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BGJHS 2013-2014 Pacing Guide (8th Grade Pre-Algebra) First Quarter Date Aug. 6-9 Unit Goals Students will solve problems involving radicals. Students will classify numbers as rational or irrational and use approximations to compare irrational numbers. Aug.12-16 Students will solve problems involving radicals. Students will classify numbers as rational or irrational and use approximations to I Can Statements I can evaluate square roots of small perfect squares. Common Core/ Program Studies 8.EE.2 – 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. 8.NS.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.EE.2 – 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. 8.NS.2 – Use rational approximations of irrational numbers to compare the size of I can find the solution(s) of equations of the form x2 = p. I can use reasoning to determine between which two consecutive whole numbers a square root will fall. I can plot the estimated value of an irrational number on a number line. I can estimate the value of an irrational number by rounding to a specific place value. I can estimate the value of an irrational number by rounding to a specific place value. I can estimate the value of an expression involving square roots by using the order of operations. I can use estimated values to compare two or more irrational or rational numbers. I can find the solution of equations of the Aug.19-23 compare irrational numbers. form x3 = p. Students will classify numbers as rational or irrational based on decimal expansions. I can classify a number as rational or irrational based on its decimal expansion. irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions. I can evaluate cube roots of small perfect cubes. 8.NS.1 - Understand informally that every number has a decimal expansion; the rational numbers are those with decimal expansions that terminate in 0s or eventually repeat. Know that other numbers are called irrational. 8.G.6 – Explain a proof of the Pythagorean Theorem and its converse. I can use visual models to demonstrate the relationship of the three side lengths of any right triangle. 8.G.6 – Explain a proof of the Pythagorean Theorem and its converse. I can use algebraic reasoning to relate the visual model to the Pythagorean Theorem. 8.G.7 – Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in realworld and mathematical problems in two and three dimensions. I can justify that the square root of a nonperfect square will be irrational. I can convert a repeating or terminating decimal into a rational number. Students will explain a proof of the Pythagorean Theorem and apply the Pythagorean Theorem to solve real-world problems. Aug. 26-30 Students will explain a proof of the Pythagorean Theorem and apply the Pythagorean Theorem to solve real-world problems. I can use visual models to demonstrate the relationship of the three side lengths of any right triangle. I can use algebraic reasoning to relate the visual model to the Pythagorean Theorem. I can use the Pythagorean Theorem to determine if a given right triangle is a right triangle. I can calculate the length of the hypotenuse or a leg of a right triangle using the Pythagorean Theorem. I can draw a diagram and use the Pythagorean Theorem to solve real-world problems involving right triangles. Sept. 3-6 Students will calculate distance using Pythagorean Theorem. I can connect any two points on a coordinate grid to a third point so that the three points form a right triangle. 8.G.8 – Apply the Pythagorean Theorem to find the distance between two points in coordinate system. 8.EE.1 – Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 32 x 3 – 5 = 3 – 3 = 1/33 = 1/27. 8.EE.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 x 108 and the population of the world as I can calculate the distance between two points on a coordinate grid using the Pythagorean Theorem. Review for Unit 1 assessment Summative Assessment over Unit 1 - Friday Sept. 9-13 Students will use exponent rules to simplify expressions. I can evaluate expressions with exponents. I can use the product properties of exponents to simplify expressions. I can use the quotient properties of exponents to simplify expressions. Sept. 16-20 Student will use scientific notation to solve real-world problems. I can convert a number from standard notation to scientific notation. I can convert a number from scientific notation to standard notation. I can compare quantities written in scientific notation, telling how much larger or smaller 7 x 109, and determine that the world population is more than 20 times larger. one is compared to the other. Sept. 17-21 Student will use scientific notation to solve real-world problems. I can add and subtract two numbers written in scientific notation. 8.EE.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. 8.EE.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 x 108 and the population of the world as 7 x 109, and determine that the world population is more than 20 times larger. 8.EE.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). I can multiply or divide numbers written in scientific notation. I can choose appropriate units of measure when using scientific notation. I can interpret scientific notation that has been generated from technology. Interpret scientific notation that has been generated by technology. Sept. 23-27 Student will use scientific notation to solve real-world problems. I can add and subtract two numbers written in scientific notation. 