1-4 | 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 Ex., 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. 8.EE.7a Solve linear equations in one variable: a. Give example 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 equations of the form x = a, a= a, or a = b results (where a and b are different numbers). 8.EE.7b Solve linear equations in one variable: b. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. | Linear equation Y-intercept Slope-intercept form X-intercept Similar figures Corresponding sides Congruent Linear relationship Constant rate of change Direct Variation Slope Distributive Property Like Terms | I can graph proportional relationships. I can compare two different proportional relationships represented in different ways.(For ex., compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.) I can interpret the unit rate of proportional relationships as the slope of the graph.
I can identify characteristics of similar triangles. I can find the slope of a line. I can determine the y-intercept of a line. I can analyze patterns for points on a line through the origin. I can come up with an equation of the form y = mx for a line through the origin. I can use similar triangle to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane. I can solve linear equations with rational number coefficients. I can solve equations whose solutions require expanding expressions using the distributive property and/ or collecting like terms. | Document Camera Calculators Promethean Board Clicker Devices Internet Number lines Scissors Tape Compass Protractors Algebra Scales M3 Tiles Integer Cards Dice Integer Robots M3 Notebooks Walk a thon cards Geogebra I-MAC computers Rope String Styrofoam Cups | Formative may include: Clicker Quizzes Problem Sets Thumbs up Bell ringers Modeling Spot Checks Exit Slips In class questioning Computer Printouts Small Dry-erase board work Summative Assessment will be at the end of week four. It will consist of approximately 20 multiple choice questions, 2 to 4 short answer questions, and an extended response. |
5-10 | 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.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 (e.g., π2). For example, by truncating the decimal expansion of , show that is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations. Work with radicals and integer exponents. | Order of operations Evaluate Properties Negative number Positive number Integers Absolute value Opposites Additive inverse, Terminating decimal Repeating decimal Bar notation Rational numbers Irrational numbers Number line Distributive property Term | I can define and use in oral and or written language the vocabulary words. I can show that the decimal expansion of rational numbers repeats eventually. I can convert a decimal expansion which repeats eventually into a rational number. I can show informally that every number has a decimal expansion. I can approximate irrational numbers as rational numbers. I can locate (approximately) irrational numbers on a number line. I can estimate the value of expressions involving irrational numbers using rational approximations.( for ex: I can shorten the decimal Expansion of √2 is between 1 and 2, then between 1.4 and 1.5 and explain how to continue on to get better approximations. I can compare the size of irrational numbers using rational approximations. | Document Camera Calculators Promethean Board Clicker Devices Internet Number lines Scissors Tape Compass Protractors Algebra Scales M3 Tiles Integer Cards Dice Integer Robots M3 Notebooks Walk a thon cards Geogebra I-MAC computers | Formative may include: Clicker Quizzes Problem Sets Thumbs up Bell ringers Modeling Spot Checks Exit Slips In class questioning Computer Printouts Small Dry-erase board work Summative Assessment will be at the end of week 10. It will consist of approximately 20 multiple choice questions, 2 to 4 short answer questions, and an extended response. |
14-15 | 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 × 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. | Scientific notation Base Standard form Powers f 10 | I can express umbers as a single digit times an integer power of 10. I can use scientific notation to estimate very large and/or very small quantities. I can perform operations using numbers expressed in scientific notations. I can use scientific notation to express very large and very small quantities. I can compare quantities to express how much larger one is compared to the other. I can interpret scientific notation that has been generated by technology. I can choose appropriate units of measure when using scientific notation. | Document Camera Calculators Promethean Board Clicker Devices Internet Number lines Scissors Tape Compass Protractors Algebra Scales M3 Tiles Integer Cards Dice Integer Robots M3 Notebooks Walk a thon cards Geogebra I-MAC computers Snap Cubes | Formative may include: Clicker Quizzes Problem Sets Thumbs up Bell ringers Modeling Spot Checks Exit Slips In class questioning Computer Printouts Small Dry-erase board work Summative Assessment will be at the end of week 15. It will consist of approximately 20 multiple choice questions, 2 to 4 short answer questions, and an extended response. |
16-21 | 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. Function notation is not required in 8^{th} grade. 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.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.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 a 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. | Independent variable Dependent variable Vertical line test Function notation Slope Intercept form | I can identify cases in which a system of two equations in two unknowns has no solution Identify cases in which a system of two equations in two unknowns has an infinite number of solutions. Solve a system of two equations (linear) in two unknowns algebraically. Solve simple cases of systems of two linear equations in two variables by inspection. I can estimate the point(s) of intersection for a system of two equations in two unknowns by graphing the equations. I can identify functions algebraically including slope and y intercept. I can Identify functions using graphs. I can Identify functions using tables. I can Identify functions using verbal descriptions. I can compare and Contrast 2 functions with different representations. I can draw conclusions based on different representations of functions. I can recognize that a linear function is graphed as a straight line. I can recognize the equation y=mx+b is the equation of a function whose graph is a straight line where m is the slope and b is the y-intercept. Provide examples of nonlinear functions using multiple representations. I can compare the characteristics of linear and nonlinear functions using various representations. I can recognize that slope is determined by the constant rate of change. I can recognize that the y-intercept is the initial value where x=0. I can determine the rate of change from two (x,y) values, a verbal description, values in a table, or graph. I can determine the initial value from two (x,y) values, a verbal description, values in a table, or graph.
