| Confuses the concept of perimeter with area. | Plugs numbers into formulas but frequently uses the slant edge instead of the perpendicular height. | AC9M7M01 solve problems involving the area of triangles and parallelograms using established formulas and appropriate units | Deconstructs irregular composite polygons into exact triangles and parallelograms to find the total area. | Derives the area formula for a parallelogram by geometrically transforming a rectangle. |
| Counts visible faces instead of calculating 3D space. | Multiplies dimensions randomly without properly identifying the true base area of the prism. | AC9M7M02 solve problems involving the volume of right prisms including rectangular and triangular prisms, using established formulas and appropriate units | Calculates the missing dimension of a prism when the total volume and other sides are provided. | Optimizes packaging design by maximizing internal volume while minimizing the external surface area. |
| Cannot visually distinguish between a radius and a diameter. | Measures circles physically but fails to grasp the constant mathematical ratio of Pi. | AC9M7M03 describe the relationship between π and the features of circles including the circumference, radius and diameter | Manipulates the circumference formula to accurately calculate the radius of objects from their perimeter. | Proves the relationship between a circle’s circumference and the perimeter of inscribed polygons. |
| Identifies shapes purely by visual appearance rather than geometry. | Names basic polygons but cannot articulate the defining conditions of a rhombus versus a square. | AC9M7SP02 classify triangles, quadrilaterals and other polygons according to their side and angle properties; identify and reason about relationships | Constructs geometric hierarchies (e.g., proving all squares are rectangles, but not vice versa). | Deduces the exact identity of hidden polygons based strictly on a minimal set of abstract angle and side clues. |