Grade 8 Overview The Number System [NS] Know that there are numbers that are not rational, and approximate them by rational numbers. Expressions and Equations [EE] Work with radicals and integer exponents. Understand the connections among proportional relationships, lines, and linear equations. Analyze and solve linear equations and pairs of simultaneous linear equations. Mathematical Practices 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. Functions [F] Define, evaluate, and compare functions. Use functions to model relationships between quantities. Geometry [G] Understand congruence and similarity using physical models, transparencies, or geometry software. Understand and apply the Pythagorean Theorem. Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres. Statistics and Probability [SP] Investigate patterns of association in bivariate data. Chalkable April 2015 1
First Quarter First Quarter 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. [8-NS1] Textbook: pp. 221 222, 224 226, 496-500 AMSTI: Looking for Pythagoras, Inv. 4 decimal expansion irrational non-terminating numbers rational repeats eventually terminating --distinguish between rational and irrational numbers. --show that the decimal representation of rational numbers terminates in 0 s or eventually repeats. --convert a repeating decimal into a fraction. 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. [8-NS2] Textbook: pp. 497 500, 500A 500B AMSTI: LFP, Inv. 4 approximation estimate number line value --find rational approximations of irrational numbers. --compare rational and irrational numbers on a number line. --locate the approximate location of irrational numbers on a number line. --estimate the value of an irrational expression. 8.3 Know and apply the properties of integer exponents to generate equivalent numerical expressions. [8-EE1] Textbook: pp. 195-205 AMSTI: Growing, Growing, Growing -- Inv. 5 equivalent numerical expressions integer exponents --infer the properties of integer exponents. --use laws of exponents to generate equivalent numerical expressions. 8.4 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. [8-EE2] Textbook: pp. 477 481, 497 AMSTI: Looking for Pythagoras, cube root equations irrational perfect cubes perfect squares positive rational numbers square root --use square root symbols to represent solutions to equations in the form x² = p where p is a positive rational number. --use cube root symbols to represent solutions to equations in the form x³ = p where p is a positive rational number. --recognize that squaring a number and taking the square root of a number are inverse operations. --recognize that cubing a number and taking the cube root of a number are inverse operations. --evaluate square root of small perfect squares. --evaluate the cube roots of small perfect cubes. --know that 2 is irrational. Chalkable April 2015 2
First Quarter First Quarter (continued) 8.5 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. [8-EE3] Textbook: pp. 205A 205B digit integer power of ten whole number --express very small and very large numbers using scientific notation. --compare quantities expressed in scientific notation. 8.6 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. [8-EE4] Textbook: pp. 206 210, 210A 210B, 211 AMSTI: Growing, Growing, Growing Inv. 5 ACE 56, 57, 60 decimal notation scientific notation --perform operations with numbers expressed in scientific notation. --perform operations with numbers expressed in both decimal form and scientific notation. --use scientific notation to choose units of appropriate size for measurement of very large or very small quantities. --interpret scientific notation that has been generated by technology. 8.25 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. [8-SP1] Textbook: pp. 48 50, 100, 12, 155, 382, 440 444, 445, 447A 447B, 630 LTF: Guess My Age bivariate data clustering linear association non-linear association outliers positive association negative association scatter plots --construct a scatter plot for bivariate measurement data. --interpret a scatter plot for bivariate measurement data. --investigate patterns associated between two quantities using a scatter plot. --describe patterns in a scatter plot. 8.26 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.[8-sp2] Textbook: pp. 440 444, 445 intercept linear associations scatter plots slope straight liens --recognize when a scatter plot represents a linear relationship. --informally fit a straight line for scatter plots that suggest a linear association. --informally assess the model fit by judging the closeness of the data to the points on the line. Chalkable April 2015 3
First Quarter First Quarter (continued) 8.28 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. [8-SP4] Textbook: pp. 647A 647B LTF: Does Gender Make a Difference columns frequencies relative frequencies rows --recognize that categorical data can also be described numerically through the use of a two-way table. --construct a two-way table summarizing data on two categorical variables collected from the same subjects. --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. First Quarter Notes: Chalkable April 2015 4
