Carrollton Exempted Village School District Carrollton, Ohio OHIO COMMON CORE STATE STANDARDS. Curriculum Map

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1 Carrollton Exempted Village School District Carrollton, Ohio OHIO COMMON CORE STATE STANDARDS Curriculum Map Course Title: Grade 8 Math Quarter 1 Academic Year: Essential Questions for this Unit: How do you use rational and irrational numbers? How are rational and irrational numbers placed on a number line? Unit Core Standards Sample Instructional Strategies and Differentiation Number System 8.NS.1: Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number. 8.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., n 2 ). For example, by truncating the decimal expansion of square root 2, show that the Indirect Instruction Problem Solving Inquiry Concept Attainment Experiential Instruction Educational Games Think Pair Share Model Building Independent Instruction Research Homework Computer Interactive Instruction Activities Debates Assessment 8.NS.1: Students will distinguish between rational and irrational numbers, recognizing that any number that can be expressed as a fraction is a rational number. 8.NS.2: Students will hypothesize and create a number line with the use of rational and irrational numbers.

2 square root is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations. Discussion Direct Instruction Vocabulary: real numbers, rational numbers, irrational numbers, repeating decimal, terminating decimal, integers, whole numbers, natural numbers Resources: McDougal Littel Book 3 Chapters 5 and 9, Measure Up, Buckle Down, McDougal Littel Pre-Algebra, Chapters 5 and 9, People s Common Core, Algebra Structure and Method, Chapter 11

3 Carrollton Exempted Village School District Carrollton, Ohio OHIO COMMON CORE STATE STANDARDS Curriculum Map Course Title: Grade 8 Math Quarter 1 Academic Year: Essential Questions for this Unit: How can you represent very large and very small numbers? Can you explain the geometric properties of integer exponents, square roots and cube roots? Unit Core Standards Sample Instructional Strategies and Differentiation Expressions & 8.EE.2: Use square root and cube root Indirect Instruction Equations symbols to represent solutions to Problem Solving Roots equations of the form x 2 = p and x 3 = p, Inquiry Scientific Notation where p is a positive rational number. Concept Attainment Integer Exponents Evaluate square roots of small perfect Experiential Instruction squares and cube roots of small perfect Educational Games Assessment 8.EE.2: Students will represent solutions to equations of the form x 2 =p, x 3 =p, and explain to a small group.

4 cubes. Know that square root of 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 x 10 8 and the population of the world as 7 x 10 9, 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 sized 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.1: Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3 2 x 3-5 = 1/3 3 = 1/27. Think Pair Share Model Building Independent Instruction Research Homework Computer Interactive Instruction Activities Debates Discussion Direct Instruction 8.EE.3: Students will use scientific notation to express very large or vary small numbers. Students will solve problems using addition, subtraction, or multiplication, and expressing the answer in scientific notation. 8.EE.4: Students will compare and contrast quantities using powers of ten. Students will use scientific notation to show appropriate size and measurement with the use of technology. 8.EE.1: Students will generate equivalents numerical expressions when multiplying, dividing, or raising a power to a power. Students will generate equivalent expressions using numerical bases and the law of exponents.

5 Vocabulary: square root, cube root, law of exponents, power, scientific notation, standard form of a number Resources: McDougal Littel Book 3 Chapter, Measure Up, Buckle Down, McDougal Littel Pre-Algebra Chapter, People s Common Core, Algebra Structure and Method Chapter Carrollton Exempted Village School District Carrollton, Ohio OHIO COMMON CORE STATE STANDARDS Curriculum Map Course Title: Grade 8 Math Quarter 1 Academic Year: Essential Questions for this Unit: 1. How can we use equations to determine solutions to real life problems? Unit Core Standards Sample Instructional Strategies and Differentiation Solve Linear 8.EE.7: Solve linear equations in one Indirect Instruction Equations variable. Problem Solving a. Give examples of linear equations in one Inquiry variable with one solution, infinitely many Concept Attainment solutions, or no solutions. Show which of Experiential Instruction these possibilities is the case by Educational Games successively transforming the given Think Pair Share equation into simpler forms, until an Model Building Assessment 8.EE.7: Students will construct and solve equations given real life situations. Students will apply distributive property and collecting like terms to solve