8.EE.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 x 108 and the population of the world as 7 x 109, and determine that the world population is more than 20 times larger. 8.EE.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. I can multiply or divide numbers written in scientific notation. I can choose appropriate units of measure when using scientific notation. I can interpret scientific notation that has been generated from technology. Review for Unit 2 assessment Summative Assessment over Unit 2 - Friday Sept. 30-Oct. 2 Oct. 3 - 11 Reteaching of Unit 1 and 2 Fall Break Reteaching of Unit 1 and 2 Reteaching of Unit 1 and 2 Fall Break Fall Break BGJHS 2013-2014 Pacing Guide (8th Grade Pre-Algebra) Second Quarter Date Unit Goal Oct. 14-18 Students will solve a one-variable equation. I Can Statements I can solve linear equations with one variable. Common Core/Program Studies 8.EE.7a – Solve linear equations in one variable. 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 successfully 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.EE.7b – Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. 8.EE.7a – Solve linear equations in one variable. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the I can solve linear equations with rational number coefficients. Oct. 21-25 Students will solve a one-variable I can solve linear equations with one variable. equation. I can solve linear equations with rational number coefficients. case by successfully 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). Oct. 28-Nov. Students will solve a one-variable I can solve linear equations with 1 one variable. equation. 8.EE.7b – Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. 8.EE.7a – Solve linear equations in one variable. 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 successfully 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.EE.7b – Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive I can give examples of linear equations that have one solution, infinitely many solutions, or no solutions. I can solve linear equations with rational number coefficients. I can solve multi-step equations that require the use of the distributive property and combining like terms. property and collecting like terms. Nov. 4-8 Students will solve a one-variable I can solve linear equations with one variable. equation. 8.EE.7a – Solve linear equations in one variable. 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 successfully 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.EE.7b – Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. 8.F.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. I can give examples of linear equations that have one solution, infinitely many solutions, or no solutions. I can solve linear equations with rational number coefficients. I can solve multi-step equations that require the use of the distributive property and combining like terms. Review for Unit 3 assessment Summative Assessment over Unit 3 - Friday Nov. 11-15 Students will define, evaluate, and I can explain that a function represents a relationship between compare functions. an input and an output. I can identify a function from a set of ordered pairs, a table, or a graph. I can give examples of relationships that are non-linear functions (from a table, graph, ordered pairs). Nov. 18-22 Students will use functions to I can match the graph of a model relationships between function to a given situation. quantities. I can write a story that describes 8.F.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 8.EE.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. the functional relationship between two variables depicted Students will graph, interpret, and on a graph. compare proportional relationships. I can create a graph of function that describes the relationship between two variables. I can graph proportional relationships in the coordinate plane. I can use a graph, a table, or an equation to determine the unit rate of a proportional relationship and use the unit rate to make comparisons between various proportional relationships. I can justify that the graph of a proportional relationship will always intersect the origin (0,0) of the graph. Nov. 25-26 Students will graph, interpret, and I can graph proportional compare proportional relationships. relationships in the coordinate 8.EE.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. 8.F.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. 8.F.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 8.EE.5 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different plane. I can use a graph, a table, or an equation to determine the unit rate of a proportional relationship and use the unit rate to make comparisons between various proportional relationships. I can justify that the graph of a proportional relationship will always intersect the origin (0,0) of the graph. Dec. 2-6 Students will define, evaluate, and Review for Unit 4 compare functions. assessment Summative Assessment Students will use functions to over Unit 4 - Friday model relationships between quantities. Students will graph, interpret, and compare proportional relationships. ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed. Dec. 9-13 Leaving This week extra due to days Will probably be finishing missed during the semester. function unit due to missing (EXPLORE, STAR, BENCHMARK TESTING, days throughout the semester ETC.) Leaving This week extra due to days missed during the semester. (EXPLORE,STAR/SMI,BENCHMARK TESTING/CIITS, ETC.) Dec. 16-20 FINAL EXAMS AND REVIEW FINAL EXAMS AND REVIEW FINAL EXAMS AND REVIEW Dec. 23Jan. 3 Winter break Winter break Winter break BGJHS 2013-2014 Pacing Guide (insert grade level here) Third Quarter Date Unit Goal Jan 6-10 Students will calculate the slope of a linear function given a graph, table, ordered pairs, equation, or realworld problem. I Can Statement Common Core/Program of Studies I can interpret the unit rate of a proportional relationship as the slope of the graph. 8.EE.6 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 and the equation y = mx + b for a line intercepting the vertical axis at b. I can use similar triangles to explain why the slope is the same between any two distinct points on a non-vertical line in the coordinate plane. I can calculate slope from a table, ordered pairs, or real world situation. Jan 13-17 Students will identify properties of a linear function. I can explain why the equation y =mx + b represents a linear function and interpret the slope and y-intercept in relation to the function. I can determine the properties of a function written in algebraic form (e.g., rate of change, meaning of y-intercept, linear, non-linear). I can determine the properties of a function when given the inputs and outputs in a table. I can determine the properties of a function represented as a graph. I can determine the properties of a function when given the situation verbally. Jan. 21-24 Students will identify properties of a linear function. I can compare the properties of two functions that are represented differently (e.g., as an equation, in a table, graphically or a verbal 8.EE.6 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 and the equation y = mx + b for a line intercepting the vertical axis at b. 8.F.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 = 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. 8.F.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. 8.F.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. 8.F.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 representation). I can write a linear function that models a given situation verbally, as a table of x and y values, or as a graph. I can define the initial value/y-intercept of the function in relation to the situation. represented by an algebraic expression, determine which function has the greater rate of change. 8.F.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. I can define the rate of change in relation to the situation. I can define the y-intercept in relation to the situation. Jan. 27-31 Students will compare properties of a linear function. I can compare the properties of two functions that are represented differently (e.g., as an equation, in a table, graphically or a verbal representation). Review for Unit 5 assessment Summative Assessment over Unit 5 - Friday Feb. 3-7 Students will solve systems of equations. 8.F.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 8.F.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. I can use the graphs of two linear equations to estimate the solution of the system. 8.EE.8: Analyze and solve pairs of simultaneous linear equations. I can solve a system of two equations by graphing. 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. 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. Feb. 10-14 Students will solve systems of equations. 1. I can solve a system of two equations using linear combinations (elimination.) 8.EE.8: Analyze and solve pairs of simultaneous linear equations. 2. I can solve a system of two equations 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. by inspection. Feb. 18-21 Students will solve systems of equations. I can solve real-world and mathematical problems that involve a system of two equations using graphing, substitution, linear combinations (elimination), or inspection. Review for Unit 6 assessment Summative Assessment over 8.EE.8: Analyze and solve pairs of simultaneous linear equations. c. Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair. Unit 6 - Friday Feb. 24-28 Students will transform figures on the I can define and identify a translation. 8.G.1 abc Verify experimentally the properties of rotations, reflections, and translations: a. Lines are taken to lines, and line segments coordinate plane. I can define and identify a reflection. I can define and identify a rotation. I can describe the changes occurring to the x and y coordinates of a figure after a translation. I can describe the changes occurring to the x and y coordinates of a figure after a reflection. to line segments of the same length. b. Angles are taken to angles of the same measure. c. Parallel lines are taken to parallel lines. 8.G.3 Describe the effect of dilations, translations, rotations, and reflections on twodimensional figures using coordinates. I can describe the changes occurring to the x and y coordinates of a figure after a rotation. I can translate a figure on a coordinate plane and use prime notation to describe the new points. I can reflect a figure on a coordinate plane and use prime notation to describe the new points. I can rotate a figure on a coordinate plane and use prime notation to describe the new points. Mar. 3-7 Students will justify whether two figures are congruent or I can describe the changes occurring to the x and y coordinates of a figure after 8.G.2 Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence similar based on the transformation that has taken place. a dilation. I can define congruency and identify the congruency symbol. I can use corresponding sides and angles to write a congruence statement. I can describe the sequence of rotations, reflections, and/or translations that will make a two-dimensional figure congruent to another figure. of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. 