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Eighth Grade * Common Core Mathematics Domain Target Number System Cluster Target * I know there are numbers that are not rational and I can approximate them with rational numbers. Number System * I know there are numbers that are not rational and I can approximate them with rational numbers. Domain & Standard Learning Target A Specific Example Standard Number System * Number System * Number System * Number System * Number System * Number System 8.NS-1. Know that numbers that are not I can explain the difference between rational and Rational numbers can be expressed rational are called irrational. Understand irrational numbers. as a fraction of integers. informally that every number has a decimal 8.NS-1 expansion; for rational numbers show that the All rational numbers repeat as a decimal expansion repeats eventually, and I can identify and explain the decimal expansion for decimal. (If you define terminating convert a decimal expansion which repeats rational numbers. decimals as repeating zeros) eventually into a rational number. 8.NS-2. Use rational approximations of irrational numbers to compare the size of I can find the approximate value of a irrational numbers irrational numbers, locate them approximately by a system of better approximations. on a number line diagram, and estimate the 8.NS-2 Expressions and Equations * Expressions and Equations 8.EE-1 value of expressions (e.g., pi2). 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. * Expressions and Equations * 8.EE-1. Know and apply the properties of integer exponents to generate equivalent numerical expressions. For * Expressions and Equations I can simplify expressions with integer exponents. * I can work with radicals and integer exponents. 8.EE-3 8.EE-4 print date 1/18/13 I can evaluate the square roots of small perfect squares. the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots I can evaluate the cube roots of small perfect cubes. of small perfect cubes. Know that √2 is I know 2 is irrational. irrational. 8.EE-3. Use numbers expressed in the form of a single digit times an integer power of 10 to I can express very large and small numbers in scientific estimate very large or very small quantities, ! ! notation. 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. 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. * Express 2.999… as a fraction of integers in lowest terms. John says that 3.121231234… is rational because it repeats. Jane says it is irrational. Explain who is correct and why. Between what two integers is √120 located? Expressions and Equations Simplify 32 x 3-5 example, 32 × 3–5 = 3–3 = (1/3)3 = 1/27. I can solve simple equations involving squares and 8.EE-2. Use square root and cube root Solve for x: x3 = 27 symbols to represent solutions to equations of cubes. 8.EE-2 Number System Find the √3 to two decimal places by Find the √12 accurate to 1 decimal place a series of division estimates. without a calculator. I can locate the approximate the value of an irrational Point on the number line where the number on a number line. square root of 15 is located. Expressions and Equations ONE Example of Assessment * * Expressions and Equations Simplify 23 x 3-3 x 2-4 x 35 Solve for x: 2x2 + 3x2 = 35 Find the square root of 36. Find the cube root of 27. Find the cube root of 27. What is the square root of 49? Is 2 rational or irrational? * Identify each as rational or irrational. 1 2 4 Express the number 3, 480, 000 in Write the number equivalent to 3.5 X 10-3 in scientific notation. ! standard ! ! notation. I can determine the proportional difference between How many times larger is 4 x 103 scientific numbers. than 4 x 10-3? I can add, subtract, multiply, and divide combinations of Calculate (3 x 104)(4 x 103) numbers in scientific notation. The distance from Vonnie's house to I can appropriately use scientific notations and units of the capital is 4.2 x 105 meters. What measurement in real-world situations. would it be in km? John's spreadsheet displays a I can explain scientific notation generated by technology. number as 5.3E-2. How would this be written in scientific notation? The population of the United States is about 3 x 108 and the population of India is 1.2 x 109. How many times larger is India's population? Calculate (6 x 10-3) divided by 4, 000. The speed of light is 3x108m/sec. The sun is 150,000,000km from the sun. How long does it take light to reach the earth? How would a calculator or spreadsheet display a number in scientific notation like 3.5 x 10-7? page 1 of 6 Eighth Grade * Common Core Mathematics Domain Target Cluster Target Domain & Standard 8.EE-5 I understand the connections between proportional relationships, lines, and linear equations. I can create and explain the attributes of linear equations. 