US homeschool curriculum · 7th grade

7th Grade Math

A self-paced online Math course for 7th grade: 49 lessons across 11 units. A short placement quiz finds the right starting point, practice adapts as your child answers, and every lesson is marked automatically with progress reported to you.

• Every lesson has at least two different question styles, with hints and step-by-step worked solutions.
• Struggling triggers a gentler re-teach and a warm-up on the missing building block — never a visible drop in score.
• Work this course at its own level: a child can take 7th Grade Math alongside a different grade in Language Arts.

What your child learns

The scope and sequence below is generated from the live curriculum, so it is always what the app actually teaches.

• Number and place value

  • Write a number in scientific notation: Can write a large or small number in scientific notation, a × 10ⁿ.
  • Write a scientific notation number as an ordinary number: Can convert a number written in scientific notation back into an ordinary number.
  • Compare numbers in scientific notation: Can compare and order numbers written in scientific notation.
  • Laws of exponents: multiplying and dividing: Can multiply and divide powers of the same base by adding or subtracting the exponents.
  • Zero and negative exponents: Knows that a⁰ = 1 and can work out a negative power as a fraction.

• Addition and subtraction

  • Upper and lower bounds: Can find the upper and lower bound of a number rounded to a given accuracy.
  • Multi-step problems with fractions and decimals: Can solve a real-life problem in several steps using whole numbers, fractions, decimals and percents.

• Multiplication and division

  • Density: Can use density = mass ÷ volume to find any of the three quantities.
  • Multiply and divide with scientific notation: Can multiply and divide two numbers given in scientific notation.

• Fractions (and decimals, percentages)

  • Compound interest: Can calculate the value of savings or a loan after repeated percentage growth.
  • Reverse percentage: Can find the original amount before a percentage increase or decrease.
  • Percentage of another quantity, with units: Can work out what percentage one quantity is of another, converting units first if needed.
  • Repeating decimals to fractions: Can convert a repeating decimal to a fraction.

• Measurement

  • Volume and surface area of a cylinder: Can calculate the volume and curved surface area of a cylinder.
  • the Pythagorean theorem: the hypotenuse: Can use the Pythagorean theorem to find the length of the hypotenuse.
  • the Pythagorean theorem: a shorter side: Can use the Pythagorean theorem to find the length of a shorter side.

• Geometry: properties of shapes

  • Conditions for congruent triangles: Can say which condition (SSS, SAS, ASA, RHS) proves two triangles are congruent.
  • Similar shapes: Can use a scale factor to find a missing length or area in similar shapes.
  • Multi-step angle problems: Can combine angle facts, such as the exterior angle theorem, to solve a problem.
  • Can these sides make a triangle?: Can tell whether three lengths can make a triangle, and which third side is possible.
  • Cross-sections of solids: Can name the flat shape made by slicing a prism, pyramid, cylinder, cone or sphere.

• Geometry: position and direction

  • Slope between two points: Can find the slope of the line joining two coordinates.
  • Equation of a line through a point: Can find the equation of a line given its slope and one point on it.

• Statistics

  • Scatter plots and correlation: Can say whether a scatter plot shows positive, negative or no correlation.
  • Line of best fit: Can use the equation of a line of best fit to estimate a value.
  • Estimate the mean from grouped data: Can estimate the mean of grouped data using midpoints.
  • Compare two distributions: Can use the mean and range to compare two sets of data.
  • Random and representative samples: Can tell a sample that represents a whole group from one that is biased.
  • From a sample to the whole group: Can use a random sample to estimate a number for the whole group.
  • How far apart are two data sets?: Can compare the difference between two means with the spread of the data.

• Algebra

  • Multiply two binomials: Can expand and simplify (x + a)(x + b).
  • Factor a quadratic expression: Can factor x² + bx + c into two parentheses.
  • System of equations by elimination: Can solve a pair of linear system of equations by adding or subtracting them.
  • System of equations by substitution: Can solve a pair of system of equations by substituting one into the other.
  • Rearrange a formula: Can rearrange a real-world formula to make a different letter the subject.
  • Equations with unknowns on both sides: Can solve an equation with the letter on both sides.
  • Form and solve an equation from a word problem: Can turn a word problem into an equation and solve it.
  • Quadratic sequences: Can find the next term of a quadratic sequence.
  • Rewrite an expression to see what it means: Can rewrite an expression such as a + 0.05a as 1.05a and say what it shows.

• Ratio, proportion and rates of change

  • Direct proportion: Can find the constant of proportionality and use y = kx.
  • Inverse proportion: Can recognize inverse proportion and use y = k/x.
  • Currency conversion: Can convert between currencies using an exchange rate.
  • Scale drawings and maps: Can find a real distance from a map scale.
  • Unit rates with fractions: Can find a unit rate when the amounts are fractions, such as 1/2 mile in 1/4 hour.

• Probability

  • Probability from a Venn diagram: Can use a Venn diagram (described by its overlapping counts) to find a probability.
  • Tree diagrams: independent events: Can multiply along the branches of a tree diagram for independent events.
  • Tree diagrams: combined outcomes: Can find the probability of at least one success across two independent trials.
  • Relative frequency: Can use a relative frequency to predict the number of times something will happen.
  • Mutually exclusive events: Can add probabilities of mutually exclusive events.

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