# Calculations

## Multiplication inquiry

Mathematical inquiry processes: Identify properties; generate examples and counter-examples. Conceptual field of inquiry: Multiplication of numbers with two and more digits; algebraic expressions.

Mathematical inquiry processes: Notice properties; generate examples; conjecture, generalise and prove. Conceptual field of inquiry: Sum of integers and other types of numbers; collect like terms; Yang Hui's (Pascal's) Triangle.

## Division inquiry 2

Mathematical inquiry processes: Verify, explore more cases and reason. Conceptual field of inquiry: Product and quotient of integers; commutativity.

## Multiplication inequalities inquiry

Mathematical inquiry processes: Verify; rearrange; conjecture and generalise. Conceptual field of inquiry: Multiplication of positive integers; permutations.

## Decimal multiplication inquiry

Mathematical inquiry processes: Identify and analyse structure; generate other examples; extend a pattern; graph results. Conceptual field of inquiry: Sum and product of integers and decimals.

## Sum and product of integers inquiry

Mathematical inquiry processes: Explore; generate other examples; conjecture, generalise, reason and prove. Conceptual field of inquiry: Sum and product of integers.

Mathematical inquiry processes: Verify; identify and analyse structure; generate other examples; reason. Conceptual field of inquiry: Addition and subtraction; sum and difference of integers; commutative law.

## Division inquiry 1

Mathematical inquiry processes: Verify; identify and analyse structure; generate other examples; reason. Conceptual field of inquiry: Quotient of integers; division.

## Order of operations inquiry

Mathematical inquiry processes: identify properties; generate more examples; extend a pattern. Conceptual field of inquiry: Order of operations. ## Inequalities inquiry

Mathematical inquiry processes: Verify; generate more examples; identify patterns and reason. Conceptual field of inquiry: Addition and inequalities.

## Negative numbers inquiry

Mathematical inquiry processes: Extend patterns; generate examples; reason. Conceptual field of inquiry: Operations with negative numbers (including multiplication and division).

# Number line

## Place value inquiry

Mathematical inquiry processes: Make connections; generate examples and problems. Conceptual field of inquiry: Place value in the decimal number system.

## Prime factors inquiry

Mathematical inquiry processes: Interpret; Analyse and extend structure. Conceptual field of inquiry: Prime and composite numbers: prime factors.

## Powers of 10 inquiry

Mathematical inquiry processes: Make connections; extend patterns; reason. Conceptual field of inquiry: Multiplication and division by powers of 10.

# Factors and multiples

## Product of factors inquiry

Mathematical inquiry processes: Verify the particular case; generate more examples; conjecture and generalise. Conceptual field of inquiry: Factors and indices.

## Number of factors inquiry

Mathematical inquiry processes: Identify and extend patterns; conjecture; generate examples and counter-examples; reason. Conceptual field of inquiry: Factors; geometric sequences.

## Factors and prime factors inquiry

Mathematical inquiry processes: Explore by testing particular cases; verify and explain. Conceptual field of inquiry: Factors, prime factors and indices.

## HCF and LCM inquiry 1

Mathematical inquiry processes: Test the generalisation with particular cases. Conceptual field of inquiry: Highest common factor and lowest common multiple. ## HCF and LCM inquiry 2

Mathematical inquiry processes: Find pairs of numbers that satisfy the condition; extend to other cases; generalise. Conceptual field of inquiry: Highest common factor and lowest common multiple.

# Fractions and decimals

Mathematical inquiry processes: Identify and create patterns; conjecture and generalise. Conceptual field of inquiry: Addition and subtraction of fractions.

## Sum and product of fractions inquiry

Mathematical inquiry processes: Search for examples that satisfy the condition; conjecture, generalise and prove. Conceptual field of inquiry: Addition and multiplication of fractions (extended to subtraction and division).

## Sum of unit fractions inquiry

Mathematical inquiry processes: Search for examples that satisfy the condition; conjecture, generalise and prove. Conceptual field of inquiry: Addition of fractions; unit fractions.

## Fraction and decimal conversion inquiry

Mathematical inquiry processes: Test particular cases; identify different types of cases; conjecture and generalise. Conceptual field of inquiry: Fraction-decimal conversion; product of prime factors; terminating and recurring decimals.

## Fractions inequality inquiry

Mathematical inquiry processes: Identify structure, generate examples; generalise and prove. Conceptual field of inquiry: Subtraction of fractions; inequalities.

## Dividing fractions inquiry

Mathematical inquiry processes: Reason; extend to other cases; generalise. Conceptual field of inquiry: Division of fractions; reciprocals.

## Mixed numbers inquiry

Mathematical inquiry processes: Verify; analyse structure; find more examples; generalise and prove. Conceptual field of inquiry: Subtraction and division of mixed numbers by integers.

## Fraction of a number inquiry

Mathematical inquiry processes: Verify, generate more examples; generalise and prove. Conceptual field of inquiry: Fraction of a number; equivalence.

## Recurring decimals inquiry

Mathematical inquiry processes: Compare and contrast; test other cases; find rules. Conceptual field of inquiry: Conversion of fractions to decimals; terminating and recurring decimals.

# Percentages

## Percentages inquiry

Mathematical inquiry processes: Verify; test other cases; conjecture, generalise and prove. Conceptual field of inquiry: Percentages, including percentages greater than 100; percentage of a number.

## Percentage change inquiry

Mathematical inquiry processes: Interpret; apply in different contexts. Conceptual field of inquiry: Percentage of a number; percentage increase and decrease; reverse percentage to find an initial amount.

# Ratio and proportion

## Ratio inquiry

Mathematical inquiry processes: Make connections; generate examples; find patterns and rules. Conceptual field of inquiry: Multiplicative relationships; multiplier; reciprocal.

## Rectangle ratios inquiry 1

Mathematical inquiry processes: Interpret; explore; test particular cases; reason; relate to context. Conceptual field of inquiry: Comparison and simplification of ratios; equivalent ratios; similarity; algebraic manipulation.

## Rectangle ratios inquiry 2

Mathematical inquiry processes: Interpret; explore; test particular cases; reason; relate to context. Conceptual field of inquiry: Comparison and simplification of ratios; equivalent ratios; similarity; algebraic manipulation.

# Indices and surds

## Indices inquiry

Mathematical inquiry processes: Interpret; make connections; identify and extend patterns; reason and explain. Conceptual field of inquiry: Squares and indices; the relationship between integers and their product.

## Squares and cubes inquiry

Mathematical inquiry processes: Verify; identify and extend patterns; reason. Conceptual field of inquiry: Square and cube numbers.

## Laws of exponents inquiry

Mathematical inquiry processes: Make connections; test different cases; infer and explain rules. Conceptual field of inquiry: Laws of exponents (indices).

## Base and index inquiry

Mathematical inquiry processes: Make connections; test different cases; infer and explain rules. Conceptual field of inquiry: Base and index numbers; square numbers.

## Surds inquiry

Mathematical inquiry processes: Verify; reason; extend to other cases and generalise; prove. Conceptual field of inquiry: Surds; mixed numbers and improper fractions.