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Ohio's Academic Content Standards in Mathematics

By the end of grade 7

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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 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)
  
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 7
1.Select appropriate units for measuring derived measurements; e.g., miles per hour, revolutions per minute. (ORC Resources)
2.Convert units of area and volume within the same measurement system using proportional reasoning and a reference table when appropriate; e.g., square feet to square yards, cubic meters to cubic centimeters. (ORC Resources)
3.Estimate a measurement to a greater degree of precision than the tool provides. (ORC Resources)
4.Solve problems involving proportional relationships and scale factors; e.g., scale models that require unit conversions within the same measurement system. (ORC Resources)
5.Analyze problem situations involving measurement concepts, select appropriate strategies, and use an organized approach to solve narrative and increasingly complex problems. (ORC Resources)
6.Use strategies to develop formulas for finding area of trapezoids and volume of cylinders and prisms. (ORC Resources)
7.Develop strategies to find the area of composite shapes using the areas of triangles, parallelograms, circles and sectors. (ORC Resources)
8.Understand the difference between surface area and volume and demonstrate that two objects may have the same surface area, but different volumes or may have the same volume, but different surface areas. (ORC Resources)
9.Describe what happens to the surface area and volume of a three-dimensional object when the measurements of the object 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 7
1.Use proportional reasoning to describe and express relationships between parts and attributes of similar and congruent figures. (ORC Resources)
2.Determine sufficient (not necessarily minimal) properties that define a specific two-dimensional figure or three-dimensional object. For example: a. Determine when one set of figures is a subset of another; e.g., all squares are rectangles. b. Develop a set of properties that eliminates all but the desired figure; e.g., only squares are quadrilaterals with all sides congruent and all angles congruent. (ORC Resources)
3.Use and demonstrate understanding of the properties of triangles. For example: a. Use Pythagorean Theorem to solve problems involving right triangles. b. Use triangle angle sum relationships to solve problems. (ORC Resources)
4.Determine necessary conditions for congruence of triangles. (ORC Resources)
5.Apply properties of congruent or similar triangles to solve problems involving missing lengths and angle measures. (ORC Resources)
6.Determine and use scale factors for similar figures to solve problems using proportional reasoning. (ORC Resources)
7.Identify the line and rotation symmetries of two-dimensional figures to solve problems. (ORC Resources)
8.Perform translations, reflections, rotations and dilations of two-dimensional figures using a variety of methods (paper folding, tracing, graph paper). (ORC Resources)
9.Draw representations of three-dimensional geometric objects from different views. (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 7
1.Represent and analyze patterns, rules and functions with words, tables, graphs and simple variable expressions. (ORC Resources)
2.Generalize patterns by describing in words how to find the next term. (ORC Resources)
3.Recognize and explain when numerical patterns are linear or nonlinear progressions; e.g., 1,3,5,7... is linear and 1,3,4,8,16... is nonlinear. (ORC Resources)
4.Create visual representations of equation-solving processes that model the use of inverse operations. (ORC Resources)
5.Represent linear equations by plotting points in the coordinate plane. (ORC Resources)
6.Represent inequalities on a number line or a coordinate plane. (ORC Resources)
7.Justify that two forms of an algebraic expression are equivalent, and recognize when an expression is simplified; e.g., 4m = m + m + m + m or a * 5 + 4 = 5a + 4. (ORC Resources)
8.Use formulas in problem-solving situations. (ORC Resources)
9.Recognize a variety of uses for variables; e.g., placeholder for an unknown quantity in an equation, generalization for a pattern, formula. (ORC Resources)
10.Analyze linear and simple nonlinear relationships to explain how a change in one variable results in the change of another. (ORC Resources)
11.Use graphing calculators or computers to analyze change; e.g., distance-time relationships. (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 7
1.Read, create and interpret box-and-whisker plots, stem-and-leaf plots, and other types of graphs, when appropriate. (ORC Resources)
2.Analyze how decisions about graphing affect the graphical representation; e.g., scale, size of classes in a histogram, number of categories in a circle graph. (ORC Resources)
3.Analyze a set of data by using and comparing combinations of measures of center (mean, mode, median) and measures of spread (range, quartile, interquartile range), and describe how the inclusion or exclusion of outliers affects those measures. (ORC Resources)
4.Construct opposing arguments based on analysis of the same data, using different graphical representations. (ORC Resources)
5.Compare data from two or more samples to determine how sample selection can influence results. (ORC Resources)
6.Identify misuses of statistical data in articles, advertisements, and other media. (ORC Resources)
7.Compute probabilities of compound events; e.g., multiple coin tosses or multiple rolls of number cubes, using such methods as organized lists, tree diagrams and area models. (ORC Resources)
8.Make predictions based on theoretical probabilities, design and conduct an experiment to test the predictions, compare actual results to predicted results, and explain differences. (ORC Resources)