Grade 8 MATHEMATICS MINI-CURRICULUM GUIDE

Transcription

1 TUCSON UNIFIED SCHOOL DISTRICT Grade 8 MATHEMATICS MINI-CURRICULUM GUIDE Version 1.1

2 Contents I. Mission Statement, Philosophy and Goals II. TUSD Scope & Sequence III. AZCCR Standards IV. Textbook Guide V. Cluster Emphases (Major, Supporting, Additional)

3 Scope & Sequence Mathematics: Grade 8 While using this document, please note the following: 1. District-wide Assessments will follow the Quarterly Scope & Sequences. 2. Major Clusters listed at the end of each Semester reflect the content emphases at each grade level. These are the areas of intensive focus, where students need fluent understanding and application of the core. These are also provided because curriculum, instruction and assessment at each grade must reflect the focus and emphasis of the standards. The following are some recommendations for using the cluster level emphases: Do Use the guidance to inform instructional decisions regarding time and other resources spent on clusters of varying degrees of emphasis. Allow the focus on the major work of the grade to open up the time and space to bring the Standards for Mathematical Practice to life in mathematics instruction through sense making, reasoning, arguing and critiquing, modeling, etc. Evaluate instructional materials taking the cluster level emphases into account. The major work of the grade must be presented with the highest possible quality; the supporting work of the grade should indeed support the major focus, not detract from it. Set priorities for other implementation efforts taking the emphases into account, such as staff development; new curriculum development; or revision of existing formative or summative testing at the state, district or school level. Don t Neglect any material in the standards. (Instead, use the information provided to connect Supporting Clusters to the other work of the grade.) Sort clusters from Major to Supporting, and then teach them in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters. Use the cluster headings as a replacement for the standards. All features of the standards matter from the practices to surrounding text to the particular wording of individual content standards. Guidance is given at the cluster level as a way to talk about the content with the necessary specificity yet without going so far into detail as to compromise the coherence of the standards.

4 Mathematics Content Focus: Turning decimal expansions into fractions and deepening understanding of the meaning of decimal expansions sets a firm foundation for understanding irrational numbers. Students will learn that the square roots of perfect squares are rational numbers, and that the square roots of nonperfect squares, such as or, are examples of irrational numbers. Further work with exponents, including scientific notation, naturally flow from the understanding of squares and cubes. TUSD Scope & Sequence: 8 th Grade Math 1 st Quarter 2 nd Quarter Number theory, Expressions, and Equations Congruence, Similarity, and Functions Mathematical Practice Focus: Mathematics Content Focus: 1: Through the study of linear equations, Students analyze the characteristics students contextualize equation and relationships of shapes and representations of real-life problems by structures, engage in logical writing equation representations reasoning, and use tools and 2: Students reason abstractly by constructing techniques to determine measurement. the integer exponent operation rules. Students learn that geometry and 3: Students construct arguments by creating measurement are useful in equations that have one solution, infinite representing and solving problems in solutions or no solutions and then defend their the real world as well as in equations. mathematics. 5: Students may use a CAS (Computer Algebra System), graphing software, data Students understand that functions software, or other technology tools to explore describe relationships and will be able solving linear equations to compare and construct a function. 6: Through exploration of scientific notation, students should see that precision is relative to need. 7: Scientific notation also offers a chance for students to make use of the structure of numbers. Target Standards: 8.NS.A EE.A EE.C.7 Mathematical Practice Focus: 1: Students seek the meaning of a problem and look for efficient ways to represent and solve it. 2: Students represent a wide variety of real world contexts through the use of real numbers and variables in mathematical expressions, equations, and inequalities 3: Students justify their reasoning for choosing a particular sequence 4: Students manipulate figures to learn the properties of similar and congruent figures. 5: Students draw pictures, use applets, or write equations to model a linear function 6: Students use clear and precise language in their discussions 7: Students routinely seek patterns or structures to solve problems. 8: Students use repeated reasoning to understand algorithms and make generalizations about patterns. Target Standards: 8.G.A EE.B.6 8.F.A F.B.4-5 Complementary Standards: no additional standards Complementary Standards: 8.F.A.1, 3 Foundational Standards: Foundational Standards: 7.NS.A EE.A EE.B EE.C.9 7.G.A G.B RP.A.1-3 Semester Constant Major Clusters: (Domains are in parentheses) 8.EE.A Work with radicals and integer exponents. (Expressions and Equations) 8.EE.B Understand the connections between proportional relationships, lines, and linear equations. (Expressions and Equations) 8.EE.C Analyze and solve linear equations and pairs of simultaneous linear equations. (Expressions and Equations) 8.F.A Define, evaluate, and compare functions. (Functions) 8.G.B Understand and apply the Pythagorean Theorem. (Geometry) 8.G.A Understand congruence and similarity using physical models, transparencies, or geometry software. (Geometry)

