Ohio's Academic Content Standards in Mathematics

Grade Level Indicators

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.

PreK | K | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12
Prekindergarten
1.  Count to 10 in the context of daily activities and play. (ORC Resources) 2.  Touch objects and say the number names when counting in the context of daily activities and play. (ORC Resources) 3.  Demonstrate one-to-one correspondence when counting objects. (ORC Resources) 4.  Determine "how many" in sets of 5 or fewer objects. (ORC Resources) 5.  Construct two sets of objects each containing the same number of objects. (ORC Resources) 6.  Compare sets of equal, more, and fewer and use the language of comparison (i.e., equal, more and fewer). (ORC Resources) 7.  Group and regroup a given set in the context of daily activities and play (e.g., 5 blocks can be 2 blue and 3 green or 1 blue and 4 green). (ORC Resources) 8.  Represent quantity using invented forms (e.g., child's marks to represent a quantity of objects). (ORC Resources) 9.  Write numerical representations (e.g., scribbles, reversals) or numerals in meaningful context (e.g., play situations). (ORC Resources) 10.  Identify and name numerals 0-9. (ORC Resources) 11.  Compare and order whole numbers up to 5. (ORC Resources) 12.  Identify some coins (e.g., penny, dime, quarter). (ORC Resources) 13.  Recognize that coins have different values. (ORC Resources) 14.  Construct sets with more or fewer objects than a given set. (ORC Resources) 15.  Count on (forward) using objects such as cards, number cubes or dominoes that have familiar dot patterns. (ORC Resources) 16.  Join two sets of objects to make one large set in the context of daily routines of play (e.g., combining 2 bags of raisins, each containing 3 pieces; combining 2 groups of blocks, each containing 3 blocks). (ORC Resources) 17.  Distribute equally a set of objects into 2 or more smaller sets. (ORC Resources)

PreK | K | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12
Kindergarten
1.  Compare and order whole numbers up to 10. (ORC Resources) 2.  Explain rules of counting, such as each object should be counted once and that order does not change the number. (ORC Resources) 3.  Count to twenty; e.g., in play situations or while reading number books. (ORC Resources) 4.  Determine "how many" in sets (groups) of 10 or fewer objects. (ORC Resources) 5.  Relate, read and write numerals for single-digit numbers (0 to 9). (ORC Resources) 6.  Construct multiple sets of objects each containing the same number of objects. (ORC Resources) 7.  Compare the number of objects in two or more sets when one set has one or two more, or one or two fewer objects. (ORC Resources) 8.  Represent and use whole numbers in flexible ways, including relating, composing and decomposing numbers; e.g., 5 marbles can be 2 red and 3 green or 1 red and 4 green. (ORC Resources) 9.  Identify and state the value of a penny, nickel and dime. (ORC Resources) 10.  Model and represent addition as combining sets and counting on, and subtraction as take-away and comparison. For example: a. Combine and separate small sets of objects in contextual situations; e.g., add or subtract one, two, or another small amount. b. Count on (forward) and count back(backward) on a number line between 0 and 10. (ORC Resources) 11.  Demonstrate joining multiple groups of objects, each containing the same number of objects; e.g., combining 3 bags of candy, each containing 2 pieces. (ORC Resources) 12.  Partition or share a small set of objects into groups of equal size; e.g., sharing 6 stickers equally among 3 children. (ORC Resources) 13.  Recognize the number or quantity of sets up to 5 without counting; e.g., recognize without counting the dot arrangement on a domino as 5. (ORC Resources)

