Ohio's Academic Content Standards in Mathematics

By the end of grade 2

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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. Indicators for 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)

Measurement Standard
Students estimate and measure to a required degree of accuracy and precision by selecting and using appropriate units, tools, and technologies. Indicators for grade 2 1. Identify and select appropriate units of measure for: a. length - centimeters, meters, inches, feet, or yards; b. volume (capacity) - liters, cups, pints, or quarts; c. weight - grams, ounces, or pounds; and d. time - hours, half-hours, quarter-hours, or minutes and time designations a.m. or p.m. (ORC Resources) 2. Establish personal or common referents for units of measure to make estimates and comparisons; e.g., the width of a finger is a centimeter, a large bottle of soda pop is 2 liters, a small paper clip weighs about one gram. (ORC Resources) 3. Describe and compare the relationships among units of measure, such as centimeters and meters; inches, feet and yards; cups, pints and quarts; ounces and pounds; and hours, half-hours, and quarter-hours; e.g., how many inches in a foot? (ORC Resources) 4. Tell time to the nearest minute interval on digital and to the nearest 5 minute interval on analog (dial) timepieces. (ORC Resources) 5. Estimate and measure the length and weight of common objects, using metric and U.S. customary units, accurate to the nearest unit. (ORC Resources) 6. Select and use appropriate measurement tools; e.g., a ruler to draw a segment 3 inches long, a measuring cup to place 2 cups of rice in a bowl, a scale to weigh 50 grams of candy. (ORC Resources) 7. Make and test predictions about measurements, using different units to measure the same length or volume. (ORC Resources)

Geometry and Spatial Sense Standard
Students identify, classify, compare and analyze characteristics, properties and relationships of one-, two- and three-dimensional geometric figures and objects. Students use spatial reasoning, properties of geometric objects, and transformations to analyze mathematical situations and solve problems. Indicators for grade 2 1. Identify, describe, compare, and sort three-dimensional objects (i.e., cubes, spheres, prisms, cones, cylinders and pyramids) according to the shape of the faces or the numbers of faces, edges, or vertices. (ORC Resources) 2. Predict what new shapes will be formed by combining or cutting apart existing shapes. (ORC Resources) 3. Recognize two-dimensional shapes and three-dimensional objects from different positions. (ORC Resources) 4. Identify and determine whether two-dimensional shapes are congruent (same shape and size) or similar (same shape different size) by copying or using superposition (lay one thing on top of another). (ORC Resources) 5. Create and identify two-dimensional figures with line symmetry; e.g., what letter shapes, logos, polygons are symmetrical? (ORC Resources)

Patterns, Functions and Algebra Standard
Students use patterns, relations and functions to model, represent and analyze problem situations that involve variable quantities. Students analyze, model and solve problems using various representations such as tables, graphs and equations. Indicators for grade 2 1. Extend simple number patterns (both repeating and growing patterns), and create similar patterns using different objects, such as using physical materials or shapes to represent numerical patterns. (ORC Resources) 2. Use patterns to make generalizations and predictions; e.g., determine a missing element in a pattern. (ORC Resources) 3. Create new patterns with consistent rules or plans, and describe the rule or general plan of existing patterns. (ORC Resources) 4. Use objects, pictures, numbers and other symbols to represent a problem situation. (ORC Resources) 5. Understand equivalence and extend the concept to situations involving symbols; e.g., 4 + 5 = 9 and 9 = 4 + 5 and 4 + 5 = 3 + 6 = + ... (ORC Resources) 6. Use symbols to represent unknown quantities and identify values for symbols in an expression or equation using addition and subtraction; e.g., + = 10, - 2 = 4. (ORC Resources) 7. Describe qualitative and quantitative changes, especially those involving addition and subtraction; e.g., a student growing taller versus a student growing two inches in one year. (ORC Resources)

Data Analysis and Probability Standard
Students pose questions and collect, organize, represent, interpret and analyze data to answer those questions. Students develop and evaluate inferences, predictions and arguments that are based on data. Indicators for grade 2 1. Pose questions, use observations, interviews and surveys to collect data, and organize data in charts, picture graphs and bar graphs. (ORC Resources) 2. Read, interpret and make comparisons and predictions from data represented in charts, line plots, picture graphs and bar graphs. (ORC Resources) 3. Read and construct simple timelines to sequence events. (ORC Resources) 4. Write a few sentences to describe and compare categories of data represented in a chart or graph, and make statements about the data as a whole. (ORC Resources) 5. Identify untrue or inappropriate statements about a given set of data. (ORC Resources) 6. Recognize that data may vary from one population to another; e.g., favorite TV shows of students and of parents. (ORC Resources) 7. List some of the possible outcomes of a simple experiment, and predict whether given outcomes are more, less or equally likely to occur. (ORC Resources) 8. Use physical models and pictures to represent possible arrangements of 2 or 3 objects. (ORC Resources)