5 Mathematics Content Focus: Students explore linear relationships through functions and their graphs. For example, students learn that proportional relationships are part of a broader group of linear functions, and they are able to identify whether a relationship is linear. Nonlinear functions are included for comparison. Students also recognize that graphed lines with one point of intersection (different slopes) will have one solution, parallel lines (same slope, different y- intercepts) will have no solutions, and lines that are the same (same slope, same y- intercept) will have infinitely many solutions. Target Standards: 8.EE.B.5 8.EE.C.8 TUSD Scope & Sequence: 8 th Grade Math 3 rd Quarter 4 th Quarter Linear Relationships Pythagorean Theorem, Volume and Bivariate Data Mathematical Practice Focus: Mathematics Content Focus: 1: Students check their thinking by asking In Unit 6, students apply their themselves, What is the most efficient way to knowledge of triangles to various solve the problem?, Does this make sense?, real-world 2-D and 3-D situations. and Can I solve the problem in a different, Students also find the volume of even easier, way? objects, but also missing dimensions 2: Students determine the most practical such as the radius or height. solution representation. Students apply experiences with 4: Students model problems symbolically, coordinate planes and linear graphically, contextually, and with a table. functions in the study of association Students solve systems of linear equations and between two variables related to a compare properties of functions in different question of interest. forms. 7: Students routinely seek patterns or structures to model and solve problems. 8: Students use repeated reasoning to understand algorithms and make generalizations about patterns. Target Standards: 8.G.B G.C.9 8.SP.A.1-4 Complementary Standards: 8.EE.C.7 8.SP.A.1-3 Complementary Standards: 8.NS.A.1, 2 Foundational Standards: Determine unit rate. Apply proportional relationships. Solve equations with numeric and graphical representations of solutions. Calculate slope/rate of change. Semester Constant Major Clusters: (Domains are in parentheses) 8.EE.A Work with radicals and integer exponents. (Expressions and Equations) 8.EE.B Understand the connections between proportional relationships, lines, and linear equations. (Expressions and Equations) 8.EE.C Analyze and solve linear equations and pairs of simultaneous linear equations. (Expressions and Equations) 8.F.A Define, evaluate, and compare functions. (Functions) 8.G.B Understand and apply the Pythagorean Theorem. (Geometry) 8.G.A Understand congruence and similarity using physical models, transparencies, or geometry software. (Geometry) Mathematical Practice Focus: 1: Students make sense of more complicated, multi-step Pythagorean problems. 2: Students represent real world contexts through the use of real numbers and variables in mathematical expressions, equations, and inequalities 3: Students prove whether a triangle is a right triangle or not. 4: Students form expressions, equations, or inequalities from real world contexts and connect symbolic and graphical representations 5: Students determine when certain tools or data are appropriate. 6: Students attend to precision by noticing that precision is relative to need. 8: Students use repeated reasoning to understand algorithms and make generalizations about patterns. Foundational Standards: Calculate the area of circles using pi. (7.G.B.4) Rewrite expressions in different forms. (7.EE.A.2) Square and cube numbers and calculate square and cube roots. (8.EE.A.2)

