This document was intended to be used digitally. This means that many of the supporting resources can only be accessed through the internet and/or through the hyper-links created within the document itself. In order to activate the link properties hold down the control (Ctrl) key and mouse over the linked information. A hand should appear and you should be able to left-click the link to access the resource. Contained within the curriculum map you will find dually-aligned 8th grade NM and standards, as well as, the remaining 8th grade and NM standards that weren t able to be dually-aligned. Each learning target is supported by resources for student practice activities and application of math practices. Additional clarification and examples for each learning target can be found in the Envisioning the Standards and Lesson Plan sections. Table of Contents Units Envisioning the Standards pp. 51-83 Standards for Mathematical Practice pp. 84-86 Unit Number Unit Title Suggested Length Sample Lesson 1 pp. 2-4 Input-Output Relationships 5 Days Unit 1 Lesson Plan 2 pp. 5-9 Linear Functions 7 Days Unit 2 Lesson Plan 3 pp. 10-13 Patterns in Bivariate Data 10 Days Unit 3 Lesson Plan 4 pp. 14-15 Linear Equations 7 Days Unit 4 Lesson Plan 5 pp. 16-18 Formulating and Solving Systems of Linear Equations 10 Days Unit 5 Lesson Plan 6 pp. 19-20 Analytic Methods for Solving Systems of Linear Equations 10 Days Unit 6 Lesson Plan 7 pp. 21-26 Pythagorean Theorem 7 Days Unit 7 Lesson Plan 8 pp. 27-30 Working with Exponents 7 Days Unit 8 Lesson Plan 9 pp. 31-38 Measurement of Geometry 15 Days Unit 9 Lesson Plan 10 pp. 39-41 Introducing Transformations 4 Days Unit 10 Lesson Plan 11 pp. 42-43 Understanding Congruence Through Transformations 8 Days Unit 11 Lesson Plan 12 pp. 44-46 Understanding Similarity 5 Days Unit 12 Lesson Plan 13 pp. 47-48 Relationships in Geometric Figures 5 Days Unit 13 Lesson Plan 14 p. 49 Ratios and Proportions 10 Days Unit 14 Lesson Plan 15 p. 50 Probability 5 Days Unit 15 Lesson Plan 1
Domain: Functions Cluster: Define Evaluate and Compare Function Unit 1: Input-Output Relationships Why is the concept of the rate of change such an important one for a scientist? // 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. Function Notation is not required in grade 8 Using a rule, students can determine if an expression is a function or not a function. Function Expression Input Equation Output Domain Range Independent variable Dependent variable Ordered pair Slope Rate of change Increasing Decreasing Linear Non-linear : Three core lessons in power point format dealing with functions: ain%5d=f%3a+functions&filters%5bstandard%5d=8.f.1%3a+unders tand+that+a+function+is+a+rule+... Online multiple choice exam on identifying functions: http://www.regentsprep.org/regents/math/algebra/ap3/funcprac.htm : Several PDF resources: http://www.sharemylesson.com/taxonomysearchresults.aspx?mod e=browse¶metrics=90011,90116,90556,93660 2.Reason abstractly and quantitatively 4.Model with mathematics 6. Attend to precision 8.Look for and express regularity and repeated reasoning Several lessons: http://betterlesson.com/directory/middle_school/relations_and_functions 2
Domain: Functions Cluster: Define Evaluate and Compare Function Unit 1: Input-Output Relationships Why is the concept of the rate of change such an important one for a scientist? // 8.F.A.2 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or buy 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. Given different representations of a function, students are able to compare and contrast properties and are able to match models to real world situations. Function Expression Input Equation Output Domain Range Independent variable Dependent variable Ordered pair Slope Rate of change Increasing Decreasing Linear Non-linear Three PowerPoint based lessons on modeling functions: ain%5d=f%3a+functions&filters%5bstandard%5d=8.f.2%3a+compa re+properties+of+two+functions+e... is included with extension of lesson by having student solve real world situations representing functions as rules and graphs: http://www.mathplanet.com/education/algebra-1/discoveringexpressions,-equations-and-functions/representing-functions-asrules-and-graphs quantitatively 6.Attend to precision 8. Look for and express regularity and repeated reasoning 3
Domain: Functions Cluster: Use functions to model relationships between quantities. Unit 1: Input-Output Relationships Why is the concept of the rate of change such an important one for a scientist? // 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. Students can analyze a graph to describe qualitatively the functional relationship between two quantities. Students determine where the function is increasing or decreasing, linear or nonlinear. Function Expression Input Equation Output Domain Range Independent variable Dependent variable Ordered pair Slope Rate of change Increasing Decreasing Linear Non-linear 5 core lessons in powerpoint format that demonstrates the rate of change as a function: ain%5d=f%3a+functions&filters%5bstandard%5d=8.f.5%3a+descri be+qualitatively+the+functional... Students are given a short formative assessment at the end of the lesson. Ie Dan rides his bicycle to school. The graph below shows his distance away from home with respect to (t) time, in minutes. For what time frame is Dan traveling the fastest? When was he stopped? How Do You Make an Approximate Graph From a Word Problem? http://www.virtualnerd.com/common-core/grade-8/8_ffunctions/b/5 quantitatively 6.Attend to precision 8. Look for and express regularity and repeated reasoning 4
