Math+Grade+Level+Indicators

Ohio Content Standards

   Number, Number Sense and Operations A. Use place value structure of the base-ten number system to read, write, represent and compare whole numbers and decimals. (03-04) 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. (03)

3. Use mathematical language and symbols to compare and order; e.g., less than, greater than, at most, at least, <, >, =, greater than/equal to, less than/equal to. (03)

 B. Recognize and generate equivalent representations for whole numbers, fractions and decimals. (03-04) 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. (03)

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. (03)

 C. Represent commonly used fractions and mixed numbers using words and physical models. (03-04) 5. Represent fractions and mixed numbers using words, numerals and physical models. (03)

 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. (03-04) 3. Use mathematical language and symbols to compare and order; e.g., less than, greater than, at most, at least, <, >, =, greater than/equal to, less than/equal to. (03)

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. (03)

 E. Recognize and classify numbers as prime or composite and list factors. (03-04)

F. Count money and make change using both coins and paper bills. (03-04) 4. Count money and make change using coins and paper bills to ten dollars. (03)

 G. Model and use commutative and associative properties for addition and multiplication. (03-04) 11. Model and use the commutative and associative properties for addition and multiplication. (03)

 H. Use relationships between operations, such as subtraction as the inverse of addition and division as the inverse of multiplication. (03-04) 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). (03)

 I. Demonstrate fluency in multiplication facts with factors through 10 and corresponding divisions. (03-04) 13. Demonstrate fluency in multiplication facts through 10 and corresponding division facts. (03)

 J. Estimate the results of whole number computations using a variety of strategies, and judge the reasonableness. (03-04) 15. Evaluate the reasonableness of computations based upon operations and the numbers involved; e.g., considering relative size, place value and estimates. (03)

 K. Analyze and solve multi-step problems involving addition, subtraction, multiplication and division of whole numbers. (03-04) 12. Add and subtract whole numbers with and without regrouping. (03)

14. Multiply and divide 2- and 3-digit numbers by a single-digit number, without remainders for division. (03)

 L. Use a variety of methods and appropriate tools (mental math, paper and pencil, calculators) for computing with whole numbers. (03-04) 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. (03)

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. (03)

 M. Add and subtract commonly used fractions with like denominators and decimals, using models and paper and pencil. (03-04)  Measurement <span style="color: rgb(237, 185, 64)"> A. Select appropriate units for perimeter, area, weight, volume (capacity), time and temperature, using: - objects of uniform size; - U.S. customary units; e.g., mile, square inch, cubic inch, second degree Fahrenheit, and other units as appropriate; - metric units; e.g., millimeter, kilometer, square centimeter, kilogram, cubic centimeter, degree Celsius, and other units as appropriate. (03-04) 1. Identify and select appropriate units for measuring: a. length - miles, kilometers and other units of measure as appropriate. b. volume (capacity) - gallons; c. weight - ounces, pounds, grams, or kilograms; d. temperature - degrees (Fahrenheit or Celsius). (03)

4. Read thermometers in both Fahrenheit and Celsius scales. (03)

<span style="color: rgb(240, 182, 66)"> B. Know that the number of units is inversely related to the size of the unit for any item being measured. (03-04)

C. Develop common referents for units of measure for length, weight, volume (capacity) and time to make comparisons and estimates. (03-04) 2. Establish personal or common referents to include additional units; e.g., a gallon container of milk; a postage stamp is about a square inch. (03)

5. Estimate and measure length, weight and volume (capacity), using metric and U.S. customary units, accurate to the nearest 1/2 or 1/4 unit as appropriate. (03)

<span style="color: rgb(243, 199, 48)"> D. Identify appropriate tools and apply counting techniques for measuring side lengths, perimeter and area of squares, rectangles, and simple irregular two-dimensional shapes, volume of rectangular prisms, and time and temperature. (03-04) 4. Read thermometers in both Fahrenheit and Celsius scales. (03)

6. Use appropriate measurement tools and techniques to construct a figure or approximate an amount of specified length, weight or volume (capacity); e.g., construct a rectangle with length 2 and 1/2 inches and width 3 inches, fill a measuring cup to the 3/4 cup mark. (03)

