NAEP Mathematics Content Strand 3

Image of a bullet. Subtopic can be assessed at this grade level.
Image of a triangle. Subtopic should not be assessed at this grade level.
Image of a pound sign. Subtopic may be introduced at a simple level
(such as using a manipulative or pictorial model).

Grade
Geometry and Spatial Sense  4   8   12 
1. Describe, visualize, draw, and construct geometric figures
a. Draw or sketch a figure given a verbal description (open-ended
    items)		 Image of a bullet. Image of a bullet. Image of a bullet.
b. Given a figure, write a verbal description of its geometric qualities Image of a triangle. Image of a bullet. Image of a bullet.
2. Investigate and predict results of combining, subdividing, and changing shapes (such as paper folding, dissecting, tiling, rearranging pieces of solids) Image of a bullet. Image of a bullet. Image of a bullet.
3. Identify the relationship (congruence, similarity) between a figure and its image under a transformation
a. Use motion geometry (informal: lines of symmetry, flips, turns, slides) Image of a bullet. Image of a bullet. Image of a bullet.
b. Use transformations (translations, rotations, reflections, dilations,
    symmetry)
    i. Synthetic Image of a triangle. Image of a pound sign. Image of a bullet.
    ii. Algebraic Image of a triangle. Image of a triangle. Image of a bullet.
4. Describe the intersection of two or more geometric figures
a. Two dimensional Image of a triangle. Image of a bullet. Image of a bullet.
b. Planar cross-section of a solid Image of a triangle. Image of a bullet. Image of a bullet.
5. Classify figures in terms of congruence and similarity, and informally apply these relationships using proportional reasoning where appropriate Image of a triangle. Image of a bullet. Image of a bullet.
6. Apply geometric properties and relationships in solving problems
a. Use concepts of "between," "inside," "on," and "outside" Image of a bullet. Image of a bullet. Image of a triangle.
b. Use the Pythagorean relationship to solve problems Image of a triangle. Image of a bullet. Image of a bullet.
c. Apply properties of ratio and proportion with respect to similarity Image of a triangle. Image of a pound sign. Image of a bullet.
e. Solve problems involving right triangle trigonometric applications Image of a triangle. Image of a triangle. Image of a bullet.
7. Establish and explain relationships involving geometric concepts
a. Make conjectures Image of a bullet. Image of a bullet. Image of a bullet.
b. Validate and justify conclusions and generalizations Image of a bullet. Image of a bullet. Image of a bullet.
c. Use informal induction and deduction Image of a pound sign. Image of a bullet. Image of a bullet.
8. Represent problem situations with geometric models and apply properties of figures in meaningful contexts to solve mathematical and real-world problems Image of a bullet. Image of a bullet. Image of a bullet.
9. Represent geometric figures and properties algebraically using coordinates and vectors
a.Use properties of lines (including distance, midpoint, slope,
    parallelism, perpendicularity) to describe figures algebraically		 Image of a triangle. Image of a pound sign. Image of a bullet.
b. Algebraically describe conic sections and their properties Image of a triangle. Image of a triangle. Image of a bullet.
c. Use vectors in problem situations (addition, subtraction, scalar
    multiplication, dot product)		 Image of a triangle. Image of a triangle. Image of a bullet.

Back to Chapter 3

Mathematics Framework for the 2003 National Assessment of Educational Progress