6 Arizona s College and Career Ready Standards Mathematics Grade 8 Standards Arizona s College and Career Ready Standards Mathematics 8 th Grade Standards 1. Formulating and reasoning about expressions and equations, including modeling an association in bivariate data with a linear equation, and solving linear equations and systems of linear equations Students use linear equations and systems of linear equations to represent, analyze, and solve a variety of problems. Students recognize equations for proportions (y/x = m or y = mx) as special linear equations (y = mx + b), understanding that the constant of proportionality (m) is the slope, and the graphs are lines through the origin. They understand that the slope (m) of a line is a constant rate of change, so that if the input or x-coordinate changes by an amount A, the output or y-coordinate changes by the amount m A. Students also use a linear equation to describe the association between two quantities in bivariate data (such as arm span vs. height for students in a classroom). At this grade, fitting the model, and assessing its fit to the data are done informally. Interpreting the model in the context of the data requires students to express a relationship between the two quantities in question and to interpret components of the relationship (such as slope and y-intercept) in terms of the situation. Students strategically choose and efficiently implement procedures to solve linear equations in one variable, understanding that when they use the properties of equality and the concept of logical equivalence, they maintain the solutions of the original equation. Students solve systems of two linear equations in two variables and relate the systems to pairs of lines in the plane; these intersect, are parallel, or are the same line. Students use linear equations, systems of linear equations, linear functions, and their understanding of slope of a line to analyze situations and solve problems. 2. Grasping the concept of a function and using functions to describe quantitative relationships Students grasp the concept of a function as a rule that assigns to each input exactly one output. They understand that functions describe situations where one quantity determines another. They can translate among representations and partial representations of functions (noting that tabular and graphical representations may be partial representations), and they describe how aspects of the function are reflected in the different representations. 3. Analyzing two- and three-dimensional space and figures using distance, angle, similarity, and congruence, and understanding and applying the Pythagorean Theorem Students use ideas about distance and angles, how they behave under translations, rotations, reflections, and dilations, and ideas about congruence and similarity to describe and analyze two-dimensional figures and to solve problems. Students show that the sum of the angles in a triangle is the angle formed by a straight line, and that various configurations of lines give rise to similar triangles because of the angles created when a transversal cuts parallel lines. Students understand the statement of the Pythagorean Theorem and its converse, and can explain why the Pythagorean Theorem holds, for example, by decomposing a square in two different ways. They apply the Pythagorean Theorem to find distances between points on the coordinate plane, to find lengths, and to analyze polygons. Students complete their work on volume by solving problems involving cones, cylinders, and spheres. The Number System - Know that there are numbers that are not rational, and approximate them by rational numbers. 8.NS.A.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.A.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, show that 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 - Work with radicals and integer exponents. 8.EE.A.1: Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, = 3 3 = 1/3 3 = 1/27. 8.EE.A.2: Use square root and cube root symbols to represent solutions to equations of the form x 2 = p and x 3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that is irrational. 8.EE.A.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 and the population of the world as , and determine that the world population is more than 20 times larger. 8.EE.A.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.

7 Understand the connections between proportional relationships, lines, and linear equations. 8.EE.B.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.B.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. Analyze and solve linear equations and pairs of simultaneous linear equations. 8.EE.C.7: Solve linear equations in one variable. 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). b. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. 8.EE.C.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. 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 of points, determine whether the line through the first pair of points intersects the line through the second pair. Functions - Define, evaluate, and compare functions. 8.F.A.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. (Note: Function notation is not required in Grade 8.) 8.F.A.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.A.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 = 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) and (3,9), which are not on a straight line. Use functions to model relationships between quantities. 8.F.B.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.B.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. Geometry - Understand congruence and similarity using physical models, transparencies, or geometry software. 8.G.A.1: 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.A.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.A.3: Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. 8.G.A.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 8.G.A.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. Understand and apply the Pythagorean Theorem. 8.G.B.6: Explain a proof of the Pythagorean Theorem and its converse. 8.G.B.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.B.8: Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres. 8.G.C.9: Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. Statistics and Probability - Investigate patterns of association in bivariate data. 8.SP.A.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.A.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.A.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.A.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? Mathematical Practices 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.

