Ohio 8.MP MATHEMATICAL PRACTICES The s for Mathematical Practice describe the skills that mathematics educators should seek to develop in their students. The descriptions of the mathematical practices in this document provide examples of how student performance will change and grow as students engage with and master new and more advanced mathematical ideas across the grade levels. 8.MP.1 Make Sense of problems and persevere in solving them. In Grade 8, students solve real-world problems through the application of algebraic and geometric concepts. Students seek the meaning of a problem and look for efficient ways This practice is evident in every lesson. Icons indicate which practice is emphasized in the lesson. to represent and solve it. They may check their thinking by asking themselves, What is the most efficient way to solve the problem?, Does this make sense?, and Can I solve the problem in a different way? 8.MP.2 Reason abstractly and quantitatively. In Grade 8, students represent a wide variety of real-world contexts through the use of real numbers and variables in mathematical expressions, equations, and inequalities. They examine patterns in data and assess the degree of linearity of functions. Students contextualize to understand the meaning of the number(s) or variable(s) as related to the problem and decontextualize to manipulate symbolic representations by applying properties of operations. Activities that use this practice have an icon located throughout the book. Please reference Teachers Manual FM10-FM11. Example: On page M1-10, Activity 1.2 has icon in header. 8.MP.3 Construct viable arguments and critique the reasoning of others. In Grade 8, students construct arguments using verbal or written explanations accompanied by expressions, equations, inequalities, models, and graphs, tables, and other data displays (e.g., box plots, dot plots, histograms, etc.). They further refine their mathematical communication skills through mathematical discussions in which they critically evaluate their own thinking and the thinking of other students. They pose questions like How did you get that?, Why is that true? Does that always work? They explain their thinking to others and respond to others thinking. Activities that use this practice have an icon located throughout the book. Please reference Teachers Manual FM10-FM11. Example: On page M1-10, Activity 1.2 has icon in header. Ohio : Course 3 1
Ohio 8.MP.4 Model with mathematics. In Grade 8, students model problem situations symbolically, graphically, in tables, and contextually. Working with the new concept of a function, students learn that relationships between variable quantities in the real-world often satisfy a dependent relationship, in that one quantity determines the value of another. Students form expressions, equations, or inequalities from real-world contexts and connect symbolic and graphical representations. Students solve systems of linear equations and compare properties of functions provided in different forms. Students use scatterplots to represent data and describe associations between variables. Students need many opportunities to connect and explain the connections between the different representations. They should be able to use all of these representations as appropriate to a problem context. Students should be encouraged to answer questions such as What are some ways to represent the quantities? or How might it help to create a table, chart, graph, or? 8.MP.5 Use appropriate tools strategically. Students consider available tools (including estimation and technology) when solving a mathematical problem and decide when certain tools might be helpful. For instance, students in Grade 8 may translate a set of data given in tabular form to a graphical representation to compare it to another data set. Students might draw pictures, use applets, or write equations to show the between the angles created by a transversal that intersects parallel lines. Teachers might ask, What approach are you considering? or Why was it helpful to use? Activities that use this practice have an icon located throughout the book. Please reference Teachers Manual FM10-FM11. Example: On page M1-77, Activity 5.3 has icon in header. Activities that use this practice have an icon located throughout the book. Please reference Teachers Manual FM10-FM11. Example: On page M1-77, Activity 5.3 has icon in header. 