8.G.4 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. I can identify the corresponding angles and sides when given similar figures and use the similarity symbol to write a similarity statement. . I can describe a sequence of transformations to prove or disprove that two given figures are similar. Mar. 10-12 Students will use parallel lines and facts about triangles to calculate interior and exterior angle measures. I can prove that the sum of any triangle's interior angles will have the same measure as a straight angle. Students will prove similarity of triangles using the angle-angle similarity I can find an unknown angle (interior or exterior) using the exterior angle theorem. I can identify angle relationships created when parallel lines are cut by a transversal. I can prove triangles are similar using the 8.G.5 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. postulate. Mar. 13-14 angle-angle criterion. 3rd quarter break BGJHS 2013-2014 Pacing Guide (8th Grade Pre-Algebra) Fourth Quarter Date Unit Goal Mar. 17-21 Students will use parallel lines and facts about triangles to calculate interior and exterior angles. Mar. 24-28 I Can Statement I can prove that the sum of any triangle's interior angles will have the same measure as a straight angle. I can identify angle relationships created when parallel lines are cut by a transversal. Students will prove similarity of triangles using the angleangle similarity postulate. I can find an unknown angle (interior or exterior) using the exterior angle theorem. Students will find the volume I can use the formula to find the Common Core/Program of Studies 8.G.5 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 I can prove triangles are similar using the angle-angle criterion. 8.G.7: Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world of three dimensional figures. volume of a cone. Students will use Pythagorean theorem to calculate distances in a threedimensional figure. I can use the formula to find the volume of a sphere. I can use the formula to find the volume of a cylinder. and mathematical problems in two and three dimensions. 8.G.9: Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve realworld and mathematical problems. I can find the radii, height, or approximate for pi when given the volume of a cone, cylinder, or sphere. I can solve real-world problems involving the volume of cylinders, cones, and spheres. I can draw a diagram to find right triangles in a three-dimensional figure and use the Pythagorean Theorem to calculate various dimensions. Review for Unit 7 assessment Summative Assessment over Unit 7 - Friday Mar. 31-April 4 SPRING BREAK SPRING BREAK April 7-11 I can identify patterns or trends, Students will such as clustering, outliers, positive create scatterplots and or negative association, linear association, and nonlinear SPRING BREAK 8.SP.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 determine patterns in the data. association. I can construct a scatter plot on a coordinate grid representing the relationship between two data sets. I can interpret the patterns of association in a data sample. I can recognize whether or not data plotted on a scatter plot have a linear association. negative association, linear association, and nonlinear association. 8.SP.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. I can draw a straight trend line (line of best fit) to approximate the linear relationship between the plotted points of two data sets. April 14-17 Good Friday I can determine the equation of the trend line that approximates the linear relationship between the plotted points of two data sets. Students will create scatterplots and write equations I can interpret the y-intercept of the for the trend equation in the context of the line. collected data. I can interpret the slope of the equation in the context of the collected data. I can use the equation of the trend line to summarize the given data and make predictions regarding 8.SP.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. additional data points. April 21-25 Students will use bivariate categorical data to construct two-way table and to determine relative frequencies. I can create a two-way table to record the frequencies of bivariate categorical values. I can determine the relative frequencies for rows and/or columns of a two-way table. Review for Unit 8 assessment Summative Assessment over Unit 8 - Friday April 28-May 2 May 5-9 May 12-16 8.SP.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? Final Exam Review TESTING? Final Exam Review Final Exam Review TESTING? TESTING? Final Exam Review and Final Exams will be given Final Exam Review and Final Exams will be given Final Exam Review and Final Exams will be given May 19-22 May 20 election day Last day for students May 22 Pacing Guide should be sent to administrators on the Skydrive and will be used for walk-throughs.