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 the place value of whole numbers to ten-thousands place including expanded notation for all arithmetic operations.
Develop understanding of multiplication and related division facts through multiple strategies and representations.
Relate multiplication and division as inverse operations.
Solve multiplication and division problems using various representations.
Understand the meaning and uses of fractions.
Use various strategies and models to compare and order fractions and identify equivalent fractions.
Add and subtract fractions with like denominators using various models.
Check For Understanding
Represent whole numbers up to 10,000 using various models (such as base-ten blocks, number lines, place-value charts) and in standard form, written form, and
Understand and use the symbols =, to signify order and comparison.
Use parentheses to indicate grouping.
Use a variety of methods to perform mental computations and compare the efficiency of those methods.
Use highest order value (such as tens or hundreds digit) to make simple estimates.
Solve a variety of addition and subtraction story problems including those with irrelevant information.
Represent multiplication using various representations such as equal-size groups, arrays, area models, and equal jumps on number lines.
Represent division using various representations such as successive subtraction, the number of equal jumps, partitioning, and sharing.
Describe contexts for multiplication and division facts.
Understand that symbols such as , 1/3, and represent numbers called unit fractions.
Identify fractions as parts of whole units, as parts of sets, as locations on number lines, and as division of two whole numbers.
Compare fractions using drawings, concrete objects, and benchmark fractions.
Understand that when a whole is divided into equal parts to create unit fractions, the sum of all the parts adds up to one.
State Performance Indicator
Read and write numbers up to 10,000 in numerals and up to 1,000 in words.
Identify the place value of numbers in the ten-thousands, thousands, hundreds, tens, and ones positions.
Convert between expanded and standard form with whole numbers to 10,000.
Compare and order numbers up to 10,000 using the words less than, greater than, and equal to, and the symbols , =.
Identify various representations of multiplication and division.
Recall basic multiplication facts through 10 times10 and the related division facts.
Compute multiplication problems that involve multiples of ten using basic number facts.
Solve problems that involve the inverse relationship between multiplication and division.
Solve contextual problems involving the addition (with and without regrouping) and subtraction (with and without regrouping) of two- and three digit whole numbers.
Identify equivalent fractions given by various representations.
Recognize and use different interpretations of fractions.
Name fractions in various contexts that are less than, equal to, or greater than one.
Recognize, compare, and order fractions (benchmark fractions, common numerators, or common denominators).
Add and subtract fractions with like denominators.