US homeschool curriculum · 5th grade

5th Grade Math

A self-paced online Math course for 5th grade: 51 lessons across 10 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 5th 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

  • Numbers to 10,000,000: Can read and write numbers up to ten million and say what each digit is worth.
  • Round to any degree of accuracy: Can round any whole number to the nearest 10 up to the nearest million.
  • Calculate across zero: Can find the difference between negative and positive numbers.
  • Order numbers to 10,000,000: Can order and compare numbers up to ten million.

• Addition and subtraction

  • Mental calculations with large numbers: Can add or subtract large numbers mentally using place value.
  • Order of operations: Can work out a calculation with parentheses, multiplication and addition in the right order.
  • Multi-step problems: Can solve a problem with three steps, choosing the operations.
  • Estimate and check: Can estimate an answer by rounding and check with the inverse operation.
  • Write expressions from words: Can write and read a numerical expression for a phrase such as 'add 8 and 7, then multiply by 2'.

• Multiplication and division

  • Long multiplication (4-digit × 2-digit): Can multiply a four-digit number by a two-digit number.
  • Long division: Can divide a number up to four digits by a two-digit number.
  • Remainders as fractions and decimals: Can write the answer to a division as a decimal or a mixed number.
  • Greatest common factor and lowest common multiple: Can find the greatest common factor or lowest common multiple of two numbers.
  • Multiply decimals by whole numbers: Can multiply a number with up to two decimal places by a one-digit number.
  • Divide decimals by whole numbers: Can divide a decimal by a one-digit number.
  • Multiply and divide decimals by 10, 100 and 1,000: Can move the digits to multiply or divide a decimal by 10, 100 or 1,000.

• Fractions (and decimals, percentages)

  • Simplify fractions: Can write a fraction in its simplest form.
  • Compare fractions with different denominators: Can compare and order fractions, including ones greater than 1.
  • Add and subtract fractions with different denominators: Can add and subtract fractions with different denominators, using equivalent fractions.
  • Multiply fractions: Can multiply two proper fractions and simplify the answer.
  • Divide a fraction by a whole number: Can divide a proper fraction by a whole number.
  • Fractions, decimals and percentages: Can convert between fractions, decimals and percentages, including eighths.
  • Percentages of amounts: Can find any percentage of an amount, such as 35% of 240.
  • Fractions of amounts: Can find a non-unit fraction of an amount, such as 5/8 of 96.
  • Multiplying makes bigger or smaller: Can tell whether a product will be bigger or smaller than a number without working it out.

• Measurement

  • Convert units, including miles and kilometers: Can convert between metric units with decimals and between miles and kilometers.
  • Area of triangles and parallelograms: Can calculate the area of a triangle or parallelogram from its base and height.
  • Volume of a rectangular prism: Can calculate the volume of a rectangular prism using length × width × height.
  • Missing sides of composite shapes: Can find a missing side length of an L-shape and then its perimeter or area.
  • Money problems with decimals: Can multiply and divide amounts of money in dollars and cents.
  • Convert customary units: Can convert between customary units of length, weight and capacity.

• Geometry: properties of shapes

  • Angles in a triangle: Can find the missing angle in a triangle.
  • Angles in quadrilaterals and regular polygons: Can find a missing angle in a quadrilateral and the interior angle of a regular polygon.
  • Vertically opposite angles: Can use vertically opposite angles and angles on a line to find a missing angle.
  • Parts of a circle: Knows that the diameter is twice the radius and can name the parts of a circle.
  • Faces, edges and vertices of prisms and pyramids: Can count the faces, edges and vertices of a prism or pyramid.
  • Classify 2D figures: Can sort quadrilaterals into categories and subcategories by their properties.

• Geometry: position and direction

  • Coordinates in four quadrants: Can read and place points in all four quadrants.
  • Reflect and translate in four quadrants: Can reflect a point in an axis or translate it, in any quadrant.

• Statistics

  • The mean: Can calculate the mean of a set of numbers.
  • Pie charts: Can use the fraction or percentage of a pie chart to find how many.
  • Line graphs: Can read a line graph's values from a table and describe the change.
  • Line plots and fraction operations: Can use a line plot of fractions to find totals and equal shares.

• Algebra

  • Use a simple formula: Can substitute a number into a formula such as cost = 3n + 2.
  • Linear number sequences: Can continue a sequence and find the rule for the nth term.
  • Solve a missing-number equation: Can find the unknown in an equation such as 3x + 4 = 19.
  • Two unknowns: Can find two numbers from their sum and difference.

• Ratio, proportion and rates of change

  • Share in a ratio: Can share an amount in a given ratio.
  • Scale factors: Can dilate a length by a scale factor and find a missing length in similar shapes.
  • One number as a percentage of another: Can work out what percentage one amount is of another.
  • Ratio and proportion problems: Can use a ratio to find an unknown quantity, such as ingredients in a recipe.

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