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