Standard: Students will understand numerical concepts and mathematical operations.

5-8 Benchmark N.1: Understand numbers, ways of representing numbers, relationships among numbers, and number systems.

5.N.1.1 Compare and order using concrete or illustrated models:

5.N.1.2 Demonstrate understanding of the magnitude of the value of numbers from thousandths to millions, including common

5.N.1.3 Represent place value using concrete or illustrated models up to one billion (1,000,000,000).

5.N.1.4 Interpret percents as part of a hundred (i.e., find decimal and percent equivalents for common fractions, explain how they

5.N.1.5 Identify and represent on a number line decimals, fractions, and mixed numbers.

5.N.1.6 Identify prime and composite numbers to 50.

6.N.1.1 Compare and order rational numbers.

6.N.1.2 Use equivalent representations for rational numbers (e.g., integers, decimals, fractions, percents, ratios, numbers with

6.N.1.3 Use appropriate representations of positive rational numbers in the context of real-life applications.

6.N.1.4 Identify greatest common factor and least common multiples for a set of whole numbers.

6.N.1.5 Identify and represent on a number line decimals, fractions, mixed numbers, and positive and negative integers.

7.N.1.1 Determine the absolute value of rational numbers.

7.N.1.2 Illustrate the relationships among natural (i.e., counting) numbers, whole numbers, integers, rational and irrational numbers.

7.N.1.3 Use properties of the real-number system to explain reasoning and to formulate and solve real-world problems.

7.N.1.4 Read, write, and compare rational numbers in scientific notation (e.g., positive and negative powers of 10) with

7.N.1.5 Simplify numerical expressions using order of operations.

8.N.1.1 Sort numbers by their properties (e.g., prime, composite, square, square root).

8.N.1.2 Demonstrate the magnitude of rational numbers (e.g., trillions to millions).

Standard: Students will understand numerical concepts and mathematical operations.

5-8 Benchmark N.2: Understand the meaning of operations and how they relate to one another.

5.N.2.1 Explain and perform whole number division and express remainders as a whole number or a fractional part as appropriate

5.N.2.2 Add and subtract decimals.

5.N.2.3 Add and subtract fractions and mixed numbers without regrouping and express answers in simplest form.

5.N.2.4 Find the factors and multiples of whole numbers.

5.N.2.5 Use arithmetic operations and inverse relationships to represent and solve real-world problems.

5.N.2.6 Identify and represent on a number line decimals, fractions, and mixed numbers.

5.N.2.7 Demonstrate proficiency with division, including one- and two-digit divisors.

5.N.2.8 Solve simple problems involving the addition and subtraction of fractions and mixed numbers.

5.N.2.9 Represent and use fractions and decimals in equivalent forms.

6.N.2.1 Calculate multiplication and division problems using contextual situations.

6.N.2.2 Factor a whole number into a product of its primes.

6.N.2.3 Demonstrate the relationship and equivalency among ratios and percents.

6.N.2.4 Use proportions to solve problems.

6.N.2.5 Explain and perform:

6.N.2.6 Determine the least common multiple and the greatest common divisor of whole numbers and use them to solve problems

7.N.2.1 Add, subtract, multiply, and divide rational numbers (e.g., integers, fractions, terminating decimals) and take positive

7.N.2.2 Convert terminating decimals into reduced fractions.

7.N.2.3 Calculate given percentages of quantities and use them to solve problems (e.g., discounts of sales, interest earned, tips,

7.N.2.4 Add and subtract fractions with unlike denominators.

7.N.2.5 Multiply, divide, and simplify rational numbers by using exponent rules.

7.N.2.6 Understand the meaning of the absolute value of a number:

Standard: Students will understand numerical concepts and mathematical operations.

5-8 Benchmark N.3: Compute fluently and make reasonable estimates.

5.N.3.1 Add, subtract, multiply, and divide whole numbers.

5.N.3.2 Add and subtract decimals.

5.N.3.3 Use estimation strategies to verify the reasonableness of calculated results.

5.N.3.4 Explain how the estimation strategy impacts the result.

5.N.3.5 Relate the basic arithmetic operations to one another (e.g., multiplication and division are inverse operations).

5.N.3.6 Simplify numerical expressions using order of operations.

5.N.3.7 Recognize and explain the differences between exact and approximate values.

