# Algebra prompts

# Expressions and proof

**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.

**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.

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

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

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

**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

**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.

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

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

**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

**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.

**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.

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

**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

**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.

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

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

# Quadratic functions

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

**Mathematical inquiry processes: **Test different cases; generalise and prove. **Conceptual field of inquiry: **Factorisation of quadratic expressions; quadratic formula; the discriminant.

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

**Mathematical inquiry processes:**** **Explore, change representations; reason and prove. **Conceptual field of inquiry:** Function notation; substitution; graphs of quadratic and cubic functions.

# Coordinates and graphs

**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.

**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.

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

**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.

**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.

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

# Functions

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

# Calculus

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

**Mathematical inquiry processes:**** **Explore, change representations; reason and prove. **Conceptual field of inquiry:** Differentiation; gradient function; graphs of quadratic and cubic functions.

# Miscellaneous

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

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