High School | Mathematics | Computation
Numbers and operations on numbers play fundamental roles in helping us make sense of the world around us. Operations such as addition, subtraction, multiplication and division, as well as the ability to find powers and roots, extend the notion of numbers to create tools to model situations and solve problems in our everyday lives. Discussing and solving problems related to budgets, comparing prices on merchandise, understanding the nature of interest charges, measuring fuel consumption and calculating the trajectory for space travel would all be impossible without a sense of numbers and numerical operations. All people must develop this sense of numbers and operations and be able to use it to solve problems using mental computation, paper-and-pencil algorithms, calculators and computers.
Demonstrate knowledge and use of numbers and their representations in a broad range of theoretical and practical settings:
- Identify and apply the associative, commutative, distributive and identity properties of real numbers, including special numbers such as pi and square roots.
- Perform addition, subtraction and multiplication of complex numbers and graph the results in the complex plane.
Investigate, represent and solve problems using number facts, operations (addition, subtraction, multiplication, division) and their properties, algorithms and relationships:
- Select and use appropriate arithmetic operations in practical situations including calculating wages after taxes, developing a budget and balancing a checkbook.
- Identify, represent and apply numbers expressed in exponential, logarithmic and scientific notation using contemporary technology.
Compute and estimate using mental mathematics, paper-and-pencil methods, calculators and computers:
- Determine whether exact values or approximations are appropriate (e.g., bid a job, determine gas mileage for a trip).
- Determine the level of accuracy needed for computations involving measurement and irrational numbers.
Solve problems using comparison of quantities, ratios, proportions and percents:
- Solve problems involving recipes or mixtures, financial calculations and geometric similarity using ratios, proportions and percents.
- Solve problems involving loans, mortgages and other practical applications involving geometric patterns of growth.
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