PreK | K | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12
Grade 1
1.  Use ordinal numbers to order objects; e.g., first, second, third. (ORC Resources) 2.  Recognize and generate equivalent forms for the same number using physical models, words and number expressions; e.g., concept of ten is described by "10 blocks", full tens frame, numeral 10, 5 + 5, 15 - 5, one less than 11, my brother's age. (ORC Resources) 3.  Read and write the numerals for numbers to 100. (ORC Resources) 4.  Count forward to 100, count backwards from 100, and count forward or backward starting at any number between 1 and 100. (ORC Resources) 5.  Use place value concepts to represent whole numbers using numerals, words, expanded notation and physical models with ones and tens. For example: a. Develop a system to group and count by twos, fives and tens. b. Identify patterns and groupings in a 100's chart and relate to place value concepts. c. Recognize the first digit of a two-digit number as the most important to indicate size of a number and the nearness to 10 or 100. (ORC Resources) 6.  Identify and state the value of a penny, nickel, dime, quarter and dollar. (ORC Resources) 7.  Determine the value of a small collection of coins (with a total value up to one dollar) using 1 or 2 different type coins, including pennies, nickels, dimes and quarters. (ORC Resources) 8.  Show different combinations of coins that have the same value. (ORC Resources) 9.  Represent commonly used fractions using words and physical models for halves, thirds and fourths, recognizing fractions are represented by equal size parts of a whole and of a set of objects. (ORC Resources) 10.  Model, represent and explain addition as combining sets (part + part = whole) and counting on. For example: a. Model and explain addition using physical materials in contextual Situations. b. Draw pictures to model addition. c. Write number sentences to represent addition. d. Explain that adding two whole numbers yields a larger whole number. (ORC Resources) 11.  Model, represent and explain subtraction as take-away and comparison. For example: a. Model and explain subtraction using physical materials in contextual situations. b. Draw pictures to model subtraction. c. Write number sentences to represent subtraction. d. Explain that subtraction of whole numbers yields an answer smaller than the original number. (ORC Resources) 12.  Use conventional symbols to represent the operations of addition and subtraction. (ORC Resources) 13.  Model and represent multiplication as repeated addition and rectangular arrays in contextual situations; e.g., four people will be at my party and if I want to give 3 balloons to each person, how many balloons will I need to buy? (ORC Resources) 14.  Model and represent division as sharing equally in contextual situations; e.g., sharing cookies. (ORC Resources) 15.  Demonstrate that equal means the same as" using visual representations. (ORC Resources) 16.  Develop strategies for basic addition facts, such as: a. counting all; b. counting on; c. one more, two more; d. doubles; e. doubles plus or minus one; f. make ten; g. using tens frames; h. identity property (adding zero). (ORC Resources) 17.  Develop strategies for basic subtraction facts, such as: a. relating to addition (for example, think of 7 - 3 = ? as 3 plus? equals 7"); b. one less, two less; c. all but one (for example, 8 - 7, 5 - 4); d. using tens frames; and e. missing addends. (ORC Resources)

PreK | K | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12
Grade 2
1.  Use place value concepts to represent, compare and order whole numbers using physical models, numerals and words, with ones, tens and hundreds. For example: a. Recognize 10 can mean "10 ones" or a single entity (1 ten) through physical models and trading games. b. Read and write 3-digit numerals (e.g., 243 as two hundred forty three, 24 tens and 3 ones, or 2 hundreds and 43 ones, etc.) and construct models to represent each. (ORC Resources) 2.  Recognize and classify numbers as even or odd. (ORC Resources) 3.  Count money and make change using coins and a dollar bill. (ORC Resources) 4.  Represent and write the value of money using the ¢ sign and in decimal form when using the $ sign. (ORC Resources) 5.  Represent fractions (halves, thirds, fourths, sixths and eighths), using words, numerals and physical models. For example: a. Recognize that a fractional part can mean different amounts depending on the original quantity. b. Recognize that a fractional part of a rectangle does not have to be shaded with contiguous parts. c. Identify and illustrate parts of a whole and parts of sets of objects. d. Compare and order physical models of halves, thirds and fourths in relations to 0 and 1. (ORC Resources) 6.  Model, represent and explain subtraction as comparison, take-away and part-to-whole; e.g., solve missing addend problems by counting up or subtracting, such as "I had six baseball cards, my sister gave me more, and I now have ten. How many did she give me?" can be represented as 6 + ? = 10 or 10 - 6 = ?. (ORC Resources) 7.  Model, represent and explain multiplication as repeated addition, rectangular arrays and skip counting. (ORC Resources) 8.  Model, represent and explain division as sharing equally and repeated subtraction. (ORC Resources) 9.  Model and use the commutative property for addition. (ORC Resources) 10.  Demonstrate fluency in addition facts with addends through 9 and corresponding subtractions; e.g., 9 + 9 = 18, 18 - 9 = 9. (ORC Resources) 11.  Add and subtract multiples of 10. (ORC Resources) 12.  Demonstrate multiple strategies for adding and subtracting 2- or 3-digit whole numbers, such as: a. compatible numbers; b. compensatory numbers; and c. informal use of commutative and associative properties of addition. (ORC Resources) 13.  Estimate the results of whole number addition and subtraction problems using front-end estimation, and judge the reasonableness of the answers. (ORC Resources)

