$x$Pre-Algebra

Integers: The Full Number Line

Integers are the whole numbers and their negatives. Move along the line to add and subtract, use the sign rules for multiplying, and track an elevator, a bank account and a frozen lake.

Building Blocks of Numbers

Every number is built from primes, like molecules from atoms. Find factor rectangles, use divisibility shortcuts, factor with trees, and know when a problem wants a GCF or an LCM.

Fractions, All Four Ways

Equivalent fractions, the lowest common denominator, multiplying as area and dividing as "how many fit". Plus the Egyptian way of writing fractions, and a famous camel puzzle.

Decimals Without Fear

Zoom into the number line, compare and round, multiply and divide without losing the point, and discover which fractions turn into decimals that never end.

Proportions Everywhere

Ratios, unit rates and proportions: scale a recipe, read a map, find a tree's height from its shadow, and see every proportional relationship as a line through zero.

Percent Detective

Convert between fractions, decimals and percents, then solve every kind of percent problem with one equation. Includes the shop that raises prices 10% and then lowers them 10%.

Every Fraction, Positive and Negative

Rational numbers are all the fractions, negatives included. Place them on the line, compute with signs, sort repeating from ending decimals, and meet a number that is not rational at all.

Powers and Roots

Discover the exponent rules by counting factors, see why anything to the zero power is 1, write the size of an atom in scientific notation, and squeeze a square root between two whole numbers.

The Language of Algebra

Variables, expressions and equations — what each one is for. Translate words into algebra, substitute, expand with rectangles, collect like terms, and read a magic trick backwards.

Solving for the Unknown

Balance two-step equations, handle x on both sides, write equations from stories, and find out why multiplying an inequality by a negative flips it.

Mapping Relationships

Plot points in all four quadrants, turn a table of values into a graph, discover which tables make straight lines, and measure distances along the grid.

Shapes, Circles and Pythagoras

Angles in a triangle, areas of every basic shape, the number pi, the most famous theorem in mathematics, and the volume of a can of soup.

Data and Chance

Describe data with mean, median, mode and range, then predict chance events and test your predictions by rolling a thousand dice in a second.