## Standards.CCK-8 History

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<p><strong>7.EE-1.</strong> Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. <br />

<p><strong><a href="CC7EE-1" target="_blank">7.EE-1.</a></strong> Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. <br />

<p><strong><a href="CC8S-1" target="_blank">8.S-1.</a></strong> 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. <br />

<strong><a href="CC8S-2" target="_blank">8.S-2.</a></strong> 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. <br />

<strong><a href="CC8S-3" target="_blank">8.S-3.</a></strong> Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height. </p>

<strong><a href="CC8S-4" target="_blank">8.S-4.</a></strong> 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. For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores?

<p><strong><a href="CC8SP-1" target="_blank">8.S-1.</a></strong> 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. <br />

<strong><a href="CC8SP-2" target="_blank">8.S-2.</a></strong> 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. <br />

<strong><a href="CC8SP-3" target="_blank">8.S-3.</a></strong> Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height. </p>

<strong><a href="CC8SP-4" target="_blank">8.S-4.</a></strong> 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. For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores?

<p><strong>8.NS-1.</strong> 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. <br />

<strong>8.NS-2.</strong> 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., π<sup>2</sup>). For example, by truncating the decimal expansion of √2, show that √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations. </p>

<p><strong><a href="CC8NS-1" target="_blank">8.NS-1.</a></strong> 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. <br />

<strong><a href="CC8NS-2" target="_blank">8.NS-2.</a></strong> 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., π<sup>2</sup>). For example, by truncating the decimal expansion of √2, show that √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations. </p>

<p><strong>8.EE-1.</strong> Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3<sup>2</sup> × 3<sup>–5</sup> = 3<sup>–3</sup> = 1/3<sup>3</sup> = 1/27. <br />

<strong>8.EE-2.</strong> Use square root and cube root symbols to represent solutions to equations of the form x<sup>2</sup> = p and x<sup>3</sup> = 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. <br />

<strong>8.EE-3.</strong> 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. For example, estimate the population of the United States as 3 × 10<sup>8</sup> and the population of the world as 7 × 10<sup>9</sup> , and determine that the world population is more than 20 times larger. <br />

<strong>8.EE-4.</strong> 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 (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.</p>

<p><strong><a href="CC8EE-1" target="_blank">8.EE-1.</a></strong> Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3<sup>2</sup> × 3<sup>–5</sup> = 3<sup>–3</sup> = 1/3<sup>3</sup> = 1/27. <br />

<strong><a href="CC8EE-2" target="_blank">8.EE-2.</a></strong> Use square root and cube root symbols to represent solutions to equations of the form x<sup>2</sup> = p and x<sup>3</sup> = 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. <br />

<strong><a href="CC8EE-3" target="_blank">8.EE-3.</a></strong> 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. For example, estimate the population of the United States as 3 × 10<sup>8</sup> and the population of the world as 7 × 10<sup>9</sup> , and determine that the world population is more than 20 times larger. <br />

<strong><a href="CC8EE-4" target="_blank">8.EE-4.</a></strong> 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 (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.</p>

<p><strong>8.EE-5.</strong> Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed. <br />

<strong>8.EE-6.</strong> 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. </p>

<p><strong><a href="CC8EE-5" target="_blank">8.EE-5.</a></strong> Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed. <br />

<strong><a href="CC8EE-6" target="_blank">8.EE-6.</a></strong> 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. </p>

<p><strong>8.EE-7.</strong> Solve linear equations in one variable. <br />

<p><strong><a href="CC8EE-7" target="_blank">8.EE-7.</a></strong> Solve linear equations in one variable. <br />

<strong>8.EE-8.</strong> Analyze and solve pairs of simultaneous linear equations. <br />

<strong><a href="CC8EE-8" target="_blank">8.EE-8.</a></strong> Analyze and solve pairs of simultaneous linear equations. <br />

<p><strong>8.F-1.</strong> 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. (Function notation is not required in Grade 8.) <br />

<strong>8.F-2.</strong> Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change. <br />

<strong>8.F-3.</strong> 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. For example, the function A = s2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line. </p>

<p><strong><a href="CC8F-1" target="_blank">8.F-1.</a></strong> 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. (Function notation is not required in Grade 8.) <br />

