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 place value of numbers from hundredths to the hundred-thousands place.
Develop fluency with multiplication and single-digit division.
Identify prime and composite numbers.
Understand and use the connections between fractions and decimals.
Add and subtract fractions with like and unlike denominators.
Solve problems involving whole numbers, fractions, and/or decimals using all four arithmetic operations.
Check For Understanding
Compose and decompose quantities according to place value.
Understand decimal notation as an extension of the base-ten number system.
Multiply two- and three-digit whole numbers.
Understand and use a reliable algorithm for multiplying multi-digit numbers and dividing numbers by a single-digit divisor accurately and efficiently.
Understand that division by zero is undefined.
Divide three-digit whole numbers by one-digit divisors fluently with pencil and paper.
Identify factors of whole numbers and model factors and products beyond basic multiplication facts using arrays and area models.
Generate equivalent forms of whole numbers, decimals, and common fractions (e.g., 1/10, , , ).
Compare equivalent forms whole numbers, fractions, and decimals to each other and to benchmark numbers.
Use models to understand division as the inverse of multiplication, partitioning, and repeated subtraction.
Use models, benchmarks, and equivalent forms to compare fractions/decimals and locate them on the number line.
Understand and use decimal numbers up to hundredths and write them as fractions.
Solve multi-step problems of various types using whole numbers, fractions, and decimals.
Understand the role of the remainder in division.
State Performance Indicator
Read and write numbers from hundredths to hundred-thousands in numerals and in words.
Locate and place mixed numbers on the number line.
Identify the place value of a specified digit in a number and the quantity it represents.
Find factors, common factors, multiples, and common multiples of two numbers.
Generate equivalent forms of common fractions and decimals and use them to compare size.
Use the symbols and = to compare common fractions and decimals in both increasing and decreasing order.
Convert improper fractions into mixed numbers and/or decimals.
Add and subtract proper fractions with like and unlike denominators and simplify the answer.
Add and subtract decimals through hundredths.
Solve contextual problems using whole numbers, fractions, and decimals.
Solve problems using whole number multi-digit multiplication.
Solve problems using whole number division with one- or two-digit divisors.