# Expressions and proof

## Number line inquiry

Mathematical inquiry processes: Interpret; test particular cases; conjecture, generalise and prove; extend to other cases. Conceptual field of inquiry: Multiplication; algebraic notation, terms and expressions.

## Steps inquiry

Mathematical inquiry processes: Interpret; identify patterns; conjecture, generalise and prove; extend to other cases. Conceptual field of inquiry: Multiplication and addition; algebraic notation, terms and expressions. ## Squaring numbers inquiry

Mathematical inquiry processes: Verify; extend the pattern; generalise and prove. Conceptual field of inquiry: Square numbers; algebraic notation; rearrangement of expressions.

## Difference of two squares inquiry

Mathematical inquiry processes: Verify; extend the pattern; generalise and prove. Conceptual field of inquiry: Difference of square numbers; rearrangement of algebraic expressions.

## Difference of two cubes inquiry

Mathematical inquiry processes: Verify; extend the pattern; generalise and prove. Conceptual field of inquiry: Difference of cube numbers; rearrangement of algebraic expressions. ## Cube numbers inquiry

Mathematical inquiry processes: Verify; extend the pattern; generalise and prove. Conceptual field of inquiry: Product of cube numbers; algebraic notation, terms and expressions.

# Manipulating algebra

## Substitution inquiry

Mathematical inquiry processes: Generate examples and counter-examples; conjecture and reason; change conditions. Conceptual field of inquiry: Substitution of different types of numbers into expressions.

## Expanding brackets inquiry

Mathematical inquiry processes: Verify; extend patterns; create and test examples; reason. Conceptual field of inquiry: Expansion of brackets; algebraic expressions. ## Binomial expansion inquiry

Mathematical inquiry processes: Verify; extend the pattern; find counter-examples; reason. Conceptual field of inquiry: Binomial expansion; factorisation; Yang Hui's (Pascal's) Triangle. ## Algebraic fractions

Mathematical inquiry processes: Identify structure; test cases; generalise and prove. Conceptual field of inquiry: Sum and difference of fractions; difference of two squares; algebraic manipulation.

# Sequences

## Intersecting sequences inquiry

Mathematical inquiry processes: Notice connections; generate examples and counter-examples; conjecture and generalise. Conceptual field of inquiry: Linear sequences; term-to-term and position-to-term rules; algebraic expressions.

## Forming a sequence inquiry

Mathematical inquiry processes: Explore; generate examples and counter-examples; find sets that satisfy conditions. Conceptual field of inquiry: Position-to-term rules; algebraic expressions; graphing a solution set.

## Product of two terms inquiry

Mathematical inquiry processes: Explore; generate examples and counter-examples; generalise and prove. Conceptual field of inquiry: Position-to-term rules; algebraic expressions.

## Linear and quadratic sequences inquiry

Mathematical inquiry processes: Notice connections; generate more examples with the same properties; analyse structure. Conceptual field of inquiry: Position-to-term rules for linear and quadratic sequences; algebraic expressions.

# Equations and formulae

## Solving equations inquiry

Mathematical inquiry processes: Identify structure; create example sets and generalise. Conceptual field of inquiry: Equations with the unknown on both sides; rearrangement of algebraic terms.

Mathematical inquiry processes: Identify structure; create example sets and generalise. Conceptual field of inquiry: Fractional equations with the unknown on both sides; algebraic generalisation.

## Solving simultaneous equations inquiry

Mathematical inquiry processes: Identify structure and notice properties; create example sets and generalise. Conceptual field of inquiry: Simultaneous equations; algebraic proof.

Mathematical inquiry processes: Generate examples; analyse structure; determine necessary conditions. Conceptual field of inquiry: Expansion of brackets; factorisation of quadratic expressions.

## Coefficients inquiry

Mathematical inquiry processes: Test different cases; generalise and prove. Conceptual field of inquiry: Factorisation of quadratic expressions; quadratic formula; solutions to quadratic equations.

## Formulae inquiry

Mathematical inquiry processes: make connections; generate examples and counter-examples; conjecture, generalise and prove. Conceptual field of inquiry: formulae linked to arrays; algebraic expressions.

## Completing the square inquiry

Mathematical inquiry processes: Explore; generate examples; conjecture; reason. Conceptual field of inquiry: Completing the square; graphs of quadratic functions; turning point; algebraic manipulation .

# Coordinates and graphs

## Straight line graphs inquiry

Mathematical inquiry processes: Explore; make connections; change the prompt; reason and analyse structure. Conceptual field of inquiry: Substitution; the coordinate plane; gradient of straight lines; intercepts of the y- and x-axes.

## Intersecting lines inquiry

Mathematical inquiry processes: Find relationships; change the prompt; conjecture, generalise and prove. Conceptual field of inquiry: The coordinate plane; gradient of straight lines; simultaneous equations. ## Graphing inequalities inquiry

Mathematical inquiry processes: Verify; explore; set constraints; generate more examples. Conceptual field of inquiry: Plot straight lines; represent inequalities graphically.

## Coordinates inquiry

Mathematical inquiry processes: Extend patterns; generate examples; find relationships; generalise. Conceptual field of inquiry: The coordinate plane; gradients of parallel and perpendicular lines; coordinates and polygons.

## Equation of a circle inquiry

Mathematical inquiry processes: Verify a particular case; test other cases; generalise and prove. Conceptual field of inquiry: Equation of a circle; equations of perpendicular lines; mid-points of straight lines; solving simultaneous equations.

## Distance-time graph inquiry

Mathematical inquiry processes: Interpret and reason; generate examples. Conceptual field of inquiry: Distance-time graphs, speed.

# Calculus ## Area under a curve

Mathematical inquiry processes: Explore; generate examples; test cases; generalise and prove. Conceptual field of inquiry: Trapezium rule; integration; definite integrals; points of intersection.

# Functions ## Composite functions

Mathematical inquiry processes: test particular cases; make conjectures about relationships; generalise and prove. Conceptual field of inquiry: function notation; inverse functions; composite functions.

# Miscellaneous

## Sets and Venn diagrams inquiry

Mathematical inquiry processes: Interpret and reason; generate examples. Conceptual field of inquiry: Set notation; elements of sets; Venn diagrams.

## Matrices inquiry

Mathematical inquiry processes: Interpret and reason; identify connections; generate examples. Conceptual field of inquiry: Matrix addition and subtraction.