US homeschool curriculum · 8th grade

8th Grade Math

A self-paced online Math course for 8th grade: 42 lessons across 8 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 8th 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

  • Simplify a radical: Can simplify a radical such as √50 to 5√2.
  • Multiply and divide radicals: Can multiply or divide two radicals, simplifying the result.
  • Rationalize a denominator: Can rewrite a fraction like 1/√2 with a whole-number denominator.
  • Fractional exponents: Can evaluate a power with a fractional exponent, such as 16^(1/2) or 8^(2/3).
  • Add and subtract in scientific notation: Can add or subtract two numbers given in scientific notation.
  • Estimate square roots: Can place a square root between two whole numbers and estimate it to one decimal place.
  • Rational and irrational numbers: Can tell whether a number is rational or irrational.

• Measurement

  • Volume of cones and spheres: Can calculate the volume of a cone and of a sphere.

• Geometry: properties of shapes

  • Trigonometry: find a missing side: Can use sine, cosine or tangent to find a missing side in a right triangle.
  • Trigonometry: find a missing angle: Can use the inverse trigonometric ratios to find a missing angle.
  • Exact trigonometric values: Knows the exact sine, cosine and tangent of 0°, 30°, 45°, 60° and 90°.
  • Angles of elevation and depression: Can solve a real-world problem using an angle of elevation or depression.
  • Circle theorem: angle in a semicircle: Knows that the angle in a semicircle is a right angle, and can use it to find another angle.
  • Circle theorem: angle at the center: Knows that the angle at the center is twice the angle at the circumference.
  • Arc length and sector area: Can find the length of an arc or the area of a sector.
  • Is it a right triangle?: Can use the Pythagorean theorem backwards to test whether a triangle is a right triangle.

• Geometry: position and direction

  • Distance between two points: Can find the distance between two coordinates using the Pythagorean theorem.
  • Midpoint of a line segment: Can find the midpoint of a line joining two coordinates.
  • Congruent figures and rigid motions: Can name the slide, flip or turn that takes one figure onto another, and knows these keep figures congruent.

• Statistics

  • Quartiles and the five-number summary: Can find the minimum, lower quartile, median, upper quartile and maximum of a data set.
  • Interquartile range: Can calculate the interquartile range of a data set.
  • Compare box plots: Can use the median and interquartile range from two box plots to compare two data sets.
  • Judge a line of fit: Can choose the straight line that fits a scatter plot best and say why a line fits badly.

• Algebra

  • Expand a perfect square: Can expand and simplify (x + a)².
  • Difference of two squares: Can factor an expression of the form a² − b².
  • Factor a quadratic with a leading coefficient: Can factor an expression like 2x² + 7x + 3.
  • Solve a quadratic using the formula: Can use the quadratic formula to solve an equation of the form ax² + bx + c = 0.
  • Complete the square: Can write x² + bx + c in the form (x + p)² + q.
  • Function notation: evaluate f(x): Can evaluate f(x) for a given value of x.
  • Function notation: solve f(x) = k: Can find x when f(x) is given a value.
  • Simplify an algebraic fraction: Can simplify an algebraic fraction by canceling a common factor.
  • Rearrange a formula with a square or root: Can solve a formula that involves a square or a square root for a chosen variable.
  • What is a function?: Can tell whether a rule or a set of pairs is a function.
  • Compare two functions: Can compare two functions when one is an equation and the other is a table.
  • Describe a graph in words: Can match a graph to a story and say whether it is increasing or decreasing, linear or nonlinear.

• Ratio, proportion and rates of change

  • Direct proportion with squares and cubes: Can solve a problem where y is proportional to x² or x³.
  • Inverse proportion with squares: Can solve a problem where y is inversely proportional to x².
  • Pressure: Can use pressure = force ÷ area to find any of the three quantities.
  • Multi-step compound measures problems: Can solve a problem that combines two compound measures, such as speed and cost.

• Probability

  • Set notation: Can say what ∪, ∩ and ' mean, and match a description to the right notation.
  • Venn diagram counts with set notation: Can find n(A ∩ B), n(A ∪ B) or n(A′) from a described Venn diagram.
  • Tree diagrams without replacement: Can find a probability from a tree diagram when items are not replaced.

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