All lessons

Course

7th Grade Math

Work with proportions and percents, compute with negative numbers, solve two-step equations, and find probability.

Work through the lessons in order, from proportional relationships to independent problem-solving. By the end, you can find the constant of proportionality from a table, graph, or equation and solve percent problems with tax, discounts, and interest. You can add, subtract, multiply, and divide positive and negative fractions and decimals. You can simplify, expand, and factor expressions and solve two-step equations and inequalities. You can use scale drawings, find unknown angles, and find the circumference and area of circles and the surface area and volume of prisms. You can find the probability of simple and compound events and use random samples to compare populations.

How to use these lessons

  • Start at the lesson marked Do this. Go on when you can do the line under the title by yourself.
  • Play the Games first. Then take the Quizzes. Eight of ten correct passes. The Worksheets are on paper. The answers are at the bottom.
  • Each lesson builds on the one before it. If a lesson is hard, go back one.
  • Use a number line for negative numbers, a percent bar for percent problems, and a compass and ruler for circles and scale drawings. Flip coins and roll dice to test probability. Check each equation by putting your answer back in.

Each lesson has games, quizzes, and worksheets.

0 of 42

Proportional Relationships

  1. 1Unit Rates with FractionsFind a unit rate when the quantities are fractions.
    • Walk 1/2 mile in 1/4 hour: find miles per hour.
    • Divide fractions to find the rate.
    • Compare two rates.
  2. 2Recognize Proportional RelationshipsTell if two quantities are in a proportional relationship.
    • Check for equal ratios in a table.
    • Check that the graph is a straight line through the origin.
    • Find relationships that are not proportional.
  3. 3Constant of ProportionalityFind the constant of proportionality from a table, graph, or story.
    • Find k = y/x in a table.
    • Read k from the point (1, k) on a graph.
    • Explain what k means in the story.
  4. 4Write Proportional EquationsWrite an equation such as y = kx.
    • Write t = 0.08p for sales tax.
    • Use the equation to find missing values.
    • Explain what (0, 0) means on the graph.
  5. 5Proportion Word ProblemsSolve multi-step ratio problems.
    • Set up and solve a proportion.
    • Use a unit rate instead.
    • Check that the answer makes sense.

Percent Applications

  1. 6Percent Increase and DecreaseFind the percent increase or decrease.
    • Find the change, then divide by the original.
    • Find a new amount after a 20% increase.
    • Use a percent bar model.
  2. 7Tax, Tips, and MarkupsFind the total cost with tax, a tip, or a markup.
    • Find 8% tax on a $45 purchase.
    • Find a 15% tip.
    • Multiply by 1.08 in one step.
  3. 8Discounts and Simple InterestFind sale prices and simple interest.
    • Find the price after a 30% discount.
    • Use I = P × r × t.
    • Compare two deals.
  4. 9Percent ErrorFind how far an estimate is from the actual value as a percent.
    • Find the difference between estimate and actual.
    • Divide by the actual value.
    • Compare the accuracy of two estimates.

Operations with Rational Numbers

  1. 10Add IntegersAdd positive and negative integers.
    • Use a number line and counters.
    • Know that a number and its opposite add to 0.
    • Add −8 + 5 and −4 + (−6).
  2. 11Subtract IntegersSubtract integers by adding the opposite.
    • Rewrite 3 − (−5) as 3 + 5.
    • Find the distance between two integers.
    • Solve temperature-change problems.
  3. 12Add and Subtract Rational NumbersAdd and subtract positive and negative fractions and decimals.
    • Find −2.5 + 4.75.
    • Find −3/4 − 1/2.
    • Use properties to add in any order.
  4. 13Multiply and Divide IntegersMultiply and divide positive and negative integers.
    • Explain why (−1)(−1) = 1.
    • Use sign rules for products and quotients.
    • Know −(p/q) = (−p)/q = p/(−q).
  5. 14Multiply and Divide Rational NumbersMultiply and divide positive and negative fractions and decimals.
    • Find −2/3 × 3/8.
    • Find −4.2 ÷ 0.6.
    • Know you cannot divide by 0.
  6. 15Fractions to DecimalsChange a fraction to a decimal that ends or repeats.
    • Use long division to change 3/8 to 0.375.
    • Change 2/3 to 0.666…
    • Write a repeating decimal with a bar.
  7. 16Rational Number Word ProblemsSolve real-world problems with all four operations on rational numbers.
    • Solve problems about money, temperature, and elevation.
    • Use the order of operations.
    • Check that the sign of the answer makes sense.

Expressions

  1. 17Simplify ExpressionsCombine like terms with rational coefficients.
    • Simplify 3x − 5 + 2x + 1/2.
    • Add and subtract terms with negative coefficients.
    • Check by substituting a value.
  2. 18Expand and FactorUse the distributive property to expand and factor expressions.
    • Expand −2(3x − 4).
    • Factor 6x + 9 as 3(2x + 3).
    • Factor out a negative number.
  3. 19Rewrite ExpressionsRewrite an expression to see a problem in a new way.
    • See that a + 0.05a = 1.05a means a 5% increase.
    • Write a perimeter in two ways.
    • Explain what each form shows.

