To become ready for college and career, high school students work independently and confidently to learn to study math across a broad spectrum, from pure math to real-world applications.
Numerical skill and quantitative reasoning remain crucial as high school students move forward with algebra. Algebra, functions, and geometry are important not only as math subjects but also because they are the language of technical subjects and the sciences. In a data-rich world, statistics and probability offer powerful ways of drawing conclusions from data and dealing with uncertainty.
In high school, students use math creatively to analyze a real-world situation, which is sometimes called “mathematical modeling.” This modeling is used throughout the following six major content areas: numbers and quantities, algebra, functions, modeling, geometry, and statistics and probability.
Examples of Your Child’s Work at School:
Numbers and Quantities
- Work with rational and irrational numbers that include rational exponents (e.g., rewriting (53) ½ as 5√5).
- Solve problems with a wide range of units and solve problems by thinking about units (e.g., “The Trans-Alaska Pipeline System is 800 miles long and cost $8 billion to build. Divide one of these numbers by the other. What is the meaning of the answer?”; “Greenland has a population of 56,700 and a land area of 2,175,600 square kilometers. By what factor is the population density of the United States, 80 persons per square mile, larger than the population density of Greenland?”).
- Solve real-world and mathematical problems by writing and solving nonlinear equations, such as quadratic equations (ax2 + bx + c = 0).
- Interpret algebraic expressions and transform them purposefully to solve problems (e.g., while solving a problem about a loan with interest rate r and principal P, see the expression P(1+r)n as a product of P with a factor not depending on P).
- Analyze functions algebraically and graphically, and work with functions presented in different forms (e.g., if given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum).
- Work with function families and understand their behavior (such as linear, quadratic, and exponential functions).
- Analyze real-world situations by using mathematics to understand the situation better and optimize, troubleshoot or make an informed decision (e.g., estimate water and food needs in a disaster area, or use volume formulas and graphs to find an optimal size for an industrial package).
- Prove theorems about triangles and other figures (e.g., the angles in a triangle add to 180º).
- Solve applied problems that involve trigonometry of right triangles.
- Use coordinates and equations to describe geometric properties algebraically (e.g., write the equation for a circle with given center and radius using Pythagorean Theorem).
Statistics and Probability
- Make inferences and justify conclusions from sample surveys, experiments, and observational studies.
- Work with probability and use ideas from probability in everyday situations (e.g., compare the chance that a person who smokes will develop lung cancer to the chance that a person who develops lung cancer smokes).