Ohio's Academic Content Standards in Mathematics

By the end of grade 6

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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 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)

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 6 1. Understand and describe the difference between surface area and volume. (ORC Resources) 2. Use strategies to develop formulas for finding circumference and area of circles, and to determine the area of sectors; e.g., 1/2 circle, 2/3 circle, 1/3 circle, 1/4 circle. (ORC Resources) 3. Estimate perimeter or circumference and area for circles, triangles and quadrilaterals, and surface area and volume for prisms and cylinders by: a. estimating lengths using string or links, areas using tiles or grid, and volumes using cubes; and b. measuring attributes (diameter, side lengths, or heights) and using established formulas for circles, triangles, rectangles, parallelograms and rectangular prisms. (ORC Resources) 4. Determine which measure (perimeter, area, surface area, volume) matches the context for a problem situation; e.g., perimeter is the context for fencing a garden, surface area is the context for painting a room. (ORC Resources) 5. Understand the difference between perimeter and area, and demonstrate that two shapes may have the same perimeter, but different areas or may have the same area, but different perimeters. (ORC Resources) 6. Describe what happens to the perimeter and area of a two-dimensional shape when the measurements of the shape are changed; e.g. length of sides are doubled. (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 6 1. Classify and describe two-dimensional and three-dimensional geometric figures and objects by using their properties; e.g., interior angle measures, perpendicular/parallel sides, congruent angles/sides. (ORC Resources) 2. Use standard language to define geometric vocabulary: vertex, face, altitude, diagonal, isosceles, equilateral, acute, obtuse, etc. (ORC Resources) 3. Use multiple classification criteria to classify triangles; e.g., right scalene triangle. (ORC Resources) 4. Identify and define relationships between planes; i.e., parallel, perpendicular and intersecting. (ORC Resources) 5. Predict and describe sizes, positions and orientations of two-dimensional shapes after transformations such as reflections, rotations, translations and dilations. (ORC Resources) 6. Draw similar figures that model proportional relationships; e.g., model similar figures with a 1 to 2 relationship by sketching two of the same figure, one with corresponding sides twice the length of the other. (ORC Resources) 7. Build three-dimensional objects built with cubes and sketch the two-dimensional representations of each side; i.e., projection sets. (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 6 1. Represent and analyze patterns, rules and functions, using physical materials, tables and graphs. (ORC Resources) 2. Use words and symbols to describe numerical and geometric patterns, rules and functions. (ORC Resources) 3. Recognize and generate equivalent forms of algebraic expressions, and explain how the commutative, associative and distributive properties can be used to generate equivalent forms; e.g., perimeter as 2(1 + w) or 21 + 2w. (ORC Resources) 4. Solve simple linear equations and inequalities using physical models, paper and pencil, tables and graphs. (ORC Resources) 5. Produce and interpret graphs that represent the relationship between two variables. (ORC Resources) 6. Evaluate simple expressions by replacing variables with given values, and use formulas in problem-solving situations. (ORC Resources) 7. Identify and describe situations with constant or varying rates of change, and compare them. (ORC Resources) 8. Use technology to analyze change; e.g., use computer applications or graphing calculators to display and interpret rate of change. (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 6 1. Read, construct and interpret line graphs, circle graphs and histograms. (ORC Resources) 2. Select, create and use graphical representations that are appropriate for the type of data collected. (ORC Resources) 3. Compare representations of the same data in different types of graphs, such as a bar graph and circle graph. (ORC Resources) 4. Understand the different information provided by measures of center (mean, mode and median) and measures of spread (range). (ORC Resources) 5. Describe the frequency distribution of a set of data, as shown in a histogram or frequency table, by general appearance or shape; e.g., number of modes, middle of data and level of symmetry, outliers. (ORC Resources) 6. Make logical inferences from statistical data. (ORC Resources) 7. Design an experiment to test a theoretical probability and explain how the results may vary. (ORC Resources)

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