6.N.3.1 Estimate quantities involving rational numbers using various estimations.

6.N.3.2 Use estimates to check reasonableness of results and make predictions in situations involving rational numbers.

6.N.3.3 Determine if a problem situation calls for an exact or approximate answer and perform the appropriate computation.

6.N.3.4 Compare and order positive and negative fractions, decimals, and mixed numbers and place them on a number line.

6.N.3.5 Convert fractions to decimals and percents and use these representations in estimations, computations, and applications.

6.N.3.6 Interpret and use ratios in different contexts.

6.N.3.7 Compute and perform multiplication and division of fractions and decimals and apply these procedures to solving

7.N.3.1 Use estimation to check reasonableness of results, and use this information to make predictions in situations involving

7.N.3.2 Convert fractions to decimals and percents and use these representations in estimations, computations, and applications.

7.N.3.3 Read, write, and compare rational numbers in scientific notation (e.g., positive and negative powers of 10) with

7.N.3.4 Calculate the percentage of increases and decreases of a quantity.

7.N.3.5 Add and subtract fractions with unlike denominators.

7.N.3.6 Use the inverse relationship between raising to a power and extracting the root of a perfect square integer.

8.N.3.1 Formulate algebraic expressions that include real numbers to describe and solve real-world problems.

8.N.3.2 Use a variety of computational methods to estimate quantities involving real numbers.

8.N.3.3 Differentiate between rational and irrational numbers.

8.N.3.4 Use real number properties to perform various computational procedures and explain how they were used.

8.N.3.5 Perform and explain computations with rational numbers, pi, and first-degree algebraic expressions in one variable in a

8.N.3.6 Select and use appropriate forms of rational numbers to solve real-world problems including those involving proportional

8.N.3.7 Approximate, mentally and with calculators, the value of irrational numbers as they arise from problem situations.

8.N.3.8 Express numbers in scientific notation (including negative exponents) in appropriate problem situations using a calculator.

8.N.3.9 Estimate answers and use formulas to solve application problems involving surface area and volume.

Standard: Students will understand algebraic concepts and applications.

5-8 Benchmark A.1: Understand patterns, relations, and functions.

5.A.1.1 Identify and graph ordered pairs in the first quadrant of the coordinate plane.

5.A.1.2 Describe, represent, and analyze patterns and relationships.

5.A.1.3 Identify, describe, and continue patterns presented in a variety of formats (e.g., numeric, visual, oral, written, kinesthetic,

5.A.1.4 Generate a pattern using a written description.

6.A.1.1 Solve problems involving proportional relationships.

6.A.1.2 Graph ordered pairs in the coordinate plane.

6.A.1.3 Explain and use symbols to represent unknown quantities and variable relationships.

6.A.1.4 Explain and use the relationships among ratios, proportions, and percents.

6.A.1.5 Make generalizations based on observed patterns and relationships.

7.A.1.1 Identify and continue patterns presented in a variety of formats.

7.A.1.2 Represent a variety of relationships using tables, graphs, verbal rules, and possible symbolic notation, and recognize the

7.A.1.3 Simplify numerical expressions by applying properties of rational numbers, and justify the process used.

7.A.1.4 Interpret and evaluate expressions involving integer powers and simple roots.

7.A.1.5 Graph and interpret linear functions.

7.A.1.6 Solve problems involving rate, average speed, distance, and time.

8.A.1.1 Move between numerical, tabular, and graphical representations of linear relationships.

8.A.1.2 Use variables to generalize patterns and information presented in tables, charts, and graphs:

Standard: Students will understand algebraic concepts and applications.

5-8 Benchmark A.2: Represent and analyze mathematical situations and structures using algebraic symbols.

5.A.2.1 Compute the value of the expression for specific numerical values of the variable.

5.A.2.2 Use a letter to represent an unknown number.

5.A.2.3 Understand the differences between the symbols for “less than”, “less than or equal to”, “greater than”, and “greater than or

6.A.2.1 Solve problems involving proportional relationships.

6.A.2.2 Use letters to represent an unknown in an equation.

6.A.2.3 Solve one-step linear equations and inequalities in one variable with positive whole-number solutions.

6.A.2.4 Demonstrate that a variable can represent a single quantity that changes.