<strong><a href="CC8F-2" target="_blank">8.F-2.</a></strong> Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change. <br />

<strong><a href="CC8F-3" target="_blank">8.F-3.</a></strong> 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. For example, the function A = s2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line. </p>

<p><strong>8.F-4.</strong> 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. <br />

<strong>8.F-5.</strong> 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. </p>

<p><strong><a href="CC8F-4" target="_blank">8.F-4.</a></strong> 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. <br />

<strong><a href="CC8F-5" target="_blank">8.F-5.</strong> 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. </p>

<p><strong>8.G-1.</strong> Verify experimentally the properties of rotations, reflections, and translations: <br />

<p><strong><a href="CC8G-1" target="_blank">8.G-1.</a></strong> Verify experimentally the properties of rotations, reflections, and translations: <br />

<strong>8.G-2.</strong> 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. <br />

<strong>8.G-3.</strong> Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. <br />

<strong>8.G-4.</strong> 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. <br />

<strong>8.G-5.</strong> 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. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so. </p>

<strong><a href="CC8G-2" target="_blank">8.G-2.</a></strong> 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. <br />

<strong><a href="CC8G-3" target="_blank">8.G-3.</a></strong> Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. <br />

<strong><a href="CC8G-4" target="_blank">8.G-4.</a></strong> 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. <br />

<strong><a href="CC8G-5" target="_blank">8.G-5.</a></strong> 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. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so. </p>

<p><strong>8.G-6</strong>. Explain a proof of the Pythagorean Theorem and its converse. <br />

<strong>8.G-7.</strong> Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. <br />

<strong>8.G-8.</strong> Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. </p>

<p><strong><a href="CC8G-6" target="_blank">8.G-6.</a></strong> Explain a proof of the Pythagorean Theorem and its converse. <br />

<strong><a href="CC8G-7" target="_blank">8.G-7.</a></strong> Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. <br />

<strong><a href="CC8G-8" target="_blank">8.G-8.</a></strong> Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. </p>

<p><strong>8.G-9.</strong> Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. </p>

<p><strong><a href="CC8G-9" target="_blank">8.G-9.</a></strong> Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. </p>

<p><strong>8.S-1.</strong> 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. <br />

<strong>8.S-2.</strong> 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. <br />

<strong>8.S-3.</strong> Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height. </p>

<strong>8.S-4.</strong> 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. For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores?

<p><strong><a href="CC8S-1" target="_blank">8.S-1.</a></strong> 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. <br />

<strong><a href="CC8S-2" target="_blank">8.S-2.</a></strong> 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. <br />

<strong><a href="CC8S-3" target="_blank">8.S-3.</a></strong> Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height. </p>

<strong><a href="CC8S-4" target="_blank">8.S-4.</a></strong> 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. For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores?

<strong>8.EE-2.</strong> 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. <br />

<strong>8.EE-3.</strong> 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. For example, estimate the population of the United States as 3 × 108 and the population of the world as 7 × 109 , and determine that the world population is more than 20 times larger. <br />

<strong>8.EE-2.</strong> Use square root and cube root symbols to represent solutions to equations of the form x<sup>2</sup> = p and x<sup>3</sup> = 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. <br />

<strong>8.EE-3.</strong> 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. For example, estimate the population of the United States as 3 × 10<sup>8</sup> and the population of the world as 7 × 10<sup>9</sup> , and determine that the world population is more than 20 times larger. <br />

<strong>8.NS-2.</strong> 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). For example, by truncating the decimal expansion of √2, show that √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations. </p>

<strong>8.NS-2.</strong> 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., π<sup>2</sup>). For example, by truncating the decimal expansion of √2, show that √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations. </p>

<p><strong>8.EE-1.</strong> Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 32 × 3–5 = 3–3 = 1/33 = 1/27. <br />

<p><strong>8.EE-1.</strong> Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3<sup>2</sup> × 3<sup>–5</sup> = 3<sup>–3</sup> = 1/3<sup>3</sup> = 1/27. <br />

<p><strong>7.RP-1.</strong> 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.<br />

<strong> 7.RP-2.</strong> Recognize and represent proportional relationships between quantities. <br />

<p><strong><a href="CC7RP-1" target="_blank">7.RP-1.</a></strong> 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.<br />