7. Make estimates for perimeter, area and volume using links, tiles, cubes and other models. (03)

<span style="color: rgb(239, 186, 42)"> E. Tell time to the nearest minute. (03-04) 3. Tell time to the nearest minute and find elapsed time using a calendar or a clock. (03) <span style="font-size: 75%; color: rgb(238, 89, 237)"> Geometry and Spatial Sense <span style="color: rgb(238, 240, 61)"> A. Provide rationale for groupings and comparisons of two-dimensional figures and three-dimensional objects. (03-04) 1. Analyze and describe properties of two-dimensional shapes and three-dimensional objects using terms such as vertex, edge, angle, side and face. (03)

<span style="color: rgb(234, 238, 73)"> B. Describe and identify points, lines and planes in the environment. (03-04)

C. Describe and identify intersecting, parallel and perpendicular lines or segments in the environment. (03-04)

D. Identify and draw right, obtuse, acute and straight angles. (03-04) 2. Identify and describe the relative size of angles with respect to right angles as follows: a. Use physical models, like straws, to make different sized angles by opening and closing the sides, not by changing the side lengths. b. Identify, classify and draw right, acute, obtuse and straight angles. (03)

<span style="color: rgb(242, 237, 69)"> E. Use attributes to describe, classify and sketch plane figures and build solid objects. (03-04) 1. Analyze and describe properties of two-dimensional shapes and three-dimensional objects using terms such as vertex, edge, angle, side and face. (03)

5. Build a three-dimensional model of an object composed of cubes; e.g., construct a model based on an illustration or actual object. (03)

<span style="color: rgb(234, 236, 65)"> F. Develop definitions of classes of shapes. (03-04)

G. Find and name locations in coordinate systems. (03-04) 3. Find and name locations on a labeled grid or coordinate system; e.g., a map or graph. (03)

<span style="color: rgb(244, 241, 62)"> H. Identify and describe line and rotational symmetry in two-dimensional shapes and designs. (03-04) 4. Draw lines of symmetry to verify symmetrical two-dimensional shapes. (03)

<span style="color: rgb(241, 240, 55)"> I. Describe, identify and model reflections, rotations and translations, using physical materials. (03-04)