6 equivalent equation of the form x = a, a =a, or a=b results (where a and b are different numbers). b. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. Independent Instruction Research Homework Computer Interactive Instruction Activities Debates Discussion Direct Instruction equations. Vocabulary: solution, coefficient, distributive property, like terms, simplify, solve Resources: McDougal Littel Book 3 Chapter, Measure Up, Buckle Down, McDougal Littel Pre-Algebra Chapter, People s Common Core, Algebra Structure and Method Chapter

7 Carrollton Exempted Village School District Carrollton, Ohio OHIO COMMON CORE STATE STANDARDS Curriculum Map Course Title: Grade 8 Math Quarter 2 Academic Year: Essential Questions for this Unit: 1.In what way is a function a rule? 2. What real world scenarios model linear and nonlinear relationships? Unit Core Standards Sample Instructional Strategies and Differentiation Linear Functions 8.F.1: Understand that a function is a rule Indirect Instruction that assigns to each input exactly one Problem Solving output. The graph of a function is the set Inquiry of ordered pairs consisting of an input and Concept Attainment the corresponding output. Experiential Instruction Assessment 8.F.1: Students will determine whether two ordered pairs form a function and explain. Students will identify

8 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 examples, the function, A= s^2 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), (3, 9), which are not on a straight line. 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 the line through the origin and the equation y = mx +b for a line intercepting the vertical axis at b. Educational Games Think Pair Share Model Building Independent Instruction Research Homework Computer Interactive Instruction Activities Debates Discussion Direct Instruction functions from equations, graphs, and tables/ordered pairs. 8.F.3: Students will understand that linear functions have a constant rate of change between any two points. Students will use equations, graphs, and tables to categorize functions as linear or nonlinear. 8.EE.6: Using a graph, students will construct triangles between two points on a line and compare sides to understand that the slope (ratio of rise to run) is the same between any two points on a line. Students will analyze the relationship between the graphs of two nonvertical lines, including slope and y-intercept. Vocabulary: proportional, unit rate, slope, coordinate plane, linear, nonlinear, linear equation, coefficient, solution, equivalent, distributive property, ordered pair, function, input, output, vertical line test, rate of change, y-intercept

9 Resources: McDougal Littel Book 3 Chapter, Measure Up, Buckle Down, McDougal Littel Pre-Algebra Chapter, People s Common Core, Algebra Structure and Method Chapter Carrollton Exempted Village School District Carrollton, Ohio OHIO COMMON CORE STATE STANDARDS Curriculum Map Course Title: Grade 8 Math Quarter 2 Academic Year: Essential Questions for this Unit: 1.What real life scenarios model linear systems? 2. What does a solution to a linear system mean? Unit Core Standards Sample Instructional Strategies and Differentiation Linear Systems 8.EE.8: Analyze and solve pairs of Indirect Instruction simultaneous linear equations. Problem Solving Inquiry a. Understand that solutions to a system of Concept Attainment Assessment 8.EE.8: Students will graph two linear equations on the same coordinate plane and determine the number of

10 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. c. Solve real world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs, determine whether the line through the first pair of points intersects the line through the second pair. Experiential Instruction Educational Games Think Pair Share Model Building Independent Instruction Research Homework Computer Interactive Instruction Activities Debates Discussion Direct Instruction solutions that exist. The students will also solve a real life problem dealing with linear systems. Vocabulary: linear system, no solution, infinitely many solutions, one solution, intersecting lines, parallel lines, same line Resources: McDougal Littel Book 3 Chapter, Measure Up, Buckle Down, McDougal Littel Pre-Algebra Chapter, People s Common Core, Algebra Structure and Method Chapter

