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