**Algebraic Equations**Worksheets: 4Study Guides: 1**The Pythagorean Theorem**Worksheets: 4Study Guides: 1**Using Integers**Worksheets: 4Study Guides: 1**Using Probability**Worksheets: 3Study Guides: 1### 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: Read, create and interpret box-and-whisker plots, stem-and-leaf plots, and other types of graphs, when appropriate.

#### DAP.3. Grade Level Indicator: Statistical Methods: 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.

#### DAP.7. Grade Level Indicator: Probability: 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.

#### DAP.8. Grade Level Indicator: Probability: Make predictions based on theoretical probabilities, design and conduct an experiment to test the predictions, compare actual results to predicted results, and explain differences.

#### DAP.A. Read, create and use line graphs, histograms, circle graphs, box-and-whisker plots, stem-and-leaf plots, and other representations when appropriate.

#### DAP.B. Interpret data by looking for patterns and relationships, draw and justify conclusions, and answer related questions.

#### DAP.C. Evaluate interpretations and conclusions as additional data are collected, modify conclusions and predictions, and justify new findings.

#### DAP.E. Collect, organize, display and interpret data for a specific purpose or need.

#### DAP.F. Determine and use the range, mean, median and mode to analyze and compare data, and explain what each indicates about the data.

#### DAP.I. Describe the probability of an event using ratios, including fractional notation.

#### DAP.J. Compare experimental and theoretical results for a variety of simple experiments.

### 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.1. Grade Level Indicator: Characteristics and Properties: Use proportional reasoning to describe and express relationships between parts and attributes of similar and congruent figures.

#### GSS.2. Grade Level Indicator: Characteristics and Properties: Determine sufficient (not necessarily minimal) properties that define a specific two-dimensional figure or three-dimensional object. For example:

##### GSS.2.a. Determine when one set of figures is a subset of another; e.g., all squares are rectangles.

##### GSS.2.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.

#### GSS.3. Grade Level Indicator: Characteristics and Properties: Use and demonstrate understanding of the properties of triangles. For example:

##### GSS.3.a. Use Pythagorean Theorem to solve problems involving right triangles.

#### GSS.6. Grade Level Indicator: Transformation and Symmetry: Determine and use scale factors for similar figures to solve problems using proportional reasoning.

#### GSS.7. Grade Level Indicator: Transformation and Symmetry: Identify the line and rotation symmetries of two-dimensional figures to solve problems.

#### GSS.8. Grade Level Indicator: Visualization and Geometric Models: Perform translations, reflections, rotations and dilations of two-dimensional figures using a variety of methods (paper folding, tracing, graph paper).

#### GSS.A. Identify and label angle parts and the regions defined within the plane where the angle resides.

#### GSS.B. Draw circles, and identify and determine the relationships among the radius, diameter, center and circumference.

#### GSS.C. Specify locations and plot ordered pairs on a coordinate plane.

#### GSS.D. Identify, describe and classify types of line pairs, angles, two-dimensional figures and three-dimensional objects using their properties.

#### GSS.E. Use proportions to express relationships among corresponding parts of similar figures.

#### GSS.F. Describe and use the concepts of congruence, similarity and symmetry to solve problems.

#### GSS.G. Describe and use properties of triangles to solve problems involving angle measures and side lengths of right triangles.

#### GSS.J. Apply properties of equality and proportionality to solve problems involving congruent or similar figures; e.g., create a scale drawing.

### 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.3. Grade Level Indicator: Use Measurement Techniques and Tools: Estimate a measurement to a greater degree of precision than the tool provides.

#### M.4. Grade Level Indicator: Use Measurement Techniques and Tools: Solve problems involving proportional relationships and scale factors; e.g., scale models that require unit conversions within the same measurement system.

#### M.8. Grade Level Indicator: Use Measurement Techniques and Tools: 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.

#### M.9. Grade Level Indicator: Use Measurement Techniques and Tools: 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.

#### M.A. Select appropriate units to measure angles, circumference, surface area, mass and volume, using: U.S. customary units; e.g., degrees, square feet, pounds, and other units as appropriate; metric units; e.g., square meters, kilograms and other units as appropriate.

#### M.B. Convert units of length, area, volume, mass and time within the same measurement system.

#### M.C. Identify appropriate tools and apply appropriate techniques for measuring angles, perimeter or circumference and area of triangles, quadrilaterals, circles and composite shapes, and surface area and volume of prisms and cylinders.

#### M.D. Select a tool and measure accurately to a specified level of precision.

#### M.F. Analyze and explain what happens to area and perimeter or surface area and volume when the dimensions of an object are changed.

#### M.G. Understand and demonstrate the independence of perimeter and area for two-dimensional shapes and of surface area and volume for three-dimensional shapes.

