Middle School — Learning Stage Pages

Lines and Angles

An angle measures a turn between two directions. A line describes a straight path that continues indefinitely. Together, they let us describe corners, crossings, slopes and the shape…

Surface Areas and Volumes

Surface area measures the size of an object’s boundary. Volume measures the space it occupies or encloses. Wrapping a box and filling a box are different measurement problems,…

Points, Lines and Planes

Points, lines and planes describe location, direction and flatness. They are the basic objects used to state geometric relationships precisely. A dot can mark a location, a drawn…

Geometric Shapes in Maths

A geometric shape is identified by properties such as its boundaries, angles, lengths and dimensions. Those properties remain meaningful when the shape is moved, turned or drawn at…

Area and Perimeter of Shapes

Perimeter measures the distance around a boundary. Area measures the size of a region. A fence follows a boundary; paving covers a region. The same drawing can support…

Decimals

A metric ruler locating 2.6 centimetres as 26 millimetres: six millimetres beyond the 2 cm mark. Decimals use base-ten place value to write whole amounts and fractional parts…

Factoring in Algebra

Factoring rewrites an expression as a product of simpler factors. It is the reverse of expansion. Factoring exposes multiplicative structure that can make equations easier to solve and…

Systems of Linear Equations

A system of linear equations asks for values that satisfy two or more linear equations at the same time. For two variables, a solution is an ordered pair…

Linear Equations

A linear equation in one variable can be written as ax+b=cax+b=c, where aa, bb and cc are constants and a≠0a\ne0. Solving means finding every input that makes the…

Linear Inequalities

A linear inequality compares two expressions using <<, >>, ≤\le or ≥\ge. Its solution is usually a set of values rather than a single number. Most equation-solving operations…

Expressions and Algebraic Expressions

An expression represents a mathematical value. It can contain numbers, variables, operations, powers and grouping symbols, but it does not state that two quantities are equal. Algebraic expressions…

Like Terms and Simplifying Expressions

Simplifying an algebraic expression means rewriting it in an equivalent form that is easier to read or use. One of the first tools is combining like terms: terms…