2026 7 Maths Unit 1.1 Rubric

Actual Rubrics are based on teacher-elaborations of selected content descriptors for the assessment that sufficiently map to all of the Achievement Standard components.

Achievement Standard Rationaliser for Assessment Construction (Non-Assessment Specific)

Achievement Standard Component	E	D	C	B	A
Students represent natural numbers in expanded form and as products of prime factors, using exponent notation.	Incorrectly represent numbers in expanded form and when using exponent notation.	Needs support to represent natural numbers or use prime factors; makes frequent notation errors.	Students represent natural numbers in expanded form and as products of prime factors, using exponent notation.	Consistently and accurately uses prime factors and exponent notation without error.	Masterfully applies prime factorization and exponent rules to solve complex, multi-step problems.
Students solve problems involving addition and subtraction of integers.	Incorrectly add or subtract integers.	Can solve basic integer problems but struggles with negative numbers or word problems.	Students solve problems involving addition and subtraction of integers.	Efficiently solves complex problems involving integer operations, including negative values.	Applies integer addition and subtraction smoothly to novel, abstract mathematical situations.
They solve problems involving squares of numbers and square roots of perfect square numbers.	Does not recognize squares or square roots.	Identifies some perfect squares but struggles to apply them to problem-solving.	They solve problems involving squares of numbers and square roots of perfect square numbers.	Accurately solves complex problems involving squares and roots, showing clear working.	Extends knowledge of squares and roots to estimate non-perfect squares or solve higher-order problems.
Students use algebraic expressions to represent situations, describe the relationships between variables from authentic data and substitute values into formulas to determine unknown values.	Incorrectly uses algebraic expressions and when substituting values.	Partially describes relationships or makes errors when substituting values into formulas.	Students use algebraic expressions to represent situations, describe the relationships between variables from authentic data and substitute values into formulas to determine unknown values.	Consistently forms accurate algebraic expressions and flawlessly substitutes values into multi-step formulas.	Synthesizes multiple algebraic expressions to model and solve highly complex or abstract scenarios.
They use all 4 operations in calculations involving positive fractions and decimals, choosing efficient calculation strategies.	Cannot calculate with fractions or decimals.	Performs basic operations but often chooses inefficient strategies or makes errors.	They use all 4 operations in calculations involving positive fractions and decimals, choosing efficient calculation strategies.	Fluently applies all 4 operations to fractions and decimals, consistently utilizing the most efficient strategies.	Solves complex, multi-layered word problems involving fractions and decimals, justifying their strategic choices.

Content Descriptor Rubric for Content Rationalisation (Non-task specific)

E	D	C	B	A
Fails to identify prime numbers.	Lists prime factors but struggles to write them using exponent notation.	AC9M7N02 represent natural numbers as products of powers of prime numbers using exponent notation	Applies prime factorization to efficiently calculate the Highest Common Factor and Lowest Common Multiple.	Generalizes prime factorization to prove mathematical properties of large numbers.
Misunderstands basic place value boundaries.	Expands numbers additively but omits powers of 10.	AC9M7N03 represent natural numbers in expanded notation using place value and powers of 10	Fluently converts between expanded form, standard form, and large powers of 10.	Synthesizes place value concepts to manipulate and calculate numbers in scientific notation.
Struggles to conceptually order negative numbers.	Orders integers correctly but relies heavily on manipulatives or number lines to calculate.	AC9M7N07 compare, order and solve problems involving addition and subtraction of integers	Models multi-step, real-world scenarios (e.g., fluctuating temperatures, elevation changes) using integer operations.	Evaluates mathematical claims involving absolute value and infinite sets of integers.
Cannot mathematically distinguish between a number and its square.	Memorizes early perfect squares up to 100 but cannot reverse the process to find roots.	AC9M7N01 describe the relationship between perfect square numbers and square roots, and use squares of numbers and square roots of perfect square numbers to solve problems	Estimates the roots of non-perfect squares to the nearest whole number.	Estimates square roots of numbers to some number of decimal places.
Treats variables as empty placeholders without mathematical meaning.	Evaluates formulas only when explicit, step-by-step guidance is provided.	AC9M7A01 recognise and use variables to represent everyday formulas algebraically and substitute values into formulas to determine an unknown	Rearranges algebraic formulas to make a different variable the subject before substituting values.	Critiques the limitations of specific formulas when applied to extreme real-world values.
Cannot translate worded phrases into mathematical symbols.	Writes simple expressions but frequently omits necessary brackets or order of operations.	AC9M7A02 formulate algebraic expressions using constants, variables, operations and brackets	Simplifies complex, self-generated expressions down to their most efficient mathematical form.	Designs generalized algebraic proofs to explain recurring arithmetic patterns.
Views fractions and decimals as completely separate concepts.	Identifies basic equivalencies but scales number lines incorrectly when plotting them or incorrectly uses order symbols	AC9M7N04 find equivalent representations of rational numbers and represent rational numbers on a number line	Interpolates accurately between closely spaced rational numbers on unscaled axes.	Demonstrates the density of rational numbers by generating continuous values between any two points.
Attempts operations but ignores place value or common denominators.	Executes calculations mechanically but struggles to select the correct operation for word problems.	AC9M7N06 use the 4 operations with positive rational numbers including fractions, decimals and percentages to solve problems using efficient calculation strategies	Mentally estimates outcomes before calculating to self-correct complex rational arithmetic.	Designs or solves original, multi-layered word problems that require mixed rational operations to solve.