8.EE-6 I can solve linear equations and pairs of simultaneous linear equations to answer real-world problems. Standard 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.EE-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. Learning Target A Specific Example I can explain proportional relationships with a graph. Car A Car B If the horizontal axis is time and the vertical axis is distance for a moving car, what do you know about each vehicle? What would you need to know before you can Car B's rate can be expressed as accurately compare the speed of Car A and Car B? s=10 miles/5 min. I can compare two proportional relationships when one is Car A a graph and the other an equation. Explain how you can use right triangles to prove the slope is the same no matter what two points you choose on a line. I can explain the constant slope of a line using points on the line and similar triangles I can determine the equation of a line given on a coordinate graph. ONE Example of Assessment 5 What is the equation of the line displayed at the left if it crosses the y-axis at 5 and has a slope of -1/3? 8.EE-7. Solve linear equations in one variable. 8.EE-7a 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). Simplify the following equation until you can determine whether it will have one, none, or an infinite I can classify linear equations that have one solution, solution set and explain how you infinite solutions, and no solutions. know. How many solutions will the following equation have? 3(4x - 7) + 5 = 2(6x -8) 12x - 3 = 4(3 + 3x) 8.EE-7. Solve linear equations in one variable. 8.EE-7b I can analyze and solve linear equations and pairs of simultaneous 8.EE-8a linear equations. 8.EE-8b print date 1/18/13 b. Solve linear equations with rational number coefficients, including equations whose I can solve any linear equation with rational numbers. solutions require expanding expressions using the distributive property and collecting like terms. 8.EE-8. Analyze and solve pairs of simultaneous linear equations. 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.EE-8. Analyze and solve pairs of simultaneous linear equations. Solve for x: 2 1 5( x + 3) " 4 = (x " 8) " x 5 2 ! 5 2 1 2 1 ( x + 3) " 4 = (x " ) + 2 x 2 5 2 3 2 ! If you know that a pair of I can explain how a solution to a pair of simultaneous simultaneous linear equations have equations relates to the intersection of their graphs. no common solution, how would you describe their graphs? I can solve a system of linear equations algebraically. Solve for y: Solve algebraically: 2x - y = 5 x + y = -2 Graph to find the solution: x-y=4 x + y = -2 If you know that a pair of simultaneous linear equations have only one solution of x=3 and y=-5, what all the details you can say about their graphs? Solve algebraically: 2x - 4y = -6 y=3 Graph to find the solution: x-y=4 2 x = -2 + 2y b. Solve systems of two linear equations in two variables algebraically, and estimate I can solve a system of linear equations graphically. solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + How many solutions for this system? 2y = 5 and 3x + 2y = 6 have no solution I can determine solutions or special conditions to simple Write an equation that will have an infinite x-y=4 because 3x + 2y cannot simultaneously be 5 linear simultaneous equations mentally. solution set with the equation 2x - y = 7. 2 x = 8 + 2y and 6. page 2 of 6 Eighth Grade * Common Core Mathematics Domain Target Domain & Standard Cluster Target Standard Learning Target A Specific Example ONE Example of Assessment 8.EE-8. Analyze and solve pairs of simultaneous linear equations. 8.EE-8c Functions * Functions * Functions * 8.F-1 c. Solve real-world and mathematical I can solve real-world problems using simultaneous problems leading to two linear equations in equations. 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. Functions * Functions * Functions * Functions * Functions * I can define and explain in my words what function is 8.F-1. Understand that a function is a rule that assigns to each input exactly one output. and how it relates to input/output tables at earlier grades. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. [1] print date 1/18/13 Functions * Functions * Functions * Functions * Write the definition of a function and Explain the different ways a function may be give an example. displayed. From an in-out table, list the ordered List the ordered pairs from the rule; "add 3" pairs and graph the points. and then graph the line from these pairs. 8.F-2 8.F-2. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in I can compare the properties of two functions that are Click on link to the right to see the tables, or by verbal descriptions). For Matching graphs, tables, and example, given a linear function represented displayed in different ways (equation, graph, table, or function match game available on the equations words) internet. 