1. Understands operations and properties of the real number system
a. solve problems using addition, subtraction, multiplication, and division of rational numbers
b. apply the order of operations
c. determine whether the properties hold (e.g., commutative, associative, distributive) for given operations on a number system
d. compare, classify, and order real numbers
e. perform operations involving exponents, including negative exponents
f. simplify and approximate radicals
g. represent and compare very large and very small numbers (e.g., scientific notation)
2. Understands the relationships among fractions, decimals, and percents
a. convert among fractions, decimals, and percents
b. represent fractions, decimals, and percents using various models
3. Knows how to use ratio reasoning to solve problems
a. apply the concept of a ratio and use ratio language and notation to describe a relationship between two quantities
b. compute unit rates
c. use ratio reasoning to convert rates
d. solve problems involving scale factors
4. Knows how to use proportional relationships to solve real-world problems
a. recognize and represent proportional and inversely proportional relationships between two quantities
b. use proportional relationships to solve multistep ratio and percent problems
5. Knows how to use basic concepts of number theory (e.g., divisibility, prime factorization, multiples) to solve problems
a. recognize relationships involving prime and composite numbers
b. solve problems involving odd or even numbers
c. solve problems involving factors, multiples, and divisibility
6. Knows a variety of strategies to determine the reasonableness of results
a. recognize the reasonableness of results within the context of a given problem
b. test the reasonableness of results using estimation
c. estimate absolute and relative error in the numerical answer to a problem
I.Numbers and Operations