PreK | K | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12
Grade 3
1.  Identify and generate equivalent forms of whole numbers; e.g., 36, 30 + 6, 9 x 4, 46 - 10, number of inches in a yard. (ORC Resources) 2.  Use place value concepts to represent whole numbers and decimals using numerals, words, expanded notation and physical models. For example: a. Recognize 100 means "10 tens" as well as a single entity (1 hundred) through physical models and trading games. b. Describe the multiplicative nature of the number system; e.g., the structure of 3205 as 3 x 1000 plus 2 x 100 plus 5 x 1. c. Model the size of 1000 in multiple ways; e.g., packaging 1000 objects into 10 boxes of 100, modeling a meter with centimeter and decimeter strips, or gathering 1000 pop-can tabs. d. Explain the concept of tenths and hundredths using physical models, such as metric pieces, base ten blocks, decimal squares or money. (ORC Resources) 3.  Use mathematical language and symbols to compare and order; e.g., less than, greater than, at most, at least, <, >, =, , . (ORC Resources) 4.  Count money and make change using coins and paper bills to ten dollars. (ORC Resources) 5.  Represent fractions and mixed numbers using words, numerals and physical models. (ORC Resources) 6.  Compare and order commonly used fractions and mixed numbers using number lines, models (such as fraction circles or bars), points of reference (such as more or less than 1/2), and equivalent forms found using physical or visual models. (ORC Resources) 7.  Recognize and use decimal and fraction concepts and notations as related ways of representing parts of a whole or a set; e.g., 3 of 10 marbles are red can also be described as 3/10 and 3 tenths are red. (ORC Resources) 8.  Model, represent and explain multiplication; e.g., repeated addition, skip counting, rectangular arrays and area model. For example: a. Use conventional mathematical symbols to write equations for word problems involving multiplication. b. Understand that, unlike addition and subtraction, the factors in multiplication and division may have different units; e.g., 3 boxes of 5 cookies each. (ORC Resources) 9.  Model, represent and explain division; e.g., sharing equally, repeated subtraction, rectangular arrays and area model. For example: a. Translate contextual situations involving division into conventional mathematical symbols. b. Explain how a remainder may impact an answer in a real-world situation; e.g., 14 cookies being shared by 4 children. (ORC Resources) 10.  Explain and use relationships between operations, such as: a. relate addition and subtraction as inverse operations; b. relate multiplication and division as inverse operations; c. relate addition to multiplication (repeated addition); d. relate subtraction to division (repeated subtraction). (ORC Resources) 11.  Model and use the commutative and associative properties for addition and multiplication. (ORC Resources) 12.  Add and subtract whole numbers with and without regrouping. (ORC Resources) 13.  Demonstrate fluency in multiplication facts through 10 and corresponding division facts. (ORC Resources) 14.  Multiply and divide 2- and 3-digit numbers by a single-digit number, without remainders for division. (ORC Resources) 15.  Evaluate the reasonableness of computations based upon operations and the numbers involved; e.g., considering relative size, place value and estimates (ORC Resources)

PreK | K | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12
Grade 4
1.  Identify and generate equivalent forms of fractions and decimals. For example: a. Connect physical, verbal and symbolic representations of fractions, decimals and whole numbers; e.g., 1/2, 5/10, "five tenths," 0.5, shaded rectangles with half, and five tenths. b. Understand and explain that ten tenths is the same as one whole in both fraction and decimal form. (ORC Resources) 2.  Use place value structure of the base-ten number system to read, write, represent and compare whole numbers through millions and decimals through thousandths. (ORC Resources) 3.  Round whole numbers to a given place value. (ORC Resources) 4.  Identify and represent factors and multiples of whole numbers through 100, and classify numbers as prime or composite. (ORC Resources) 5.  Use models and points of reference to compare commonly used fractions. (ORC Resources) 6.  Use associative and distributive properties to simplify and perform computations; e.g., use left to right multiplication and the distributive property to find an exact answer without paper and pencil, such as 5 x 47 = 5 x 40 + 5 x 7 = 200 + 35 = 235. (ORC Resources) 7.  Recognize that division may be used to solve different types of problem situations and interpret the meaning of remainders; e.g., situations involving measurement, money. (ORC Resources) 8.  Solve problems involving counting money and making change, using both coins and paper bills. (ORC Resources) 9.  Estimate the results of computations involving whole numbers, fractions and decimals, using a variety of strategies. (ORC Resources) 10.  Use physical models, visual representations, and paper and pencil to add and subtract decimals and commonly used fractions with like denominators. (ORC Resources) 11.  Develop and explain strategies for performing computations mentally. (ORC Resources) 12.  Analyze and solve multi-step problems involving addition, subtraction, multiplication and division using an organized approach, and verify and interpret results with respect to the original problem. (ORC Resources) 13.  Use a variety of methods and appropriate tools for computing with whole numbers; e.g., mental math, paper and pencil, and calculator. (ORC Resources) 14.  Demonstrate fluency in adding and subtracting whole numbers and in multiplying and dividing whole numbers by 1- and 2-digit numbers and multiples of ten. (ORC Resources)

