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

24 courses

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Mathematics · Grade 7

Proportional Relationships and Graphs

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).

  • 4 lessons
  • About 90 min
  • Quiz: 10 questions
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Mathematics · Grade 7

Percent Change and Multi-Step Applications

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.

  • 4 lessons
  • About 95 min
  • Quiz: 10 questions
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Mathematics · Grade 7

Add and Subtract Rational Numbers

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.

  • 4 lessons
  • About 90 min
  • Quiz: 10 questions
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Mathematics · Grade 7

Multiply and Divide Rational Numbers

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.

  • 4 lessons
  • About 90 min
  • Quiz: 10 questions
Free starter

Mathematics · Grade 7

Expressions and Structural Reasoning

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.

  • 4 lessons
  • About 90 min
  • Quiz: 10 questions
Free starter

Mathematics · Grade 7

Equations and Inequalities

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.

  • 4 lessons
  • About 95 min
  • Quiz: 10 questions

Mathematics · Grade 7

Scale Drawings and Geometric Constructions

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.

  • 4 lessons
  • About 95 min
  • Quiz: 11 questions

Mathematics · Grade 7

Circles, Angles and Area

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.

  • 4 lessons
  • About 95 min
  • Quiz: 11 questions

Mathematics · Grade 7

Surface Area, Volume and Slicing Solids

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.

  • 4 lessons
  • About 95 min
  • Quiz: 11 questions

Mathematics · Grade 7

Sampling and Comparing Populations

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.

  • 4 lessons
  • About 95 min
  • Quiz: 11 questions

Mathematics · Grade 7

Chance Models and Compound Probability

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.

  • 4 lessons
  • About 95 min
  • Quiz: 11 questions

Mathematics · Grade 7

Multi-Step Modeling, Critique and Transfer

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.

  • 4 lessons
  • About 100 min
  • Quiz: 11 questions

Mathematics · Grade 8

Rational and Irrational Numbers

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.

  • 4 lessons
  • About 90 min
  • Quiz: 10 questions
Free starter

Mathematics · Grade 8

Exponents and Scientific Notation

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.

  • 4 lessons
  • About 90 min
  • Quiz: 10 questions
Free starter

Mathematics · Grade 8

Proportional Relationships and Slope

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.

  • 4 lessons
  • About 95 min
  • Quiz: 10 questions
Free starter

Mathematics · Grade 8

Linear Equations and Reasoning

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.

  • 4 lessons
  • About 90 min
  • Quiz: 10 questions
Free starter

Mathematics · Grade 8

Systems of Linear Equations

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.

  • 4 lessons
  • About 95 min
  • Quiz: 10 questions
Free starter

Mathematics · Grade 8

Functions and Multiple Representations

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.

  • 5 lessons
  • About 100 min
  • Quiz: 11 questions

Mathematics · Grade 8

Transformations and Congruence

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.

  • 4 lessons
  • About 90 min
  • Quiz: 10 questions

Mathematics · Grade 8

Similarity and Angle Relationships

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.

  • 4 lessons
  • About 95 min
  • Quiz: 10 questions

Mathematics · Grade 8

The Pythagorean Theorem

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.

  • 4 lessons
  • About 90 min
  • Quiz: 10 questions

Mathematics · Grade 8

Volume of Cylinders, Cones and Spheres

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.

  • 4 lessons
  • About 90 min
  • Quiz: 10 questions

Mathematics · Grade 8

Scatter Plots and Two-Variable Data

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.

  • 4 lessons
  • About 95 min
  • Quiz: 10 questions

Mathematics · Grade 8

Model, Explain and Prepare for Algebra

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.

  • 4 lessons
  • About 100 min
  • Quiz: 11 questions