Domain: Functions Unit 2: Linear Functions Cluster: Use functions to model relationships between quantities. Why is it necessary to keep certain relationships proportional? 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 Students can determine the rate of change (slope) and initial value (y-intercept) from different representations of a linear function, such as graphs, equations, and tables. Students understand rate of change and initial value in context of the problem. Function Model Linear relationship Relationship Linear Function Graph Slope Proportional relationship Similar Vertical axis Axis Vertical Rate of change // Three core lessons and two misconception examples in a PowerPoint format on linear functions. ain%5d=f%3a+functions&filters%5bstandard%5d=8.f.4%3a+constr uct+a+function+to+model+a+linea... is given at end of lessons ie Show an image of a restaurant price board or menu. -Are the prices slopes or y- intercepts? -What does each mean as it pertains to the restaurant? - There is an unseen value for each of the prices, what is it (slope or y- intercept)? -What does the unseen value mean as it pertains to the restaurant? Constructing functions to model linear relationships between two quantities: http://learnzillion.com/lessonsets/357-constructing-functions-tomodel-linear-relationships-between-two-quantities quantitatively. 8. Look for and express regularity in repeated reasoning. 5
Domain: Functions Unit 2: Linear Functions Cluster: Define, Evaluate, and Compare Function Why is it necessary to keep certain relationships proportional? 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= 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. Students can write an equation of a line in the form y = mx + b. Students can identify the slope and y-intercept from the equation. Students can give examples of linear and nonlinear functions. Function Model Linear relationship Relationship Linear Function Graph Slope Proportional relationship Similar Vertical axis Axis Vertical Rate of change // 4 core lessons in recognizing functions in a PowerPoint format: ain%5d=f%3a+functions&filters%5bstandard%5d=8.f.3%3a+interpr et+the+equation+y+%3d+mx+%2b+b+as+... is included at end of lesson with an extension ie It is said that a person s wingspan equals their height. Measure your wingspan and height, in inches, along with a few other friends of different heights (with their permission, of course). Let height be (x) and wingspan be (y). Is this linear? Will it ever be? Why or why not? interpret the equation y-mx+b http://www.virtualnerd.com/common-core/grade-8/8_ffunctions/a/3 quantitatively. 8. Look for and express regularity in repeated reasoning. 6
Domain: Functions Unit 2: Linear functions Cluster: Use functions to model relationships between quantities Why is it necessary to keep certain relationships proportional? 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. Students can analyze a graph to describe qualitatively the functional relationship between two quantities. Students can determine if the function is increasing or decreasing. The is on linear functions. Function Model Linear relationship Relationship Linear Function Graph Slope Proportional relationship Similar Vertical axis Axis Vertical Rate of change // 5 core lessons in PowerPoint format having to do with various topics in functions: ain%5d=f%3a+functions&filters%5bstandard%5d=8.f.5%3a+descri be+qualitatively+the+functional... Lesson provides an extension at end ie Describe a real world scenario for each of the three increasing profiles: - Increasing at an increasing rate - Increasing at a constant rate - Increasing at a decreasing rate modeling with functions http://www.opusmath.com/common-core-standards/8.f.5-describequalitatively-the-functional-relationship-between-two-quantities quantitatively. 8. Look for and express regularity in repeated reasoning. 7
Domain: Expressions and Equations Unit 2: Linear Functions Cluster: Understand the connections between proportional relationships, lines, and linear equations. Why is it necessary to keep certain relationships proportional? 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. Students can graph proportional relationships and understand that the unit rate of the proportional relationship is the slope. Students can compare characteristics of proportional relationships by analyzing different representations such as tables, graphs, or equations. Function Model Linear relationship Relationship Linear Function Graph Slope Proportional relationship Similar Vertical axis Axis Vertical Rate of change // 5 core lessons in PowerPoint format in graphing rate of change: %5D=math&query=&filters%5Bdomain%5D=EE%3A+Expressions+and +Equations&filters%5Bstandard%5D=8.EE.5%3A+Graph+proportional +relationships%2c+int... Extension provided at end of lesson provides a very good formative assessment ie. Comparing complicated rates (fractions): Brent takes 28 minutes to complete 1work order forms. Josh takes 36 41minutes to complete 7work order 2forms. Who works faster? proportional relationships and slope http://www.cpm.org/pdfs/state_supplements/proportional_relation ships_slope.pdf quantitatively. 8. Look for and express regularity in repeated reasoning. 8