6.A.2.5 Demonstrate how changes in one variable affect other variables.

7.A.2.1 Write verbal expressions and sentences as algebraic expressions and equations:

7.A.2.2 Use variables and appropriate operations to write an expression, an equation, or an inequality that represents a verbal

7.A.2.3 Use the order of operations to evaluate algebraic expressions.

7.A.2.4 Simplify numerical expressions by applying properties of rational numbers.

7.A.2.5 Graph linear functions and identify slope as positive or negative.

7.A.2.6 Use letters as variables in mathematical expressions to describe how one quantity changes when a related quantity changes.

8.A.2.1 Demonstrate the difference between an equation and an expression.

8.A.2.2 Solve two-step linear equations and inequalities in one variable with rational solutions.

8.A.2.3 Evaluate formulas using substitution.

8.A.2.4 Demonstrate understanding of the relationships between ratios, proportions, and percents and solve for a missing term in a

8.A.2.5 Graph solution sets of linear equations in two variables on the coordinate plane.

8.A.2.6 Formulate and solve problems involving simple linear relationships, find percents of a given number, variable situations,

8.A.2.7 Use symbols, variables, expressions, inequalities, equations, and simple systems of equations to represent problem

Standard: Students will understand algebraic concepts and applications.

5-8 Benchmark A.3: Use mathematical models to represent and understand quantitative relationships.

5.A.3.1 Use mathematical models to represent and explain mathematical concepts and procedures.

5.A.3.2 Understand and use mathematical models such as:

5.A.3.3 Demonstrate how a situation can be represented in more than one way.

6.A.3.1 Develop and use mathematical models to represent and justify mathematical relationships found in a variety of situations.

6.A.3.2 Create, explain, and use mathematical models such as:

7.A.3.1 Create scale models and use them for dimensional drawings.

7.A.3.2 Understand and use the coordinate plane to graph ordered pairs and linear equations.

7.A.3.3 Select and use an appropriate model for a particular situation.

8.A.3.1 Generate different representations to model a specific numerical relationship given one representation of data (e.g., a table,

Standard: Students will understand algebraic concepts and applications.

5-8 Benchmark A.4: Analyze changes in various contexts.

5.A.4.1 Recognize and create patterns of change from everyday life using numerical or pictorial representations.

5.A.4.2 Generalize patterns of change and recognize the same general patterns presented in different representations.

6.A.4.1 Represent and explain changes using one-step equations with one variable.

6.A.4.2 Solve problems that involve change using proportional relationships.

6.A.4.3 Use ratios to predict changes in proportional situations.

6.A.4.4 Use tables and symbols to represent and describe proportional and other relationships involving conversions, sequences,

6.A.4.5 Generate formulas to represent relationships involving changes in perimeter.

7.A.4.1 Use variables and appropriate operations to write an expression, an equation, and/or an inequality that represents a verbal

7.A.4.2 Interpret and evaluate expressions involving integer powers and simple roots as they relate to change.

7.A.4.3 Graph and interpret linear functions as they are used to solve problems.

7.A.4.4 Solve two-step equations and inequalities with one variable over the rational numbers, interpret the solution or solutions in

8.A.4.1 Use graphs, tables, and algebraic representations to make predictions and solve problems that involve change.

8.A.4.2 Estimate, find, and justify solutions to problems that involve change using tables, graphs, and algebraic expressions.

8.A.4.3 Use appropriate problem-solving strategies (e.g., drawing a picture, looking for a pattern, systematic guessing and

8.A.4.4 Solve multi-step problems that involve changes in rate, average speed, distance, and time.

8.A.4.5 Analyze problems that involve change by identifying relationships, distinguishing relevant from irrelevant information,

8.A.4.6 Generalize a pattern of change using algebra and show the relationship among the equation, graph, and table of values.

8.A.4.7 Recognize the same general pattern of change presented in different representations.

Standard: Students will understand geometric concepts and applications.

5-8 Benchmark G.1: Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop

5.G.1.1 Identify, describe, and classify two-dimensional shapes and three-dimensional figures by their properties.

5.G.1.2 Recognize and describe properties of regular polygons having up to ten sides.

5.G.1.3 Identify faces, edges, and bases on three-dimensional objects.

