# data[].attributes.body
Find area of triangles, quadrilaterals and polygons by composing/decomposing.

# data[].attributes.body
Apply the formulas V = lwh and V = Bh to find volumes of right rectangular prisms with fractional edge lengths.

# data[].attributes.body
Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side.

# data[].attributes.body
Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures.

# data[].attributes.body
Solve problems involving scale drawings of geometric figures, such as computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.

# data[].attributes.body
Draw two-dimensional geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides.

# data[].attributes.body
Describe the shape of the two-dimensional face of the figure that results from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.

# data[].attributes.body
Understand the concept of a ratio including the distinctions between part:part and part:whole and the value of a ratio; part/part and part/whole. Use ratio language to describe a ratio relationship between two quantities.

# data[].attributes.body
Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship, including the use of units.

# data[].attributes.body
Use ratio and rate reasoning to solve real-world and mathematical problems.

# data[].attributes.body
Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship, including the use of units.

# data[].attributes.body
Fluently divide multi-digit numbers using the standard algorithm.

# data[].attributes.body
Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

# data[].attributes.body
Use prime factorization to find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two relatively prime numbers.

# data[].attributes.body
Understand that positive and negative numbers are used together to describe quantities having opposite directions or values to represent quantities in real-world contexts, explaining the meaning of zero in each situation.

# data[].attributes.body
Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.

# data[].attributes.body
Understand ordering and absolute value of rational numbers.

# data[].attributes.body
Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.

# data[].attributes.body
Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers.

# data[].attributes.body
Understand that a set of data collected to answer a statistical question has a distribution, which can be described by its center (median, mean, and/or mode), spread (range, interquartile range), and overall shape.

# data[].attributes.body
Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.

# data[].attributes.body
Display numerical data in plots on a number line, including dot plots, histograms, and box plots.

# data[].attributes.body
Write and evaluate numerical expressions involving whole-number exponents.

# data[].attributes.body
Write, read, and evaluate expressions in which letters stand for numbers.

# data[].attributes.body
Apply the properties of operations to generate equivalent expressions.

# data[].attributes.body
Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them).

# data[].attributes.body
Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.

# data[].attributes.body
Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.

# data[].attributes.body
Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.

# data[].attributes.body
Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such in-equalities on number line diagrams.

# data[].attributes.body
Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation.

# data[].attributes.body
Summarize numerical data sets in relation to their context.

# data[].attributes.body
Circles and measurement

# data[].attributes.body
Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write simple equations and use them to solve for an unknown angle in a figure.

# data[].attributes.body
Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write simple equations and use them to solve for an unknown angle in a figure.

# data[].attributes.body
Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units.

# data[].attributes.body
Recognize and represent proportional relationships between quantities.

# data[].attributes.body
Use proportional relationships to solve multi-step ratio, rate, and percent problems.

# data[].attributes.body
Apply and extend previous understandings of addition and subtraction to add and subtract integers and other rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.

# data[].attributes.body
Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide integers and other rational numbers.

# data[].attributes.body
Solve real-world and mathematical problems involving the four operations with integers and other rational numbers.

# data[].attributes.body
Apply properties of operations to add, subtract, factor, and expand linear expressions with rational coefficients.

# data[].attributes.body
Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related.

# data[].attributes.body
Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies.

# data[].attributes.body
Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.

# data[].attributes.body
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.

# data[].attributes.body
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.

# data[].attributes.body
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.

# data[].attributes.body
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 ½ indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.

# data[].attributes.body
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.

# data[].attributes.body
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.

# data[].attributes.body
Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.

# data[].attributes.body
Verify experimentally the properties of rotations, reflections, and translations.

# data[].attributes.body
Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.

# data[].attributes.body
Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.

# data[].attributes.body
Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.

# data[].attributes.body
Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles.

# data[].attributes.body
Understand the relationship among the sides of a right triangle. Analyze and justify the Pythagorean Theorem.

# data[].attributes.body
Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.

# data[].attributes.body
Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.

# data[].attributes.body
Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

# data[].attributes.body
Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.

# data[].attributes.body
Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g.,π²).

# data[].attributes.body
Know and apply the properties of integer exponents to generate equivalent numerical expressions.

# data[].attributes.body
Use square root and cube root symbols to represent solutions to equations of the form x² = p and x³ = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.

# data[].attributes.body
Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other.

# data[].attributes.body
Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities. Interpret scientific notation that has been generated by technology.

# data[].attributes.body
Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.

# data[].attributes.body
Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

# data[].attributes.body
Solve linear equations in one variable.

# data[].attributes.body
Analyze and solve pairs of simultaneous linear equations.

# data[].attributes.body
Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.

# data[].attributes.body
Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.

# data[].attributes.body
Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept.

# data[].attributes.body
Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables.

# data[].attributes.body
Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.

# data[].attributes.body
Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions)

# data[].attributes.body
Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear.

# data[].attributes.body
Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.

# data[].attributes.body
Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

# data[].attributes.headline
Arithmetic w/Polynomials & Rational Expressions

# data[].attributes.subject
Arithmetic w/Polynomials & Rational Expressions

# data[].attributes.headline
Interpreting Categorical & Quantitative Data

# data[].attributes.subject
Interpreting Categorical & Quantitative Data

# data[].attributes.headline
Similarity, Right Triangles, and Trigonometry

# data[].attributes.subject
Similarity, Right Triangles, and Trigonometry