square roots or rounded values as asked.
Mathematics · Grade 8
Learners extend base-times-height to cylinders, discover that a cone holds one third of the matching cylinder, and find sphere volumes with the 1 : 2 : 3 relationship among a cone, a sphere and a cylinder. They give exact answers in terms of π and approximate answers with π ≈ 3.14, then work backward to missing heights and radii (using square and cube roots) and find the volume of composite solids in real situations.
Mathematics · Grade 8
Learners plot paired data and describe the pattern in a scatter plot: direction, linear or nonlinear form, clusters and outliers, without confusing association with cause. They fit straight lines informally and judge them by how close the points are, use a line's equation to predict and to interpret slope and intercept in context, and finish with two-way tables, using relative frequencies to decide whether two categorical variables seem associated.
Mathematics · Grade 8
This capstone pulls the year together for algebra. Learners build linear models from descriptions, tables and two points, solve and critique linear equations (including ones with no or infinitely many solutions), and model real choices with systems of equations. They then use the Pythagorean theorem in context, critique predictions made far outside the data, and retrieve exponent, scientific-notation and function skills from earlier in the year.
Mathematics · Grade 9
A fast but serious consolidation of the number sense algebra depends on: computing with signed rational numbers and proving why the sign rules work, reasoning with ratios and unit rates, handling percent change (including why successive changes do not simply add), and checking whether a quantitative result or claim is reasonable.
Mathematics · Grade 9
Learners write expressions from words and contexts and read the meaning of each part, use the properties of operations to produce and justify equivalent expressions (and to disprove false equivalences with counterexamples), evaluate formulas carefully, and use units and dimensional analysis to convert quantities and check that formulas make sense.
Mathematics · Grade 9
Learners solve multi-step linear equations as chains of justified moves, recognize equations with no solution or infinitely many, rearrange formulas, and solve linear and compound inequalities, including a clear explanation of why multiplying by a negative reverses the inequality. The course ends by modeling budgets, capacities and schedules with equations and inequalities and interpreting the answers in context.
Mathematics · Grade 9
Learners read the story a graph tells, compute slope from points, tables and graphs and interpret it as a rate with units, write and graph lines in slope-intercept, point-slope and standard form (including horizontal and vertical lines), and measure the average rate of change of curved relationships over an interval.
Mathematics · Grade 9
Learners define a function as a rule that gives each input exactly one output and test relations in mappings, tables, graphs and equations. They use function notation to evaluate and interpret statements like h(2) = 30, describe domain, range and key features of graphs, and compare functions given in different representations, including arithmetic sequences seen as linear functions.
Mathematics · Grade 9
Learners connect the table, equation, graph and words of a linear model, interpret rate of change and initial value with their units, and build models from two facts while checking that every representation agrees. They then decide when a prediction is trustworthy, spot invalid extrapolations, and finish with the full cycle of graphing, solving and interpreting. An optional honors lesson critiques two plausible models of a cooling cup of tea.
Mathematics · Grade 9
Learners solve pairs of linear equations by graphing, substitution and elimination, prove why elimination is valid, and classify systems by their number of solutions. They model ticket sales, mixtures and plan comparisons with systems, then graph linear inequalities and systems of inequalities to find and interpret feasible combinations under real constraints.
Mathematics · Grade 9
Learners derive the laws of integer exponents from the meaning of repeated multiplication (including zero and negative exponents), then build exponential functions y = a·b^x^ and interpret their initial value, growth or decay factor and percent rate. They contrast constant differences with constant ratios, see why exponential growth eventually overtakes any linear growth, and model compound interest, depreciation, half-life and geometric sequences.
Mathematics · Grade 9
Learners add, subtract and multiply polynomials with the distributive property and area models, then reverse multiplication by factoring: greatest common factors, trinomials (including leading coefficients other than 1) and the special forms difference of squares and perfect-square trinomials. They learn to factor completely, to see structure such as x^4^ − 81, and to check any factorization by multiplying or substituting.
Mathematics · Grade 9
Learners read the vertex, axis of symmetry, intercepts and direction of a parabola from its standard, vertex and factored forms, then solve quadratic equations by factoring, square roots, completing the square and the quadratic formula, using the discriminant to predict the number of real solutions. Projectile and area models end the course, with attention to rejecting solutions that make no sense. An optional honors lesson derives the quadratic formula.
Mathematics · Grade 9
Learners summarize distributions with center, spread, shape and outliers, look for associations in two-way tables using conditional relative frequencies, and describe scatterplots with direction, form, strength and correlation. They fit and interpret linear models, judge fit with residuals, and critique claims that confuse correlation with causation, ignore lurking variables, extrapolate, or use misleading graphs.