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-3 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. I can define, evaluate, and compare functions. I can explain the important attributes of functions and use them to model relationships. I can explain how the graph of a function relates to its set of ordered pairs. The length of a rectangle is twice its Two tables and 3 chairs together cost $2,000 width. The perimeter is 30. Find its whereas 3 tables and 2 chairs together cost dimensions. $2,500. Find the cost of a table and a chair. I can rewrite linear equations in the form of y = mx + b. Rewrite 3x - 5y = 10 as a linear equation in slope-intercept form. Write an equation for the linear function where the slope = 2 and the y-intercept is 3. I can recognize when an equation is a linear function. Explain why 2x - y = 7 is a linear function. Select all the functions that are linear. x - y = 3; y = -2; 1/2x = 3y; 1/x + y = 2 I can generate functions that are not linear and explain why they are not linear. Bob says that 1/x + y = 3 is linear because Generate a function that is not linear there are no exponents. Sally disagrees. and explain why. Who is correct and why? page 3 of 6 I can explain the important attributes of functions and use them to model Domain relationships. Target Eighth Grade * Common Core Mathematics Domain & Standard Cluster Target 8.F-4 I can use functions to model relationships between quantities. 8.F-5 Geometry * Geometry * Geometry * Geometry Standard Learning Target 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-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. A Specific Example I can create an equation to model two quantities that are linear. I can determine the rate of change when given a linear relationship shown by a table or graph. 8.G-1c 8.G-2 I can explain congruence and similarity in a variety of ways. 8.G-3. print date 1/18/13 I can explain congruence, similarity, the Pythagorean Y 2 4 6 5 7 9 I can determine the initial value when given a linear relationship shown by a table or graph. I can explain what the a linear relationship in I can explain what the linear relationship in a After driving a 20 miles, Todd has 5 gallons in his motorcycle. Driving rate of change means when given another 100 miles he now has 3 gal a real-world situation. in his tank. How many miles per initial value means when given a gallon is he getting? How much gas did he start with? real-world situation. The graph at the right has a slope of -1/3. What function describes this graph and what is the rate of change? 5 Week John is saving for a new 3 smart phone shown by the table. Write the equation 4 the describes this table. How 5 much money did he start with and what does the slope tell you? Money $ 55 $ 62 $ 69 Describe the areas of the graph shown at the left as increasing, decreasing, constant, linear, and nonlinear. I can describe where a graph is increasing, decreasing, constant, linear, and nonlinear. Sketch a graph that is increasing at a constant rate, then becomes constant, and finally begins to decrease at a slow constant rate. * Geometry * Geometry * Sketch a graph that describes Amy walking to school at a constant rate, then realizing she dropped her book goes back and gets it and then runs the rest of the way to school. Geometry * Geometry * Geometry 8.G-1. Verify experimentally the properties of I can demonstrate and explain what happens to a line when it is rotated, reflected, and translated by various rotations, reflections, and amounts. translations: Describe what a line will look like after being rotated by 180 degrees. What will the line described by y = x look like after being reflected on the y-axis? a. Lines are taken to lines, and line segments I can demonstrate and explain what happens to a line to line segments of the segment when it is rotated, reflected, and translated by same length. various amounts. What transformations are necessary to make segment A match segment B? Draw segment A after being rotated about the point shown by 180 degrees. * Geometry * Geometry * I can sketch a graph if I am told where and how it is increasing, decreasing, constant, linear, and nonlinear. Geometry * Geometry * Geometry * Geometry 8.G-1a 8.G-1b Create an equation from the table shown and describe the rate of change. ONE Example of Assessment X A B 8.G-1. Verify experimentally the properties of rotations, reflections, and I can demonstrate and explain what happen to a angle translations: when it is rotated, reflected, and translated by various amounts. b. Angles are taken to angles of the same measure. 8.G-1. Verify experimentally the properties of I can demonstrate and explain what happen to parallel rotations, reflections, and lines when they are rotated, reflected, and translated by translations: various amounts. c. Parallel lines are taken to parallel lines. 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 of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. I can define congruence in terms of rotating, reflecting, or translating the first to obtain the second. I can specifically name the rotation, reflection, or translation of one 2-D shape necessary to obtain the second congruent figure. 