1. 1 REQUIREMENT INFORMATIONASSESSMENT INFORMATION TD3 Textbook Resource Glencoe Math: Course 3 Note: The Standards in each unit are not required to be taught in order. Every attempt should be made to teach material in the quarter to which it has been assigned. NWEA/MAP Assessment AZMerit Assessment AZMerit is a computer-based test which provides engaging questions and measures critical thinking skills for college and career readiness. For schools that are not yet ready, a paper-based version is available. AZMerit is aligned to Arizona’s state learning standards which detail what students should be able to do at each grade level. The test is designed to measure student learning and progress towards readiness for college and career. HOW TO READ THE CURRICULUM MAP Standards are grouped into units in each quarter. Example : Quarter 1: Unit 1 Knowledge for each standard appears directly adjacent to the strand and standard identification. When part of a standard is crossed out, that part of the standard will be addressed in a later unit. “Big Ideas” are what the students will understand by the end of the unit. “Essential Questions” stimulate ongoing thinking of “Big Ideas.” Key terms come from the Standards as well as additional academic words to support instruction. Standards are labeled by grade level (8), domain (EE), cluster (A), and standard (1). Example: 8.EE.A.1. The Big Ideas, Essential Questions, and Key Terms are student friendly language.( They are also highlighted in Blue) Tempe Elementary School District #3 8th GRADE - MATH 3/1/2016Tempe Elementary School District #3 8 TH GRADE NWEA/MAP INFORMATION Spring National Norm (2011) 245

2. Overview of Math Domains for 8 th Grade The Number System (NS) Know that there are numbers that are not rational, and approximate them by rational numbers. Expressions and Equations (EE) 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. Functions (F) Define, evaluate, and compare functions. Use functions to model relationships between quantities. Geometry (G) Understand congruence and similarity using physical models, transparencies, or geometry software. Understand and apply the Pythagorean Theorem. Solve real‐world and mathematical problems involving volume of cylinders, cones and spheres. Statistics and Probability (SP) Investigate patterns of association in bivariate data. 23/1/2016Tempe Elementary School District #3 8th GRADE - MATH

3. Standards for Mathematical Practices (MP) Standards Students are expected to: Explanations and Examples 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 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 or variable as related to the problem and decontextualize to manipulate symbolic representations by applying properties of operations. 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). 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?”, and “Does that always work?” They explain their thinking to others and respond to others’ thinking. 8.MP.4. Model with mathematics. In Grade 8, students model problem situations symbolically, graphically, tabularly, and contextually. 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. 3 8th GRADE - MATH 3/1/2016Tempe Elementary School District #3

4. Standards for Mathematical Practices (MP), continued Standards Students are expected to: Explanations and Examples 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 relationships between the angles created by a transversal. 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. 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. 8.MP.8. Look for and express regularity in repeated reasoning. In Grade 8, students use repeated reasoning to understand algorithms and make generalizations about patterns. Students use iterative processes to determine more precise rational approximations for irrational numbers. During multiple opportunities to solve and model problems, they notice that the slope of a line and rate of change are the same value. Students flexibly make connections between covariance, rates, and representations showing the relationships between quantities. 4 8th GRADE - MATH 3/1/2016Tempe Elementary School District #3

5. 8 th Grade Key Terms ALL CAPS Term = second and final year of appearance 5 alternate exterior angles alternate interior angles altitude angle of rotation base area bivariate data center of dilation center of rotation chord clustering coefficient constant converse correlation corresponding angles corresponding sides cube root deductive reasoning dependent variable diameter dilation domain elimination exponential form exterior angles frequency function function table gradient hypotenuse independent variable inductive reasoning input interior angles irrational number leg line of best fit linear linear association linear function mapping negative association nonlinear nonlinear function nonlinear association outlier output perfect cube perfect square pi (π) positive association power proof Pythagorean Theorem qualitative variable quantitative variable radical sign (  ) radius rate of change real number reflection remote interior angle repeating decimal rise rotation rotational symmetry run scale factor scatter plot scientific notation similar slant height slope slope-intercept form square root standard deviation standard form equation system of equations terminating decimal theorem transformation translation transversal two-way table univariate data x-intercept y-intercept 3/1/2016Tempe Elementary School District #3 8th GRADE - MATH

