# Mathematics Common Core Cluster. Mathematics Common Core Standard. Domain

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1 Mathematics Common Core Domain Mathematics Common Core Cluster Mathematics Common Core Standard Number System Know that there are numbers that are not rational, and approximate them by rational numbers. Number System Know that there are numbers that are not rational, and approximate them by rational numbers. NS.8.1 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. NS.8.2 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^2). For example, by truncating the decimal expansion of 2 (square root 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. Expressions & Equations Work with radicals and integer exponents. EE.8.1 Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3^2 3^( 5) = 3^( 3) = 1/(3^3) = 1/27. Expressions & Equations Work with radicals and integer exponents. EE.8.2 Use square root and cube root symbols to represent solutions to equations of the form x^2 = p and x^3 = 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. Page 1 of 35

2 Expressions & Equations Work with radicals and integer exponents. EE.8.3 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 10^8 and the population of the world as 7 10^9, and determine that the world population is more than 20 times larger. Expressions & Equations Work with radicals and integer exponents. EE.8.4. 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. Expressions & Equations Understand the connections between proportional relationships, lines, and linear equations. EE.8.5 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. Expressions & Equations Understand the connections between proportional relationships, lines, and linear equations. EE.8.6 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. Page 2 of 35

3 Expressions & Equations Analyze and solve linear equations and pairs of simultaneous linear equations. EE.8.7 Solve linear equations in one variable. Expressions & Equations Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. EE.8.7.a Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers). Expressions & Equations Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. EE.8.7.b Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. Expressions & Equations Analyze and solve linear equations and pairs of simultaneous linear equations. EE.8.8 Analyze and solve pairs of simultaneous linear equations. Expressions & Equations Analyze and solve linear equations and pairs of simultaneous linear equations. EE.8.8.a Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously. Expressions & Equations Analyze and solve linear equations and pairs of simultaneous linear equations. EE.8.8.b Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6. Functions Define, evaluate, and compare functions. F.8.1 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 ) Page 3 of 35

4 Functions Define, evaluate, and compare functions. F.8.2 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. Functions Define, evaluate, and compare functions. F.8.3 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 = s^2 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. Functions Use functions to model relationships between quantities. F.8.4 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. Functions Use functions to model relationships between quantities. F.8.5 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. Geometry Understand congruence and G.8.1 Verify experimentally the properties of rotations, similarity using physical models, reflections, and translations: transparencies, or geometry -- a. Lines are taken to lines, and line segments to line software. segments of the same length. -- b. Angles are taken to angles of the same measure. -- c. Parallel lines are taken to parallel lines. Page 4 of 35

5 Geometry Understand congruence and G.8.2 Understand congruence and similarity using physical similarity using physical models, models, transparencies, or geometry software. Understand transparencies, or geometry that a two-dimensional figure is congruent to another if the software. 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. Geometry Understand congruence and G.8.3 Describe the effect of dilations, translations, rotations similarity using physical models, and reflections on two-dimensional figures using transparencies, or geometry coordinates. software. Geometry Understand congruence and G.8.4 Understand that a two-dimensional figure is similar to similarity using physical models, another if the second can be obtained from the first by a transparencies, or geometry sequence of rotations, reflections, translations, and dilations; software. given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them. Page 5 of 35

6 Geometry Understand congruence and G.8.5 Use informal arguments to establish facts about the similarity using physical models, angle sum and exterior angle of triangles, about the angles transparencies, or geometry created when parallel lines are cut by a transversal, and the software. angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the three angles appear to form a line, and give an argument in terms of transversals why this is so. Geometry Understand and apply the Pythagorean Theorem. G.8.6 Explain a proof of the Pythagorean Theorem and its converse. Geometry Geometry Understand and apply the Pythagorean Theorem. Understand and apply the Pythagorean Theorem. G.8.7 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. G.8.8 Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. Geometry Solve real-world and mathematical problems involving volume of cylinders, cones and spheres. G.8.9 Know the formulas for the volume of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. Statistics & Probability Investigate patterns of association in bivariate data. SP.8.1 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. Statistics & Probability Investigate patterns of association in bivariate data. SP.8.2 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. Statistics & Probability Investigate patterns of association in bivariate data. SP.8.3 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. Page 6 of 35