I can construct a function to model a linear relationship between two quantities. Relate the rate of change and initial value to real world quantities in a linear function in terms of the situation modeled and in terms of its graph or a table of values. I can analyze a graph and describe the functional relationship between two quantities using the qualities of the graph. I can sketch a graph given a verbal description of its qualitative features. I can interpret the relationship between x and y values by analyzing a graph. | Document Camera Calculators Promethean Board Clicker Devices Internet Number lines Scissors Tape Compass Protractors Algebra Scales M3 Tiles Integer Cards Dice Integer Robots M3 Notebooks Walk a thon cards Geogebra I-MAC computers Snap Cubes | Formative may include: Clicker Quizzes Problem Sets Thumbs up Bell ringers Modeling Spot Checks Exit Slips In class questioning Computer Printouts Small Dry-erase board work Summative Assessment will be at the end of week 21. It will consist of approximately 20 multiple choice questions, 2 to 4 short answer questions, and an extended response. |
22-23 | 8.EE.8a 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.8b Analyze and solve pairs of simultaneous linear 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. 8.EE.8c 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. | Parent function Linear function Linear equation Y-intercept Slope-intercept Form X-intercept | I can solve linear equations with rational number coefficients. I can solve equations whose solutions require expanding expressions using the distributive property and/ or collecting like terms. I can identify the solution(s) to a system of two linear equations in two variables as the point(s) of intersection of their graphs. I can describe the point(s) of intersection between two lines as points that satisfy both equations simultaneously. I can define “inspection”. Identify cases in which a system of two equations in two unknowns has no solution. I can identify cases in which a system of two equations in two unknowns has an infinite number of solutions. I can solve a system of two equations (linear) in two unknowns algebraically. I can solve simple cases of systems of two linear equations in two variables by inspection. I can estimate the point(s) of intersection for a system of two equations in two unknowns by graphing the equations. I can define “inspection”. I can identify cases in which a system of two equations in two unknowns has no solution I can identify cases in which a system of two equations in two unknowns has an infinite number of solutions. I can solve a system of two equations (linear) in two unknowns algebraically. I can solve simple cases of systems of two linear equations in two variables by inspection. I can estimate the point(s) of intersection for a system of two equations in two unknowns by graphing the equations. | Document Camera Calculators Promethean Board Clicker Devices Internet Number lines Scissors Tape Compass Protractors Algebra Scales M3 Tiles Integer Cards Dice Integer Robots M3 Notebooks Walk a thon cards Geogebra I-MAC computers Snap Cubes | Formative may include: Clicker Quizzes Problem Sets Thumbs up Bell ringers Modeling Spot Checks Exit Slips In class questioning Computer Printouts Small Dry-erase board work Summative Assessment will be at the end of week 23. It will consist of approximately 20 multiple choice questions, 2 to 4 short answer questions, and an extended response. |
24-29 | 8.G.1abc Verify experimentally the properties of rotations, reflections, and translations: a. Lines are taken to lines, and line segments 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.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. 8.G.3 Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. 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. 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 three angles appear to form a line, and give an argument in terms of transversals why this is so. 8.G.6 Explain a proof of the Pythagorean Theorem and it’s converse. 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 Apply the Pythagorean Theorem to find the distance between two points in a coordinate system 8.G.9 Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. | Rotation Center of rotation Rotational symmetry Transformation Image Translation Reflection Line of symmetry Reflection Translation Dilations Similar figures Corresponding parts Congruent Similar figures Scale drawing Scale Scale model Dilations proofs Legs Hypotenuse Pythagorean theorem Circles Radius Diameter Circumference Pi Sector Central angle Composite figure Area Perimeter Surface area Regular pyramid Similar solids Volume | I can define & identify rotations, reflections, and translations. I can identify corresponding sides & corresponding angles. Understand prime notation to describe an image after a translation, reflection, or rotation. I can identify center of rotation. I can identify direction and degree of rotation. I can identify line of reflection. I can use physical models, transparencies, or geometry software to verify the properties of rotations, reflections, and translations (ie. Lines are taken to lines and line segments to line segments of