6. Tempe Elementary School District #36 7 The first examples in each cell are examples of discrete things. These are easier for students and should be given before the measurement examples. 4 The language in the array examples shows the easiest form of array problems. A harder form is to use the terms rows and columns: The apples in the grocery window are in 3 rows and 6 columns. How many apples are in there? Both forms are valuable. 5 Area involves arrays of squares that have been pushed together so that there are no gaps or overlaps, so array problems include these especially important measurement situations. 3/1/2016 8th GRADE - MATH

7. Quarter 1 Unit 1 Suggested Number of Days: 8 Days Big Ideas/Enduring Understandings: Rotations, reflections, and translations move the figure while maintaining congruency. Essential Questions: What happens when figures undergo a rotation, reflection, or translation? Standards for Mathematical Practice: 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. Cluster G.A: Understand congruence and similarity using physical models, transparencies, or geometry software. Key Terms AZCCRSKnowledgeSkills reflection rotation center of rotation rotational symmetry transformation translation 8.G.A.1 Rotations Reflections Translations V ERIFY 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. Resources: http://bit.ly/1qj1Ywn 7 8th GRADE - MATH 3/1/2016Tempe Elementary School District #3

8. Quarter 1 Unit 2 Suggested Number of Days: 11 Days Big Ideas/Enduring Understandings: Congruency between two figures is determined by the sequence of transformations. Essential Questions: How can congruency between two figures be determined? Standards for Mathematical Practice: 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. Cluster G.A: Understand congruence and similarity using physical models, transparencies, or geometry software. Key Terms AZCCRSKnowledgeSkills angle of rotation 8.G.A.2 Congruence Rotations Reflections Translations Sequence U NDERSTAND 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 Also in Q1-Unit 3 Two-dimensional figures Coordinates D ESCRIBE the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. Resources: http://bit.ly/24XtcvD 8 8th GRADE - MATH 3/1/2016Tempe Elementary School District #3

9. Quarter 1 Unit 3 Suggested Number of Days: 10 Days Big Ideas/Enduring Understandings: Geometric figures can change size and/or position during dilations and other transformations while maintaining proportional attributes. Essential Questions: How do ratios and similarity relate to dilations? Standards for Mathematical Practice: 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. Cluster G.A: Understand congruence and similarity using physical models, transparencies, or geometry software. Key Terms AZCCRSKnowledgeSkills similar dilation center of dilation scale factor 8.G.A.3 Also in Q1-Unit 2 Dilations Translations Rotations Reflections Coordinates Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. 8.G.A.4 Similarity Sequence 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. Resources: http://bit.ly/1NtBP9p 9 8th GRADE - MATH 3/1/2016 Tempe Elementary School District #3

10. Quarter 1 Unit 4 Suggested Number of Days: 14 Days Big Ideas/Enduring Understandings: Irrational numbers are expressed symbolically or approximated to a close rational number because they are non-repeating, non-terminating decimals. Between any two rational numbers there are an infinite number of rational and irrational numbers. Essential Questions: How are irrational numbers expressed? How many numbers are between two rational numbers? Standards for Mathematical Practice: 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. Cluster NS.A: Know that there are numbers that are not rational, and approximate them by rational numbers. EE.A: Work with radicals and integer exponents. Key Terms AZCCRSKnowledgeSkills irrational number repeating decimal terminating decimal real number pi (π) square root cube root square root sign cube root sign perfect square perfect cube radical sign (√) 8.NS.A.1 Irrational numbersKnow 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.A.2 Irrational number comparisonsUse 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.,  2 ). Note: 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. 10 8th GRADE - MATH 3/1/2016Tempe Elementary School District #3

11. 8.EE.A.2 Square root Cube root U SE 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. E VALUATE square roots of small perfect squares and cube roots of small perfect cubes. K NOW that √2 is irrational. Resources: http://bit.ly/23OxmA2 11 8th GRADE - MATH 3/1/2016Tempe Elementary School District #3

12. Quarter 2 Unit 5 Suggested Number of Days: 12 Days Big Ideas/Enduring Understandings: The sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse. The Pythagorean Theorem can be used to find the distance between the two points when those points form the hypotenuse. Essential Questions: What is the relationship between the sides of a right triangle? How can the distance between two points be found? Standards for Mathematical Practice: 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. Cluster G.B: Understand and apply the Pythagorean Theorem. Key Terms AZCCRSKnowledgeSkills proof theorem leg hypotenuse Pythagorean Theorem converse exterior angles interior angles alternate exterior angles alternate interior angles corresponding angles deductive reasoning inductive reasoning 8.G.B.6 Pythagorean Theorem Converse E XPLAIN a proof of the Pythagorean Theorem and its converse. 8.G.B.7 Pythagorean Theorem Real-world problems A PPLY 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 Pythagorean Theorem Distance A PPLY the Pythagorean Theorem to FIND the distance between two points in a coordinate system. Resources: http://bit.ly/1Tby5d0 12 8th GRADE - MATH 3/1/2016 Tempe Elementary School District #3

