Cluster: Use random sampling to draw inferences about a population

Standard: Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

Degree of Alignment: Not Rated (0 users)

Cluster: Use random sampling to draw inferences about a population

Standard: Use random sampling to draw inferences about a population. Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be.

Degree of Alignment: Not Rated (0 users)

Cluster: Draw, construct, and describe geometrical figures and describe the relationships between them.

Standard: Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.

Degree of Alignment: Not Rated (0 users)

Cluster: Draw, construct, and describe geometrical figures and describe the relationships between them.

Standard: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

Degree of Alignment: Not Rated (0 users)

Cluster: Solve real-life and mathematical problems involving angle measure, area, surface area, and volume

Standard: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

Degree of Alignment: Not Rated (0 users)

Cluster: Solve real-life and mathematical problems involving angle measure, area, surface area, and volume

Standard: Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

Degree of Alignment: Not Rated (0 users)

Cluster: Solve real-life and mathematical problems involving angle measure, area, surface area, and volume

Standard: Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

Degree of Alignment: Not Rated (0 users)

Cluster: Investigate chance processes and develop, use, and evaluate probability models

Standard: Design and use a simulation to generate frequencies for compound events. For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood?

Degree of Alignment: Not Rated (0 users)

Cluster: Investigate chance processes and develop, use, and evaluate probability models

Standard: Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., “rolling double sixes”), identify the outcomes in the sample space which compose the event.

Degree of Alignment: Not Rated (0 users)

Cluster: Investigate chance processes and develop, use, and evaluate probability models

Standard: Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.

Degree of Alignment: Not Rated (0 users)

Cluster: Investigate chance processes and develop, use, and evaluate probability models

Standard: Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times.

Degree of Alignment: Not Rated (0 users)

Cluster: Investigate chance processes and develop, use, and evaluate probability models

Standard: Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.

Degree of Alignment: Not Rated (0 users)

Cluster: Investigate chance processes and develop, use, and evaluate probability models

Standard: Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected.

Degree of Alignment: Not Rated (0 users)

Cluster: Investigate chance processes and develop, use, and evaluate probability models

Standard: Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies?

Degree of Alignment: Not Rated (0 users)

Cluster: Investigate chance processes and develop, use, and evaluate probability models

Standard: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.

Degree of Alignment: Not Rated (0 users)

Cluster: Draw informal comparative inferences about two populations

Standard: Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.

Degree of Alignment: Not Rated (0 users)

Cluster: Draw informal comparative inferences about two populations

Standard: Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable.

Degree of Alignment: Not Rated (0 users)

Cluster: Investigate chance processes and develop, use, and evaluate probability models

Standard: Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.

Degree of Alignment: Not Rated (0 users)

Cluster: Analyze proportional relationships and use them to solve real-world and mathematical problems

Standard: Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

Degree of Alignment: Not Rated (0 users)

Cluster: Analyze proportional relationships and use them to solve real-world and mathematical problems

Standard: Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.

Degree of Alignment: Not Rated (0 users)

Cluster: Analyze proportional relationships and use them to solve real-world and mathematical problems

Standard: Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.

Degree of Alignment: Not Rated (0 users)

Cluster: Analyze proportional relationships and use them to solve real-world and mathematical problems

Standard: Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.

Degree of Alignment: Not Rated (0 users)

Cluster: Analyze proportional relationships and use them to solve real-world and mathematical problems

Standard: Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

Degree of Alignment: Not Rated (0 users)

Cluster: Analyze proportional relationships and use them to solve real-world and mathematical problems

Standard: Recognize and represent proportional relationships between quantities.

Degree of Alignment: Not Rated (0 users)

Cluster: Analyze proportional relationships and use them to solve real-world and mathematical problems

Standard: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction (1/2)/(1/4) miles per hour, equivalently 2 miles per hour.

Degree of Alignment: Not Rated (0 users)

Cluster: Mathematical practices

Standard: Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.

Degree of Alignment: Not Rated (0 users)

Cluster: Mathematical practices

Standard: Construct viable arguments and critique the reasoning of others. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.