6.G.1.1 Identify, describe, and classify the properties of, and the relationships between, plane and solid geometric figures:

6.G.1.2 Classify angles as right, obtuse, or straight.

6.G.1.3 Describe the properties of geometric figures that include regular polygons, circles, ellipses, cylinders, cones, spheres, and

6.G.1.4 Classify polygons as regular or irregular.

6.G.1.5 Classify triangles as scalene, isosceles, or equilateral and by angles (i.e., right, acute, and obtuse).

6.G.1.6 Identify angle, line, segment, and ray and use the symbols for each.

6.G.1.7 Describe the relationship between radius, diameter, and circumference of a circle.

7.G.1.1 Classify geometric figures as similar or congruent.

7.G.1.2 Understand the concept of a constant (e.g., pi) and use the formulas for the circumference and area of a circle.

7.G.1.3 Explain and use the Pythagorean theorem.

7.G.1.4 Determine the radius, diameter, and circumference of a circle and explain their relationship.

7.G.1.5 Use properties to classify solids including pyramids, cones, prisms, and cylinders.

8.G.1.1 Recognize, classify, and discuss properties of all geometric figures including point, line, and plane.

8.G.1.2 Identify arc, chord, and semicircle and explain their attributes.

8.G.1.3 Use the Pythagorean theorem and its converse to find the missing side of a right triangle and the lengths of the other line

Standard: Students will understand geometric concepts and applications.

5-8 Benchmark G.2: Specify locations and describe spatial relationships using coordinate geometry and other representational

5.G.2.1 Recognize perpendicular and parallel lines.

6.G.2.1 Use coordinate geometry to describe location on a plane.

6.G.2.2 Recognize skewed lines in space.

7.G.2.1 Construct and use coordinate graphs to plot simple figures, determine lengths and areas related to them, and determine the

8.G.2.1 Represent, formulate, and solve distance and geometry problems using the language and symbols of algebra and the

Standard: Students will understand geometric concepts and applications.

5-8 Benchmark G.3: Apply transformations and use symmetry to analyze mathematical situations.

5.G.3.1 Identify line of symmetry in simple geometric figures.

6.G.3.1 Identify line of symmetry with rotation and scaling.

7.G.3.1 Determine how perimeter and area are affected by changes of scale.

8.G.3.1 Describe the symmetry of three-dimensional figures.

8.G.3.2 Describe and perform single and multiple transformations that include rotation, reflection, translation, and dilation (i.e.,

Standard: Students will understand geometric concepts and applications.

5-8 Benchmark G.4: Use visualization, spatial reasoning, and geometric modeling to solve problems.

5.G.4.1 Understand and compute the perimeter of regular polygons.

5.G.4.2 Identify and explain circumference, radius, and diameter.

6.G.4.1 Use appropriate technology, manipulatives, constructions, or drawings to recognize or compare geometric

7.G.4.1 Compute the perimeter and area of common geometric shapes and use the results to find measures of less

7.G.4.2 Identify and describe the properties of two-dimensional figures:

8.G.4.1 Understand angle relationships formed by parallel lines cut by a transversal.

8.G.4.2 Recognize and apply properties of corresponding parts of similar and congruent triangles and quadrilaterals.

8.G.4.3 Represent and solve problems relating to size, shape, area, and volume using geometric models.

8.G.4.4 Develop and use formulas for area, perimeter, circumference, and volume.

8.G.4.5 Construct two-dimensional patterns for three-dimensional models (e.g., cylinders, prisms, cones).

Standard: Students will understand measurement systems and applications.

5-8 Benchmark M.1: Understand measurable attributes of objects and the units, systems, and processes of measurement.

5.M.1.1 Understand properties (e.g., length, area, weight, volume) and select the appropriate type of unit for measuring each using

5.M.1.2 Select and use appropriate units and tools to measure according to the degree of accuracy required in a particular problemsolving

5.M.1.3 Solve problems involving linear measurement, weight, and capacity (e.g., measuring to the nearest sixteenth of an inch or

5.M.1.4 Perform one-step conversions within a system of measurement (e.g., inches to feet, centimeters to meters).

6.M.1.1 Perform multi-step conversions of measurement units to equivalent units within a given system (e.g., 36 inches equals 3

6.M.1.2 Estimate measurement in both U.S. customary and metric units.