Domain: Expressions and Equations Unit 2: Linear Functions Cluster: Understand the connections between proportional relationships, lines, and linear equations. Why is it necessary to keep certain relationships proportional? 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. Students understand that triangles are similar when there is a constant rate of proportionality between them. Students can use a graph to construct triangles between two points on a line and compare the sides to understand that the slope (ratio of rise to run) is the same between any two points on a line. Function Model Linear relationship Relationship Linear Function Graph Slope Proportional relationship Similar Vertical axis Axis Vertical Rate of change // 5 core lessons in PowerPoint format having to do with proportional relationships: %5D=math&query=&filters%5Bdomain%5D=EE%3A+Expressions+and +Equations&filters%5Bstandard%5D=8.EE.5%3A+Graph+proportional +relationships%2c+int... There is a short formative quiz at end of the lesson. Ie Use similar triangles to demonstrate that the equation of a line through 334 unit on using similar triangles to find slope http://www.glencoe.com/sites/washington/support_student/additio nal_lessons/course_2/18_23_wa_se_gr7_adllsn_onln.pdf quantitatively. 8. Look for and express regularity in repeated reasoning. 9
Domain: Statistics and Probability Cluster: Investigate patterns of association in bivariate data. Unit 3: Patterns in Bivariate Data Why should we use models to represent real world situations? 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. Students can represent numerical data on a scatter plot to examine the relationships between two quantities. They analyze scatter plots to determine if the relationship has positive, negative, nor no association, and if the relationship is linear or non-linear *note Students must also be able to find central tendency for a set of data. Using a set of data the students must also construct and interpret: frequency tables, histograms, box and whisker plots, line plots, bar line and pie graphs Scatter Plot Interpret Quantities Model Positive associate Negative association Slope Intercept Relative frequencies Row Column Summarizing Linear model Bivariate Informally assess Frequencies // 3 core lessons in PowerPoint format having to do with making and using scatter plots: ain%5d=sp%3a+statistics+and+probability&filters%5bstandard%5d= 8.SP.1%3A+Construct+and+interpret+scatter+plots... The extension activity at the end of the lesson provides a very good formative assessment ie. Find a data table in your local newspaper that compares two pieces of data. Construct a scatter plot using the data found. Write a general statement about the relationship that the scatter plot shows. lesson on constructing and interpreting scatter plots http://www.graniteschools.org/depart/teachinglearning/curriculumi nstruction/math/secondarymathematics/math%207%20lessons/41- NewMath7LessonHApr3ScatterPlots.pdf 6. Attend to precision 10
Domain: Statistics and Probability Cluster: Investigate patterns of association in bivariate data. Unit 3: Patterns in Bivariate Data Why should we use models to represent real world situations? 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. Students can analyze a scatter plot to determine if there is a linear association. If a linear association is determined, the student fits the scatter plot with a straight line. Students need to pick the linear model that is closest to each of the data points. Scatter Plot Interpret Quantities Model Positive associate Negative association Slope Intercept Relative frequencies Row Column Summarizing Linear model Bivariate Informally assess Frequencies // 1 core lesson in PowerPoint format having to do with drawing a line of best fit: ain%5d=sp%3a+statistics+and+probability&filters%5bstandard%5d= 8.SP.2%3A+Know+that+straight+lines+are+widely+u... There is an extension activity at the end of the lessons that serve as a very good formative assessment ie Find a data table in your local newspaper that compares two pieces of data. Construct a scatter plot using the data found. Informally draw the line of best fit. Use this line to predict 3 values that were not observed activity on modeling relationship between two variables http://www.graniteschools.org/depart/teachinglearning/curriculumi nstruction/math/secondarymathematics/math%207%20lessons/41- NewMath7LessonHApr3ScatterPlots.pdf 6. Attend to precision 11
