Resource Type: Lessons Discipline: Mathematics Grades: Grades 8–11 Professional Commentary: Students use graphs, tables, number lines, verbal descriptions, and symbolic representations to analyze the domains of various functions. An activity sheet, discussion questions, lesson extensions, and suggestions for assessment are included.... Resource Type: Lessons Discipline: Mathematics Grades: Grades 8–12 Professional Commentary: Students model successive discounts as a composition of functions and show that, in general, function composition is not commutative. They study the graphs of the discount functions to find the values for which different orders of successive discounts yield equal results. An activity sheet, discussion questions, lesson extensions, suggestions for assessment, and prompts for teacher reflection are included.... Resource Type: Lessons Discipline: Mathematics Grades: Grades 10–12 Professional Commentary: As a culminating activity to instruction in functions, linear equations, and proportional reasoning, students are introduced to the mathematics of bicycles. Students pair up to investigate bicycle-related relationships, such as wheel diameter and coasting distance or frame tubing size and weight allowances.... 4 NAEP Assessment Item, Grade 12: Solve a Function Using Substitution Resource Type: Assessments Discipline: Mathematics Grades: Grades 9–12 Professional Commentary: This item asks students to evaluate the composition of a quadratic function with a linear function for x=2. This multiple-choice question is a sample test item used in grade 12 in the 1992 National Assessment of Educational Progress (see About NAEP).... 5 NAEP Assessment Item, Grade 12: Given a Graph, Find the Value Resource Type: Assessments Discipline: Mathematics Grades: Grades 9–12 Professional Commentary: Students must find the value of a composition of functions by looking at the graphs of the functions. This multiple-choice question is a sample test item used in grade 12 in the 1990 National Assessment of Educational Progress (see About NAEP).... 6 NAEP Assessment Item, Grade 12: Determine composition of two functions Resource Type: Assessments Discipline: Mathematics Grades: Grades 10–12 Professional Commentary: Students are asked to find the composition of two functions. This constructed-response question is a "hard" test item used in grade 12 of the 2005 National Assessment of Educational Progress (see About NAEP).... 7 NAEP Assessment Item, Grade 12: Evaluate a Quadratic Function Resource Type: Assessments Discipline: Mathematics Grades: Grades 8–12 Professional Commentary: Students are asked to evaluate a quadratic function for a noninteger value of x. They have the option of using a calculator.... 8 NAEP Assessment Item, Grade 12: Given a Graph, Find the Value Resource Type: Assessments Discipline: Mathematics Grades: Grades 7–10 Professional Commentary: Students must determine the value of a function by looking at its graph. This multiple-choice question is a sample test item used in grade 12 in the 1990 National Assessment of Educational Progress (see About NAEP).... 9 Linearity in the World Around Us Resource Type: Content Supports -- Activities and rich problems Discipline: Mathematics Grades: Grades 8–10 Professional Commentary: Several real-world situations motivate the study of linear functions, their parameters, and behaviors. The contextual situations lead to the abstraction of function and provide tools for understanding and long-term memory.... Resource Type: Content Supports -- Reference materials Discipline: Mathematics Grades: Grades 12–Postsecondary Professional Commentary: Students will find tutorials, Java applets, drills, computer programs, quizzes, and LiveMath notebooks and animations on a variety of precalculus topics. More than 100 subsections of the site address polynomial, rational, exponential, trigonometric, and logarithmic functions, as well as piecewise definitions, parametric equations, and polar coordinates.... |