| Uses trial and error exclusively, lacking an algebraic method. | Solves one-step equations using inverse operations but fails on multi-step problems. | AC9M7A03 solve one-variable linear equations with natural number solutions; verify the solution by substitution | Isolates variables in equations featuring multiple terms on both sides of the equal’s sign. | Formulates linear equations from ambiguous real-world data to pinpoint exact intersecting solutions. |
| Reads single data points but ignores the overall trend. | Identifies if a graph goes up or down but cannot describe the mathematical rate of change. | AC9M7A04 describe relationships between variables represented in graphs of functions from authentic data | Interpolates and extrapolates data reliably, identifying exactly where the graphical model loses accuracy. | Hypothesizes the external physical or economic factors causing specific anomalies in the graphed function. |
| Sees no connection between visual patterns and numerical sequences. | Extends a visual pattern physically but struggles to abstract it into a generic mathematical rule. | AC9M7A05 generate tables of values from visually growing patterns or the rule of a function; describe and plot these relationships on the Cartesian plane | Transitions seamlessly between the nth term formula, the table of values, and the Cartesian plot. | Proves mathematically why two seemingly different visual patterns generate the exact same algebraic function. |
| Randomly changes values in a formula without tracking outcomes. | Uses digital tools to alter variables but cannot predict the result before calculating. | AC9M7A06 manipulate formulas involving several variables using digital tools, and describe the effect of systematic variation in the values of the variables | Maps out direct and inverse proportionalities when isolating specific variables within the formula. | Models the cascading mathematical impact of simultaneous, multi-variable adjustments in a complex digital system. |
| Draws overlapping shapes without recognizing spatial movement. | Performs single translations but distorts the shape’s proportions during rotations. | AC9M7SP03 describe transformations of a set of points using coordinates in the Cartesian plane, translations and reflections on an axis, and rotations about a given point | Executes combined sequences of transformations while maintaining perfect geometric congruence. | Determines the single minimal transformation required to replace a complex, multi-step sequence. |
| Truncates numbers arbitrarily regardless of the following digit. | Rounds correctly in isolation but fails to use it as a tool to check final answers. | AC9M7N05 round decimals to a given accuracy appropriate to the context and use appropriate rounding and estimation to check the reasonableness of solutions | Strategically rounds up or down based on real-world constraints (e.g., material limits) rather than strict math rules. | Calculates the maximum percentage error introduced into a system by continuous rounding / compounding errors. |