### 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.A. Clarify problem-solving situation and identify potential solution processes; e.g., consider different strategies and approaches to a problem, restate problem from various perspectives.

#### MP.B. Apply and adapt problem-solving strategies to solve a variety of problems, including unfamiliar and non-routine problem situations.

#### MP.C. Use more than one strategy to solve a problem, and recognize there are advantages associated with various methods.

#### MP.D. Recognize whether an estimate or an exact solution is appropriate for a given problem situation.

#### MP.E. Use deductive thinking to construct informal arguments to support reasoning and to justify solutions to problems.

#### MP.F. Use inductive thinking to generalize a pattern of observations for particular cases, make conjectures, and provide supporting arguments for conjectures.

### 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: Demonstrate an understanding of place value using powers of 10 and write large numbers in scientific notation.

#### NNSO.2. Grade Level Indicator: Number and Number Systems: Explain the meaning of exponents that are negative or 0.

#### NNSO.4. Grade Level Indicator: Meaning of Operations: Use order of operations and properties to simplify numerical expressions involving integers, fractions and decimals.

#### NNSO.5. Grade Level Indicator: Meaning of Operations: Explain the meaning and effect of adding, subtracting, multiplying and dividing integers; e.g., how adding two integers can result in a lesser value.

#### NNSO.6. Grade Level Indicator: Computation and Estimation: Simplify numerical expressions involving integers and use integers to solve real-life problems.

#### NNSO.8. Grade Level Indicator: Computation and Estimation: Develop and analyze algorithms for computing with percents and integers, and demonstrate fluency in their use.

#### NNSO.9. Grade Level Indicator: Computation and Estimation: Represent and solve problem situations that can be modeled by and solved using concepts of absolute value, exponents and square roots (for perfect squares).

#### NNSO.A. Represent and compare numbers less than 0 through familiar applications and extending the number line.

#### NNSO.B. Compare, order and convert among fractions, decimals and percents.

#### NNSO.C. Develop meaning for percents, including percents greater than 100 and less than 1.

#### NNSO.D. Use models and pictures to relate concepts of ratio, proportion and percent.

#### NNSO.E. Use order of operations, including use of parenthesis and exponents to solve multi-step problems, and verify and interpret the results.

#### NNSO.F. Apply number system properties when performing computations.

#### NNSO.G. Apply and explain the use of prime factorizations, common factors, and common multiples in problem situations.

#### NNSO.H. Use and analyze the steps in standard and non-standard algorithms for computing with fractions, decimals and integers.

#### NNSO.I. Use a variety of strategies, including proportional reasoning, to estimate, compute, solve and explain solutions to problems involving integers, fractions, decimals and percents.

### 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.11. Grade Level Indicator: Analyze Change: Use graphing calculators or computers to analyze change; e.g., distance-time relationships.

#### PFA.2. Grade Level Indicator: Use Patterns, Relations and Functions: Generalize patterns by describing in words how to find the next term.

#### PFA.3. Grade Level Indicator: Use Patterns, Relations and Functions: 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.

#### PFA.5. Grade Level Indicator: Use Algebraic Representations: Represent linear equations by plotting points in the coordinate plane.

#### PFA.6. Grade Level Indicator: Use Algebraic Representations: Represent inequalities on a number line or a coordinate plane.

#### PFA.7. Grade Level Indicator: Use Algebraic Representations: Justify that two forms of an algebraic expression are equivalent, and recognize when an expression is simplified.

#### PFA.8. Grade Level Indicator: Use Algebraic Representations: Use formulas in problem-solving situations.

#### PFA.9. Grade Level Indicator: Use Algebraic Representations: Recognize a variety of uses for variables; e.g., placeholder for an unknown quantity in an equation, generalization for a pattern, formula.

#### PFA.A. Describe, extend and determine the rule for patterns and relationships occurring in numeric patterns, computation, geometry, graphs and other applications.

#### PFA.B. Represent, analyze and generalize a variety of patterns and functions with tables, graphs, words and symbolic rules.

#### PFA.C. Use variables to create and solve equations and inequalities representing problem situations.

#### PFA.D. Use symbolic algebra to represent and explain mathematical relationships.

#### PFA.E. Use rules and variables to describe patterns, functions and other relationships.

#### PFA.G. Write, simplify and evaluate algebraic expressions.

#### PFA.H. Solve linear equations and inequalities symbolically, graphically and numerically.

#### PFA.J. Use formulas in problem-solving situations.

#### PFA.K. Graph linear equations and inequalities.

#### PFA.L. Analyze functional relationships, and explain how a change in one quantity results in a change in the other.

#### PFA.M. Approximate and interpret rates of change from graphical and numerical data.

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