6.M.1.3 Select and use units of appropriate size and type to measure angles (e.g., degrees, radians), perimeter, area, and capacity in

6.M.1.4 Use standard units of linear measurement to the nearest sixteenth of an inch; metric measurements to the nearest

7.M.1.1 Choose appropriate units of measure and ratios to recognize new equivalences (e.g., 1 square yard equals 9 square feet) to

7.M.1.2 Select and use the appropriate size and type of unit for a given measurement situation.

7.M.1.3 Compare masses, weights, capacities, geometric measures, times, and temperatures within measurement systems.

7.M.1.4 Approximate the relationship between standard and metric measurement systems (e.g., inches and centimeters, pounds and

7.M.1.5 Use measures expressed as rates and measures expressed as products to solve problems, check the units of the solutions,

8.M.1.1 Understand the concept of volume and use the appropriate units in common measuring systems (e.g., cubic

8.M.1.2 Use changes in measurement units (e.g., square inches, cubic feet) to perform conversions from one-, two-, and threedimensional

Standard: Students will understand measurement systems and applications.

5-8 Benchmark M.2: Apply appropriate techniques, tools, and formulas to determine measurements.

5.M.2.1 Solve measurement problems using appropriate tools involving length, perimeter, weight, capacity, time, and temperature.

5.M.2.2 Select and use strategies to estimate measurements including length, distance, capacity, and time.

5.M.2.3 Apply strategies and use tools for estimating and measuring the perimeter of regular and irregular shapes.

6.M.2.1 Apply various measurement techniques and tools, units of measure, and degrees of accuracy to find accurate rational

6.M.2.2 Select and use formulas for perimeters of squares and rectangles.

6.M.2.3 Select and use strategies to estimate measurements including angle measure and capacity.

6.M.2.4 Select and justify the selection of measurement tools, units of measure, and degrees of accuracy appropriate to the given

7.M.2.1 Apply strategies and formulas to find missing angle measurements in triangles and quadrilaterals.

7.M.2.2 Select and use formulas to determine the circumference of circles and the area of triangles, parallelograms, trapezoids, and

7.M.2.3 Solve problems involving scale factors, ratios, and proportions.

8.M.2.1 Use ratios and proportions to measure hard-to-measure objects.

8.M.2.2 Use estimation to solve problems.

8.M.2.3 Use proportional relationships in similar shapes to find missing measurements.

8.M.2.4 Apply strategies to determine the surface area and volume of prisms, pyramids, and cylinders.

8.M.2.5 Perform conversions with multiple terms between metric and U.S. standard measurement systems.

8.M.2.6 Estimate volume in cubic units.

8.M.2.7 Solve simple problems involving rates and derived measurements for such properties as velocity and density.

Standard: Students will understand how to formulate questions, analyze data, and determine probabilities.

5-8 Benchmark D.1: Formulate questions that can be addressed with data and collect, organize, and display relevant data to

5.D.1.1 Construct, read, analyze, and interpret tables, charts, graphs, and data plots.

5.D.1.2 Construct, interpret, and analyze data from graphical representations and draw simple conclusions using bar graphs, line

5.D.1.3 Display, analyze, compare, and interpret different data sets, including data sets of different sizes.

5.D.1.4 Organize and display single-variable data in appropriate graphs and representations.

5.D.1.5 Organize, read, and display numerical (quantitative) and non-numerical (qualitative) data in a clear, organized, and accurate

5.D.1.6 Formulate questions and identify data to be collected to correctly answer a question.

6.D.1.1 Use statistical representations to analyze data.

6.D.1.2 Draw and compare different graphical representations of the same data.

6.D.1.3 Use mean, median, mode, and range to describe data.

6.D.1.4 Sketch circle graphs to display data.

6.D.1.5 Solve problems by collecting, organizing, displaying and interpreting data.

6.D.1.6 Compare different samples of a population with the entire population and determine the appropriateness of using a sample.

6.D.1.7 Conduct and explain sampling techniques such as observations, surveys, and random sampling for gathering data.

6.D.1.8 Determine the median for a rational number data set containing an odd number of data points.

6.D.1.9 Calculate and explain the median for a whole number data set containing an even number of data points.

6.D.1.10 Explain advantages and disadvantages of using various display formats for a specific data set.

