# Number prompts

# Calculations: addition and subtraction

**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.

**Mathematical inquiry processes: **Explore other cases; identify patterns; conjecture and generalise. **Conceptual field of inquiry: **Sum of integers; prime factorisation; factors.

**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.

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

# Calculations: multiplication and division

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

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

**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.

**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: **Quotient of integers; division.

# Order of operations

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

# Number line and place value

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

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

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

# Factors and multiples

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

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

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

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

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

**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

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

**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).

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

**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.

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

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

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

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

**Mathematical inquiry processes:** Extend a pattern; find connections; generalise; reason about structure.** ****Conceptual field of inquiry: **Division of whole numbers by fractions; division and multiplication.

# Decimals and percentages

**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.

**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.

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

**Mathematical inquiry processes: **Explore; set conditions; test different cases; conjecture and reason. **Conceptual field of inquiry:** Compound interest and depreciation; percentages.

# Ratio and proportion

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

**Mathematical inquiry processes: **Make connections; generate examples; express in general form. **Conceptual field of inquiry:** Direct and inverse proportion; multiplicative relationships; reciprocal; equation.

**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.

**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

**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.

**Mathematical inquiry processes:** Verify; test other cases; create alternative representations; reason. **Conceptual field of inquiry:** Square and cube roots; laws of exponents; graphs of functions with roots; differentiation.

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

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

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

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