J. Describe a motion or series of transformations that show two shapes are congruent. (03-04) <span style="font-size: 75%; color: rgb(234, 108, 114)"> <span style="color: rgb(81, 80, 211)">Patterns, Functions and Algebra  <span style="color: rgb(74, 87, 186)"><span style="color: rgb(62, 35, 190)"><span style="color: rgb(71, 55, 230)"><span style="color: rgb(34, 78, 226)"><span style="color: rgb(226, 54, 106)">A. Analyze and extend patterns, and describe the rule in words. (03-04)   1. Extend multiplicative and growing patterns, and describe the pattern or rule in words. (03) 2. Analyze and replicate arithmetic sequences with and without a calculator. (03) <span style="color: rgb(222, 43, 43)">B. Use patterns to make predictions, identify relationships, and solve problems. (03-04) 3. Use patterns to make predictions, identify relationships, and solve problems. (03) <span style="color: rgb(229, 42, 42)">C. Write and solve open sentences and explain strategies. (03-04) 5. Write, solve and explain simple mathematical statements, such as 7 + triangle > 8 or triangle + 8 = 10. (03) 6. Express mathematical relationships as equations and inequalities. (03) <span style="color: rgb(230, 45, 45)">D. Represent an unknown quantity as a variable using a symbol, including letters. (03-04) E. Use variables to create and solve equations representing problem situations. (03-04) 4. Model problem situations using objects, pictures, tables, numbers, letters and other symbols. (03) <span style="color: rgb(234, 52, 52)">F. Construct and use a table of values to solve problems associated with mathematical relationships. (03-04) 7. Create tables to record, organize and analyze data to discover patterns and rules. (03) <span style="color: rgb(214, 76, 76)">G. Describe how a change in one variable affects the value of a related variable. (03-04) 8. Identify and describe quantitative changes, especially those involving addition and subtraction; e.g., the height of water in a glass becoming 1 centimeter lower each week due to evaporation. (03)   <span style="font-size: 150%; color: rgb(77, 245, 229)">        Data Analysis and Probability <span style="font-size: 75%; color: rgb(155, 248, 246)"><span style="color: rgb(159, 74, 176)">A. Gather and organize data from surveys and classroom experiments, including data collected over a period of time. (03-04) 1. Collect and organize data from an experiment, such as recording and classifying observations or measurements, in response to a question posed. (03) <span style="color: rgb(161, 73, 171)">B. Read and interpret tables, charts, graphs (bar, picture, line, line plot), and timelines as sources of information, identify main idea, draw conclusions, and make predictions. (03-04) 4. Support a conclusion or prediction orally and in writing, using information in a table or graph. (03) 5. Match a set of data with a graphical representation of the data. (03) 7. Analyze and interpret information represented on a timeline. (03) <span style="color: rgb(164, 66, 184)">C. Construct charts, tables and graphs to represent data, including picture graphs, bar graphs, line graphs, line plots and Venn diagrams. (03-04) 6. Translate information freely among charts, tables, line plots, picture graphs and bar graphs; e.g., create a bar graph from the information in a chart. (03) <span style="color: rgb(166, 68, 197)">D. Read, interpret and construct graphs in which icons represent more than a single unit or intervals greater than one; e.g., each (bicycle picture) = 10 bicycles or the intervals on an axis are multiples of 10. (03-04) 2. Draw and interpret picture graphs in which a symbol or picture represents more than one object. (03) 3. Read, interpret and construct bar graphs with intervals greater than one. (03) <span style="color: rgb(153, 79, 171)">E. Describe data using mode, median and range. (03-04) 8. Identify the mode of a data set and describe the information it gives about a data set. (03) <span style="color: rgb(160, 69, 181)">F. Conduct a simple probability experiment and draw conclusions about the likelihood of possible outcomes. (03-04) 9. Conduct a simple experiment or simulation of a simple event, record the results in a chart, table or graph, and use the results to draw conclusions about the likelihood of possible outcomes. (03) <span style="color: rgb(147, 67, 173)">G. Identify and represent possible outcomes, such as arrangements of a set of up to four members and possible combinations from several sets, each containing 2 or 3 members. (03-04) 10. Use physical models, pictures, diagrams and lists to solve problems involving possible arrangements or combinations of two to four objects. (03) <span style="color: rgb(168, 101, 179)">H. Use the set of possible outcomes to describe and predict events. (03-04) <span style="color: rgb(168, 101, 179)">   <span style="font-size: 75%; color: rgb(241, 85, 220)">    Mathematical Processes  A. Apply and justify the use of a variety of problem-solving strategies; e.g., make an organized list, guess and check. (03-04) B. Use an organized approach and appropriate strategies to solve multi-step problems. (03-04)  C. Interpret results in the context of the problem being solved; e.g., the solution must be a whole number of buses when determining the number of buses necessary to transport students. (03-04) D. Use mathematical strategies to solve problems that relate to other curriculum areas and the real world; e.g., use a timeline to sequence events; use symmetry in artwork. (03-04)  E. Link concepts to procedures and to symbolic notation; e.g., model 3 x 4 with a geometric array, represent one-third by dividing an object into three equal parts. (03-04) F. Recognize relationships among different topics within mathematics; e.g., the length of an object can be represented by a number. (03-04)  G. Use reasoning skills to determine and explain the reasonableness of a solution with respect to the problem situation. (03-04) H. Recognize basic valid and invalid arguments, and use examples and counter examples, models, number relationships, and logic to support or refute. (03-04)  I. Represent problem situations in a variety of forms (physical model, diagram, in words or symbols), and recognize when some ways of representing a problem may be more helpful than others. (03-04) J. Read, interpret, discuss and write about mathematical ideas and concepts using both everyday and mathematical language. (03-04)  K. Use mathematical language to explain and justify mathematical ideas, strategies and solutions. (03-04)