Domain: Statistics and Probability Cluster: Investigate patterns of association in bivariate data. Unit 3: Patterns in Bivariate Data Why should we use models to represent real world situations? 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. Students can write an equation to represent a line modeling a linear association on a scatter plot. Students can interpret the slope and y-intercept of the line in context of the problem. Scatter Plot Interpret Quantities Model Positive associate Negative association Slope Intercept Relative frequencies Row Column Summarizing Linear model Bivariate Informally assess Frequencies // 3 core lessons in PowerPoint format dealing with scatter plots, lline of best fit, and finding the y-iintercept: ain%5d=sp%3a+statistics+and+probability&filters%5bstandard%5d= 8.SP.3%3A+Use+the+equation+of+a+linear+model+to... Find a data table in your local newspaper that compares two pieces of data. Construct a scatter plot using the data found. Informally draw the line of best fit. Find the y-intercept for this data using this graph. Explain what the y-intercept represents within the context of the problem. the meaning of slope and intercept http://www.purplemath.com/modules/slopyint.htm 6. Attend to precision 12
Domain: Statistics and Probability Cluster: Investigate patterns of association in bivariate data. Unit 3: Patterns in Bivariate Data Why should we use models to represent real world situations? 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? Students can use and understand that a two-way table provides a way to organize data between two categorical variables. Students can calculate the relative frequencies to describe associations. Scatter Plot Interpret Quantities Model Positive associate Negative association Slope Intercept Relative frequencies Row Column Summarizing Linear model Bivariate Informally assess Frequencies // 3 core lesssons in PowerPoint format dealing with categorizing bivariate data: ain%5d=sp%3a+statistics+and+probability&filters%5bstandard%5d= 8.SP.4%3A+Understand+that+patterns+of+associati... There is an extension at the end of the lesson that provides a very good formative assessment. Ie. Observe the students in your class and create a two way table that displays the combinations on hair color and eye color. The hair color categories are light and dark. The eye color categories are also light and dark. Create a Venn Diagram to summarize this data. Use the diagram to construct a two way table. tutorials on understanding the patters associated with bivariate date http://www.virtualnerd.com/common-core/grade-8/8_sp-statisticsprobability/a/4 6. Attend to precision 13
Domain: Expressions and Equations Cluster: Analyze and solve linear equations and pairs of simultaneous linear equations. Unit 4: Linear Equations Why is it important to know whether an equation has one solution, no solutions, or an infinite amount of solutions? // 8.EE.C.7.a Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers.) Students can create and solve linear equations in one variable that results in one, infinitely many, or no solutions. All three are required Linear Equation Variable Equivalent equation Rational Coefficients Rational number coefficients Solution Expanding expressions Distributive property Like terms 1 core lesson and 5 support lessons in PowerPoint format dealing with solving linear equations: ain%5d=ee%3a+expressions+and+equations&filters%5bstandard%5 D=8.EE.7a%3A+Give+examples+of+linear+equations+in+... There are very good extensions at the end of the activity that serve as a very good formative assessment. Ie What can you tell about the structure of an equation that has no solution? webpage on solving linear equations http://www.purplemath.com/modules/solvelin.htm 6. Attend to precision 7. Look for and make use of structure 8. Look for and express regularity in repeated reasoning. 14
Domain: Expressions and Equations Cluster: Analyze and solve linear equations and pairs of simultaneous linear equations. Unit 4: Linear Equations Why is it important to know whether an equation has one solution, no solutions, or an infinite amount of solutions? // 8.EE.C.7b Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. Students can solve linear equations in one variable including distributive property and combining like terms. Some equations should include rational coefficients other than integers. Linear Equation Variable Equivalent equation Rational Coefficients Rational number coefficients Solution Expanding expressions Distributive property Like terms 6 core lessons and 3 supporting lessons in PowerPoint format dealing with solving linear equations: ain%5d=ee%3a+expressions+and+equations&filters%5bstandard%5 D=8.EE.7b%3A+Solve+linear+equations+with+rational+... There are extension activities that serve as a very good formative assessment at the end of the lesson. Ie Explain how to determine which operation will be done first when solving two step equations. webpage on using the distributive property http://www.algebrahelp.com/lessons/simplifying/distribution/ 6. Attend to precision 7. Look for and make use of structure 8. Look for and express regularity in repeated reasoning. 15