Equations and Inequalities

  1. 20Two-Step EquationsSolve equations such as 3x + 5 = 20.
    • Undo addition, then multiplication.
    • Solve equations of the form p(x + q) = r.
    • Check by substituting the answer.
  2. 21Equations with Fractions and DecimalsSolve two-step equations with fractions, decimals, and negative numbers.
    • Solve 0.4x − 2 = 6.
    • Solve 2/3 x + 1 = −5.
    • Clear fractions by multiplying both sides.
  3. 22Two-Step InequalitiesSolve and graph inequalities such as 2x − 3 > 7.
    • Solve like an equation.
    • Flip the sign when you multiply or divide by a negative.
    • Graph and explain the solution.
  4. 23Equation and Inequality Word ProblemsWrite and solve an equation or inequality for a word problem.
    • Define the variable.
    • Write and solve the equation or inequality.
    • Explain the answer in the story.

Geometry

  1. 24Scale DrawingsUse a scale to find real lengths and areas.
    • Use 1 cm = 5 m to find a real length.
    • Redraw a figure at a new scale.
    • Find a real area from a scale drawing.
  2. 25Draw TrianglesDraw a triangle from given angles or sides.
    • Draw a triangle with a ruler and protractor.
    • Find when three lengths can make a triangle.
    • Find when the conditions make one, many, or no triangles.
  3. 26Cross SectionsDescribe the shape you get when you slice a solid.
    • Slice a prism parallel and perpendicular to its base.
    • Slice a pyramid.
    • Match cross sections to solids.
  4. 27Angle RelationshipsUse supplementary, complementary, vertical, and adjacent angles to find an unknown angle.
    • Know complementary angles add to 90° and supplementary angles to 180°.
    • Know vertical angles are equal.
    • Write and solve an equation for an unknown angle.
  5. 28Circumference of a CircleFind the circumference of a circle.
    • Measure circles to discover π.
    • Use C = πd and C = 2πr.
    • Find the diameter from the circumference.
  6. 29Area of a CircleFind the area of a circle.
    • Cut a circle into wedges to see why A = πr².
    • Find the area from the radius or the diameter.
    • Find the area of a semicircle.
  7. 30Area and Surface Area of Composite FiguresFind the area of composite figures and the surface area of prisms.
    • Split a figure into rectangles, triangles, and circles.
    • Subtract a cut-out area.
    • Find the surface area of a prism.
  8. 31Volume of PrismsFind the volume of any right prism.
    • Use V = B × h.
    • Find the volume of a triangular prism.
    • Find the volume of a composite solid.

Probability

  1. 32Probability of an EventWrite a probability as a number from 0 to 1.
    • Know 0 is impossible, 1/2 is equally likely, and 1 is certain.
    • Find the probability of rolling a 5.
    • Describe events as likely or unlikely.
  2. 33Experimental ProbabilityEstimate probability from the results of an experiment.
    • Flip a coin 50 times and record the results.
    • Compare experimental and theoretical probability.
    • See that more trials get closer to the theory.
  3. 34Probability ModelsMake a probability model and use it to predict.
    • Make a uniform model for a fair spinner.
    • Make a model from observed data.
    • Predict how many times an event will happen.
  4. 35Compound EventsFind the probability of two events with lists, tables, and tree diagrams.
    • List the outcomes of flipping a coin and rolling a die.
    • Draw a tree diagram.
    • Find the probability of rolling two sixes.
  5. 36SimulationsDesign a simulation to estimate a probability.
    • Use random numbers to model an event.
    • Run many trials.
    • Estimate the probability from the results.

Sampling and Statistics

  1. 37Samples and PopulationsTell a random sample from a biased one.
    • Define population and sample.
    • Explain why random samples represent a population.
    • Find the bias in a survey.
  2. 38Make Inferences from SamplesUse a random sample to estimate something about a population.
    • Estimate the number of students who prefer a lunch option.
    • Take several samples and compare them.
    • Explain how much the estimates vary.
  3. 39Compare Two PopulationsCompare two groups using center and spread.
    • Compare two box plots or dot plots.
    • Compare the difference in means to the spread.
    • Decide if the difference is meaningful.

Review, Mixed Practice, and Challenges

  1. 40Proportions, Rational Numbers, and Equations ReviewSolve mixed problems with proportions, percents, rational numbers, and equations.
    • Find and use a constant of proportionality.
    • Compute with negative numbers.
    • Solve two-step equations and inequalities.
  2. 41Geometry, Probability, and Statistics ReviewSolve mixed problems with circles, angles, volume, probability, and samples.
    • Find circumference, area, and volume.
    • Find unknown angles.
    • Find probabilities and make inferences.
  3. 42Seventh Grade Math ChallengeComplete mixed questions covering the major units.
    • Choose a strategy without being told.
    • Solve multi-step problems.
    • Find the areas that need more practice.