Second Quarter Second Quarter 8.7 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. [8-EE5] Textbook: pp. 408 410, 412 413, 415 419, 422 424, 436 437, 453A 453B LTF: Detecting Linear Motion graph proportional relationship slope unit rate --graph proportional relationships. --interpret the unit rate as a slope of the graph of a proportional relationship. --compare two different proportional relationships represented in different ways. 8.8 Use similar triangles to explain why the slope m is the same between any two distinct point on a nonvertical 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. [8-EE6] Textbook: pp. 420 425, 430 436, 437A 437B, 439-444 coordinate plane equation non-vertical line origin similar triangles slope vertical axis --use similar triangles to explain why the slope m is the same between any two distinct points on a nonvertical line in the coordinate plane. --derive the equation y = mx for a line through the origin. --derive the equation y = mx + b for a line intercepting the vertical axis at b. 8.9 Solve linear equations in one variable. [8-EE7] Textbook: pp. 91 101, 103 105, 120 132 linear equations AMSTI: Say It With Symbols, Inv. 1, 2, 3, and 4 8.9.a. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. 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). [8-EE7a] Textbook: pp. 131-132 equivalent equation simultaneous linear equations --give examples of linear equations in one variable with one solution. --give examples of linear equations in one variable with infinitely many solutions. --give examples of linear equations in one variable with no solutions. --use inverse operations and the properties of equality to solve linear equations in one variable. --interpret the number of solutions to a linear equation. Chalkable April 2015 5
Second Quarter Second Quarter (continued) 8.9.b. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. [8-EE7b] Textbook: pp. 91 101, 103 105, 107, 120 136 coefficients distributive property equations linear equations --solve linear equations with rational number coefficients and variables on both sides of the equation. --solve linear equations involving the distributive property. --solve linear equations involving collecting like terms. 8.11 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.) [8-F1] Textbook: pp. 401 406 LTF: Reading the Graph function graph input ordered pairs output --distinguish between functions and non-functions using equations, graphs, and tables 8.12 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [8-F2] Textbook, pp. 408 412, 414 425, 430 437, 453A 453B algebraically function graphically tables verbal descriptions --compare properties of two functions each represented in a different way 8.13 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. [8-F3] Textbook: pp. 408 412, 412A 412B, 430-435 Inv. 4 equation linear function non-linear function --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 LTF: Translation of Linear Functions 8.27 Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept.[8-sp3] Textbook: pp. 422 425, 431, 433 435, 437C 437D, 440-444 bivariate data equation intercept linear model slope --use the equation of a linear model to solve problems in the context of a linear problem. --interpret the slope of the equation of a linear model in the context of the problem. --interpret the y-intercept of the equations of a linear model in the context of the problem. Second Quarter Notes: Chalkable April 2015 6
Third Quarter Third Quarter 8.10 Analyze and solve pairs of simultaneous linear equations. [8-EE8] Textbook: pp. 453 458, 458A 458B, 459 simultaneous linear equations 8.10.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. [8-EE8a] Textbook: pp. 454-458 graphs intersection linear equations points of intersection simultaneously variables --define the solution to a system of equations as the intersection of their lines 8.10.b.Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. [8-EE8b] Textbook: pp. 453, 454 455, 458A 458B, 459 algebraically equations estimate graphing linear equations --solve systems of two linear equations in two variables algebraically --estimate the solution of two linear equations by graphing the equations --solve simple cases of a system of two linear equations by inspection --recognize that parallel lines have no solution and the same slope but different y-intercepts --recognize that two equations with the same slope and the same y-intercept have infinite solutions 8.10.c.Solve real-world and mathematical problems leading to two linear equations in two variables. [8-EE8c] Textbook: pp. 456-458 --solve real world problems leading to two linear equations in two variables 8.14 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. [8-F4] Textbook: pp. 422, 431 437, 439-445 AMSTI: Say It With Models, Inv. 2 LTF: Calculating Average Rates of Change LTF: What Really Bugs Me LTF: Reading the Graph function graph initial value of the function linear relationship rate of change table of values --construct a function to model a linear relationship between two quantities. --determine the rate of change 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. --determine the 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. Chalkable April 2015 7