Domain: Expressions and Equations Cluster: Analyze and solve linear equations and pairs of simultaneous linear equations. Unit 5: Formulating and Solving Systems of Linear Equations What are some ways in which we could find one set of answers for many variations of the same situation? // 8.EE.C.8a 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. Students can explain that the solution to a system of linear equations is the point of intersection on the graph of the two linear equations. Students can look at a graph of a system of linear equations and determine if there is one, infinitely many, or no solution. System Linear equation Variable Intersection Graph Systems of two linear equations Solution Algebraically Coordinates Core lesson in PowerPoint format dealing with slope and solving systems of equations. ain%5d=ee%3a+expressions+and+equations&filters%5bstandard%5 D=8.EE.8a%3A+Understand+that+solutions+to+a+system... There is a multiple choice assessment at the end of the unit. 1. Make sense of problems and persevere in solving them. quantitatively. 6. Attend to precision games on solving systems of equations http://www.coolmath.com/algebra/12-2x2-systems-of-equations/ 16
Domain: Expressions and Equations Cluster: Analyze and solve linear equations and pairs of simultaneous linear equations. Unit 5: Formulating and Solving Systems of Linear Equations What are some ways in which we could find one set of answers for many variations of the same situation? // 8.EE.C.8b 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. Students can estimate the solution to a system of linear equations by using a graph. System Linear equation Variable Intersection Graph Systems of two linear equations Solution Algebraically Coordinates 7 core lessons and several supporting lessons in PowerPoint format dealing with solving systems of equations: http://learnzillion.com/lessons?utf8=%e2%9c%93&filters%5bsubje ct%5d=math&query=&filters%5bgrade%5d%5b%5d=8&filters%5bd omain%5d=ee%3a+expressions+and+equations&filters%5bstandar d%5d=8.ee.8b%3a+solve+systems+of+two+linear+equations... There is an extension at the end of the lesson that can serve as a very good formative assessment. Ie When we solve the systems of equations y=2x and y=x, what is our solution? What does it mean? notes on solving systems of equations with two variables http://tutorial.math.lamar.edu/classes/alg/systemstwovrble.aspx 1. Make sense of problems and persevere in solving them. quantitatively. 6 Attend to precision 17
Domain: Expressions and Equations Cluster: Analyze and solve linear equations and pairs of simultaneous linear equations. Unit 5: Formulating and Solving Systems of Linear Equations What are some ways in which we could find one set of answers for many variations of the same situation? // 8.EE.C.8c 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. Given a real-world problem that results in a system of linear equations, students can estimate the solution by graphing. System Linear equation Variable Intersection Graph Systems of two linear equations Solution Algebraically Coordinates Link to a PDF file that talks about solving systems of equations: http://infinity.cos.edu/algebra/blakely%20text/chapter%209/9.1.pdf A set of real world problems to be solved. http://www.algebraclass.com/solving-systems-of-equations.html real world problems involving systems of equations http://www.purplemath.com/modules/systprob.htm 1. Make sense of problems and persevere in solving them. quantitatively. 6 Attend to precision 18
Domain: Expressions and Equations Cluster: Analyze and solve linear equations and pairs of simultaneous linear equations. Unit 6: Analytic Methods for Solving Systems of Linear Equations. Why do we model certain situations by graphing the linear equation? 8.EE.C.8b 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. Students can solve a system of linear equations by applying the substitution and elimination methods. Estimate Solutions Equation Systems of linear equations Linear equation Intersect Simultaneously // 6 core lessons and several supporting lessons in PowerPoint format that deals with solving systems of equations: ain%5d=ee%3a+expressions+and+equations&filters%5bstandard%5 D=8.EE.8b%3A+Solve+systems+of+two+linear+equations... There are extensions at the end of the lesson that can serve as a good formative assessment. Ie Does the system of linear equations y=2x and y=2x+1 have infinitely many solutions? Explain your answer. practice problems on graphing systems http://hotmath.com/help/gt/genericalg1/section_5_1.html 1. Make sense of problems and persevere in solving them. quantitatively. 6 Attend to precision 19
Domain: Expressions and Equations Cluster: Analyze and solve linear equations and pairs of simultaneous linear equations. Unit 6: Analytic Methods for Solving Systems of Linear Equations. Why do we model certain situations by graphing the linear equation? 8.EE.C.8c 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. Given a real-world problem that results in a system of linear equations, students can solve by applying the substitution and elimination methods. Estimate Solutions Equation Systems of linear equations Linear equation Intersect Simultaneously // Lesson in PDF format that talks about solving systems of equations: http://www.nsa.gov/academia/_files/collected_learning/high_school /algebra/real_world_systems_of_linear_equations.pdf There is a series of open ended questions at the end of the activity. PowerPoint on systems of equations http://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd =6&ved=0CEoQFjAF&url=http%3A%2F%2Fteachers.henrico.k12.va.us %2Fmath%2Fhcpsalgebra2%2FDocuments%2F3-1%2F2006_3_1.ppt&ei=7vzmUYnqJLCQyQGd1IGYDg&usg=AFQjCNGC R7UhVDSwNx0fAiT4eZbw4jx6eA&bvm=bv.49405654,bs.1,d.aWc 1. Make sense of problems and persevere in solving them. quantitatively. 6 Attend to precision 20
