Search every subject world, from Preschool to Grade 12. The first five courses of every subject path are free.
34 courses
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
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
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 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 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 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 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 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 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
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 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
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 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.