6.D.1.11 Formulate and solve problems by collecting, organizing, displaying, and interpreting data.

7.D.1.1 Describe how data representations influences interpretation.

7.D.1.2 Select and use appropriate representation for presenting collected data and justify the selection.

7.D.1.3 Use measures of central tendency and spread to describe a set of data.

7.D.1.4 Choose between median and mode to describe a set of data and justify the choice for a particular situation.

7.D.1.5 Determine the quartiles of a data set.

7.D.1.6 Identify ordered pairs of data from a graph and interpret the data in terms of the situation depicted by the graph.

7.D.1.7 Use various scales and formats to display the same data set.

7.D.1.8 Identify and explain the misleading representations of data.

7.D.1.9 Collect, organize, and represent data sets that have one or more variables and identify relationships among variables within

7.D.1.10 Compute the minimum, lower quartile, median, upper quartile, and maximum of a data set.

7.D.1.11 Identify and explain the effects of scale and/or interval changes on graphs of whole number data sets.

7.D.1.12 Use and explain sampling techniques (e.g., observations, surveys, and random sampling) for gathering data.

7.D.1.13 Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, identifying missing

8.D.1.1 Represent two numerical variables on a plot, describe how the data points are distributed, and identify relationships that

8.D.1.2 Generate, organize, and interpret real numbers in a variety of situations.

8.D.1.3 Organize, analyze, and display appropriate quantitative and qualitative data to address specific questions including:

8.D.1.4 Select the appropriate measure of central tendency to describe a set of data for a particular problem situation.

8.D.1.5 Simulate an event selecting and using different models.

8.D.1.6 Develop an appropriate strategy using a variety of data from surveys, samplings, estimations, and inferences to address a

Standard: Students will understand how to formulate questions, analyze data, and determine probabilities.

5-8 Benchmark D.2: Select and use appropriate statistical methods to analyze data.

5.D.2.1 Organize and display single-variable data in appropriate graphs and representations and determine which types of graphs

5.D.2.2 Use fractions and percentages to compare data sets of different sizes.

5.D.2.3 Correctly rank the values of a numerical data set containing simple fractions and decimals, identify maximum and

6.D.2.1 Choose an appropriate graphical format to organize and represent data.

6.D.2.2 Describe the effects of missing or incorrect data.

6.D.2.3 Compute and analyze statistical measurements for data sets:

6.D.2.4 Use data samples of a population and describe the characteristics and limitations of the sample.

6.D.2.5 Identify different ways of selecting a sample (e.g., convenience sampling, responses to a survey, random sampling) and

6.D.2.6 Explain how the way a question is asked in a survey might influence the results obtained.

6.D.2.7 Identify data that represent sampling errors and explain why the sample and the display might be biased.

6.D.2.8 Identify claims based on statistical data and, in sample cases, evaluate the validity and usefulness of the claims.

7.D.2.1 Choose and justify appropriate measures of central tendencies (e.g., mean, median, mode, range) to describe given or

7.D.2.2 Know various ways to display data sets (e.g., stem and leaf plot, box and whisker plot, scatter plots) and use these forms to

7.D.2.3 Use the analysis of data to make convincing arguments.

7.D.2.4 Use appropriate technology to gather and display data sets and identify the relationships that exist among variables within

7.D.2.5 Use data samples of a population and describe the characteristics and limitations of the sample.

7.D.2.6 Identify data that represent sampling errors and explain why the sample and the display might be biased.

7.D.2.7 Identify claims based on statistical data and evaluate the validity of the claims.

8.D.2.1 Use changes in scales, intervals, or categories to help support a particular interpretation of data.

8.D.2.2 Generate, organize, and interpret real number and other data in a variety of situations.

8.D.2.3 Analyze data to make decisions and to develop convincing arguments from data displayed in a variety of formats including:

8.D.2.4 Interpret and analyze data from graphical representations and draw simple conclusions (e.g., line of best fit).

8.D.2.5 Evaluate and defend the reasonableness of conclusions drawn from data analysis.

8.D.2.6 Use appropriate central tendency and spread as a means for effective decision-making in analyzing data and outliers.

8.D.2.7 Identify simple graphic misrepresentations and distortions of sets of data (e.g., unequal interval sizes, omission of parts of

8.D.2.8 Use appropriate technology to display data as lists, tables, matrices, graphs, and plots and to analyze the relationships of

Standard: Students will understand how to formulate questions, analyze data, and determine probabilities.

