Academic Standard

Number and Operations
Tennessee Diploma Project
Grade range: 
Conceptual StrandThe Number and Operations Standard describes deep and fundamental understanding of, and proficiency with, counting, numbers, and arithmetic, as well as an understanding of number systems and their structures.Guiding QuestionHow do students develop number sense that allows them to naturally decompose numbers, use particular numbers as referents, solve problems using the relationships among operations and knowledge about the base-ten system, estimate a reasonable result for a problem, and have a disposition to make sense of numbers, problems, and results?
Elements within this Standard
Grade Level Expectation
Extend understandings of addition, subtraction, multiplication and division to integers.
Understand and work with the properties of and operations on the system of rational numbers.
Develop an understanding of and apply proportionality.
Use ratios, rates and percents to solve single- and multi-step problems in various contexts.
Understand and work with squares, cubes, square roots and cube roots.
Introduce the concept of negative exponents.
Understand and use scientific notation.
Check For Understanding
Understand that the set of rational numbers includes any number that can be written as a ratio of two integers in which the denominator is not zero.
Develop and analyze algorithms and compute efficiently with integers and rational numbers.
Recognize that rational numbers satisfy the commutative and associative laws of addition and multiplication and the distributive law.
Understand that a and a are additive inverses and are located the same distance from zero on the number line; relate distance from zero to absolute value.
Understand that (a) = a for any number a.
Use the number line to demonstrate addition and subtraction with integers.
Write number sentences to solve contextual problems involving ratio and percent.
Apply ratios, rates, proportions and percents (such as discounts, interest, taxes, tips, distance/rate/time, and percent increase or decrease).
Efficiently compare and order rational numbers and roots of perfect squares/cubes; determine their approximate locations on a number line.
Recognize that when a whole number is not a perfect square, then its square root is not rational and cannot be written as the ratio of two integers.
Estimate square/cube roots and use calculators to find approximations.
Recognize that the square root of m times n equals the square root of m plus the square root of n and that the square root of m squared equals m.
Use the meaning of negative exponents to represent small numbers; translate between scientific and standard notation.
Express numbers in scientific notation and recognize its importance in representing the magnitude of a number.
Report results of calculations appropriately in a given context (i.e. using rules of rounding, degree of accuracy, and/or significant digits).
State Performance Indicator
Simplify numerical expressions involving rational numbers.
Compare rational numbers using appropriate inequality symbols.
Use rational numbers and roots of perfect squares/cubes to solve contextual problems.
Determine the approximate location of square/cube roots on a number line.
Solve contextual problems that involve operations with integers.
Express the ratio between two quantities as a percent, and a percent as a ratio or fraction.
Use ratios and proportions to solve problems.