11 Carrollton Exempted Village School District Carrollton, Ohio OHIO COMMON CORE STATE STANDARDS Curriculum Map Course Title: Grade 8 Math Quarter 2 Academic Year: Essential Questions for this Unit: 1.How do proportional relationships and equations help to solve problems? 2. How do you sign and resent functions? Unit Core Standards Sample Instructional Strategies and Differentiation Linear 8.F.4: Construct a function to model a Indirect Instruction Relationships linear relationship between two quantities. Problem Solving Determine the rate of change and initial Inquiry value of the function from a description of Concept Attainment Assessment 8.F.4: Students will describe the relationship based on the (x,y) values to determine and interpret the rate of

12 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 in 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. 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 greatest rate of change. 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 Experiential Instruction Educational Games Think Pair Share Model Building Independent Instruction Research Homework Computer Interactive Instruction Activities Debates Discussion Direct Instruction change and initial value of the function. 8.F.5: Students will sketch and describe graphs where function is increasing, decreasing, linear, or nonlinear. 8.F.2: Students will compare functions with algebra, graphs, tables, and descriptions. Students will compare two functions from different representations. 8.EE.5: Students will compare graphs, tables and equations of proportional relationships. Students will identify the unit rate (or slope) in graphs, tables and equations to compare two proportional relationships represented in different ways.

13 equation to determine which of two moving objects has greater speed. Vocabulary: proportional, unit rate, slope, coordinate plane, linear, nonlinear, linear equation, coefficient, solution, equivalent, distributive property, ordered pair, function, input, output, vertical line test, rate of change, y-intercept Resources: McDougal Littel Book 3 Chapter, Measure Up, Buckle Down, McDougal Littel Pre-Algebra Chapter, People s Common Core, Algebra Structure and Method Chapter Carrollton Exempted Village School District Carrollton, Ohio OHIO COMMON CORE STATE STANDARDS Curriculum Map Course Title: Grade 8 Math Quarter 3 Academic Year: Essential Questions for this Unit: 1. How do you investigate patterns in real-world applications? Unit Core Standards Sample Instructional Strategies and Differentiation Statistics and 8.SP.2: Know that straight lines are widely Indirect Instruction Probability used to model relationships between two Problem Solving quantitative variables. For scatter plots that Inquiry suggest a linear association, informally fit a Concept Attainment Assessment 8.SP.2: Students will determine the relationship between straight lines and two quantitative variables by

14 straight line, and informally assess the model fit by judging the closeness of the data points to the line. 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.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 tow 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. 8.SP.3: Use the equation of a linear model to solve problems in the context of Experiential Instruction Educational Games Think Pair Share Model Building Independent Instruction Research Homework Computer Interactive Instruction Activities Debates Discussion Direct Instruction using scatter plots. 8.SP.1: Students will construct and interpret scatter plots for coordinate planes by describing patterns such as clustering, outliers, positive or negative associations, linear, and nonlinear associations. 8.SP.4: Students will describe possible associations between two variables by using relative frequencies calculated for rows or columns. 8.SP.3: Students will evaluate and solve linear models on coordinate plane by interpreting the slope and intercept.

15 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. Vocabulary: bivariate data, scatter plot, linear model, clustering, linear association, nonlinear association, outliers, positive association, negative association, categorical data, two-way table, relative frequency Resources: McDougal Littel Book 3 Chapter, Measure Up, Buckle Down, McDougal Littel Pre-Algebra Chapter, People s Common Core, Algebra Structure and Method Chapter Carrollton Exempted Village School District Carrollton, Ohio OHIO COMMON CORE STATE STANDARDS Curriculum Map Course Title: Grade 8 Math Quarter 3 Academic Year: Essential Questions for this Unit: 1.How do we apply and relate different geometric properties within the real-world? Unit Core Standards Sample Instructional Strategies and Assessment Differentiation Geometric 8.G.1: Verify experimentally the properties Indirect Instruction 8.G.1: Students will use