13. Quarter 2 Unit 6 Suggested Number of Days: 11 Days Big Ideas/Enduring Understandings: When graphing a linear equation, the slope determines the slant of the line. Representing equations in different symbolic forms allow for patterns to be identified and for equivalency to be determined. Essential Questions: What does the slope determine when graphing a linear equation? Why are there different ways of representing equations? Standards for Mathematical Practice: 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. Cluster EE.B: Understand the connections between proportional relationships, lines, and linear equations. Key Terms AZCCRSKnowledgeSkills slope rise run gradient y-intercept x-intercept standard form equation slope-intercept form 8.EE.B.5 SlopeGraph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. Note: 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 Slope y = mx + b 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. Resources: http://bit.ly/1Tb8a7a 13 8th GRADE - MATH 3/1/2016Tempe Elementary School District #3

14. Quarter 2 Unit 7 Suggested Number of Days: 16 Days Big Ideas/Enduring Understandings: Functions can be represented in multiple ways for the purpose of comparing rate of change. In a linear function, for each input there is one output that is determined by the rate of change. Information about a real-world context can be shown graphically, symbolically, and verbally in terms of its function. Essential Questions: Why are functions represented in multiple ways? What is the relationship between the input and output of a linear function? How can real-world functional relationships be represented? Standards for Mathematical Practice: 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. Cluster F.A: Define, evaluate, and compare functions. F.B: Use functions to model relationships between quantities. Key Terms AZCCRSKnowledgeSkills domain function function table input output vertical line test dependent variable independent variable mapping linear linear function constant rate of change 8.F.A.1 Function Graph of a function U NDERSTAND 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 Properties of functionsC OMPARE properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). Note: 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. 14 8th GRADE - MATH 3/1/2016Tempe Elementary School District #3

15. 8.F.A.3 Also in Q3-Unit 10 Linear functionI NTERPRET the equation y = mx + b as defining a linear function, whose graph is a straight line; GIVE examples of functions that are not linear. Note: 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. 8.F.B.4 Linear relationship Rate of change C ONSTRUCT a function to model a linear relationship between two quantities. D ETERMINE 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. Resources: http://bit.ly/1Tb8gvi 15 8th GRADE - MATH 3/1/2016Tempe Elementary School District #3

16. Quarter 2 Unit 8 Suggested Number of Days: 7 Days Big Ideas/Enduring Understanding: The correlation between bivariate data shows to what degree the variables affect one another. Essential Questions: What does the correlation between bivariate data show? Standards for 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. Cluster SP.A: Investigate patterns of association in bivariate data. Key Terms AZCCRSKnowledgeSkills scatter plot univariate data bivariate data quantitative variable qualitative variable clustering outlier positive association negative association linear association nonlinear nonlinear association correlation line of best fit 8.SP.A.1 Scatter plotsConstruct 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 Quantitative variablesKnow 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. Resources: http://bit.ly/1Op3TuP 16 8th GRADE - MATH 3/1/2016Tempe Elementary School District #3

17. Quarter 3 Unit 9 Suggested Number of Days: 7 Days Big Ideas/Enduring Understanding: The line of best fit can help determine an approximate linear equation for a set of data which can then be used to make inferences. Essential Questions: How can the line of best fit assist in making inferences about a set of data? Standards for 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. Cluster SP.A: Investigate patterns of association in bivariate data. Key Terms AZCCRSKnowledgeSkills frequency standard deviation two-way table 8.SP.A.3 Linear model Slope Intercept Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. Note: 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 Bivariate data Relative frequencies 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. 17 8th GRADE - MATH 3/1/2016Tempe Elementary School District #3

18. Note: 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? Resources: http://bit.ly/1NtC2Ju 18 8th GRADE - MATH 3/1/2016Tempe Elementary School District #3

19. Quarter 3 Unit 10 Suggested Number of Days: 10 Days Big Ideas/Enduring Understandings: There is no constant relationship between the input and output of a nonlinear function because the slope changes. Essential Questions: What is the relationship between the input and output of a nonlinear function? Standards for Mathematical Practice: 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. Cluster F.A: Define, evaluate, and compare functions. F.B: Use functions to model relationships between quantities. Key Terms AZCCRSKnowledgeSkills nonlinear function 8.F.A.3 Also in Q2-Unit 7 Linear function Nonlinear function 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. Note: 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. 8.F.B.5 Functional relationshipsDescribe 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. Resources: http://bit.ly/27kT9nj 19 8th GRADE - MATH 3/1/2016 Tempe Elementary School District #3