8.MP.6 Attend to precision. In Grade 8, students continue to refine their mathematical communication skills by using clear and precise language in their discussions with others and in their own reasoning. Students use appropriate terminology when referring to the number system, functions, geometric figures, and data displays. Teachers might ask, What mathematical language, definitions, or properties can you use to explain? Activities that use this practice have an icon located throughout the book. Please reference Teachers Manual FM10-FM11. Example: On page M1-28, Activity 2.4 has icon in header. Ohio : Course 3 2
Ohio 8.MP.7 Look for and make use of structure. Students routinely seek patterns or structures to model and solve problems. In Grade 8, students apply properties to generate equivalent expressions and solve equations. Students examine patterns in tables and graphs to generate equations and describe relationships. Additionally, students experimentally verify the effects of transformations and describe them in terms of congruence and similarity. Activities that use this practice have an icon located throughout the book. Please reference Teachers Manual FM10-FM11. Example: On page M1-41, Activity 3.1 has icon in header. 8.MP.8 Look for an express regularity in repeated reasoning. In Grade 8, students use repeated reasoning to understand the slope formula and to make sense of rational and irrational numbers. Through multiple opportunities to model linear relationships, they notice that the slope of the graph of the linear relationship and the rate of change of the associated function are the same. For example, as students repeatedly check whether points are on the line with a slope of 3 that goes through the point (1, 2), they might abstract the equation of the line in the form yy 2 xx 1 = 3. Students should be encouraged to answer questions such as How would we prove that? or How is this situation like and different from other situations using these operations? Activities that use this practice have an icon located throughout the book. Please reference Teachers Manual FM10-FM11. Example: On page M1-41, Activity 3.1 has icon in header. Ohio : Course 3 3
Ohio 8.NS NUMBER SYSTEM Know that there are numbers that are not rational, and approximate them by rational numbers (s 8.NS.1 3). 8.NS.1 Know that real numbers are either rational or irrational. Understand informally that every number has a decimal expansion which is repeating, terminating, or is non-repeating and non-terminating. 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., Π 2). 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. 8.NS.3 Understand how to perform operations and simplify radicals with emphasis on square roots. TEXTBOOK: Module 4 T1L1: Number Sort (M4-7 thru M4-16) T1L2: Rational and Irrational Numbers (exclude converting a decimal expansion into a rational number. (M4-17 thru M4-30) SKILLS PRACTICE: Module 4, Expanding Number Systems Topic 1: Real Number System (pp. 109 111) MATHia: Module, Expanding Number Systems Unit: Rational and Irrational Numbers Workspace: Introduction to Irrational Numbers TEXTBOOK: Module 4 T1L3: The Real Numbers (M4-31 thru M4-50) SKILLS PRACTICE: Module 4, Expanding Number Systems Topic 1: Real Number System (pp. 109 111) MATHia: Module, Expanding Number Systems Unit: Rational and Irrational Numbers Workspace: Graphing Real Numbers on a Number Line; Ordering Rational and Irrational Numbers MATHia: Module, Quadratics Unit: Simplification and Operations with Radicals Workspace: Simplifying Radicals; Adding and Subtracting Radicals; Multiplying Radicals Ohio : Course 3 4
