Algebra Algebra is the essence of mathematical thought. Learning to generalise basic number skills into the abstract idea of unknowns and variables will be the initial focus. The thought of fluidly moving between the multiple representations of some of the content is very important. These representations are equations, tables and graphs. Number and spatial patterns will be covered which introduce the idea of discrete and continuous variables.
NZC achievement objectives will be developed from level 4 through to Level 5 and where suitable Level 6 as follows: Level 4 Equations and expressions Form and solve simple linear equations. Patterns and relationships Generalise properties of multiplication and division with whole numbers. Use graphs, tables, and rules to describe linear relationships found in number and spatial patterns. Level 5 Equations and expressions Form and solve linear and simple quadratic equations. Patterns and relationships Generalise the properties of operations with fractional numbers and integers. Relate tables, graphs, and equations to linear and simple quadratic relationships found in number and spatial patterns. Level 6 Equations and expressions Form and solve linear equations and inequations, quadratic and simple exponential equations, and simultaneous equations with two unknowns. Patterns and relationships Generalise the properties of operations with rational numbers, including the properties of exponents. Relate graphs, tables, and equations to linear, quadratic, and simple exponential relationships found in number and spatial patterns. Relate rate of change to the gradient of a graph. This topic of learning leads onto the Level 1 NCEA Achievement Standards AS91027, AS91028 and AS91029.