7 Statistics & Probability Investigate patterns of association in bivariate data. SP.8.4 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? Page 7 of 35

8 Algebra 1 Suggested Resources Months Taught Quarter Assessed Algeba 1 1-3, 3-8, Buckle Down, Tasks October 1st Algebra 1 1-3, 3-8, Buckle Down, Tasks October 1st Algebra 1 1-2, 8-1, 8-3, 8-4, 8-5, Buckle Down, Tasks February 2nd Algebra 1 1-2, Buckle Down, Tasks October 1st Page 8 of 35

9 Algebra 1 8-2, Course 3 w/s 12-5, Buckle Down, Tasks February 3rd Algebra 1 8-3, Course 3 w/s 12-3,w/s 12-5, Activity labs 2-8a, 12-3b, Buckle Down, Tasks, February 3rd Algebra 1 5-5, 5-6, Course 3 Activity lab 11-4a, Buckle Down, Tasks November 2nd Algebra 1 6-1, 6-2, 6-4,6-5,6-6, Buckle Down, Tasks November 2nd Page 9 of 35

10 Algebra 1 2-1,3-2,3-2,3-6,3-7,4-1, 4- January 2,4-3,4-4,7-5, Buckle Down Tasks 3rd Algebra 1 3-1, 3-2, 3-3, 3-6, 3-7, 4-1, 4-2, 4-3, 4-4, 7-5, Buckle Down, Tasks January 3rd Algebra 1 2-4, 3-2, 3-3, 3-6, 3-7, Buckle Down, Tasks January 3rd Algebra 1 7-1, 7-2, 7-3, 7-4, 7-6, Buckle Down, Tasks February 3rd Algebra 1 7-1,7-4, 7-6, Buckle Down, Tasks, February 3rd Algebra 1 7-2, 7-3, 7-4, Buckle Down, Tasks February 3rd Algebra 1 1-4, 3-1, 5-1, 5-2, Buckle Down, Tasks November 2nd Page 10 of 35

11 Algebra 1 1-4, 5-4, Buckle Down, Tasks November 2nd Algebra 1 5-3, Course 3 w/s 11-5, w/s 11-7 Buckle Down, Tasks November, January 2nd, 3rd Algebra 1 5-1, 5-2,6-3, Course 3 Activity lab 3-5b, 11-4a, Buckle Down, Tasks November 2nd Algebra 5-1, 5-2, 5-5, Course 3 w/s 11-2, w/s 11-6, Buckle Down, Tasks November, January 2nd, 3rd Course 3 w/s 3-6, w/s3-7, w/s3-8 Activity Lab 3-7a, 3-8a, Buckle Down, Tasks August 1st Page 11 of 35

12 Course 3 w/s 7-3, Buckle Down, Tasks September 1st Course 3 w/s 3-6, w/s 3-7, w/s 3-8, w/s 4-5, Buckle Down, Tasks September 1st Course 3 w/s 4-4, w/s 4-5, Buckle Down, Tasks September 1st Page 12 of 35

13 Course 3 w/s 4-4, w/s 7-2, Buckle Down, Tasks, Activity Lab 7-5a, Supplemental material September, March 1st, 4th Algebra 1 3-9, 3-9A, Buckle Down, Tasks October 2nd Algebra 1 3-9, 3-9A, Buckle Down, Tasks October 2nd Algebra #49-55, Course 3 w/s 3-4, Buckle Down, Tasks October 2nd Course 3 w/s 8-6, w/s 8-7, w/s 8-8, Buckle Down, Tasks April 4th Algebra 1 1-5,Course 3 Activity lab 9-7a, Buckle Down, Tasks December 2nd Algebra 1 6-7, Buckle Down, Tasks December 2nd Algebra 1 6-7, Buckle Down, Tasks, Supplemental material December 2nd Page 13 of 35

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