9 8 th Grade Math Textbook Guide - Overview Textbook Resources (8 th Grade Math) Quarter Target Standards Complementary Standards HOLT Mathematics: Chapters 2, 4, 11, 12 Math In Context: Algebra Rules! It s All The Same: Section D Graphing Equations Looking At An Angle: Section E. Patterns and Figures: Section C, Revisiting Numbers: Sections A, B, E Connected Math: CC Investigation 1 - Exponents Growing, Growing, Growing: Investigations 1-2, 4-5 Looking for Pythagoras: Investigations NS EE EE.7 (none) HOLT Mathematics: Chapters 3, 4, 5, 7, 8, 11, 12, 13 Math in Context: Algebra Rules! Graphing Equations It s All The Same: Sections A, B, C, E Level 2 Triangles and Beyond: Section E Looking at Angles Patterns and Symbols Revisiting Numbers Ups and Downs: Investigations A, B, C Connected Math: Frogs, Fleas, and Painted Cubes: Investigations 1-4 Growing, Growing, Growing: Investigations 1-4 Kaleidoscopes, Hubcaps, and Mirrors: Investigations 1-5 Looking for Pythagoras: Investigations 2 Moving Straight Ahead: Investigations 1-5 Say It With Symbols: Investigations 1-4 Stretching and Shrinking: Investigations 2 The Shapes of Algebra: Investigations G EE.6 8.F F.1, 3

10 Textbook Resources (8 th Grade Math) Quarter Target Standards Complementary Standards Thinking With Mathematical Models: Investigations 1-3 Variables and Patterns: Investigations 1-4 HOLT Mathematics: Chapter , 9.7, 11 and 12 Math in Context: Revisiting Numbers Algebra Rules! Graphing Equations Insights into Data 3 8.EE.5, 8 8.EE.7 8.SP.1-3 Connected Math Looking or Pythagoras Investigations 2 Samples and Population Investigation 4 HOLT Mathematics: Chapters 2, 4, 5, 8, 9.7, 8, 12.7 Math In Context: Insights into Data It s All The Same: Section D Looking At An Angle: Section E Patterns and Symbols Revisiting Numbers: Sections A, E Connected Math: Filling and Wrapping: Investigations 3-5 Kaleidoscopes, Hubcaps, and Mirrors: Investigations 1-3 Looking for Pythagoras: Investigations 2-4 Samples and Population: Investigations 4 Say It With Symbols: Investigations G G.9 8.SP NS.1-2

11 8 th Grade Math Textbook Guide - Detail Textbook Resources by Standard (8 th Grade Math) 8.NS.1 HOLT Mathematics: Chapters 2.1, 4.7. Additional Pages: 67, 71, 106, 109, 200, 206, 207, 827. Math In Context: Revisiting Numbers: Sections E, Connected Math: Looking for Pythagoras: Investigations 4 8.NS.2 HOLT Mathematics: Chapters 4.6. Additional Pages: 199, 200, 206, 207. Math in Context: Revisiting Numbers: Section A, E. Connected Math: Looking for Pythagoras: Investigations 4 8.EE.1 HOLT Mathematics: Chapters 4.3 Additional Pages: 178, 205, 207. Math In Context: Revisiting Numbers: Section A, B. Connected Math: Growing, Growing, Growing: Investigations 5 8.EE.2 HOLT Mathematics: Chapters 4.5, 4.8 Additional Pages:200, 206, 207, 830. Math in Context: Revisiting Numbers: Section E. Patterns and Figures: Section C, It s All The Same: Section D, Looking At An Angle: Section E. Connected Math: Looking for Pythagoras: Investigations 2-4, CC Investigation 1 - Exponents 8.EE.3 HOLT Mathematics: Chapters 4.4 Additional Pages: 180, 205, 207 Math in Context: Revisiting Numbers: Section A, B. Connected Math: Growing, Growing, Growing: Investigations 1-2, EE.4 HOLT Mathematics: Chapters 4.4 Additional Pages: 179, 180, 205, 207 Math in Context: Revisiting Numbers: Section A, B. Connected Math: Growing, Growing, Growing: Investigations 5 8.EE.1-7 HOLT Mathematics: Chapter , 11 and 12 and extension Math in Context: Revisiting Numbers, Algebra Rules!, Graphing Equations Connected Math 8th grade: Looking or Pythagoras Investigations 2 Target Quarter Standards 1 8.NS EE EE.7 Complementary Standards (none)