Mathematics · Grade 9
A capstone investigation that pulls the year together. Learners help a fictional town plan its community fair: they formulate questions and assumptions, choose between linear and exponential models of attendance and advertising reach, build a quadratic revenue model to set a ticket price under a crowd constraint, and validate their models against new data before writing a recommendation with stated limitations.
Mathematics · Grade 10
The opening course of geometry builds the language and logic of proof. Learners work with undefined terms and precise definitions, analyze conditional statements and their converses, inverses and contrapositives, contrast inductive conjectures with deductive arguments, apply the segment and angle addition postulates, and write their first two-column and paragraph proofs, including the vertical angles theorem.
Mathematics · Grade 10
Learners begin the statistics elective by asking questions that data can answer. They identify individuals and variables, classify variables, summarize categorical data with frequencies and displays, analyze two-way tables with marginal, joint and conditional relative frequencies, judge whether two variables are associated, and consider the ethics of collecting and sharing data.
Mathematics · Grade 10
Learners carry out classical compass-and-straightedge constructions as precise procedures and explain why they work, then describe rigid motions (translations, reflections and rotations) exactly with coordinate rules. They compose transformations, find sequences that map one figure onto another, and use rotations and reflections to describe the symmetry of polygons.
Mathematics · Grade 10
Learners study where data come from. They compare sampling methods and see sampling variability in a simulation, identify sources of bias, distinguish observational studies from experiments, explain confounding, design experiments with control, random assignment, replication, blocking and blinding, and decide what conclusions a study's design allows.
Mathematics · Grade 10
Learners describe distributions of quantitative data: they choose displays, describe shape, center, spread and unusual values, compute and compare the mean, median, standard deviation and interquartile range, identify outliers with the 1.5 × IQR rule, standardize values with z-scores and percentiles, see how linear transformations change summaries, and use the empirical rule for normal distributions.
Mathematics · Grade 10
Learners define congruence through rigid motions, read congruence statements to find corresponding parts, and justify the triangle congruence criteria SSS, SAS, ASA, AAS and HL, including counterexamples showing why SSA and AAA fail. They plan and write two-column proofs of triangle congruence and then use congruent triangles (CPCTC) to prove further facts, such as the perpendicular bisector theorem.
Mathematics · Grade 10
Learners prove the triangle angle-sum and exterior angle theorems, the isosceles triangle theorem and its converse, and use the triangle inequality and the midsegment theorem. They then meet the four classical points of concurrency (circumcenter, incenter, centroid and orthocenter), prove why the circumcenter is equidistant from the vertices, and apply the centroid's 2 : 1 property.
Mathematics · Grade 10
Learners study relationships between two quantitative variables. They describe scatterplots, interpret the correlation r and its properties, build the least-squares regression line from summary statistics, interpret slope, intercept and r² in context, use residuals and residual plots to judge fit, recognize outliers and influential points, avoid extrapolation, and separate correlation from causation. An optional honors lesson straightens curved data with logarithms.
Mathematics · Grade 10
Learners prove the angle relationships formed when a transversal crosses parallel lines and use their converses to prove lines parallel. They connect parallel and perpendicular lines to slopes, write equations of such lines, use the distance and midpoint formulas, partition segments in a given ratio, and write coordinate proofs that classify triangles and quadrilaterals.
Mathematics · Grade 10
Learners build the probability tools that inference relies on: the addition and multiplication rules, conditional probability, independence and tree diagrams; discrete random variables with their means and standard deviations; binomial and geometric settings; and simulation as a way to estimate probabilities. An optional honors lesson reverses conditional probabilities with natural frequencies.
Mathematics · Grade 10
Learners study dilations and their properties, define similarity with similarity transformations, and use the AA, SAS and SSS similarity criteria to find unknown lengths, including indirect measurement with shadows. They prove the triangle proportionality (side-splitter) theorem and the Pythagorean theorem with similar triangles, and apply scale factors to maps, models, areas and volumes. An optional honors lesson develops geometric means in right triangles.
Mathematics · Grade 10
Learners treat a sample statistic as a random variable. Starting from a sampling simulation, they describe sampling variability, find the mean and standard deviation of the sampling distributions of a sample proportion and a sample mean, check when a normal model is appropriate, meet the Central Limit Theorem, and distinguish bias from variability in estimators.
