Understand numbers, ways of representing numbers, relationships among numbers, and number systems
Understand meanings of operations and how they relate to one another
Compute fluently and make reasonable estimates
Students engage in problem solving, communicating, reasoning, connecting, and representing as they:
Compare, order, estimate, and translate among integers, fractions and mixed numbers (i.e., rational numbers), decimals, and percents.
Define, compare, order, and apply frequently used irrational numbers, such as ?2 and ?.
Use ratios and proportions in the solution of problems, in particular, problems involving unit rates, scale factors, and rate of change.
Represent numbers in scientific notation, and use them in calculations and problem situations.
Apply number theory concepts, including prime factorization and relatively prime numbers, to the solution of problems.
Demonstrate an understanding of absolute value, e.g., |-3| = |3| = 3.
Apply the rules of powers and roots to the solution of problems. Extend the Order of Operations to include positive integer exponents and square roots.
Demonstrate an understanding of the properties of arithmetic operations on rational numbers. Use the associative, commutative, and distributive properties; properties of the identity and inverse elements (e.g., -7 + 7 = 0; 3/4 x 4/3 = 1); and the notion of closure of a subset of the rational numbers under an operation (e.g., the set of odd integers is closed under multiplication but not under addition).
Use the inverse relationships of addition and subtraction, multiplication and division, and squaring and finding square roots to simplify computations and solve problems, e.g. multiplying by 1/2 or 0.5 is the same as dividing by 2.
Estimate and compute with fractions (including simplification of fractions), integers, decimals, and percents (including those greater than 100 and less than 1).
Determine when an estimate rather than an exact answer is appropriate and apply in problem situations.
Select and use appropriate operations—addition, subtraction, multiplication, division, and positive integer exponents—to solve problems with rational numbers (including negatives).
Exploratory Concepts and Skills
for Grades 7-8 and Single-Subject Courses
Investigate the meaning of significant digits.
Investigate negative integral exponents and their use in scientific and calculator notation.