Domain: Geometry Cluster: Understand and apply the Pythagorean Theorem Unit 7: Pythagorean Theorem Why does the Pythagorean Theorem only work on right triangles? 8.G.B.6 Explain a proof of the Pythagorean Theorem and its converse. Students can explain what the Pythagorean Theorem and its converse are, and give an example to prove that it works. Converse Pythagorean Theorem Rational Approximations Coordinate systems Distance Square root Cube root Irrational Decimal expansion Repeat Positive rational number Evaluate Perfect squares Two dimension Three dimension Approximation Right triangle // Core lessons in PowerPoint format that talks about the Pythagorean Theorem: ain%5d=g%3a+geometry&filters%5bstandard%5d=8.g.6%3a+explai n+a+proof+of+the+pythagorean+th... There is a quiz at the end of the lesson to be used as a formative assessment. Ie. Below are the measurements of a triangle. Using the Pythagorean Theorem, classify the triangle as acute, obtuse, or right. webpage graphically showing the theorem http://www.mathsisfun.com/pythagoras.html 1. Make sense of problems and persevere in solving them. quantitatively. 3. Construct viable arguments and critique the reasoning of others. 21
Domain: Geometry Cluster: Understand and apply the Pythagorean Theorem Unit 7: Pythagorean Theorem Why does the Pythagorean Theorem only work on right triangles? 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. Students can apply the Pythagorean Theorem to find missing sides of right triangles in real-word problems involving two and three dimensional shapes. Converse Pythagorean Theorem Rational Approximations Coordinate systems Distance Square root Cube root Irrational Decimal expansion Repeat Positive rational number Evaluate Perfect squares Two dimension Three dimension Approximation Right triangle // 2 core lessons in PowerPoint format that deals with applications to the Pythagorean Theorem: ain%5d=g%3a+geometry&filters%5bstandard%5d=8.g.7%3a+apply +the+pythagorean+theorem+to+dete... There is an extension activity at the end of the activity that can be used as a formative assessment. Ie. Find the length of the diagonal if the dimensions of the laptop are 9 in by 12 in. variety of resources for the application of the Theorem http://www.ck12.org/geometry/applications-of-the-pythagorean- Theorem/ 1. Make sense of problems and persevere in solving them. quantitatively. 3. Construct viable arguments and critique the reasoning of others. 22
Domain: Geometry Cluster: Understand and apply the Pythagorean Theorem Unit 7: Pythagorean Theorem Why does the Pythagorean Theorem only work on right triangles? 8.G.B.8 Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. Students can apply the Pythagorean Theorem to find the distance between two points in a coordinate system. Converse Pythagorean Theorem Rational Approximations Coordinate systems Distance Square root Cube root Irrational Decimal expansion Repeat Positive rational number Evaluate Perfect squares Two dimension Three dimension Approximation Right triangle // 4 core lessons that talk about finding perimeter using the Pythagorean Theorem: ain%5d=g%3a+geometry&filters%5bstandard%5d=8.g.8%3a+apply +the+pythagorean+theorem+to+find... There is a good extension activity at the end of the lesson that can be used as a formative assessment. Ie. Describe how you can find the length of a line segment by creating a square using the coordinates of the vertices of the square. presentation on the Pythagorean theorem http://www.brainingcamp.com/resources/math/pythagoreanformula/lesson.php 1. Make sense of problems and persevere in solving them. quantitatively. 3. Construct viable arguments and critique the reasoning of others. 23
Domain: The Number System Cluster: Know that there are numbers that are not rational, and approximate them by rational numbers. Unit 7: Pythagorean Theorem Why does the Pythagorean Theorem only work on right triangles? 8.NS.A.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. Students can explain the difference between rational and irrational numbers, both on their own and in relation to the Pythagorean Theorem. Converse Pythagorean Theorem Rational Approximations Coordinate systems Distance Square root Cube root Irrational Decimal expansion Repeat Positive rational number Evaluate Perfect squares Two dimension Three dimension Approximation Right triangle // 5 activities in PowerPoint format that discusses rational and irrational numbers ain%5d=ns%3a+the+number+system&filters%5bstandard%5d=8.n S.1%3A+Know+that+numbers+that+are+not+ration... This is a short test on rational and irrational numbers http://www.mytestbook.com/worksheet.aspx?test_id=1347&grade= 7&subject=Math webpage presentation on rational and irrational numbers http://www.mathsisfun.com/irrational-numbers.html 1. Make sense of problems and persevere in solving them. quantitatively. 3. Construct viable arguments and critique the reasoning of others. 24
