All topics

Topics are the filing system: what the math is, at beginner, intermediate, advanced. Grades are a lookup on top of them.

Number and place value

• Counting and number sense

  Counting on, skip counting, number recognition and the early number sense that everything else is built on.

• Place value

  Tens and ones through millions and thousandths, expanded form, and reading numbers out loud correctly.

• Comparing and ordering

  Greater than, less than, equal to, and putting sets of numbers in order without guessing.

• Factors, multiples and primes

  Factor pairs, common multiples, prime and composite numbers, and prime factor trees.

• Integers and negative numbers

  Number lines below zero, absolute value, and the sign rules for all four operations.

• Estimation and rounding

  Rounding to any place, front-end estimation, and checking whether an answer is sensible.

Operations

• Addition

  Sums within 10 through multi-digit column addition with regrouping, plus the fact fluency underneath.

• Subtraction

  Taking away, counting up, and multi-digit subtraction with borrowing across zeros.

• Multiplication

  Times tables, arrays and area models, and long multiplication up to multi-digit factors.

• Division

  Sharing and grouping, division facts, remainders, and long division that a kid can follow.

• Mixed operations

  One sheet, all four operations, so a student has to choose the operation instead of repeating one.

• Order of operations

  Brackets, exponents and left-to-right rules, with the classic traps kids fall into.

• Mental math

  Bridging ten, doubles and near doubles, compensation, and other strategies worth naming.

Fractions, decimals and percents

• Fractions

  Naming, comparing, simplifying and calculating with fractions, including mixed numbers.

• Decimals

  Decimal place value, comparing, rounding, and the four operations with decimal points lined up.

• Percentages

  Percent of a number, percent change, and moving between fractions, decimals and percents.

• Ratios and proportions

  Ratio notation, equivalent ratios, unit rates and proportional reasoning problems.

Patterns and algebra

• Exponents and roots

  Powers, square roots, exponent laws and scientific notation.

• Pre-algebra

  One-step equations with a letter in them, and undoing an operation to solve.

• Algebra

  Two-step equations, and undoing the steps backwards to find the unknown.

• Patterns and sequences

  Repeating and growing patterns, term-to-term rules, and finding the nth term.

Geometry and measurement

• Geometry and shapes

  Naming 2D and 3D shapes, properties, symmetry, and transformations.

• Area, perimeter and volume

  Perimeter and area of rectangles, squares and right triangles, and the volume of a box.

• Angles

  Naming angles by sight, and working out angles on a line and in a triangle.

• Coordinate plane

  Plotting points, four quadrants, distance on a grid, and coordinate puzzles.

• Measurement and units

  Length, mass and capacity, and converting between units inside one system.

• Telling time

  Elapsed time between two clock readings, and converting between units of time.

• Money

  Totalling a shopping list and working out change, in dollars and cents.

Data, statistics and probability

• Data and graphing

  Tally charts, pictographs, bar and line graphs, and reading a graph honestly.

• Statistics

  Mean, median, mode and range, and which average actually answers the question.

• Probability

  How likely an event is, written as a fraction between impossible and certain.

Reasoning and problem solving

• Word problems

  One- and two-step story problems, with the reading strategy taught alongside the math.

• Logic puzzles

  Ranking people from clues, and matching each of them to a thing. No arithmetic — just reasoning.