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Ohio Math Standards - 8th Grade
MathScore aligns to the Ohio Math Standards for 8th Grade. The standards appear below along with the MathScore topics that match. If you click on a topic name, you will see sample problems at varying degrees of difficulty that MathScore generated. When students use our program, the difficulty of the problems will automatically adapt based on individual performance, resulting in not only true differentiated instruction, but a challenging game-like experience.
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View the Ohio Math Standards at other levels.
Number and Number Systems
* Use scientific notation to express large numbers and small numbers between 0 and 1. (Scientific Notation )* Recognize that natural numbers, whole numbers, integers, rational numbers and irrational numbers are subsets of the real number system.
Meaning of Operations
* Explain and use the inverse and identity properties and use inverse relationships (addition/subtraction, multiplication/division, squaring/square roots) in problem solving situations. (Single Variable Equations , Single Variable Equations 2 , Single Variable Equations 3 , Roots Of Exponential Expressions , Estimating Square Roots )* Apply order of operations to simplify expressions and perform computations involving integer exponents and radicals. (Simplifying Algebraic Expressions 2 , Simplifying Algebraic Expressions , Simplifying Radical Expressions , Adding and Subtracting Radical Expressions , Multiplying and Dividing Radical Expressions )
Computation and Estimation
* Use factorial notation and computations to represent and solve problem situations involving arrangements.* 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. (Estimated Multiply Divide Word Problems )
* Estimate, compute and solve problems involving rational numbers, including ratio, proportion and percent, and judge the reasonableness of solutions. (Percentage Change , Purchases At Stores , Restaurant Bills , Commissions , Proportions 2 )
* Add, subtract, multiply, divide and compare numbers written in scientific notation. (Scientific Notation 2 )
Use Measurement Techniques and Tools
* Solve and determine the reasonableness of the results for problems involving rates and derived measurements, such as velocity and density, using formulas, models and graphs. (Distance, Rate, and Time , Train Problems )* Use appropriate levels of precision when calculating with measurements.
* Derive formulas for surface area and volume and justify them using geometric models and common materials. For example, find:
- the surface area of a cylinder as a function of its height and radius; (Cylinders )
- that the volume of a pyramid (or cone) is one-third of the volume of a prism (or cylinder) with the same base area and height. (Triangular Prisms , Cylinders )
* Determine surface area for pyramids by analyzing their parts.
* Demonstrate understanding of the concepts of perimeter, circumference and area by using established formulas for triangles, quadrilaterals, and circles to determine the surface area and volume of prisms, pyramids, cylinders, spheres and cones. (Note: Only volume should be calculated for spheres and cones.) (Triangle Area , Parallelogram Area , Perimeter , Rectangular Solids , Compare Rectangle Area and Perimeter , Circle Area , Circle Circumference , Triangular Prisms , Cylinders )
* Apply proportional reasoning to solve problems involving indirect measurements or rates. (Distance, Rate, and Time )
* Find the sum of the interior and exterior angles of regular convex polygons with and without measuring the angles with a protractor. (Polygon Angles )
* Use conventional formulas to find the surface area and volume of prisms, pyramids and cylinders and the volume of spheres and cones to a specified level of precision. (Triangular Prisms , Cylinders )
Measurement Units
* Compare and order the relative size of common U.S. customary units and metric units; e.g., mile and kilometer, gallon and liter, pound and kilogram.* Use proportional relationships and formulas to convert units from one measurement system to another; e.g., degrees Fahrenheit to degrees Celsius. (Distance Conversion , Time Conversion , Volume Conversion , Weight Conversion , Temperature Conversion )
Characteristics and Properties
* Make and test conjectures about characteristics and properties (e.g., sides, angles, symmetry) of two-dimensional figures and three-dimensional objects.* Use proportions in several forms to solve problems involving similar figures (part-to-part, part-to-whole, corresponding sides between figures). (Proportions 2 )
* Recognize the angles formed and the relationship between the angles when two lines intersect and when parallel lines are cut by a transversal. (Identifying Angles , Angle Measurements 2 )
Visualization and Geometric Models
* Solve problems involving chords, radii, and arcs within the same circle.* Draw nets for a variety of prisms, pyramids, cylinders and cones.
