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 High School
- Understanding of very large and very small numbers
- Representations of very large and very small numbers
- Properties of numbers and number systems
- Rational and real numbers
- Complex numbers as solutions to quadratic equations
- Vectors and matrices as systems that have some of the properties of the real-number system
- Relationships involving whole numbers
- Multiplication, division, computing powers and roots on the magnitudes of quantities
- Addition and multiplication of vectors and matrices
- Permutations and combinations as counting techniques
- Operations with real numbers, vectors, and matrices
- Numerical computations
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Middle School
- Fractions, decimals, and percents to solve problems
- Compare and order fractions, decimals, and percents
- Percents greater than 100 and less than 1
- Ratios and proportions
- Exponential, scientific, and calculator notation
- Factors, multiples, prime factorization
- Integers - represent and compare quantities with them
- Arithmetic operations with fractions, decimals, and integers
- Associative and commutative properties of addition and multiplication
- Distributive property of multiplication over addition
- Inverse relationships of addition and subtraction, multiplication and division
- Squaring and finding square roots
- Computing with fractions and decimals
- Algorithms for computing with fractions, decimals, and integers
- Rational-number computations
- Problems involving proportions - such as scaling and finding equivalent ratios
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Elementary School
- Place-value structure of the base-ten number system
- Represent and compare whole numbers and decimals
- Equivalent representations for the same number
- Generate equivalent numbers by decomposing and composing
- Fractions as parts of unit wholes, and collection
- Fractions as locations on number lines and as divisions of whole numbers
- Size of fractions
- Equivalent forms of fractions, decimals, and percents
- Explore numbers less than 0
- Classes of numbers
- Multiplication and division of whole numbers
- Relationships between operations and properties of operations
- Distributive property (multiplication over addition)
- Basic number combinations for multiplication and division
- Adding, subtracting, multiplying, and dividing whole numbers
- Add and subtract fractions and decimals
- Computing with whole numbers
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