Mathematics · Grade 10
Learners use the Pythagorean theorem and its converse to find lengths and classify triangles, and learn the 45°–45°–90° and 30°–60°–90° relationships. They see sine, cosine and tangent as ratios that similar right triangles share, use them and their inverses to find sides and angles, connect sine and cosine of complementary angles, and solve angle-of-elevation and depression problems. An optional honors lesson introduces the Law of Sines, the Law of Cosines and the area formula ½ab sin C.
Mathematics · Grade 10
Learners turn sampling distributions into estimates with honest uncertainty. They build confidence intervals for a proportion after checking conditions, interpret intervals and confidence levels correctly, see how confidence level and sample size change the margin of error, choose a sample size for a desired margin, and construct a t interval for a mean.
Mathematics · Grade 10
Learners test claims with data. They state hypotheses, see the logic of a significance test through simulation, carry out a one-proportion z test, interpret P-values and significance levels, weigh Type I and Type II errors and power, meet the one-sample t test and randomization tests for two groups, and distinguish statistical significance from practical importance.
Mathematics · Grade 10
Learners prove the properties of parallelograms with congruent triangles, learn several ways to prove that a quadrilateral is a parallelogram, and distinguish rectangles, rhombuses and squares by their diagonals. They study trapezoids and kites, organize quadrilaterals in a hierarchy, and derive and apply the interior and exterior angle sums of polygons.
Mathematics · Grade 10
Learners relate central angles, arcs and inscribed angles and prove the inscribed angle theorem, including the right angle in a semicircle and the supplementary opposite angles of a cyclic quadrilateral. They use tangent and chord properties, compute arc lengths and sector areas, meet radian measure as arc length divided by radius, and write and analyze equations of circles on the coordinate plane.
Mathematics · Grade 10
Learners study what can go wrong. They check the conditions behind intervals and tests and see what happens when they fail, diagnose regression models with residual plots and influential points, recognize the dangers of multiple comparisons and p-hacking, untangle Simpson's paradox, and practice communicating uncertainty and the limits of generalization honestly.
Mathematics · Grade 10
In this capstone, learners carry a statistical investigation from question to report using a fictional school sleep survey. They pose questions and plan data collection, choose and carry out descriptive and inferential methods (an interval, a test, a comparison of groups and a regression), critique conditions, bias and scope, and write a clear, honest report for a general audience, while retrieving key skills from the whole elective.
Mathematics · Grade 10
Learners justify area formulas by cutting and rearranging, including an informal limit argument for the area of a circle, and explain volume formulas with Cavalieri's principle and the one-third relationship between pyramids and prisms. They compute surface areas from nets, identify cross-sections and solids of revolution, and apply density and scale factors in modeling problems. An optional honors lesson shows three pyramids filling a cube.
Mathematics · Grade 10
Learners use geometry to model and design real objects: they represent irregular objects with simple shapes and state their assumptions, explore designs numerically to find the best option under a constraint (the largest pen, the biggest open box), check whether designs satisfy limits on slope, clearance and capacity, and reason about measurement precision before communicating a recommendation.
Mathematics · Grade 10
The geometry capstone. Learners choose among two-column, paragraph, coordinate and transformation proofs for the same theorem, critique and repair flawed proofs, and complete a design brief for a fictional community-garden pavilion that draws on area, volume, similarity and trigonometry. They finish by assembling portfolio pieces: a polished proof and a design report written for a non-specialist audience.
Mathematics · Grade 11
Algebra II opens by sharpening the language of functions. Learners find domains and ranges in interval notation, including restrictions from denominators and square roots, analyze piecewise and absolute value functions, combine and compose functions (and find the domain of a composition), and use algebraic structure: testing whether functions are even or odd, decomposing composite functions, and computing average rates of change.
Mathematics · Grade 11
Learners open the calculus elective by studying how fast quantities change. They compute average rates of change with units, estimate instantaneous rates from tables and graphs using local linearity, connect position and velocity, approximate with tangent lines, and simplify difference quotients in preparation for the formal definition of the derivative.
Mathematics · Grade 11
Learners return to linear and quadratic models with Algebra II tools: piecewise-linear pricing, interpreting technology-produced lines of fit, vertex form by completing the square for maximum and minimum problems, linear–quadratic systems, and quadratic inequalities solved with sign analysis. An optional honors lesson fits a quadratic through three points with a system of three equations.
Mathematics · Grade 11
Learners make 'approaching' precise. They estimate limits from tables and graphs, compare one-sided limits, evaluate limits with limit laws, factoring and rationalizing, analyze limits involving infinity, test continuity with three conditions, classify discontinuities, and use the Intermediate Value Theorem. An optional honors lesson introduces the squeeze theorem and the limit of sin x / x.