12 Textbook Resources by Standard (8 th Grade Math) 8.G.1 HOLT Mathematics: Chpt 7.7 Math in Context: Level 2 Triangles and Beyond: E Connected Math: Stretching and Shrinking: Investigations 2, Kaleidoscopes, Hubcaps, and Mirrors: Investigations G.1a HOLT Mathematics: Chpt 7.1 Math in Context: None Connected Math: Stretching and Shrinking: Investigations 2, Kaleidoscopes, Hubcaps, and Mirrors: Investigations G.1b HOLT Mathematics: Chapters 7.1 Additional Pages: 334 Math in Context: It s All The Same: Section A. Connected Math: Stretching and Shrinking: Investigations 2, Kaleidoscopes, Hubcaps, and Mirrors: Investigations G.1c HOLT Mathematics: Chapters 7.2 Additional Pages: 334 Math in Context: It s All The Same: Section A, C, E. Connected Math: Stretching and Shrinking: Investigations 2, Kaleidoscopes, Hubcaps, and Mirrors: Investigations G.2 HOLT Mathematics: Chapters 7.7 Additional Pages: , 378 Math in Context: None Connected Math: Kaleidoscopes, Hubcaps, and Mirrors: Investigations 3 8.G.3 HOLT Mathematics: Chapters 5.6, 7.7 Additional Pages: , 258, 264, 265, , 378 Math in Context: It s All The Same: Section B. Connected Math: Stretching and Shrinking: Investigations 2, Kaleidoscopes, Hubcaps, and Mirrors: Investigations 2, 5. 8.G.4 HOLT Mathematics Chapters 5.5, 5.6 Additional Pages: , 264, 265 Math in Context: It s All The Same: Section B. Connected Math: Stretching and Shrinking: Investigations 2, Kaleidoscopes, Hubcaps, and Mirrors: Investigations 2. Target Quarter Standards 2 8.G EE.6 8.F.1-5 Complementary Standards 8.F.1, 3

13 Textbook Resources by Standard (8 th Grade Math) 8.G.1-5 HOLT Mathematics: Chapter 7, ,8.9,4.8, Math in Context: Patterns and Symbols, It s All the Same, Looking at Angle Connected Math: Looking or Pythagoras, Kaleidoscopes, Hubcaps and Mirrors Quarter Target Standards Complementary Standards 8.EE.1-7 HOLT Mathematics: Chapter , 11 and 12 and extension Math in Context: Revisiting Numbers, Algebra Rules!, Graphing Equations Connected Math 8th grade: Looking or Pythagoras Investigations 2 8.F.1 HOLT Mathematics: Chapters 3.4, 3.5, 13.4, 13.5, 13.6, 13.7 Additional Pages: 146, 147, 152, 153, , 718, 723, 724, 725. Math in Context: Ups and Downs: Investigations A, B, C, Ups and Downs: Section A, B, C. Connected Math: Variables and Patterns: Investigations 1-4, Moving Straight Ahead: Investigations 1-5, Thinking With Mathematical Models: Investigations 1-3, Growing, Growing, Growing: Investigations 1-4, Frogs, Fleas, and Painted Cubes: Investigations 1-4, Say It With Symbols: Investigations F.2 HOLT Mathematics: Chapters 13.5 Math in Context: None Connected Math: Moving Straight Ahead: Investigations 1-4, Thinking With Mathematical Models: Investigations 1, Growing, Growing, Growing: Investigations 1, Frogs, Fleas, and Painted Cubes: Investigations 1-4, The Shapes of Algebra: Investigations 2-4, Say It With Symbols: Investigations 2 8.F.1-4 HOLT Mathematics: Chapter ,13.4 Math in Context: Ups and Downs, Algebra Rules!, Patterns and Figures Connected Math: 7 th grade: Moving Straight Ahead 8.F.5 HOLT Mathematics: Chapters 3.5, 12.1, 12.2, 12.5, 13.4 Additional Pages: 648, 670, 673. Math in Context: Ups and Downs: Investigations A, C. Connected Math: Moving Straight Ahead: Investigations 1-2,4, Thinking With Mathematical Models: Investigations 2, Growing, Growing, Growing: Investigations 1-4, Frogs, Fleas, and Painted Cubes: Investigations,. 1-4, Say It With Symbols: Investigations 4. 8.EE.1-8 HOLT Mathematics: Chapter , 11 and 12 and extension Math in Context: Revisiting Numbers, Algebra Rules!, Graphing Equations Connected Math Looking or Pythagoras Investigations EE.5, 8 8.EE.7 8.SP.1-3