Ohio 8.EE EXPRESSIONS AND EQUATIONS Work with radical and integer exponents (s 8.EE.1 4). Understand the connections between proportional relationships, lines, and linear relationships (s 8.EE.5 6). Analyze and solve linear equations and inequalities and pairs of simultaneous linear equations (s 8.EE.7 8). TEXTBOOK: Module 5 T1L1: Properties of Powers with Integer Exponents (M5-7 thru M5-28) T1L2: Analyzing Properties of Powers (M5-29 thru M5-42) 8.EE.1 Understand, explain, and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3² 3 5 = 3 3 = 1/3³ = 1/27. SKILLS PRACTICE: Module 5, Applying Powers Topic 1: Exponents and Scientific Notation (pp. 123 126) MATHia: Module, Applying Powers Unit: Properties of Whole Number Exponents Workspace: Using the Product Rule and the Quotient Rule; Using the Power to a Power Rule; Using the Product to a Power Rule and the Quotient to a Power Rule; Simplifying Expressions with Negative and Zero Exponents 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.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. TEXTBOOK: Module 4 T1L3: The Real Numbers (M4-31 thru M4-45) T2L1: The Pythagorean Theorem (M4-55 thru M4-74) T2L2: The Converse of the Pythagorean Theorem (M4-75 thru M4-86) T2L4: Side Lengths in Two and Three Dimensions (M4-99 thru M4-112) SKILLS PRACTICE: Module 4, Expanding Number Systems Topic 1: Real Number System (pp. 109 111) Topic 2: The Pythagorean Theorem (pp. 112 122) MATHia: Module, Expanding Number Systems Unit: The Pythagorean Theorem Workspace: Applying the Pythagorean Theorem; Problem Solving Using the Pythagorean Theorem TEXTBOOK: Module 5 T1L3: Scientific Notation (M5-43 thru M5-60) T1L4: Operations with Scientific Notation (M5-61 thru M5-84) SKILLS PRACTICE: Module 5, Applying Powers Topic 1: Exponents and Scientific Notation (pp. 123 126) MATHia: Module, Applying Powers Unit: Scientific Notation Workspace: Using Scientific Notation; Comparing Numbers Using Scientific Notation Ohio : Course 3 5
Ohio 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.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. 8.EE.7 Solve linear equations and inequalities in one variable. TEXTBOOK: Module 5 T1L3: Scientific Notation (M5-43 thru M5-60) T1L4: Operations with Scientific Notation (M5-61 thru M5-84) SKILLS PRACTICE: Module 5, Applying Powers Topic 1: Exponents and Scientific Notation (pp. 123 126) MATHia: Module, Applying Powers Unit: Scientific Notation Workspace: Using Scientific Notation; Comparing Numbers Using Scientific Notation T1L1: Representations of Proportional Relationships (M2-7 thru M2-22) T1L2: Using Similar Triangles to Describe the Steepness of a Line (M2-23 thru M2-42) SKILLS PRACTICE: Module 2, Developing Functions Foundations Topic 1: From Proportions to Linear Relationships (pp. 19 31) Unit: Linear Models Workspace: Graphing Given an Integer Slope and y-intercept; Graphing Given a Decimal Slope and y-intercept T1L2: Using Similar Triangles to Describe the Steepness of a Line (M2-23 thru M2-42) T1L3: Exploring Slopes Using Similar Triangles (M2-43 thru M2-52) T1L4: Transformations of Lines (M2-53 thru M2-80) Unit: Linear Models Workspace: Graphing Given an Integer Slope and y-intercept; Graphing Given a Decimal Slope and y-intercept Ohio : Course 3 6
Ohio 8.EE.7.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.EE.7.b Solve single-variable linear equations and inequalities with rational number coefficients, including equations and inequalities whose solutions require expanding expressions using the distributive property and collecting like terms. 8.EE.7.c Solve single-variable absolute value equations. 8.EE.8 Analyze and solve parts of simultaneous linear equations graphically. 8.EE.8.a Understand that the solution to a pair of linear equations in two variables corresponds to the point(s) of intersection of their graphs, because the point(s) of intersection satisfy both equations simultaneously. TEXTBOOK: Module 3 T1L2: Analyzing and Solving Linear Equations (M3-17 thru M3-30) T1L3: Creating Linear Equations (M3-31 thru M3-46) SKILLS PRACTICE: Module 3, Modeling Linear Equations Topic 1: Solving Linear Equations (pp. 90 92) MATHia: Module, Modeling Linear Equations Unit: Linear Equations with Variables on Both Sides Workspace: Solving Equations with One Solution, Infinite, and No Solutions; Soring Equations by Number of Solutions TEXTBOOK: Module 3 T1L1: Equations with Variables on Both Sides (M3-7 thru M3-15) T1L3: Creating Linear Equations (M3-31 thru M3-46) SKILLS PRACTICE: Module 3, Modeling Linear Equations Topic 1: Solving Linear Equations (pp. 90 92) MATHia: Module, Modeling Linear Equations Unit: Solving Linear Equations; Linear Equations with Variables on Both Sides Workspace: Exploring Two-Step Equations; Solving