8.G-3. Describe the effect of dilations, I can explain how a translation changes a figure on a translations, rotations, and reflections on twocoordinate graph. dimensional figures using coordinates. A What will the angle at the left look like after it has been reflected on the dashed line? The lines shown at the left are parallel. Carl says that he can reflect these lines together (not independently) so they will no longer be parallel. Explain why you agree or disagree. Example: A two- dimensional figure is congruent to another if the 2nd can be obtained from the 1st by a combination of translations, rotations, and reflections. Explain how a traditional definition of congruent (two shapes that have the same size and shape) differs from the transformational definition. Name the transformations necessary to prove these two figures are congruent. If a triangle has coordinates of (0,0), What translation would change a triangle with (5,0), & (3,7). What will the coordinates of (-2,3), (4,3), & (-2, 6) to one coordinates be when it is reflected with coordinates of (-4,3), (8,3), (-4,9)? over the y-axis? page 4 of 6 I can explain congruence and similarity in a variety of ways. Domain Target Cluster Target I can explain congruence, similarity, the Pythagorean Theorem, and how to find the volume of cylinders, cones, and spheres. Eighth Grade * Common Core Mathematics Domain & Standard 8.G-4. 8.G-5 Standard 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. Learning Target I can explain how two geometric figures are similar when you can dilate, rotate or reflect or translate the first to Example: A two- dimensional figure obtain the second. is similar to another if the 2nd can be obtained from the 1st by a I can specifically name the dilation, rotation or reflection combination of translations, or translation of one geometric figure necessary to obtain rotations, reflections, and dilations. the second similar figure. I can explain why the interior angles of a triangle always Arrange three copies of the same triangle so that the sum of the three add to 180o. angles appears to form a line. 8.G-5. Use informal arguments to establish If the interior angles of a triangle are facts about the angle sum and exterior angle I can explain the measures of the exterior angles of a 0 0 0 20 , 60 , and 100 , what is the of triangles, about the angles created when o triangle and why they add to 360 . measure of each exterior angle? parallel lines are cut by a transversal, and the angle criterion for similarity of triangles. For When parallel lines are cut by a I can explain the relationship between all the angles example, arrange three copies of the same transversal, what angles are formed by parallel lines cut by a transversal. triangle so that the sum of the three angles complimentary? appears to form a line, and give an argument A drawing of a triangle is duplicated in terms of transversals why this is so. I can explain the relationship between all the angles of on a copier that increases its size by two similar triangles. 200%. Describe the angles and sides of the new figure compared to I can explain at least one method of proof of the Pythagorean Theorem. 8.G-6 8.G-6. Explain a proof of the Pythagorean Theorem and its converse. 8.G-7 8.G-7. Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. 8.G-8 8.G-8. Apply the Pythagorean Theorem to find I can find the distance between two points on a the distance between two points in a coordinate grid. coordinate system. I can explain and apply the Pythagorean Theorem. I can solve real-world problems involving the 8.G-9 volume of cylinders, cones, and spheres. print date 1/18/13 A Specific Example 8.G-9. Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. ONE Example of Assessment Explain how a traditional definition of similarity (two shapes that have the same shape but not necessarily the same size) differs from the transformational definition. Name the transformations necessary to prove these two figures are congruent. If ∆ABC is constructed between two parallel lines, prove the B 0 C A interior angles add to 180 . Bob says the exterior angles of a triangle are the same as the interior angles. Explain why you agree or disagree. When parallel lines are cut by a transversal, name all the congruent angles. A triangle has all of its sides decreased by a factor of 1/3. If one of the angles was 0 originally 30 , what is this angle on the new figure? Present a proof of the Pythagorean Theorem. (if a, b, and c are sides of a right triangle with c=hypotenuse, then a2 + b2 = c2) I can explain a proof of the converse of the Pythagorean Theorem which says, if the square of one side of a Present a proof of the converse of the Pythagorean Theorem. (if a2 + b2 = c2 then triangle is equal to the sum of the squares of the other ∆abc is a right triangle) two