20. Quarter 3 Unit 11 Suggested Number of Days: 11 Days Big Ideas/Enduring Understandings: Solving an equation is finding the value(s) of a variable for which two expressions represent the same quantity. Essential Questions: What does it mean to solve an equation? Standards for Mathematical Practice: 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. Cluster EE.C: Analyze and solve linear equations and pairs of simultaneous linear equations. Key Terms AZCCRSKnowledgeSkills coefficient 8.EE.C.7 Linear equationsSolve 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. Resources: http://bit.ly/1TbyAni 20 8th GRADE - MATH 3/1/2016 Tempe Elementary School District #3

21. Quarter 3 Unit 12 Suggested Number of Days: 17 Days Big Ideas/Enduring Understandings: Solving a system of equations means finding the points of intersection by substituting, eliminating, or graphing. Essential Questions: What does it mean to solve a system of equations? Standards for Mathematical Practice: 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. Cluster EE.C: Analyze and solve linear equations and pairs of simultaneous linear equations. Key Terms AZCCRSKnowledgeSkills system of equations elimination 8.EE.C.8 Systems of linear equationsA NALYZE and SOLVE pairs of simultaneous linear equations. a.U NDERSTAND 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.S OLVE systems of two linear equations in two variables algebraically, and ESTIMATE solutions by graphing the equations. S OLVE simple cases by inspection. Note: For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6. c.S OLVE real-world and mathematical problems leading to two linear equations in two variables. 21 8th GRADE - MATH 3/1/2016Tempe Elementary School District #3

22. Note: 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. Resources: http://bit.ly/1s86W00 22 8th GRADE - MATH 3/1/2016Tempe Elementary School District #3

23. Quarter 4 Unit 13 Suggested Number of Days: 12 Days Big Ideas/Enduring Understandings: Using exponential form enables us to write very large or very small numbers in an abbreviated way. Essential Questions: Why is exponential form useful? Standards for Mathematical Practice: 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. Cluster EE.A: Work with radicals and integer exponents. Key Terms AZCCRSKnowledgeSkills power exponential form scientific notation 8.EE.A.1 Integer exponents Numerical expressions Know and apply the properties of integer exponents to generate equivalent numerical expressions. Note: For example, 3 2  3 –5 = 3 –3 = 1/3 3 = 1/27. 8.EE.A.3 Powers of 10Use 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. Note: For example, estimate the population of the United States as 3  10 8 and the population of the world as 7  10 9, and determine that the world population is more than 20 times larger. 8th GRADE - MATH 23 3/1/2016Tempe Elementary School District #3

24. 8.EE.A.4 Scientific notation 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. Resources: http://bit.ly/1WvmjwP 8th GRADE - MATH 24 3/1/2016Tempe Elementary School District #3

25. Quarter 4 Unit 14 Suggested Number of Days: 15 Days Big Ideas/Enduring Understandings: Special angle relationships determine how to write and solve equations for angle measurements. Essential Questions: What determines how to write and solve equations for angle measurements? Standards for Mathematical Practice: 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. Cluster G.A: Understand congruence and similarity using physical models, transparencies, or geometry software. Key Terms AZCCRSKnowledgeSkills corresponding sides transversal remote interior angle 8.G.A.5 Angles Similar Triangles 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. Note: 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. Resources: http://bit.ly/1TTbhNY 8th GRADE - MATH 25 3/1/2016Tempe Elementary School District #3

26. Quarter 4 Unit 15 Suggested Number of Days: 12 Days Big Ideas/Enduring Understandings: The formulas for volume are based on the relationships of length, width, and height. Essential Questions: What is the basis for the volume formulas? Standards for Mathematical Practice: 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. Cluster G.C: Solve real-world and mathematical problems involving volume of cylinders, cones and spheres. Key Terms AZCCRSKnowledgeSkills base area altitude chord radius diameter slant height 8.G.C.9 VolumeK NOW the formulas for the volumes of cones, cylinders, and spheres and USE them to solve real-world and mathematical problems. Resources: http://bit.ly/24XuLti 8th GRADE - MATH 26 3/1/2016Tempe Elementary School District #3