<strong><a href="CC7RP-2" target="_blank">7.RP-2.</a></strong> Recognize and represent proportional relationships between quantities. <br />

<strong>7.RP-3.</strong> 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.</p>

<strong><a href="CC7RP-3" target="_blank">7.RP-3.</a></strong> 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.</p>

<p><strong>7.NS-1.</strong> Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. <br />

<p><strong><a href="CC7NS-1" target="_blank">7.NS-1.</a></strong> Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. <br />

<strong>7.NS-2.</strong> Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. <br />

<strong><a href="CC7NS-2" target="_blank">7.NS-2.</a></strong> Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. <br />

<strong>7.NS-3</strong>. Solve real-world and mathematical problems involving the four operations with rational numbers. (Computations with rational numbers extend the rules for manipulating fractions to complex fractions.)</p>

<strong><a href="CC7NS-3" target="_blank">7.NS-3</a></strong>. Solve real-world and mathematical problems involving the four operations with rational numbers. (Computations with rational numbers extend the rules for manipulating fractions to complex fractions.)</p>

<strong>7.EE-2.</strong> 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. For example, a + 0.05a = 1.05a means that “increase by 5%” is the same as “multiply by 1.05.” </p>

<strong><a href="CC7EE-2" target="_blank">7.EE-2.</a></strong> 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. For example, a + 0.05a = 1.05a means that “increase by 5%” is the same as “multiply by 1.05.” </p>

<p><strong>7.EE-3.</strong> 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. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation. <br />

<strong>7.EE-4.</strong> 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. <br />

<p><strong><a href="CC7EE-3" target="_blank">7.EE-3.</a></strong> 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. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation. <br />

<strong><a href="CC7EE-4" target="_blank">7.EE-4.</a></strong> 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. <br />

<p><strong>7.G-1.</strong> 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. <br />

<p><strong><a href="CC7G-1" target="_blank">7.G-1.</a></strong> 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. <br />

<p><strong>7.SP-1.</strong> 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. <br />

<strong>7.SP-2.</strong> 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. Draw informal comparative inferences about two populations. <br />

<strong>7.SP-3.</strong> 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. <br />

<strong>7.SP-4.</strong> 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. Investigate chance processes and develop, use, and evaluate probability models. <br />

<strong>7.SP-5.</strong> 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.<br />

<strong>7.SP-6.</strong> 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. <br />

<strong>7.SP-7.</strong> 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. <br />

<p><strong><a href="CC7SP-1" target="_blank">7.SP-1.</a></strong> 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. <br />

<strong><a href="CC7SP-2" target="_blank">7.SP-2.</a></strong> 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. Draw informal comparative inferences about two populations. <br />

<strong><a href="CC7SP-3" target="_blank">7.SP-3.</a></strong> 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. <br />

<strong><a href="CC7SP-4" target="_blank">7.SP-4.</a></strong> 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. Investigate chance processes and develop, use, and evaluate probability models. <br />

<strong><a href="CC7SP-5" target="_blank">7.SP-5.</a></strong> 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.<br />

<strong><a href="CC7SP-6" target="_blank">7.SP-6.</a></strong> 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. <br />

<strong><a href="CC7SP-7" target="_blank">7.SP-7.</a></strong> 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. <br />

<strong>7.SP-8.</strong> Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.<br />

<strong><a href="CC7SP-8" target="_blank">7.SP-8.</a></strong> Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.<br />

<strong>7.G-2.</strong> 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. <br />

<strong>7.G-3.</strong> Describe the two-dimensional figures that result from slicing three- dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. </p>

<strong><a href="CC7G-2" target="_blank">7.G-2.</a></strong> 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. <br />

<strong><a href="CC7G-3" target="_blank">7.G-3.</a></strong> Describe the two-dimensional figures that result from slicing three- dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. </p>

<p><strong>7.G-4.</strong> 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. <br />

<strong>7.G-5.</strong> 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.<br />

<strong>7.G-6.</strong> 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. </p>

<p><strong><a href="CC7G-4" target="_blank">7.G-4.</a></strong> 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. <br />

<strong><a href="CC7G-5" target="_blank">7.G-5.</a></strong> 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.<br />