the same length, angles are taken to angles of the same measure, & parallel lines are taken to parallel lines.) I can define congruency. Identify symbols for congruency. I can apply the concept of congruency to write congruent statements. I can reason that a 2-D figure is congruent to another if the second can be obtained by a sequence of rotations, reflections, translation. I can describe the sequence of rotations, reflections, translations that exhibits the congruence between 2-D figures using words. I can describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. I can describe the effects of dilations, translations, rotations, & reflections on 2-D figures using coordinates. I can define similar figures as corresponding angles are congruent and corresponding sides are proportional. I can recognize symbol for similar. I can apply the concept of similarity to write similarity statements. I can reason that a 2-D figure is similar to another if the second can be obtained by a sequence of rotations, reflections, translation, or dilation. I can describe the sequence of rotations, reflections, translations, or dilations that exhibits the similarity between 2-D figures using words and/or symbols. I can define similar triangles I can define and identify transversals I can identify angles created when parallel line is cut by transversal (alternate interior, alternate exterior, corresponding, vertical, adjacent, etc.) I can justify that the sum of interior angles equals 180. (For example, arrange three copies of the same triangle so that the three angles appear to form a line.) I can justify that the exterior angle of a triangle is equal to the sum of the two remote interior angles. I can use Angle-Angle Criterion to prove similarity among triangles. (Give an argument in terms of transversals why this is so.) I can define key vocabulary: square root, Pythagorean Theorem, right triangle, legs a & b, hypotenuse, sides, right angle, converse, base, height, proof. I can identify the legs and hypotenuse of a right triangle. I can explain a proof of the Pythagorean Theorem. I can explain a proof of the converse of the Pythagorean Theorem. I can recall the Pythagorean theorem and its converse. I can solve basic mathematical Pythagorean theorem problems and its converse to find missing lengths of sides of triangles in two and three-dimensions. I can apply Pythagorean theorem in solving real-world problems dealing with two and three-dimensional shapes. I can determine how to create a right triangle from two points on a coordinate graph. I can use the Pythagorean Theorem to solve for the distance between the two points. I can identify and define vocabulary: cone, cylinder, sphere, radius, diameter, circumference, area, volume, pi, base, height Know formulas for volume of cones, cylinders, and spheres. I can compare the volume of cones, cylinders, and spheres. I can determine and apply appropriate volume formulas in order to solve mathematical and real-world problems for the given shape. I can, given the volume of a cone, cylinder, or sphere, find the radii, height, or approximate for π. | Document Camera Calculators Promethean Board Clicker Devices Internet Number lines Scissors Tape Compass Protractors Algebra Scales M3 Tiles Integer Cards Dice Integer Robots M3 Notebooks Walk a thon cards Geogebra I-MAC computers Snap Cubes | In class questioning Computer Printouts Small Dry-erase board work Summative Assessments will be at the end of week 26 and 29. It will consist of approximately 10-15 multiple choice questions, 2 to 4 short answer questions, and an extended response. This unit will be divided between transformations/triangles and volume so there will be two summatives. |
30-33 | 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. 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.) 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? | Measures of central tendency Mean Median Mode Stem-and-leaf plot Stems Leaves Measures of variation Range Quartiles Outlier Box-and-whisker plot Histogram Outcomes bivariate | I can describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association I can construct scatter plots for bivariate measurement data I can interpret scatter plots for bivariate (two different variables such as distance and time) measurement data to investigate patterns of association between two quantities I can know that straight lines are used to model relationships between two quantitative variables I can informally assess the model fit by judging the closeness of the data points to the line. I can fit a straight line within the plotted data. I can interpret the meaning of the slope and intercept of a linear equation in terms of the situation I can solve problems using the equation of a linear model. | Document Camera Calculators Promethean Board Clicker Devices Internet Number lines Scissors Tape Compass Protractors Algebra Scales M3 Tiles Integer Cards Dice Integer Robots M3 Notebooks Walk a thon cards Geogebra I-MAC computers Snap Cubes | In class questioning Computer Printouts Small Dry-erase board work Summative Assessment will be at the end of week 33. It will consist of approximately 20 multiple choice questions, 2 to 4 short answer questions, and an extended response. |