Multi-Step Equations; Solving with Integers (No Type In); Solving with Integers (Type In) MATHia: Module, Relating Quantities and Reasoning with Equations Unit: Absolute Value Equations Workspace: Graphing Simple Absolute Value Equations Using Number Lines; Solving Absolute Value Equations TEXTBOOK: Module 3 T2L1: Point of Intersection of Linear Graphs (M3-47 thru M3-60) SKILLS PRACTICE: Module 3, Modeling Linear Equations Topic 2: Systems of Linear Equations (pp. 93 108) MATHia: Module, Modeling Linear Equations Unit: Systems of Linear Equations Workspace: Modeling Linear Systems Involving Integers; Modeling Linear Systems Involving Decimals Ohio : Course 3 7
Ohio 8.EE.8.b Use graphs to find or estimate the solution to a pair of two simultaneous linear equations in two variables. Equations should include all three solution types: one solution, no solution, and infinitely many solutions. 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.8.c Solve real-world and mathematical problems leading to pairs of 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. (Limit solutions to those that can be addressed by graphing.) TEXTBOOK: Module 3 T2L2: Systems of Linear Equations (M3-61 thru M3-74) SKILLS PRACTICE: Module 3, Modeling Linear Equations Topic 2: Systems of Linear Equations (pp. 93 108) MATHia: Module, Modeling Linear Equations Unit: Systems of Linear Equations Workspace: Modeling Linear Systems Involving Integers; Modeling Linear Systems Involving Decimals TEXTBOOK: Module 3 T2L4: Choosing a Method to Solve Linear System (NOTE: limit to solving systems graphically and with simple inspection) (M3-93 thru M3-104) SKILLS PRACTICE: Module 3, Modeling Linear Equations Topic 2: Systems of Linear Equations (pp. 93 108) MATHia: Module, Modeling Linear Equations Unit: Systems of Linear Equations Workspace: Modeling Linear Systems Involving Integers; Modeling Linear Systems Involving Decimals Ohio : Course 3 8
Ohio 8.F FUNCTIONS Define, evaluate, and compare functions (s 8.F.1 3). Use functions to model relationships between quantities (s 8.F.4 5). 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 Grade 8. 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. T3L1: Analyzing Sequences as Rules (M3-179 thru M3-188) T3L3: Defining Functional Relationships (M3-205 thru M3-222) SKILLS PRACTICE: Module 2, Developing Functions Foundations Topic 3: Introduction to Functions (pp. 70 83) Unit: Relations and Functions Workspace: Exploring Functions; Exploring Graphs of Functions; Classifying Relations and Functions T3L5: Comparing Functions Using Different Representations (M3-241 thru M3-266) T3L4: Describing Functions (M3-223 thru M2-240) SKILLS PRACTICE: Module 2, Developing Functions Foundations Topic 3: Introduction to Functions (pp. 70 83) Unit: Relations and Functions Workspace: Exploring Functions; Exploring Graphs of Functions; Classifying Relations and Functions; Identifying Key Characteristics of Graphs of Functions Ohio : Course 3 9
Ohio 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. T2 L1: Using Tables, Graphs, and Equations (M2-81 thru M2-92) T2 L2: Linear Relationships in Tables (M2-93 thru M2-108) T2 L3: Linear Relationships in Context (M2-109 thru M2-118) T2 L4: Slope-Intercept Form of a Line (M2-119 thru M2-134) T2 L5: Point-Slope Form of a Line (M2-135 thru M2-150) T2 L6: Using Linear Equations (M2-151 thru M2-178) T3 L4: Describing Functions (M3-223 thru M3-240) SKILLS PRACTICE: Module 2, Developing Function Foundations Topic 2: Linear Relationships (pp. 32 70) Topic 3: Introduction to Functions (pp. 70 83) Unit: Linear Models and the Distributive Property; Graphs of Linear Equations in Two Variables; Writing Equations of a Line Workspace: Modeling with Integer Rates of Change; Modeling with Fractional Rates of Change; Modeling using the Distributive Property over Division; Graphing Linear Equations Using a Given Method; Graphing Linear Equations Using a Chosen Method; Modeling Given Slope and a Point; Calculating Slopes; Modeling Given Two Points; Modeling Given an Initial Point; Modeling Linear Function Using Multiple Representations T3L2: Analyzing the Characteristics of Graphs of Relationships (M3-189 thru M3-204) T3L4: Describing Functions (M3-223 thru M3-240) SKILLS PRACTICE: Module 2, Developing Function Foundations Topic 3: Introduction to Functions (pp. 70 83) Unit: Relations and Functions Workspace: Identifying Key Characteristics of Graphs of Functions Ohio : Course 3 10
