US homeschool curriculum · 6th grade

6th Grade Math

A self-paced online Math course for 6th grade: 51 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 6th 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

  • Four operations with negative numbers: Can add, subtract, multiply and divide with negative numbers.
  • Decimal places and significant figures: Can round a number to a given number of decimal places or significant figures.
  • Prime factorization: Can write a number as a product of its prime factors.
  • GCF and LCM of larger numbers: Can find the GCF and LCM of two numbers up to 200.
  • Powers and roots: Can work out squares, cubes, higher powers and square roots.
  • Order of operations with powers: Can evaluate a calculation with parentheses, powers, multiplication and addition in the correct order.

• Addition and subtraction

  • Add and subtract decimals: Can add and subtract decimals with different numbers of decimal places.

• Multiplication and division

  • Multiply decimals: Can multiply two decimals, such as 2.4 × 1.5.
  • Divide by a decimal: Can divide by a decimal by scaling both numbers, such as 7.2 ÷ 0.4.
  • Estimate using one significant figure: Can estimate a calculation by rounding each number to one significant figure.

• Fractions (and decimals, percentages)

  • Add and subtract mixed numbers: Can add and subtract mixed numbers with different denominators.
  • Multiply and divide fractions: Can multiply and divide fractions, including by another fraction.
  • Percentage increase and decrease: Can increase or decrease an amount by a percentage.
  • Percentage change: Can work out the percentage change from an old value to a new one.
  • Fractions to decimals, including repeating: Can convert fractions such as 1/3 and 5/8 to decimals and recognize repeating ones.
  • Order fractions, decimals and percentages: Can put a mixed list of fractions, decimals and percentages in order.

• Measurement

  • Area of a trapezoid: Can calculate the area of a trapezoid.
  • Circumference and area of a circle: Can calculate the circumference and area of a circle using π ≈ 3.14.
  • Volume of prisms and surface area of rectangular prisms: Can find the volume of a prism and the surface area of a rectangular prism.
  • Convert units of area: Can convert between cm² and mm², and between m² and cm².

• Geometry: properties of shapes

  • Angles in parallel lines: Can find alternate, corresponding and co-interior angles.
  • Interior and exterior angles of polygons: Can find the angle sum of any polygon and the exterior angle of a regular one.
  • Properties of quadrilaterals: Can identify a quadrilateral from its sides, angles, diagonals and symmetry.

• Geometry: position and direction

  • Rotations and reflections with coordinates: Can find the image of a point after a rotation about the origin or a reflection in y = x.
  • Dilation from the origin: Can dilate a point by a scale factor with the origin as the center.
  • Distance on the coordinate plane: Can find the distance between two points that share an x or a y value.

• Statistics

  • Mean, median, mode and range: Can find all four averages and the range of a data set.
  • Averages from a frequency table: Can find the mode, median and mean from a frequency table.
  • Pie chart angles: Can work out the angle of a pie-chart sector from a frequency.
  • Two-way tables: Can complete and read a two-way table.
  • Statistical questions: Can tell a question that expects different answers from one that has a single answer.
  • Dot plots and the shape of data: Can read a dot plot and describe where the data clusters, peaks and spreads.

• Algebra

  • Collect like terms: Can simplify an expression by collecting like terms.
  • Substitute into expressions: Can substitute positive and negative numbers into an expression, including squares.
  • Expand with the distributive property: Can expand an expression like 3(x + 4).
  • Factor out a common factor: Can take out a common factor, such as 6x + 9 = 3(2x + 3).
  • Solve two-step linear equations: Can solve equations like 3x − 7 = 11 and 2(x + 3) = 14.
  • nth term of a linear sequence: Can find the nth term rule of a linear sequence and use it.
  • Straight-line graphs y = mx + c: Can find points on a line from its equation and read off the slope and intercept.
  • Inequalities: Can list the integers that satisfy an inequality such as −2 < x ≤ 3.
  • Expressions from words: Can write an expression such as '3 more than twice n' as 2n + 3.

• Ratio, proportion and rates of change

  • Simplify a ratio: Can write a ratio in its simplest form, including with mixed units.
  • Share in a three-part ratio: Can divide an amount in a ratio with three parts.
  • Direct proportion (unit rate): Can find the cost of any number of items from the cost of some.
  • Ratios as fractions and percentages: Can turn a ratio into the fraction or percentage of the whole each part represents.
  • Speed, distance and time: Can use speed = distance ÷ time to find any of the three.
  • The better buy: Can compare prices by working out the cost per unit.

• Probability

  • Probability of a single event: Can write the probability of an outcome as a fraction on the 0–1 scale.
  • Probability an event does not happen: Knows that P(not A) = 1 − P(A) and can use it.
  • Sample spaces: Can count outcomes for two events, such as two dice, and find a probability.
  • Experimental probability: Can estimate a probability from results and compare it with the theoretical value.

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