5-8 Benchmark D.3: Develop and evaluate inferences and predictions that are based on data.

5.D.3.1 Make and justify valid inferences, predictions, and arguments based on statistical analysis.

5.D.3.2 Compare a given prediction with the results of an investigation.

5.D.3.3 Use counting strategies to determine all the possible outcomes of a particular familiar event.

5.D.3.4 Find all possible outcome sets involving four or more sets of objects.

5.D.3.5 Evaluate the reasonableness of inferences that are based on data in the context of the original solution.

5.D.3.6 Identify the method used to make an inference and/or a prediction on a given data set and solve similar problems.

5.D.3.7 Determine the accuracy of a prediction or an inference based on the accuracy of the data in a given data set.

5.D.3.8 List all possible outcomes of simple events.

6.D.3.1 Identify claims based on statistical data and evaluate the validity of the claim

6.D.3.2 Conduct observations, surveys, experiments and/or simulations, record the results in charts, tables, or graphs, and use the

6.D.3.3 Find all possible combinations in a given set (e.g., the number of ways a set of books can be arranged on a shelf).

6.D.3.4 Compare expected results with actual results in a simple experiment.

7.D.3.1 Formulate and justify mathematical conjectures based on data and a general description of the mathematical question or

7.D.3.2 Analyze data to make accurate inferences, predictions, and to develop convincing arguments from data displayed in a

7.D.3.3 Approximate a line of best fit for a data set in a scatter plot form and make predictions using the simple equation of that

8.D.3.1 Describe how changes in scale, intervals, or categories influence arguments for a particular interpretation of the data.

8.D.3.2 Describe how reader bias, measurement errors, and display distortion can affect the interpretation of data, predictions, and

8.D.3.3 Conduct simple experiments and/or simulations, record results in charts, tables, or graphs, and use the results to draw

8.D.3.4 Compare expected results with experimental results and information used in predictions and inferences.

Standard: Students will understand how to formulate questions, analyze data, and determine probabilities.

5-8 Benchmark D.4: Understand and apply basic concepts of probability.

5.D.4.1 Determine probabilities through experiments and/or simulations and compare the results with mathematical expressions.

5.D.4.2 Make predictions from the results of student-generated experiments of single events.

5.D.4.3 Identify simple experiments where the probabilities of all outcomes are equal.

5.D.4.4 Describe and predict the results of a probability experiment.

5.D.4.5 Use fractions to describe the results of an experiment.

5.D.4.6 Use probability to generalize from a simple pattern or set of examples and justify why the generalization is reasonable.

6.D.4.1 List all possible outcomes for a compound event composed of two independent events and recognize whether an outcome is

6.D.4.2 Determine and compare experimental (empirical) and mathematical (theoretical) probabilities (e.g., flipping two color

6.D.4.3 Determine theoretical and experimental probabilities and use them to make predictions about events.

6.D.4.4 Represent all possible outcomes for compound events in an organized way (e.g., tables, grids, tree diagrams) and express

6.D.4.5 Use data to estimate the probability of future events (e.g., batting averages).

6.D.4.6 Represent probabilities as ratios, proportions, decimals between 0 and 1, and percentages between 0 and 100 and verify that

6.D.4.7 Describe the difference between independent and dependent events and identify situations involving independent or

7.D.4.1 Determine the probability of a compound event composed of two independent events.

7.D.4.2 Identify examples of events having the probability of one or zero.

7.D.4.3 Describe the probability of events using fractions, decimals, and percents.

7.D.4.4 Express probability as a fraction, zero, or one.

7.D.4.5 Use probability to generate convincing arguments, draw conclusions, and make decisions in a variety of situations.

7.D.4.6 Make predictions based on theoretical probabilities of compound events.

7.D.4.7 Determine the probability of a simple event or a compound event composed of a simple, independent events.

8.D.4.1 Calculate the odds of a desired outcome in a simple experiment.

8.D.4.2 Design and use an appropriate simulation to estimate the probability of a real-world event (e.g., disk toss, cube toss).

8.D.4.3 Explain the relationship between probability and odds and calculate the odds of a desired outcome in a simple experiment.