Mathematics · Grade 11
Learners connect a polynomial's degree, leading coefficient, zeros and multiplicities to the shape of its graph, divide polynomials by long and synthetic division, and use the remainder and factor theorems. They find rational zeros with the rational root theorem to solve polynomial equations, and prove polynomial identities, including one that generates Pythagorean triples.
Mathematics · Grade 11
Learners define the derivative as a limit of difference quotients, interpret it with units, connect the graphs of f and f′, and learn where derivatives fail to exist. They then derive and apply the power, sum, product and quotient rules, use the derivatives of sine, cosine, the exponential and the natural logarithm, apply the chain rule, and write tangent lines.
Mathematics · Grade 11
Learners differentiate equations that do not give y explicitly, derive the derivatives of inverse functions such as ln x, arcsin x and arctan x, solve related-rate problems about sliding ladders, spreading ripples, filling tanks and lengthening shadows, and use local linear approximation and differentials to estimate values and measurement errors.
Mathematics · Grade 11
Learners treat rational expressions like fractions with variables: they simplify, multiply, divide, add and subtract them while tracking domain restrictions, solve rational equations and detect extraneous solutions, analyze rational functions (vertical and horizontal asymptotes, holes, transformations of 1/x), and model inverse variation, combined work rates and average cost.
Mathematics · Grade 11
Learners use derivatives to analyze and optimize. They find critical points, classify extrema with the first- and second-derivative tests, study concavity and inflection points, locate absolute extrema on closed intervals, solve optimization problems such as designing a box or a fence, apply the Mean Value Theorem, and decide when a moving object speeds up or slows down. An optional honors lesson introduces L'Hôpital's rule.
Mathematics · Grade 11
Learners extend the exponent laws to rational exponents and see why a^1/n^ must mean the nth root. They simplify and combine radicals, rationalize denominators, solve radical equations while checking for extraneous solutions, and analyze square root and cube root functions and models such as a pendulum's period.
Mathematics · Grade 11
Learners discover that the area under a rate graph is the accumulated change in a quantity, approximate that accumulation with Riemann and trapezoid sums, and then define the definite integral as the limit of those sums. They evaluate integrals with geometry, properties and a symbolic rule derived from sums, build accumulation functions, and learn to say exactly when each rule or estimate applies.
Mathematics · Grade 11
Learners meet the imaginary unit i, do arithmetic with complex numbers (including powers of i, conjugates and division), and plot complex numbers in the complex plane. They solve every quadratic equation, including those with complex solutions, derive the quadratic formula by completing the square, and use the Fundamental Theorem of Algebra and conjugate pairs to count and find polynomial zeros. An optional honors lesson explains why complex zeros of real polynomials come in pairs.
Mathematics · Grade 11
Learners connect the two halves of calculus. Building on accumulation functions, they see why the derivative of an accumulated amount is the rate (Fundamental Theorem, part 1), find antiderivatives, evaluate definite integrals exactly with antiderivatives (part 2), and use the net change theorem and average value in context. An optional honors lesson handles variable upper limits with the chain rule.
Mathematics · Grade 11
Learners extend exponential models to the base e and continuous compounding, define the logarithm as the inverse of exponentiation, derive the product, quotient and power properties from the exponent laws, and use logarithms (including change of base) to solve exponential equations for doubling times, half-lives and growth rates.
Mathematics · Grade 11
Learners widen their integration toolkit with substitution, then use integrals to measure: areas between curves, volumes of solids built from disks, washers and known cross-sections, and positions recovered from velocity and acceleration. An optional honors lesson introduces integration by parts.
Mathematics · Grade 11
Learners describe how shifts, stretches, compressions and reflections change a function's equation, graph and key points, and write transformed equations from descriptions. They then find inverse functions algebraically, verify them by composition, relate their graphs by reflection in y = x, test invertibility with the horizontal line test, and restrict domains so that quadratics have inverses.
Mathematics · Grade 11
Learners write arithmetic and geometric sequences explicitly and recursively, use sigma notation, and prove the arithmetic series formula by pairing and the geometric series formula by multiplying and subtracting. They apply finite geometric series to savings plans and decide when an infinite geometric series has a sum, using it for repeating decimals and a bouncing ball.
Mathematics · Grade 11
Learners read equations about rates of change as models. They verify solutions, sketch and interpret slope fields, approximate solutions with Euler's method, solve separable equations with initial conditions, and model exponential growth and decay, Newton's law of cooling and logistic growth, including equilibrium and long-run behavior.
