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