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 the understanding of place value through millions and millionths in various contexts and representations.
Write natural numbers (to 50) as a product of prime factors and understand that this is unique (apart from order).
Develop fluency with division of whole numbers. Understand the relationship of divisor, dividend, and quotient in terms of multiplication and division.
Develop fluency with addition and subtraction of proper and improper fractions and mixed numbers; explain and model the algorithm.
Develop fluency in solving multi-step problems using whole numbers, fractions, mixed numbers, and decimals.
Check For Understanding
Identify prime numbers up to 50.
Use the prime factorization of two whole numbers to determine the greatest common factor and the least common multiple.
Use visual models, benchmarks, and equivalent forms to add and subtract commonly used fractions and decimals.
Use divisibility rules to factor numbers.
Make reasonable estimates of fraction and decimal sums and differences.
Add and subtract mixed numbers.
Understand the placement of the decimal point in calculations of multiplication and long division, including the placement in the estimation of the answer.
Understand that division by zero is undefined.
Explore numbers less than 0 by extending the number line through familiar applications (e.g., temperatures below zero, owing money, measuring elevation below sea
Use exponential notation to represent repeated multiplication of whole numbers.
State Performance Indicator
Read and write numbers from millions to millionths in various contexts.
Write the prime factorization of numbers through 50 using both exponential and standard notation.
Select a reasonable solution to a real-world division problem in which the remainder must be considered.
Solve problems involving the division of two- and three-digit whole numbers by one- and two-digit whole numbers.
Solve addition and subtraction problems involving both fractions and decimals.
Add and subtract proper and improper fractions as well as mixed numbers.
Recognize equivalent representations for the same number.
Write terminating decimals in the form of fractions or mixed numbers.
Compare whole numbers, decimals and fractions using the symbols , and =.