14 Textbook Resources by Standard (8 th Grade Math) Quarter Target Standards Complementary Standards 8.SP.1-3 HOLT Mathematics: Chapters 9.7, 12.7 Math in Context: Insights into Data Connected Math Samples and Population Investigation 4 8.NS.1 HOLT Mathematics: Chapters 2.1, 4.7. Additional Pages: 67, 71, 106, 109, 200, 206, 207, 827. Math In Context: Revisiting Numbers: Sections E, Connected Math: Looking for Pythagoras: Investigations 4 8.NS.2 HOLT Mathematics: Chapters 4.6. Additional Pages: 199, 200, 206, 207. Math in Context: Revisiting Numbers: Section A, E. Connected Math: Looking for Pythagoras: Investigations 4 8.G.6 HOLT Mathematics Chapters 4.8 Math in Context: It s All The Same: Section D. Looking At An Angle: Section E. Connected Math: Looking for Pythagoras: Investigations 3 8.G.7 HOLT Mathematics Chapters 4.8 Additional Pages: 200, 206, 267 Math in Context: It s All The Same: Section D. Looking At An Angle: Section E. Connected Math: Looking for Pythagoras: Investigations G.8 HOLT Mathematics Chapters 4.8 Math in Context: It s All The Same: Section D. Looking At An Angle: Section E. Connected Math: Looking for Pythagoras: Investigations G.9 HOLT Mathematics Chapters 8.5, 8.6, 8.9 Additional Pages: 412, , 444, 451, 452, 453. Math in Context: None Connected Math: Filling and Wrapping: Investigations 3-5, Kaleidoscopes, Hubcaps, and Mirrors: Investigations 1-3, Looking for Pythagoras: Investigations 3-4, Say It With Symbols: Investigations SP.1-4 HOLT Mathematics: Chapters 9.7, 12.7 Math in Context: Insights into Data Connected Math Samples and Population Investigation G G.9 8.SP NS.1-2

15 Major, Supporting, and Additional Clusters Some clusters require greater emphasis than the others based on the depth of the ideas, the time that they take to master, and/or their importance to future mathematics or the demands of college and career readiness. In addition, an intense focus on the most critical material at each grade allows depth in learning, which is carried out through the Standards for Mathematical Practice. Explanations of terms used: Major clusters areas of intensive focus, where students need fluent understanding and application of the core concepts Supporting clusters rethinking and linking; areas where some material is being covered, but in a way that applies core understandings Additional Clusters expose students to other subjects, though at a distinct, level of depth and intensity Depth Opportunities - Highlights some individual standards that play an important role in the content at each grade. The indicated mathematics might be given an especially in-depth treatment, as measured, for example, by the type of assessment items; the number of days; the quality of classroom activities to support varied methods, reasoning, and explanation; the amount of student practice; and the rigor of expectations for depth of understanding or mastery of skills. Note, however, that a standard can be individually important even though the indicated mathematics may require relatively little teaching time.

16 Cluster Emphasis: Grade 8 Note: Domains are in Bold. Clusters are listed under each Domain. Major Supporting Additional Expressions and Equations The Number System Geometry Work with radicals and integer exponents. Understand the connections between proportional relationships, lines, and linear equations. Analyze and solve linear equations and pairs of simultaneous linear equations. Know that there are numbers that are not rational, and approximate them by rational numbers. Work with the number system in this grade is intimately related to work with radicals, and both of these may be connected to the Pythagorean Theorem as well as to volume problems, e.g., in which a cube has known volume but unknown edge lengths. Solve real world and mathematical problems involving volume of cylinders, cones, and spheres. Functions Define, evaluate, and compare functions. Geometry Understand and apply the Pythagorean Theorem. Understand congruence and similarity using physical models, transparencies, or geometry software. Depth Opportunities: 8.EE5, 7, 8; 8.F.2; 8.G.7 Functions Use functions to model relationships between quantities. The work in this cluster involves functions for modeling linear relationships and a rate of change/initial value, which supports work with proportional relationships and setting up linear equations. Statistics and Probability Investigate patterns of association in bivariate data. Looking for patterns in scatterplots and using linear models to describe data are directly connected to the work in the Expressions and Equations clusters. Together, these represent a connection to the Standard for Mathematical Practice Model with mathematics.