<strong><a href="CC7G-6" target="_blank">7.G-6.</a></strong> 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. </p>

<strong>7.G-2.</strong> 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. <br />

<strong>7.G-3.</strong> Describe the two-dimensional figures that result from slicing three- dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. </p>

<strong>7.G-2.</strong> 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. <br />

<strong>7.G-3.</strong> Describe the two-dimensional figures that result from slicing three- dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. </p>

<p><strong>7.G-4.</strong> 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. <br />

<strong>7.G-5.</strong> 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.<br />

<strong>7.G-6.</strong> 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. </p>

<p><strong>7.G-4.</strong> 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. <br />

<strong>7.G-5.</strong> 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.<br />

<strong>7.G-6.</strong> 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. </p>

[]K-8 Standards Common Core State Standards 9-12

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<p><strong></strong> Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. </p>

<strong></strong> Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape.

<p><strong><a href="http://www.mathcasts.org/mtwiki/Standards/CC3G-1" target="_blank">3.G-1.</a></strong> Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. </p>

<strong><a href="http://www.mathcasts.org/mtwiki/Standards/CC3G-2" target="_blank">3.G-2.</a></strong> Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape.

<p><strong>3.G-1.</strong> Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. </p>

<strong>3.G-2.</strong> Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape.

<p><strong></strong> Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. </p>

<strong></strong> Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape.

<h3><a name="_K.CC_Counting_and" id="_K.CC_Counting_and"></a>K.CC Counting and Cardinality </h3>

<h4>Know number names and the count sequence. </h4>

<h4 style="color:#008000"><a name="_K.CC_Counting_and" id="_K.CC_Counting_and"></a>K.CC Counting and Cardinality </h4>

<h5 style="color:#990099">Know number names and the count sequence. </h5>

<h4>Count to tell the number of objects. </h4>

<h5 style="color:#990099">Count to tell the number of objects. </h5>

<h4>Compare numbers. </h4>

<h5 style="color:#990099">Compare numbers. </h5>

<h3><a name="_K.OA_Operations_and" id="_K.OA_Operations_and"></a>K.OA Operations and Algebraic Thinking </h3>

<h4>Understand addition as putting together and adding to, and under- stand subtraction as taking apart and taking from. </h4>

<h4 style="color:#008000"><a name="_K.OA_Operations_and" id="_K.OA_Operations_and"></a>K.OA Operations and Algebraic Thinking </h4>

<h5 style="color:#990099">Understand addition as putting together and adding to, and under- stand subtraction as taking apart and taking from. </h5>

<h3><a name="_K.NBT_Number_and" id="_K.NBT_Number_and"></a>K.NBT Number and Operations in Base Ten </h3>

<h4>Work with numbers 11–19 to gain foundations for place value. </h4>

<h4 style="color:#008000"><a name="_K.NBT_Number_and" id="_K.NBT_Number_and"></a>K.NBT Number and Operations in Base Ten </h4>

<h5 style="color:#990099">Work with numbers 11–19 to gain foundations for place value. </h5>

<h3><a name="_K.MD_Measurement_and" id="_K.MD_Measurement_and"></a>K.MD Measurement and Data </h3>

<h4>Describe and compare measurable attributes. </h4>

<h4 style="color:#008000"><a name="_K.MD_Measurement_and" id="_K.MD_Measurement_and"></a>K.MD Measurement and Data </h4>

<h5 style="color:#990099">Describe and compare measurable attributes. </h5>

<h4>Classify objects and count the number of objects in each category. </h4>

<h5 style="color:#990099">Classify objects and count the number of objects in each category. </h5>

<h3><a name="_K.G_Geometry" id="_K.G_Geometry"></a>K.G Geometry </h3>

<h4>Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres). </h4>

<h4 style="color:#008000"><a name="_K.G_Geometry" id="_K.G_Geometry"></a>K.G Geometry </h4>

<h5 style="color:#990099">Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres). </h5>

<h4>Analyze, compare, create, and compose shapes. </h4>

<h5 style="color:#990099">Analyze, compare, create, and compose shapes. </h5>

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<h2>K - Standards</h2>

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[c]Printer-friendly PDF (Word doc file available on request.)

[c]Printer-friendly PDF (Word doc file available on request.)

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