16 Transformations 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, 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-dimensional figures, describe a sequence that exhibits the similarity between them. 8.G.3: Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. Problem Solving Inquiry Concept Attainment Experiential Instruction Educational Games Think Pair Share Model Building Independent Instruction Research Homework Computer Interactive Instruction Activities Debates Discussion Direct Instruction compasses, protractors, and rulers or technology to explore figures created from translations, reflections, and rotations. Students will compare geometric shapes with their translations through flips, turns, and rotations. 8.G.2: Students will determine congruence through the comparison of corresponding parts between two-dimensional figures and their translations. 8.G.4: Students will understand similar figures have congruent angles and sides that are proportional. Similar figures are produced from dilations. Students will describe the sequence that would produce similar figures, including the scale factors. 8.G.3: Students will analyze the graphs of two-

17 dimensional figures and their translations on a coordinate plane. Vocabulary: translations, rotations, reflections, line of reflection, center of rotation, clockwise, counterclockwise, parallel lines, betweenness, congruence, similarity, dilations, image, Resources: McDougal Littel Book 3 Chapter, Measure Up, Buckle Down, McDougal Littel Pre-Algebra Chapter, People s Common Core, Algebra Structure and Method Chapter Carrollton Exempted Village School District Carrollton, Ohio OHIO COMMON CORE STATE STANDARDS Curriculum Map Course Title: Grade 8 Math Quarter 3 Academic Year: Essential Questions for this Unit: 1.How do we apply and relate different geometric properties in the real-world? Unit Core Standards Sample Instructional Strategies and Differentiation Pythagorean 8.G.6: Explain a proof of the Pythagorean Indirect Instruction Theorem Theorem and its converse. Problem Solving Assessment 8.G.6: Students will explain the Pythagorean Theorem,

18 and Geometry 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.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. Inquiry Concept Attainment Experiential Instruction Educational Games Think Pair Share Model Building Independent Instruction Research Homework Computer Interactive Instruction Activities Debates Discussion Direct Instruction understanding that the sum of the squares of the legs is equal to the square of the hypotenuse in a right triangle. Students will also understand that given three side lengths with this relationship forms a right triangle. 8.G.7: Students will employ the Pythagorean Theorem to calculate measurements in a variety of real-world contexts. 8.G.8: Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. 8.G.5: Students will prove facts about angles in a variety of geometric contexts. Vocabulary: hypotenuse, legs, Pythagorean Theorem, square root, right triangle, length, congruent, rot angle, right triangle, right triangle, exterior angles, interior angles, alternate interior angles, vertical angles, adjacent, supplementary, complimentary, corresponding, scale factor, transversal, parallel

19 Resources: McDougal Littel Book 3 Chapter, Measure Up, Buckle Down, McDougal Littel Pre-Algebra Chapter, People s Common Core, Algebra Structure and Method Chapter Carrollton Exempted Village School District Carrollton, Ohio OHIO COMMON CORE STATE STANDARDS Curriculum Map Course Title: Grade 8 Math Quarter 3 Academic Year: Essential Questions for this Unit: 1.How do we apply and relate different geometric properties with the real-world? Unit Core Standards Sample Instructional Strategies and Differentiation Volume 8.G.9 Know the formulas for the volumes Indirect Instruction of cones, cylinders, and spheres, and use Problem Solving Assessment 8.G.9: Students will model and solve real-world

20 them to solve real-world and mathematical problems. Inquiry Concept Attainment Experiential Instruction Educational Games Think Pair Share Model Building Independent Instruction Research Homework Computer Interactive Instruction Activities Debates Discussion Direct Instruction problems involving volume of cones, cylinders, and spheres by applying appropriate formulas. Vocabulary: volume, cylinder, cone, sphere, radius, height, Pi Resources: McDougal Littel Book 3 Chapter, Measure Up, Buckle Down, McDougal Littel Pre-Algebra Chapter, People s Common Core, Algebra Structure and Method Chapter

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