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
Understand and explain the procedures for multiplication and division of fractions, mixed numbers, and decimals.
Solve multi-step mathematical, contextual and verbal problems using fractions, mixed numbers, and decimals.
Understand and use ratios, rates and percents.
Understand and convert between fraction, decimal, and percent forms of rational numbers.
Develop meaning for integers; represent and compare quantities with integers.
Check For Understanding
Efficiently compare and order fractions, decimals and percents; determine their approximate locations on a number line.
Use area models to represent multiplication of fractions.
Create and solve contextual problems that lead naturally to division of fractions.
Understand ratio as a fraction used to compare two quantities by division.
Recognize a:b, a/b, and a to b as notations for ratios.
Recognize common percentages as ratios based on fractions whose denominators are 2, 3, 4, 5, or 10.
Connect ratio and rate to multiplication and division.
Recognize that a terminating decimal equals a fraction with a denominator that is a power of ten.
Recognize that the decimal form of a rational number either terminates or repeats.
Explore contexts that can be described with negative numbers (such as money, elevation, and temperature).
State Performance Indicator
Solve problems involving the multiplication and division of fractions.
Solve problems involving the addition, subtraction, multiplication, and division of mixed numbers.
Solve problems involving the addition, subtraction, multiplication, and division of decimals.
Solve multi-step arithmetic problems using fractions, mixed numbers, and decimals.
Transform numbers from one form to another (fractions, decimals, percents, and mixed numbers).
Solve problems involving ratios, rates and percents.
Locate positive rational numbers on the number line.
Locate integers on the number line.