Spatial Relationships
* Represent and analyze shapes using coordinate geometry; e.g., given three vertices and the type of quadrilateral, find the coordinates of the fourth vertex.Transformations and Symmetry
* Draw the results of translations, reflections, rotations and dilations of objects in the coordinate plane, and determine properties that remain fixed; e.g., lengths of sides remain the same under translations. (Translations and Reflections )Use Patterns, Relations and Functions
* Identify functions as linear or nonlinear based on information given in a table, graph or equation.* Relate the various representations of a relationship; i.e., relate a table to graph, description and symbolic form.
Use Algebraic Representations
* Use physical models to add and subtract monomials and polynomials, and to multiply a polynomial by a monomial. (Simplifying Algebraic Expressions , Simplifying Algebraic Expressions 2 )* Use symbolic algebra (equations and inequalities), graphs and tables to represent situations and solve problems. (Number Line Inequalities , Mixture Word Problems )
* Write, simplify and evaluate algebraic expressions (including formulas) to generalize situations and solve problems. (Algebraic Word Problems , Mixture Word Problems , Work Word Problems , Integer Word Problems , Variable Substitution 2 )
* Describe the relationship between the graph of a line and its equation, including being able to explain the meaning of slope as a constant rate of change and y-intercept in real-world problems. (Determining Slope , Graphs to Linear Equations , Graphs to Linear Equations 2 , Graphs to Linear Inequalities )
* Solve linear equations and inequalities graphically, symbolically and using technology. (Linear Equations , Single Variable Equations , Single Variable Equations 2 , Single Variable Equations 3 , Single Variable Inequalities )
* Solve 2 by 2 systems of linear equations graphically and by simple substitution. (System of Equations Substitution )
* Interpret the meaning of the solution of a 2 by 2 system of equations; i.e., point, line, no solution.
* Compute and interpret slope, midpoint and distance given a set of ordered pairs.
Analyze Change
* Differentiate and explain types of changes in mathematical relationships, such as linear vs. nonlinear, continuous vs. noncontinuous, direct variation vs. inverse variation.* Use graphing calculators or computers to analyze change; e.g., interest compounded over time as a nonlinear growth pattern.
Data Collection
* Use, create and interpret scatterplots and other types of graphs as appropriate.* Represent and analyze bivariate data using appropriate graphical displays (scatterplots, parallel box-and-whisker plots, histograms with more than one set of data, tables, charts, spreadsheets) with and without technology.
* Display bivariate data where at least one variable is categorical.
* Identify outliers on a data display; e.g., use the interquartile range to identify outliers on a box-and-whisker plot.
* Evaluate different graphical representations of the same data to determine which is the most appropriate representation for an identified purpose; e.g., line graph for change over time, circle graph for part-to-whole comparison, scatterplot for relationship between two variants.
* Differentiate between discrete and continuous data and appropriate ways to represent each.
Statistical Methods
* Interpret the relationship between two variables using multiple graphical displays and statistical measures; e.g., scatterplots, parallel box-and-whisker plots, and measures of center and spread.* Explain the mean's sensitivity to extremes and its use in comparison with the median and mode.
* Compare two sets of data using measures of center (mean, mode, median) and measures of spread (range, quartiles, interquartile range, percentiles).
* Describe how the relative size of a sample compared to the target population affects the validity of predictions.
* Make conjectures about possible relationship in a scatterplot and approximate line of best fit.
* Construct convincing arguments based on analysis of data and interpretation of graphs.
* Identify different ways of selecting samples, such as survey response, random sample, representative sample and convenience sample.
Probability
* Calculate the number of possible outcomes for a situation, recognizing and accounting for when items may occur more than once or when order is important.* Describe, create and analyze a sample space and use it to calculate probability.
* Demonstrate an understanding that the probability of either of two disjoint events occurring can be found by adding the probabilities for each and that the probability of one independent event following another can be found by multiplying the probabilities. (Probability 2 , Probability )
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