Applied 3D Nets, Cross-Sections, and Structures

Identify, describe, and classify regular and irregular polygons including triangles, quadrilaterals, and multi-sided shapes based on side and angle properties.

Explore circle properties, sort 2D shapes using logical diagrams, and investigate geometric applications in nature, engineering, and the built environment.

Identify the geometric properties of prisms and pyramids, verify Euler's formula, and connect polyhedra to their 2D folding nets.

Explore curved nets, design functional packaging, evaluate cross-sections, and build compound 3D structures.

Use rulers, set squares, and compasses to construct precise 2D lines, polygons, circles, and geometric patterns.

Create 3D representations of solid shapes using isometric, oblique, and orthographic elevation techniques as well as digital tools.

Understand angles as measures of turn, classify angle types, and estimate angle sizes in degrees using key benchmarks.

Apply angle sum rules for lines, points, triangles, and quadrilaterals to calculate missing angles and solve geometric deduction puzzles.

Accurately measure and construct acute, obtuse, and reflex angles using 180-degree and 360-degree protractors in practical and technical contexts.

Link compass points to angle turns, navigate routes using 8-point and 16-point compasses, use programmable technology, and calculate three-figure bearings.

Understand, interpret, and create scale drawings, models, architectural floor plans, and maps using ratio and graphic scales.

Plot, locate, describe, and transform coordinate points and geometric shapes on single-quadrant and four-quadrant Cartesian grids.

Identify, test, and draw lines of symmetry in 2D shapes, and create and complete intricate symmetrical patterns and pictures.

Plan, devise, conduct, collate, and communicate collaborative statistical surveys and mathematical investigations.

Construct accurate bar charts, comparative bar graphs, pictograms, and single and dual line graphs with appropriate vertical axis scales on grid paper.

Construct pie charts and stem-and-leaf diagrams by hand, and create and format professional charts using spreadsheet software.

Read and analyze bar, line, and pie charts, and calculate and evaluate statistical averages (mean, median, mode, and range) for various data sets.

Detect visual distortions, manipulative axis scales, disproportionate icons, and biased samples to draw sound, evidence-based conclusions from data.

Understand chance vocabulary, express probabilities numerically on a 0 to 1 scale, calculate theoretical probabilities, and conduct introductory coin and dice experiments.

Design probability experiments, construct sample space diagrams, analyze trial accuracy and game fairness, and apply probability to everyday decisions.