NAEP Mathematics Content Strand 5

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
Algebra and Functions  4   8   12 
1. Describe, extend, interpolate, transform, and create a wide variety of patterns and functional relationships
a. Recognize patterns and sequences Image of a bullet. Image of a bullet. Image of a bullet.
b. Extend a pattern or functional relationship Image of a bullet. Image of a bullet. Image of a bullet.
c. Given a verbal description, extend or interpolate with a pattern
    (complete a missing term)		 Image of a triangle. Image of a bullet. Image of a bullet.
d. Translate patterns from one context to another Image of a pound sign. Image of a bullet. Image of a bullet.
e. Create an example of a pattern or functional relationship Image of a bullet. Image of a bullet. Image of a bullet.
f. Understand and apply the concept of a variable Image of a pound sign. Image of a bullet. Image of a bullet.
2. Use multiple representations for situations to translate among diagrams, models, and symbolic expressions Image of a bullet. Image of a bullet. Image of a bullet.
3. Use number lines and rectangular coordinate systems as representational tools
a. Identify or graph sets of points on a number line or in a rectangular
    coordinate system		 Image of a bullet. Image of a bullet. Image of a bullet.
b. Identify or graph sets of points in a polar coordinate system Image of a triangle. Image of a triangle. Image of a bullet.
c. Work with applications using coordinates Image of a triangle. Image of a bullet. Image of a bullet.
d. Transform the graph of a function Image of a triangle. Image of a pound sign. Image of a bullet.
4. Represent and describe solutions to linear equations and inequalities to solve mathematical and real-world problems
a. Provide solution sets of whole numbers Image of a bullet. Image of a bullet. Image of a bullet.
b. Provide solution sets of real numbers Image of a pound sign. Image of a bullet. Image of a bullet.
5. Interpret contextual situations and perform algebraic operations on real numbers and algebraic expressions to solve mathematical and real-world problems
a. Perform basic operations, using appropriate tools, on real numbers
    in meaningful contexts (including grouping and order of multiple
    operations involving basic operations, exponents, and roots)		 Image of a triangle. Image of a bullet. Image of a bullet.
b. Solve problems involving substitution in expressions and formulas Image of a triangle. Image of a bullet. Image of a bullet.
c. Solve meaningful problems involving a formula with one variable Image of a triangle. Image of a bullet. Image of a bullet.
d. Use equivalent forms to solve problems Image of a triangle. Image of a bullet. Image of a bullet.
6. Solve systems of equations and inequalities using appropriate methods
a. Solve systems graphically Image of a triangle. Image of a bullet. Image of a bullet.
b. Solve systems algebraically Image of a triangle. Image of a triangle. Image of a bullet.
c. Solve systems using matrices Image of a triangle. Image of a triangle. Image of a bullet.
7. Use mathematical reasoning
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 discrete structures
a. Use finite graphs and matrices Image of a triangle. Image of a pound sign. Image of a bullet.
b. Use sequences and series Image of a triangle. Image of a triangle. Image of a bullet.
c. Use recursive relations (including numerical and graphical iteration
    and finite differences)		 Image of a triangle. Image of a triangle. Image of a bullet.
9. Solve polynomial equations with real and complex roots using a variety of algebraic and graphical methods and using appropriate tools Image of a triangle. Image of a triangle. Image of a bullet.
10. Approximate solutions of equations (bisection, sign changes, and successive approximations) Image of a triangle. Image of a pound sign. Image of a bullet.
11. Use appropriate notation and terminology to describe functions and their properties (including domain, range, function composition, and inverses) Image of a triangle. Image of a triangle. Image of a bullet.
12. Compare and apply the numerical, symbolic, and graphical properties of a variety of functions and families of functions, examining general parameters and their effect on curve shape Image of a triangle. Image of a pound sign. Image of a bullet.
13. Apply function concepts to model and deal with real-world situations Image of a triangle. Image of a pound sign. Image of a bullet.
14. Use trigonometry
a. Use triangle trigonometry to model problem situations Image of a triangle. Image of a triangle. Image of a bullet.
b. Use trigonometric and circular functions to model real-world phenomena Image of a triangle. Image of a triangle. Image of a bullet.
c. Apply concepts of trigonometry to solve real-world problems 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