Mathematics · Grade 11
In this capstone, learners investigate a fictional reservoir during a twelve-hour storm. Using inflow and outflow rates, they build an accumulation model, find when the water volume rises, falls and reaches its extremes, approximate integrals from data and judge their accuracy, connect volume and depth with related rates, extend the model with a differential equation, and write a complete, justified report.
Mathematics · Grade 11
Learners extend trigonometry from right triangles to all angles. They measure angles in radians, use the unit circle to evaluate sine, cosine and tangent of any angle, prove the Pythagorean identity sin^2^θ + cos^2^θ = 1, graph sinusoidal functions with amplitude, period, midline and phase shift, and model Ferris wheels, tides and daylight hours with invented but realistic data.
Mathematics · Grade 11
Learners build sample spaces and use the addition and multiplication rules, compute conditional probabilities from two-way tables and test for independence, use normal distributions, the empirical rule and z-scores to estimate proportions and compare values, and distinguish surveys, observational studies and experiments while judging sample estimates with simulation and margins of error.
Mathematics · Grade 11
The Algebra II capstone. Working with invented monitoring data from a fictional lake, learners decide which function family fits each data set (linear, quadratic, exponential, logarithmic or periodic), build models from key features and from transformed data, compare competing models with residuals and context, and write an investigation report that states its assumptions and limits.
Mathematics · Grade 12
Precalculus opens with building functions from situations: writing explicit formulas from geometry and business contexts, describing processes recursively, composing and inverting functions to answer chained and reverse questions, and analyzing how a model behaves on intervals with average rates of change, extreme values and domain limits. Learners finish by choosing and defending a model family for a purpose.
Mathematics · Grade 12
Learners analyze polynomial and rational functions as a precalculus student should: complete factorization over the complex numbers, end behavior and turning points, sign charts for polynomial inequalities, a full analysis of rational graphs including holes and slant asymptotes, and rational inequalities in context, such as keeping an average cost below a target.
Mathematics · Grade 12
Learners use exponential and logarithmic functions as modeling tools: cooling toward room temperature, logistic growth with a carrying capacity, straightening exponential data with a semi-log plot, and logarithmic scales such as pH and decibels. Throughout, they compare models and explain which assumptions each one makes.
Mathematics · Grade 12
Learners extend trigonometry to all six functions on the unit circle, define inverse trigonometric functions on restricted domains, verify identities with chains of justified steps, disprove false identities with counterexamples, and derive and use the sum, difference and double-angle formulas.
Mathematics · Grade 12
Learners solve trigonometric equations on an interval and in general form, then apply trigonometry to triangles that are not right triangles: the Law of Sines with its ambiguous case, the Law of Cosines, the area formula ½ab sin C, navigation with bearings, and periodic motion modeled by sine and cosine.
Mathematics · Grade 12
Learners represent quantities with both size and direction as vectors, combine them, use the dot product to measure angles and work, solve navigation and force problems, and describe motion with parametric equations such as the path of a launched ball. An optional honors lesson introduces polar coordinates.
Mathematics · Grade 12
Learners study circles, parabolas, ellipses and hyperbolas as sets of points defined by distances. They complete the square to find centers, derive the equation of a parabola from its focus and directrix, read foci and eccentricity from equations, classify conics from general equations, and use reflective properties in designs such as dishes, reflectors and orbits.
Mathematics · Grade 12
Learners prove statements about all natural numbers with mathematical induction, manipulate sigma notation, decide when an infinite geometric series converges and find its sum, expand powers with the binomial theorem and Pascal's triangle, and investigate the long-run behavior of sequences, including recursive ones.
Mathematics · Grade 12
Learners count outcomes with permutations and combinations, use expected value to compare decisions such as buying a warranty or guessing on a test, model repeated trials with the binomial distribution, and critique statistical claims: biased samples, misleading graphs, overfitted models and confusing conditional probabilities.
Mathematics · Grade 12
Learners prepare for calculus by moving from average to instantaneous rates of change: secant slopes that approach a tangent slope, difference quotients simplified with algebra, limits read from tables, graphs and formulas, informal continuity, and limits at infinity that describe end behavior.
Mathematics · Grade 12
Learners meet three directions that mathematics takes after precalculus: calculus (finding accumulated change from a rate), statistics (estimating with uncertainty from random samples), and mathematical modeling (optimizing a decision under constraints). Every learner works through all three short extensions, decides which tool fits which question, and goes deeper in the one they choose.
Mathematics · Grade 12
In this capstone, learners carry a quantitative question from start to finish: they make a vague question precise, choose and justify a model or method, compute and check results, test how sensitive conclusions are to assumptions, and explain the findings honestly to a non-specialist audience. The quiz also retrieves key skills from across the year.