Degree of Alignment: Not Rated (0 users)

Cluster: Mathematical practices

Standard: Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Statistics and Probability

Standard: Investigate chance processes and develop, use, and evaluate probability models

Indicator: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Statistics and Probability

Standard: Investigate chance processes and develop, use, and evaluate probability models

Indicator: Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Statistics and Probability

Standard: Investigate chance processes and develop, use, and evaluate probability models

Indicator: Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Statistics and Probability

Standard: Investigate chance processes and develop, use, and evaluate probability models

Indicator: Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Statistics and Probability

Standard: Draw informal comparative inferences about two populations

Indicator: Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Statistics and Probability

Standard: Draw informal comparative inferences about two populations

Indicator: Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Geometry

Standard: Solve real-life and mathematical problems involving angle measure, area, surface area, and volume

Indicator: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Geometry

Standard: Solve real-life and mathematical problems involving angle measure, area, surface area, and volume

Indicator: Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Geometry

Standard: Solve real-life and mathematical problems involving angle measure, area, surface area, and volume

Indicator: Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Statistics and Probability

Standard: Investigate chance processes and develop, use, and evaluate probability models

Indicator: Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies?

Degree of Alignment: Not Rated (0 users)

Learning Domain: Statistics and Probability

Standard: Investigate chance processes and develop, use, and evaluate probability models

Indicator: Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Ratios and Proportional Relationships

Standard: Analyze proportional relationships and use them to solve real-world and mathematical problems

Indicator: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction (1/2)/(1/4) miles per hour, equivalently 2 miles per hour.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Ratios and Proportional Relationships

Standard: Analyze proportional relationships and use them to solve real-world and mathematical problems

Indicator: Recognize and represent proportional relationships between quantities.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Ratios and Proportional Relationships

Standard: Analyze proportional relationships and use them to solve real-world and mathematical problems

Indicator: Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Statistics and Probability

Standard: Investigate chance processes and develop, use, and evaluate probability models

Indicator: Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., "rolling double sixes"ť), identify the outcomes in the sample space which compose the event.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Statistics and Probability

Standard: Investigate chance processes and develop, use, and evaluate probability models

Indicator: Design and use a simulation to generate frequencies for compound events. For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood?

Degree of Alignment: Not Rated (0 users)

Learning Domain: Statistics and Probability

Standard: Investigate chance processes and develop, use, and evaluate probability models

Indicator: Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Mathematical Practices

Standard: Mathematical practices

Indicator: Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Ratios and Proportional Relationships

Standard: Analyze proportional relationships and use them to solve real-world and mathematical problems

Indicator: Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Ratios and Proportional Relationships

Standard: Analyze proportional relationships and use them to solve real-world and mathematical problems

Indicator: Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Ratios and Proportional Relationships

Standard: Analyze proportional relationships and use them to solve real-world and mathematical problems

Indicator: Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Ratios and Proportional Relationships

Standard: Analyze proportional relationships and use them to solve real-world and mathematical problems

Indicator: Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Statistics and Probability

Standard: Use random sampling to draw inferences about a population

Indicator: Use random sampling to draw inferences about a population. Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Statistics and Probability

Standard: Use random sampling to draw inferences about a population

Indicator: Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Geometry

Standard: Draw, construct, and describe geometrical figures and describe the relationships between them.

Indicator: Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Geometry

Standard: Draw, construct, and describe geometrical figures and describe the relationships between them.

Indicator: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Geometry

Standard: Draw, construct, and describe geometrical figures and describe the relationships between them.

Indicator: Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Mathematical Practices

Standard: Mathematical practices

Indicator: Construct viable arguments and critique the reasoning of others. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and"Óif there is a flaw in an argument"Óexplain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Mathematical Practices

Standard: Mathematical practices

Indicator: Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, "Does this make sense?"ť They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Ratios and Proportional Relationships

Standard: Analyze proportional relationships and use them to solve real-world and mathematical problems.

Indicator: Recognize and represent proportional relationships between quantities.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Ratios and Proportional Relationships

Standard: Analyze proportional relationships and use them to solve real-world and mathematical problems.

Indicator: Solve multi-step real world and mathematical problems involving ratios and percentages.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Ratios and Proportional Relationships

Standard: Analyze proportional relationships and use them to solve real-world and mathematical problems.

Indicator: Compute unit rates, including those involving complex fractions, with like or different units.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Ratios and Proportional Relationships

Standard:

Indicator: Decide whether two quantities in a table or graph are in a proportional relationship.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Ratios and Proportional Relationships

Standard:

Indicator: Represent proportional relationships with equations.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Ratios and Proportional Relationships

Standard:

Indicator: Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

Degree of Alignment: Not Rated (0 users)

Learning Domain: Ratios and Proportional Relationships

Standard:

Indicator: Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.

Degree of Alignment: Not Rated (0 users)