PreK | K | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12
Grade 5
1.  Use models and visual representation to develop the concept of ratio as part-to-part and part-to-whole, and the concept of percent as part-to-whole. (ORC Resources) 2.  Use various forms of "one" to demonstrate the equivalence of fractions; e.g., 18/24 = 9/12 x 2/2 = 3/4 x 6/6. (ORC Resources) 3.  Identify and generate equivalent forms of fractions, decimals and percents. (ORC Resources) 4.  Round decimals to a given place value and round fractions (including mixed numbers) to the nearest half. (ORC Resources) 5.  Recognize and identify perfect squares and their roots. (ORC Resources) 6.  Represent and compare numbers less than 0 by extending the number line and using familiar applications; e.g., temperature, owing money. (ORC Resources) 7.  Use commutative, associative, distributive, identity and inverse properties to simplify and perform computations. (ORC Resources) 8.  Identify and use relationships between operations to solve problems. (ORC Resources) 9.  Use order of operations, including use of parentheses, to simplify numerical expressions. (ORC Resources) 10.  Justify why fractions need common denominators to be added or subtracted. (ORC Resources) 11.  Explain how place value is related to addition and subtraction of decimals; e.g., 0.2 + 0.14; the two tenths is added to the one tenth because they are both tenths. (ORC Resources) 12.  Use physical models, points of reference, and equivalent forms to add and subtract commonly used fractions with like and unlike denominators and decimals. (ORC Resources) 13.  Estimate the results of computations involving whole numbers, fractions and decimals, using a variety of strategies. (ORC Resources)

PreK | K | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12
Grade 6
1.  Decompose and recompose whole numbers using factors and exponents (e.g., 32 = 2 x 2 x 2 x 2 x 2 = 25), and explain why "squared" means "second power" and "cubed" means "third power." (ORC Resources) 2.  Find and use the prime factorization of composite numbers. For example: a. Use the prime factorization to recognize the greatest common factor (GCF). b. Use the prime factorization to recognize the least common multiple (LCM). c. Apply the prime factorization to solve problems and explain solutions. (ORC Resources) 3.  Explain why a number is referred to as being "rational," and recognize that the expression a/b can mean a parts of size 1/b each, a divided by b, or the ratio of a to b. (ORC Resources) 4.  Describe what it means to find a specific percent of a number, using real-life examples. (ORC Resources) 5.  Use models and pictures to relate concepts of ratio, proportion and percent, including percents less than 1 and greater than 100. (ORC Resources) 6.  Use the order of operations, including the use of exponents, decimals and rational numbers, to simplify numerical expressions. (ORC Resources) 7.  Use simple expressions involving integers to represent and solve problems; e.g., if a running back loses 15 yards on the first carry but gains 8 yards on the second carry, what is the net gain/loss? (ORC Resources) 8.  Represent multiplication and division situations involving fractions and decimals with models and visual representations; e.g., show with pattern blocks what it means to take 2-2/3 divided by 1/6. (ORC Resources) 9.  Give examples of how ratios are used to represent comparisons; e.g., part-to-part, part-to-whole, whole-to-part. (ORC Resources) 10.  Recognize that a quotient may be larger than the dividend when the divisor is a fraction; e.g., 6 divided by 1/2 = 12. (ORC Resources) 11.  Perform fraction and decimal computations and justify their solutions; e.g., using manipulatives, diagrams, mathematical reasoning. (ORC Resources) 12.  Develop and analyze algorithms for computing with fractions and decimals, and demonstrate fluency in their use. (ORC Resources) 13.  Estimate reasonable solutions to problem situations involving fractions and decimals; e.g., 7/8 + 12/13 = 2 and 4.23 x 5.8 25. (ORC Resources) 14.  Use proportional reasoning, ratios and percents to represent problem situations and determine the reasonableness of solutions. (ORC Resources) 15.  Determine the percent of a number and solve related problems; e.g., find the percent markdown if the original price was $140, and the sale price is $100. (ORC Resources)