Ohio 8.G GEOMETRY Understand congruence and similarity using physical models, transparencies, or geometry software. 8.G.1 Verify experimentally the properties of rotations, reflections, and translations (include examples both with and without coordinates). 8.G.1.a Lines are taken to lines, and line segments are take to line segments of the same length. TEXTBOOK: Module 1; Module 2 M1T1L1: Introduction to Congruent Figures (M1-7 thru M1-16) M1T1L2: Introduction to Rigid Motions (M1-17 thru M1-38) M2T1L4: Transformations of Lines (M2-53 thru M2-80) SKILLS PRACTICE: Module 1, Transforming Geometric Objects Topic 1: Rigid Motion Transformations (pp. 1 5) 8.G.1.b Angles are taken to angles of the same measure. 8.G.1.c Parallel lines are taken to parallel lines. MATHia: Module, Transforming Geometric Objects Unit: Rigid Motion Transformations Workspace: Translating Plane Figures; Rotating Plane Figures; Reflecting Plane Figures TEXTBOOK: Module 1 M1T1L1: Introduction to Congruent Figures (M1-7 thru M1-16) M1T1L2: Introduction to Rigid Motions (M1-17 thru M1-38) SKILLS PRACTICE: Module 1, Transforming Geometric Objects Topic 1: Rigid Motion Transformations (pp. 1 5) MATHia: Module, Transforming Geometric Objects Unit: Rigid Motion Transformations Workspace: Translating Plane Figures; Rotating Plane Figures; Reflecting Plane Figures TEXTBOOK: Module 1; Module 2 M1T1L1: Introduction to Congruent Figures (M1-7 thru M1-16) M1T1L2: Introduction to Rigid Motions (M1-17 thru M1-38) M2T1L4: Transformations of Lines (M2-53 thru M2-80) SKILLS PRACTICE: Module 1, Transforming Geometric Objects Topic 1: Rigid Motion Transformations (pp. 1 5) MATHia: Module, Transforming Geometric Objects Unit: Rigid Motion Transformations Workspace: Translating Plane Figures; Rotating Plane Figures; Reflecting Plane Figures Ohio : Course 3 11
Ohio 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. (Include examples both with and without coordinates. 8.G.3 Observe that orientation of the plane is preserved in rotations and translations, but not with reflections. Describe the effect of dilations, translations, rotations, and reflections on twodimensional figures using coordinates. TEXTBOOK: Module 1 T1L1: Introduction to Congruent Figures (M1-7 thru M1-16) T1L2: Introduction to Rigid Motions (M1-17 thru M1-38) T1L3: Translations of Figures on the Coordinate Plane (M1-39 thru M1-52) T1L4: Reflections of Figures on Coordinate Plane (M1-53 thru M1-66) T1L5: Rotations of Figures on Coordinate Plane (M1-67 thru M1-82) T1L6: Combining Rigid Motions (M1-83 thru M1-108) SKILLS PRACTICE: Module 1, Transforming Geometric Objects Topic 1: Rigid Motion Transformations (pp. 1 5) MATHia: Module, Transforming Geometric Objects Unit: Rigid Motion Transformations Workspace: Translating Plane Figures; Rotating Plane Figures; Reflecting Plane Figures; Performing One Transformation; Performing Multiple Transformations TEXTBOOK: Module 1 T1L3: Translations of Figures on Coordinate Plane (M1-39 thru M1-52) T1L4: Reflections of Figures on Coordinate Plane (M1-53 thru M1-66) T1L5: Rotations of Figures on Coordinate Plane (M1-67 thru M1-82) T1L6: Combining Rigid Motions (M1-83 thru M1-108) T2L2: Dilating Figures on the Coordinate Plane (M1-125 thru M166) SKILLS PRACTICE: Module 1, Transforming Geometric Objects Topic 1: Rigid Motion Transformations (pp. 1 5) Topic 2: Similarity (pp. 6 11) MATHia: Module, Transforming Geometric Objects Unit: Rigid Motion Transformations Workspace: Translating Plane Figures; Rotating Plane Figures; Reflecting Plane Figures; Dilating Plane Figures; Performing One Transformation; Performing Multiple Transformations Ohio : Course 3 12