Third Quarter Third Quarter (continued) 8.15 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. [8-F5] Textbook: pp. 412A 412B, 414 419, 439 AMSTI: Say It With Symbols, Inv. 4 LTF: Piecewise Functions decreasing functional relationship increasing linear non-linear qualitative features verbally --recognize if the slope of a linear function is positive, negative, zero or undefined. --recognize when a function is increasing or decreasing. --recognize when a function is linear or non-linear. --sketch a graph to model a given verbal situation. --describe a situation when given a graph. 8.16 Verify experimentally the properties of rotations, reflections, and translations: [8-G1] Textbook: pp. 705 722, 722A 722B LTF: Transformations and Tessellations reflections rotations translations --rotate geometric shapes in the coordinate plane. --reflect geometric shapes in the coordinate plane. --translate geometric shapes in the coordinate plane. 8.16.a. Lines are taken to lines, and line segment to line segments of the same length. [8-G1a] Textbook: pp. 705 722, 722A 722B LTF: The Water Park line segment lines --verify experimentally that lines that are rotated, reflected and/or translated transform to lines. --verify experimentally that line segments that are rotated, reflected and/or translated transform to line segments of the same length. 8.16.b. Angles are taken to angles of the same measure. [8-G1b] Textbook: pp. 705 722, 722A 722B angles --verify experimentally that angles that are rotated, reflected and/or translated transform to angles of the same measure. 8.16.c. Parallel lines are taken to parallel lines. [8-G1c] Textbook: pp. 722A 722B parallel lines --verify experimentally that parallel lines that are rotated, reflected and/or translated transform to parallel lines. Third Quarter Notes: Chalkable April 2015 8
Fourth Quarter Fourth Quarter 8.17 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. [8-G2] Textbook: pp. 298, 302 304, 705 709, 710 714, 715, 716 722, 722A 722B congruent reflections rotations translations two-dimensional figure --infer that a rigid transformation preserves original size and shape. --describe a sequence of transformations that exhibits the congruency between two figures. 8.18 Describe the effect of dilations, translations, rotations and reflections on two-dimensional figures using coordinates. [8-G3] Textbook: pp. 705 709, 710 716, 717 722, 723-727 coordinates dilations reflections rotations two-dimensional figures --describe the effect of dilations on two-dimensional figures using coordinates. --describe the effect of translations on twodimensional figures using coordinates. --describe the effect of rotations on twodimensional figures using coordinates. --describe the effect of reflections on twodimensional figures using coordinates. 8.19 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 twodimensional figures, describe a sequence that exhibits the similarity between them. [8-G4] Textbook: pp, 300, 302 303, 705 709, 710 716, 717 722, 723 727, 727A 727B dilations reflections rotations similar translations two-dimensional figures --determine that similar figures have angles with the same measure and sides that are proportional. --recognize that a dilation of a scale factor of greater than 1 will make the figure larger. --recognize that a dilation of a scale factor of less than 1 will make the figure smaller. --describe a sequence of transformations that exhibits the similarity between two figures. 8.20 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. [8-G5] Textbook: pp. 494, 691A -691B, 692 696, 697, 698-703 angle sum exterior angles informal argument parallel lines transversal triangles --use exploration and deductive reasoning to determine relationships that exists between interior and exterior sums of triangles. --use exploration and deductive reasoning to determine relationships that exists between angles created when parallel lines are cut by a transversal. --use exploration and deductive reasoning to determine relationships that exist between the angle-angle criterion for similarity of triangles. Chalkable April 2015 9
Fourth Quarter Fourth Quarter (continued) 8.21 Explain a proof of the Pythagorean Theorem and its converse. [8-G6] Textbook: pp. 493A 493B AMSTI: Looking for Pythagoras, Inv. 4 converse Pythagorean Theorem --explain a proof of the Pythagorean Theorem. --explain a proof of the Pythagorean Theorem converse. 8.22 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. [8-G7] Textbook: pp. 489 493, 497, 498, 509 514, 570 LTF: Pythagorean Theorem in Motion Pythagorean Theorem right triangle three-dimensions two-dimensions --apply the Pythagorean Theorem to determine unknown side lengths in right triangles in mathematical problems in two and three dimensions. --apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real world problems in two and three dimensions. 8.23 Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. [8-G8] Textbook: pp. 498, 502 coordinate system Pythagorean Theorem --apply the Pythagorean Theorem to find the distance between two points in a coordinate system. 8.24 Know the formulas for the volume of cones, cylinders, and spheres and use them to solve realworld and mathematical problems. [8-G9] Textbook: pp. 578 583, 586 591 LTF: Water Tanks and Sand Piles cone cylinder sphere volume --derive the formula for the volume of a cone. --derive the formula for the volume of a cylinder. --derive the formula for the volume of a sphere. --use the formulas to solve mathematical problems. --use the formulas to solve real-world problems. Fourth Quarter Notes: Second Semester Notes: I Can statements from ND, NC, and Utah. Chalkable April 2015 10
Assessment Schedule 1 st Nine Weeks Date: 2 nd Nine Weeks Date: 3 rd Nine Weeks Date: 4 th Nine Weeks Date: AL CCRS Standards AL CCRS Standards AL CCRS Standards AL CCRS Standards 1 2 3 4 5 6 25 26 28 7 8 9 9a 9b 11 12 13 27 10 10a 10b 10c 14 15 16 16a 16b 16c 17 18 19 20 21 22 23 24 Chalkable April 2015 11