Domain: The Number System Cluster: Know that there are numbers that are not rational, and approximate them by rational numbers. Unit 7: Pythagorean Theorem Why does the Pythagorean Theorem only work on right triangles? 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., π2). 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. Students can use a rational approximation to represent an irrational number. Students use varying approximations to describe the location of an irrational number (e.g., saying an irrational number is between 1.45 and 1.46 is more specific than saying an irrational number is between 1 and 2). Students can apply these skills to problems involving Pythagorean Theorem. Converse Pythagorean Theorem Rational Approximations Coordinate systems Distance Square root Cube root Irrational Decimal expansion Repeat Positive rational number Evaluate Perfect squares Two dimension Three dimension Approximation Right triangle // in PowerPoint format that talks about ain%5d=ns%3a+the+number+system&filters%5bstandard%5d=8.n S.2%3A+Use+rational+approximations+of+irrati... Online quiz on graphing irrational numbers on a number line http://braingenie.ck12.org/skills/106607 presentations on using a number line to estimate irrational numbers http://www.virtualnerd.com/common-core/grade-8/8_ns-numbersystem/a/2 1. Make sense of problems and persevere in solving them. quantitatively. 3. Construct viable arguments and critique the reasoning of others. 25
Domain: Expressions and Equations Cluster: Work with radicals and integer exponents. Unit 7:Pythagorean Theorem Why does the Pythagorean Theorem only work on right triangles? 8.EE.A.2 Use square root and cube root symbols to represent solutions to equations of the form =p and =p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that of is irrational. Students can solve equations in the form =p by using square roots. Students can use the square root symbol appropriately to represent solutions to these types of equations. Students can apply these skills to the Pythagorean Theorem. Converse Pythagorean Theorem Rational Approximations Coordinate systems Distance Square root Cube root Irrational Decimal expansion Repeat Positive rational number Evaluate Perfect squares Two dimension Three dimension Approximation Right triangle // 4 core lessons and several supporting activities in PowerPoint format that deal with roots: ain%5d=ee%3a+expressions+and+equations&filters%5bstandard%5 D=8.EE.2%3A+Use+square+root+and+cube+root+symbols... There is an extension at the end of the activity that may be used as a formative assessment. Ie Find one or more values of x that would make the following equation true explanation on solving quadratic equations http://www.mathsisfun.com/algebra/quadratic-equation.html 1. Make sense of problems and persevere in solving them. quantitatively. 3. Construct viable arguments and critique the reasoning of others. 26
Domain: Expressions and Equations Cluster: Work with radicals and integer exponents. Unit 8: Working with Exponents What effects do positive and negative exponents have on a number and why? // 8.EE.A.1 Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, x = = = Students can apply properties of exponents to simplify expressions involving exponents. This includes zero and negative exponents, and multiplication and division properties of exponents. Property Exponents Equivalent Numerical expressions Estimate Quantity Integer Power Operations Decimal Scientific notation Unit 8 core lessons and several supporting activities that demonstrate how to work with exponents: ain%5d=ee%3a+expressions+and+equations&filters%5bstandard%5 D=8.EE.1%3A+Know+and+apply+the+properties+of+inte... There is an extension at the end of the activity that may be used as a formative assessment. Ie Nathaniel simplified Write a short letter to Nathaniel explaining the mistake he made and giving him a suggestion to keep him from making the same mistake in the future. 6. Attend to precision 7. Look for and make use of structure 8. Look for and express regularity I repeated reasoning. simplifying expressions with exponents http://www.purplemath.com/modules/simpexpo.htm 27
Domain: Expressions and Equations Cluster: Work with radicals and integer exponents. Unit 8: Working with Exponents What effects do positive and negative exponents have on a number and why? // 8.EE.A.2 Use square root and cube root symbols to represent solutions to equations of the form =p and =p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that of 2 is irrational. Students can solve equations in the form =p by using cube roots. Students can use the cube root symbol appropriately to represent solutions to these types of equations. Property Exponents Equivalent Numerical expressions Estimate Quantity Integer Power Operations Decimal Scientific notation Unit 4 core lessons and several supporting activities that deal with square roots and cube roots: ain%5d=ee%3a+expressions+and+equations&filters%5bstandard%5 D=8.EE.2%3A+Use+square+root+and+cube+root+symbols... There is an extension at the end of the activity that may be used as a formative assessment. Ie A square has an area of 120 in2. Is the side length of this square closer to 10 in or 11 in? quadratic equation calculator http://www.math.com/students/calculators/source/quadratic.htm 6. Attend to precision 7. Look for and make use of structure 8. Look for and express regularity I repeated reasoning. 28