Ohio 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. (Include examples both with and without coordinates. 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. 8.G.6 Analyze and justify an informal proof of the Pythagorean Theorem and its converse. TEXTBOOK: Module 1 T2L1: Dilations of Figures (M1-109 thru M1-124) T2L2: Dilating Figures on the Coordinate Plane (M1-125 thru M1-140) T2L3: Mapping Similar Figures with Transformations (M1-141 thru M1-166) SKILLS PRACTICE: Module 1, Transforming Geometric Objects Topic 2: similarity (pp. 6 11) MATHia: Module, Transforming Geometric Objects Unit: Rigid Motion Transformations Workspace: Dilating Plane Figures; Performing One Transformation; Performing Multiple Transformation TEXTBOOK: Module 1 T3L1: Triangle Sum and Exterior Angle Theorem (M1-167 thru M1-180) T3L2: Angle Relationships Formed by Lines Intersected by a Transversal (M1-181 thru M1-202) T3L3: The Angle-Angle Similarity Theorem (M1-203 thru M1-212) SKILLS PRACTICE: Module 1, Transforming Geometric Objects Topic 3: Line and Angle Relationships (pp. 12 18) MATHia: Module, Transforming Geometric Objects Unit: Lines Cut by a Transversal Workspace: Classifying Angles Formed by Transversals; Reasoning About Angles Formed by Transversals; Calculating Angles Formed by Transversals TEXTBOOK: Module 4 T2L1: The Pythagorean Theorem (M4-55 thru M4-74) T2L2: Converse of Pythagorean Theorem (M4-75 thru M4-86) MATHia: Module, Expanding Number Systems Unit: The Pythagorean Theorem Workspace: Exploring the Pythagorean Theorem; Applying the Pythagorean Theorem; Problem Solving Using the Pythagorean Theorem Ohio : Course 3 13
Ohio 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 Solve real-world and mathematical problems involving volumes of cones, cylinders, and spheres. TEXTBOOK: Module 4 T2L1: The Pythagorean Theorem (M4-55 thru M4-74) T2L2: Converse of Pythagorean Theorem (M4-75 thru M4-86) T2L4: Side Lengths in Two and Three Dimensions (M4-99 thru M4-112) SKILLS PRACTICE: Module 4, Expanding Number Systems Topic 2: The Pythagorean Theorem (pp. 112 122) MATHia: Module, Expanding Number Systems Unit: The Pythagorean Theorem Workspace: Applying the Pythagorean Theorem; Problem Solving Using the Pythagorean Theorem TEXTBOOK: Module 4 T2L3: Distances in a Coordinate System (M4-87 thru M4-98) SKILLS PRACTICE: Module 4, Expanding Number Systems Topic 2: The Pythagorean Theorem (pp. 112 122) MATHia: Module, Expanding Number Systems Unit: The Pythagorean Theorem Workspace: Calculating Distances on the Coordinate Plane TEXTBOOK: Module 5 T2L1: Volume of a Cylinder (M5-85 thru M5-98) T2L2: Volume of a Cone (M5-99 thru M5-112) T2L3: Volume of a Sphere (M5-113 thru M5-122) T2L4: Volume Problems with Cylinders, Cones, and Spheres (M5-123 thru M5-132) SKILLS PRACTICE: Module 5, Applying Powers Topic 2: Volume of Curved Figures (pp. 127 139) MATHia: Module, Applying Powers Unit: Volume Workspace: Calculation Volume of Cylinders; Using Volume of Cylinders; Calculating Volume of Cones; Using Volume of Cones; Calculating Volume of Spheres; Using Volume of Spheres Ohio : Course 3 14
Ohio 8.SP STATISTICS AND PROBABILITY Investigate patterns of association in bivariate data (s 8.SP.1 4). 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, negative, or no association; and linear association and nonlinear association (GAISE Model, steps 3 and 4). 8.SP.2 Understand 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 (GAISE Model, steps 3 and 4). 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 (GAISE Model, steps 3 and 4). T4L1: Analyzing Patterns in Scatter Plots (M2-267 thru M2-288) SKILLS PRACTICE: Module 2, Developing Function Foundations Topic 4: Patterns in Bivariate Data (pp. 84 89) Unit: Lines of Best Fit Workspace: Estimating Lines of Best Fit T4L2: Drawing Line of Best Fit (M2-289 thru M2-304) T4L3: Analyzing Line of Best Fit (M2-305 thru M2-318) SKILLS PRACTICE: Module 2, Developing Function Foundations Topic 4: Patterns in Bivariate Data (pp. 84 89) Unit: Lines of Best Fit Workspace: Estimating Lines of Best Fit; Using Lines of Best Fit T4L2: Drawing Line of Best Fit (M2-289 thru M2-304) T4L3: Analyzing Line of Best Fit (M2-305 thru M2-318) T4L4: Comparing Slopes and Intercepts of Data from Experiments (M2-319 thru M2-328) SKILLS PRACTICE: Module 2, Developing Function Foundations Topic 4: Patterns in Bivariate Data (pp. 84 89) Unit: Lines of Best Fit Workspace: Estimating Lines of Best Fit; Using Lines of Best Fit Ohio : Course 3 15
Ohio 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. T4L5: Patterns of Association in Two-Way Tables (M2-329 thru M2-349) 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? Ohio : Course 3 16