sides, then the triangle is a right triangle I can solve real-world problems using the Pythagorean Theorem. I can find the volume of any cone, cylinder, or sphere. John leaves school to go home. He walks 6 blocks North and then 8 blocks west. How far is John from the school? A string connects to opposite corners of a cube in such a way as it goes through the center of the cube. How long is the string is the cube measures 5 cm on each edge? Find the distance between the two points (-3, 5) and (4, -1). Name a coordinate point that is 9 units from the point (-3, -5) and is in the first quadrant (where both coordinates are positive). Find the volume of a cylinder with a height of 7cm. and a diameter of 3cm. A cone and cylinder have the same base diameter and same volume. What is the height of the cone compared to the cylinder? A sphere is inside a 6 cm cube and I can solve real-world problems involving the volumes of touches all 6 sides. What is the cones, cylinders, or spheres. volume of the cube? A 6cm cube is constructed to hold a sphere with a diameter of 6cm. How much empty space will be in the cube? page 5 of 6 Eighth Grade * Common Core Mathematics Domain Target Statistics & Probability Domain & Cluster Target Standard Standard * Statistics & Probability * Statistics & Probability * 8.SP-1 8.SP-2 I can explain patterns of association in data with two variables (bivariate). I can explain patterns of association in data with two variables (bivariate). 8.SP-3. 8.SP-4 Created by Carl Jones, Darke County ESC, Karen Smith, Auglaize County ESC, Virginia McClain, Sidney City Schools, and Leah Fullenkamp, Waynesfield-Goshen print date 1/18/13 Learning Target Statistics & Probability 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 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. * Statistics & Probability A Specific Example * Statistics & Probability I can create a scatter plot with data involving two variables (bivariate data). ONE Example of Assessment * Statistics & Probability * Statistics & Probability Create a scatter plot with the following data Create a scatter plot with data of all your that compares student's arm span compared to their height. the ages of (web link) married couples. I can interpret a scatter plot by explaining patterns such Describe the attributes of the scatter plots addressing things like data points that as clustering, outliers, positive and negative patterns, are clustered, data points that are extreme, linear or nonlinear patterns, and linear patterns, and nonlinear patterns. whether the pattern of points go up (positive) or down (negative). I can identify linear patterns in a scatter plot and can estimate a straight line that fits the pattern. Draw a line that best fits the data in the scatterplot at the right. I can judge the quality of a line fitting a scatter plot by judging the closeness of the points to the line. Explain why the line you chose would be the best. What is the average distance from any point to the line? 8.SP-3. Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and I can create a linear model of a problem and describe intercept. how the slope and/or intercepts relate to the context of For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as the problem . meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height. 8.SP-4. Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and I can create a two-way table on data with two variables. 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 I can recognize patterns of association with categorical relative frequencies calculated for rows or data. 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 I can use the relative frequencies to find possible nights and whether or not they have assigned associations between the bivariate data. chores at home. Is there evidence that those who have a curfew also tend to have chores? [1] Function Notation is not required in Grade 8. The graph at the right models how the height of a plant in inches (yaxis) relates to the time in days (xaxis). What does the y-intercept mean in this context? What is the slope and what does it mean in the context of this problem? Create a two-way table from a population of adults that show their highest degree earned compared to their current annual salary. Create a two-way table based on students in your class and whether they have a curfew and how many hours of chores they perform a week. Total the columns and rows in your two-way table and explain any patterns you may notice about the data. Total the columns and rows in your two-way table and explain any patterns you may notice about the data. Explain whether or not you feel that students who have a curfew tend to also have chores and support your position with data from the table. Explain whether or not you feel that students who have a curfew tend to also have chores and support your position with data from the table. Created 1-3-2011 page 6 of 6