Grades
Standard
Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of [...]
Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For [...]
Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.
Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the [...]
Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described [...]
Design and use a simulation to generate frequencies for compound events. For example, use random digits as a simulation tool [...]
Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal [...]
Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for [...]
Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, [...]
Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or [...]
Recognize and represent proportional relationships between quantities.
Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing [...]
Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased [...]
Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with [...]
Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, [...]
Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on [...]
Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its [...]
Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending [...]
Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (–q). Show that the [...]
Apply properties of operations as strategies to add and subtract rational numbers.
Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. Apply and extend [...]
Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of [...]
Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero [...]
Apply properties of operations as strategies to multiply and divide rational numbers.
Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates [...]
Evaluate expressions at specific values for their variables. Include expressions that arise from formulas in real-world problems. Perform arithmetic operations, [...]
Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3(2 + [...]
Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is [...]
Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if [...]
Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can [...]
Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px [...]
Write an inequality of the form x > c or x < c to represent a constraint or condition in [...]
Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation [...]
Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it [...]
Understand that a set of data collected to answer a statistical question has a distribution which can be described by [...]
Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, [...]
Display numerical data in plots on a number line, including dot plots, histograms, and box plots.
Summarize and describe distributions. Summarize numerical data sets in relation to their context, such as by:
Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.
Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing [...]
Relating the choice of measures of center and variability to the shape of the data distribution and the context in [...]
Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing [...]
Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three [...]
Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right [...]
Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.
Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual [...]
Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.
Grades
Standard
Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of [...]
Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For [...]
Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.
Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the [...]
Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described [...]
Design and use a simulation to generate frequencies for compound events. For example, use random digits as a simulation tool [...]
Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal [...]
Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for [...]
Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, [...]
Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or [...]
Recognize and represent proportional relationships between quantities.
Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing [...]
Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased [...]
Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with [...]
Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, [...]
Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on [...]
Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its [...]
Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending [...]
Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (–q). Show that the [...]
Apply properties of operations as strategies to add and subtract rational numbers.
Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. Apply and extend [...]
Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of [...]
Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero [...]
Apply properties of operations as strategies to multiply and divide rational numbers.
Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates [...]
Evaluate expressions at specific values for their variables. Include expressions that arise from formulas in real-world problems. Perform arithmetic operations, [...]
Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3(2 + [...]
Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is [...]
Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if [...]
Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can [...]
Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px [...]
Write an inequality of the form x > c or x < c to represent a constraint or condition in [...]
Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation [...]
Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it [...]
Understand that a set of data collected to answer a statistical question has a distribution which can be described by [...]
Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, [...]
Display numerical data in plots on a number line, including dot plots, histograms, and box plots.
Summarize and describe distributions. Summarize numerical data sets in relation to their context, such as by:
Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.
Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing [...]
Relating the choice of measures of center and variability to the shape of the data distribution and the context in [...]
Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing [...]
Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three [...]
Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right [...]
Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.
Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual [...]
Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.
