Ohio Resource Center

# Ohio's Academic Content Standards in Mathematics

## Benchmarks

Number, Number Sense and Operations Standard
Students demonstrate number sense, including an understanding of number systems and operations and how they relate to one another. Students compute fluently and make reasonable estimates using paper and pencil, technology-supported and mental methods.

By the end of the K - 2 program:
 A. Use place value concepts to represent whole numbers using numerals, words and physical models. (ORC Resources) B. Recognize, classify, compare and order whole numbers. (ORC Resources) C. Represent commonly used fractions using words and physical models. (ORC Resources) D. Determine the value of a collection of coins and dollar bills. (ORC Resources) E. Make change using coins for values up to one dollar. (ORC Resources) F. Count, using numerals and ordinal numbers. (ORC Resources) G. Model, represent and explain addition as combining sets and counting on. (ORC Resources) H. Model, represent and explain subtraction as comparison, take-away and part-to-whole. (ORC Resources) I. Model, represent and explain multiplication as repeated addition, rectangular arrays and skip counting. (ORC Resources) J. Model, represent and explain division as sharing equally, repeated subtraction and rectangular arrays. (ORC Resources) K. Demonstrate fluency in addition facts with addends through 9 and corresponding subtractions. (ORC Resources) L. Demonstrate fluency in adding and subtracting multiples of 10, and recognize combinations that make 10. (ORC Resources) M. Add and subtract two-digit numbers with and without regrouping. (ORC Resources)

By the end of the 3 - 4 program:
 A. Use place value structure of the base-ten number system to read, write, represent and compare whole numbers and decimals. (ORC Resources) B. Recognize and generate equivalent representations for whole numbers, fractions and decimals. (ORC Resources) C. Represent commonly used fractions and mixed numbers using words and physical models. (ORC Resources) D. Use models, points of reference and equivalent forms of commonly used fractions to judge the size of fractions and to compare, describe and order them. (ORC Resources) E. Recognize and classify numbers as prime or composite and list factors. (ORC Resources) F. Count money and make change using both coins and paper bills. (ORC Resources) G. Model and use commutative and associative properties for addition and multiplication. (ORC Resources) H. Use relationships between operations, such as subtraction as the inverse of addition and division as the inverse of multiplication. (ORC Resources) I. Demonstrate fluency in multiplication facts with factors through 10 and corresponding divisions. (ORC Resources) J. Estimate the results of whole number computations using a variety of strategies, and judge the reasonableness. (ORC Resources) K. Analyze and solve multi-step problems involving addition, subtraction, multiplication and division of whole numbers. (ORC Resources) L. Use a variety of methods and appropriate tools (mental math, paper and pencil, calculators) for computing with whole numbers. (ORC Resources) M. Add and subtract commonly used fractions with like denominators and decimals, using models and paper and pencil. (ORC Resources)

By the end of the 5 - 7 program:
 A. Represent and compare numbers less than 0 through familiar applications and extending the number line. (ORC Resources) B. Compare, order and convert among fractions, decimals and percents. (ORC Resources) C. Develop meaning for percents, including percents greater than 100 and less than 1. (ORC Resources) D. Use models and pictures to relate concepts of ratio, proportion and percent. (ORC Resources) E. Use order of operations, including use of parenthesis and exponents to solve multi-step problems, and verify and interpret the results. (ORC Resources) F. Apply number system properties when performing computations. (ORC Resources) G. Apply and explain the use of prime factorizations, common factors, and common multiples in problem situations. (ORC Resources) H. Use and analyze the steps in standard and non-standard algorithms for computing with fractions, decimals and integers. (ORC Resources) I. Use a variety of strategies, including proportional reasoning, to estimate, compute, solve and explain solutions to problems involving integers, fractions, decimals and percents. (ORC Resources)

By the end of the 8 - 10 program:
 A. Use scientific notation to express large numbers and numbers less than one. (ORC Resources) B. Identify subsets of the real number system. (ORC Resources) C. Apply properties of operations and the real number system, and justify when they hold for a set of numbers. (ORC Resources) D. Connect physical, verbal and symbolic representations of integers, rational numbers and irrational numbers. (ORC Resources) E. Compare, order and determine equivalent forms of real numbers. (ORC Resources) F. Explain the effects of operations on the magnitude of quantities. (ORC Resources) G. Estimate, compute and solve problems involving real numbers, including ratio, proportion and percent, and explain solutions. (ORC Resources) H. Find the square root of perfect squares, and approximate the square root of non-perfect squares. (ORC Resources) I. Estimate, compute and solve problems involving scientific notation, square roots and numbers with integer exponents. (ORC Resources)

By the end of the 11 - 12 program:
 A. Demonstrate that vectors and matrices are systems having some of the same properties of the real number system. (ORC Resources) B. Develop an understanding of properties of and representations for addition and multiplication of vectors and matrices. (ORC Resources) C. Apply factorials and exponents, including fractional exponents, to solve practical problems. (ORC Resources) D. Demonstrate fluency in operations with real numbers, vectors and matrices, using mental computation or paper and pencil calculations for simple cases and technology for more complicated cases. (ORC Resources) E. Represent and compute with complex numbers. (ORC Resources)