Middle Level Mathematics (Grades 5–8) Subtest 2

For example:

• 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 shapes, regions, and solids (e.g., length, area, 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 linear dimensions of a multidimensional object on its length, area, and volume

For example:

• demonstrating knowledge of the relationships between points, lines (e.g., parallel, perpendicular, skew), rays, angles (e.g., supplementary, vertical), and planes
• applying the properties of triangles (e.g., congruence conditions, triangle inequality, classifications) and other polygons (e.g., properties of quadrilaterals, sums of interior angles) to solve mathematical and real-world problems
• applying the properties of circles (e.g., tangents, arc length, chords, inscribed angles) to solve mathematical and real-world problems
• applying the properties of three-dimensional shapes (e.g., circular cones, spheres) to solve mathematical and real-world problems
• evaluating formal and informal arguments and proofs

For example:

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