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OH.DAP. Data Analysis and Probability: 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.
DAP.1. Grade Level Indicator: Data Collection: Use, create and interpret scatterplots and other types of graphs as appropriate.
DAP.11. Grade Level Indicator: 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.
DAP.2. Grade Level Indicator: Data Collection: 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.
DAP.6. Grade Level Indicator: Statistical Methods: Make conjectures about possible relationship in a scatterplot and approximate line of best fit.
DAP.7. Grade Level Indicator: Statistical Methods: Identify different ways of selecting samples, such as survey response, random sample, representative sample and convenience sample.
DAP.A. Create, interpret and use graphical displays and statistical measures to describe data; e.g., box-and-whisker plots, histograms, scatterplots, measures of center and variability.
DAP.B. Evaluate different graphical representations of the same data to determine which is the most appropriate representation for an identified purpose.
DAP.D. Find, use and interpret measures of center and spread, such as mean and quartiles, and use those measures to compare and draw conclusions about sets of data.
DAP.G. Describe sampling methods and analyze the effects of method chosen on how well the resulting sample represents the population.
DAP.H. Use counting techniques, such as permutations and combinations, to determine the total number of options and possible outcomes.
DAP.I. Design an experiment to test a theoretical probability, and record and explain results.
DAP.J. Compute probabilities of compound events, independent events, and simple dependent events.
DAP.K. Make predictions based on theoretical probabilities and experimental results.
OH.GSS. Geometry and Spatial Sense: 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.
GSS.3. Grade Level Indicator: Characteristics and Properties: Use proportions in several forms to solve problems involving similar figures (part-to-part, part-to-whole, corresponding sides between figures).
GSS.4. Grade Level Indicator: 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.
GSS.5. Grade Level Indicator: Transformation 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.
GSS.A. Formally define geometric figures.
GSS.B. Describe and apply the properties of similar and congruent figures; and justify conjectures involving similarity and congruence.
GSS.C. Recognize and apply angle relationships in situations involving intersecting lines, perpendicular lines and parallel lines.
GSS.D. Use coordinate geometry to represent and examine the properties of geometric figures.
GSS.G. Prove or disprove conjectures and solve problems involving two- and three-dimensional objects represented within a coordinate system.
GSS.I. Use right triangle trigonometric relationships to determine lengths and angle measures.
OH.M. Measurement: Students estimate and measure to a required degree of accuracy and precision by selecting and using appropriate units, tools and technologies.
M.10. Grade Level Indicator: Use Measurement Techniques and Tools: 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.
M.3. Grade Level Indicator: Use Measurement Techniques and Tools: Use appropriate levels of precision when calculating with measurements.
M.5. Grade Level Indicator: Use Measurement Techniques and Tools: Determine surface area for pyramids by analyzing their parts.
M.6. Grade Level Indicator: 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.
M.7. Grade Level Indicator: Use Measurement Techniques and Tools: Apply proportional reasoning to solve problems involving indirect measurements or rates.
M.9. Grade Level Indicator: Use Measurement Techniques and Tools: Demonstrate understanding of the concepts of perimeter, circumference and area by using established formula 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.)
M.B. Use formulas to find surface area and volume for specified three-dimensional objects accurate to a specified level of precision.
M.C. Apply indirect measurement techniques, tools and formulas, as appropriate, to find perimeter, circumference and area of circles, triangles, quadrilaterals and composite shapes, and to find volume of prisms, cylinders, and pyramids.
M.D. Use proportional reasoning and apply indirect measurement techniques, including right triangle trigonometry and properties of similar triangles, to solve problems involving measurements and rates.
M.E. Estimate and compute various attributes, including length, angle measure, area, surface area and volume, to a specified level of precision.
OH.MP. Mathematical Processes: Students use mathematical processes and knowledge to solve problems. Students apply problem-solving and decision-making techniques, and communicate mathematical ideas.
MP.B. Apply mathematical knowledge and skills routinely in other content areas and practical situations.
MP.D. Apply reasoning processes and skills to construct logical verifications or counter-examples to test conjectures and to justify and defend algorithms and solutions.
OH.NNSO. Number, Number Sense and Operations: 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.
NNSO.1. Grade Level Indicator: Number and Number Systems: Use scientific notation to express large numbers and small numbers between 0 and 1.
NNSO.3. Grade Level Indicator: Meaning of Operations: Apply order of operations to simplify expressions and perform computations involving integer exponents and radicals.
NNSO.7. Grade Level Indicator: Computation and Estimation: Find the square root of perfect squares, and approximate the square root of non-perfect squares as consecutive integers between which the root lies.
NNSO.A. Use scientific notation to express large numbers and numbers less than one.
NNSO.C. Apply properties of operations and the real number system, and justify when they hold for a set of numbers.
NNSO.D. Connect physical, verbal and symbolic representations of integers, rational numbers and irrational numbers.
NNSO.E. Compare, order and determine equivalent forms of real numbers.
NNSO.G. Estimate, compute and solve problems involving real numbers, including ratio, proportion and percent, and explain solutions.
NNSO.H. Find the square root of perfect squares, and approximate the square root of non-perfect squares.
NNSO.I. Estimate, compute and solve problems involving scientific notation, square roots and numbers with integer exponents.
OH.PFA. Patterns, Functions and Algebra: 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.
PFA.13. Grade Level Indicator: Use Algebraic Representations: Compute and interpret slope, midpoint and distance given a set of ordered pairs.
PFA.14. Grade Level Indicator: Analyze Change: Differentiate and explain types of changes in mathematical relationships, such as linear vs. nonlinear, continuous vs. noncontinuous, direct variation vs. inverse variation.
PFA.16. Grade Level Indicator: Analyze Change: Use graphing calculators or computers to analyze change; e.g., interest compounded over time as a nonlinear growth pattern.
PFA.2. Grade Level Indicator: Use Patterns, Relation and Functions: Generalize patterns and sequences by describing how to find the nth term.
PFA.4. Grade Level Indicator: Use Algebraic Representations: Extend the uses of variables to include covariants where y depends on x.
PFA.6. Grade Level Indicator: Use Algebraic Representations: 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.
PFA.7. Grade Level Indicator: Use Algebraic Representations: Use symbolic algebra (equations and inequalities), graphs and tables to represent situations and solve problems.
PFA.8. Grade Level Indicator: Use Algebraic Representations: Write, simplify and evaluate algebraic expressions (including formulas) to generalize situations and solve problems.
PFA.9. Grade Level Indicator: Use Algebraic Representations: Solve linear equations and inequalities graphically, symbolically and using technology.
PFA.A. Generalize and explain patterns and sequences in order to find the next term and the nth term.
PFA.F. Solve and graph linear equations and inequalities.
PFA.I. Model and solve problem situations involving direct and inverse variation.
PFA.J. Describe and interpret rates of change from graphical and numerical data.
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