PreK | K | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12
Grade 7
1.  Demonstrate an understanding of place value using powers of 10 and write large numbers in scientific notation. (ORC Resources) 2.  Explain the meaning of exponents that are negative or 0. (ORC Resources) 3.  Describe differences between rational and irrational numbers; e.g., use technology to show that some numbers (rational) can be expressed as terminating or repeating decimals and others (irrational) as non-terminating and non-repeating decimals. (ORC Resources) 4.  Use order of operations and properties to simplify numerical expressions involving integers, fractions and decimals. (ORC Resources) 5.  Explain the meaning and effect of adding, subtracting, multiplying and dividing integers; e.g., how adding two integers can result in a lesser value. (ORC Resources) 6.  Simplify numerical expressions involving integers and use integers to solve real-life problems. (ORC Resources) 7.  Solve problems using the appropriate form of a rational number (fraction, decimal or percent). (ORC Resources) 8.  Develop and analyze algorithms for computing with percents and integers, and demonstrate fluency in their use. (ORC Resources) 9.  Represent and solve problem situations that can be modeled by and solved using concepts of absolute value, exponents and square roots (for perfect squares). (ORC Resources)

PreK | K | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12
Grade 8
1.  Use scientific notation to express large numbers and small numbers between 0 and 1. (ORC Resources) 2.  Recognize that natural numbers, whole numbers, integers, rational numbers and irrational numbers are subsets of the real number system. (ORC Resources) 3.  Apply order of operations to simplify expressions and perform computations involving integer exponents and radicals. (ORC Resources) 4.  Explain and use the inverse and identity properties and use inverse relationships (addition/subtraction, multiplication/division, squaring/square roots) in problem solving situations. (ORC Resources) 5.  Determine when an estimate is sufficient and when an exact answer is needed in problem situations, and evaluate estimates in relation to actual answers; e.g., very close, less than, greater than. (ORC Resources) 6.  Estimate, compute and solve problems involving rational numbers, including ratio, proportion and percent, and judge the reasonableness of solutions. (ORC Resources) 7.  Find the square root of perfect squares, and approximate the square root of non-perfect squares as consecutive integers between which the root lies; e.g., is between 11 and 12. (ORC Resources) 8.  Add, subtract, multiply, divide and compare numbers written in scientific notation. (ORC Resources)

PreK | K | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12
Grade 9
1.  Identify and justify whether properties (closure, identity, inverse, commutative and associative) hold for a given set and operations; e.g., even integers and multiplication. (ORC Resources) 2.  Compare, order and determine equivalent forms for rational and irrational numbers. (ORC Resources) 3.  Explain the effects of operations such as multiplication or division, and of computing powers and roots on the magnitude of quantities. (ORC Resources) 4.  Demonstrate fluency in computations using real numbers. (ORC Resources) 5.  Estimate the solutions for problem situations involving square and cube roots. (ORC Resources)

PreK | K | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12
Grade 10
1.  Connect physical, verbal and symbolic representations of irrational numbers; e.g., construct as a hypotenuse or on a number line. (ORC Resources) 2.  Explain the meaning of the nth root. (ORC Resources) 3.  Use factorial notation and computations to represent and solve problem situations involving arrangements. (ORC Resources) 4.  Approximate the nth root of a given number greater than zero between consecutive integers when n is an integer; e.g., the 4th root of 50 is between 2 and 3. (ORC Resources)

PreK | K | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12
Grade 11
1.  Determine what properties hold for matrix addition and matrix multiplication; e.g., use examples to show addition is commutative and when multiplication is not commutative. (ORC Resources) 2.  Determine what properties hold for vector addition and multiplication, and for scalar multiplication. (ORC Resources) 3.  Represent complex numbers on the complex plane. (ORC Resources) 4.  Use matrices to represent given information in a problem situation. (ORC Resources) 5.  Model using the coordinate plane, vector addition and scalar multiplication. (ORC Resources) 6.  Compute sums, differences and products of matrices using paper and pencil calculations for simple cases, and technology for more complicated cases. (ORC Resources) 7.  Compute sums, differences, products and quotients of complex numbers. (ORC Resources) 8.  Use fractional and negative exponents as optional ways of representing and finding solutions for problem situations; e.g., 272/3 = (271/3)2 = 9. (ORC Resources) 9.  Use vector addition and scalar multiplication to solve problems. (ORC Resources)

PreK | K | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12
Grade 12
1.  Determine what properties (closure, identity, inverse, commutative and associative) hold for operations with complex numbers. (ORC Resources) 2.  Apply combinations as a method to create coefficients for the Binomial Theorem, and make connections to everyday and workplace problem situations. (ORC Resources)

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