# Middle Level Mathematics (Grades 5–8) Subtest 2

## Subarea I.1. Shape and Space

0008
Apply principles of measurement and geometry to solve problems.

- solving problems involving conversions within and between different systems of measurement, including dimensional analysis
- solving mathematical and real-world problems involving measurable attributes of simple or composite figures and shapes (e.g., length, capacity, angle measure)
- solving mathematical and real-world problems involving indirect measurement (e.g., proportional reasoning, Pythagorean theorem, trigonometric ratios)
- solving problems involving the effects of changing the dimensions of a figure or shape on its area and volume

0009
Analyze figures and shapes in two and three dimensions.

- demonstrating knowledge of the axioms of Euclidean geometry (e.g., points, lines, planes, angles)
- applying the properties of polygons and circles to solve mathematical and real-world problems
- applying the properties of two- and three-dimensional shapes to solve mathematical and real-world problems
- evaluating formal and informal arguments and proofs

0010
Analyze figures and shapes using coordinate and transformational geometry.

- analyzing two- and three-dimensional figures and shapes in the coordinate plane
- applying geometric properties and the concepts of distance, midpoint, and slope in coordinate systems to solve mathematical and real-world problems
- applying transformations (e.g., rotations, reflections, dilations) to figures in the coordinate plane
- analyzing the use of the techniques of coordinate geometry in geometric proofs