Domain: Expressions and Equations Cluster: Work with radicals and integer exponents. Unit 8: Working with Exponents What effects do positive and negative exponents have on a number and why? // 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 7, and determine that the world population is more than 20 times larger. Students can use an expression of a single digit times an integer power of 10 to estimate significantly large or very small quantities. Students can compare these expressions to see which quantities are larger or smaller. Property Exponents Equivalent Numerical expressions Estimate Quantity Integer Power Operations Decimal Scientific notation Unit 4 core lessons in PowerPoint format that uses scientific notation: ain%5d=ee%3a+expressions+and+equations&filters%5bstandard%5 D=8.EE.3%3A+Use+numbers+expressed+in+the+form+of+... There is an extension at the end of the activity that may be used as a formative assessment. Ie Use scientific notation to estimate the number of inches in a light-year. scientific notation problem set http://lasp.colorado.edu/~bagenal/math/problems/problems1.html 6. Attend to precision 7. Look for and make use of structure 8. Look for and express regularity I repeated reasoning. 29
Domain: Expressions and Equations Cluster: Work with radicals and integer exponents. Unit 8: Working with Exponents What effects do positive and negative exponents have on a number and why? // 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. Students can simplify and solve problem situations involving scientific notation and decimals that can be better represented by scientific notation. Students can determine which situations would be best for using scientific notation. Property Exponents Equivalent Numerical expressions Estimate Quantity Integer Power Operations Decimal Scientific notation Unit 3 core activities in PowerPoint format that talk deal with using scientific notation in problems: ain%5d=ee%3a+expressions+and+equations&filters%5bstandard%5 D=8.EE.4%3A+Perform+operations+with+numbers+expre... There is an extension at the end of the activity that may be used as a formative assessment. Ie Extension Activities Let s Review Positive integer powers of 10 are of three types: Ones (e.g. one million) Tens (e.g. ten thousand) Hundreds (e.g. one hundred billion) Is a googol 10 hundred webpage that has notes on scientific notation http://www.brynmawr.edu/nsf/tutorial/ss/ssnot.html 6. Attend to precision 7. Look for and make use of structure 8. Look for and express regularity I repeated reasoning. 30
Domain: addendum: Classifying Geometric Shapes Cluster: Addendum Unit 9: Measurement in Geometry Why do we need to find volume? This addendum to the unit is included to fill the void for the bridge assessment between Common Core and New Mexico State standards. Students will be able to classify and describe basic geometric shapes by their characteristics. Triangle Symmetry Area Two-dimensional Surface area Net Volume Prism Pyramid Cone Circle Chord Radius Diameter Rhombus Quadrilateral Parallelogram Symmetry // PDF lessons that discusses shape classification: http://www.greatmathsteachingideas.com/wpcontent/uploads/2012/03/ss1.pdf There is an assessment at the end of the unit Tutorials on classifying polygons http://www.virtualnerd.com/middle-math/geometricfigures/polygons 6.Attend to precision 8. Look for and express regularity and repeated reasoning 31
Domain: Addendum: symmetry Cluster: Addendum Unit 9: Measurement in Geometry Why do we need to find volume? This addendum to the unit is included to fill the void for the bridge assessment between Common Core and New Mexico State standards Students will be able to discover symmetry with any object or shape. Triangle Symmetry Area Two-dimensional Surface area Net Volume Prism Pyramid Cone Circle Chord Radius Diameter Rhombus Quadrilateral Parallelogram Symmetry // PowerPoint presentation that discusses symmetry: http://www.slideshare.net/caniglia/symmetry-in-math-3036380 Simple quiz on symmetry. http://www.quizrevolution.com/ch/a135800/go/symmetry webpage that has different examples on symmetry http://www.mathsisfun.com/geometry/symmetry.html 8. Look for and express regularity in repeated reasoning. 32
Domain: Addendum: Area Cluster: Addendum Unit 9: Measurement in Geometry Why do we need to find volume? This addendum to the unit is included to fill the void for the bridge assessment between Common Core and New Mexico State standards Students will be able to find the area of two-dimensional geometric figures. Students will be able to find the nets and surface area of threedimensional geometric shapes. Triangle Symmetry Area Two-dimensional Surface area Net Volume Prism Pyramid Cone Circle Chord Radius Diameter Rhombus Quadrilateral Parallelogram Symmetry // Online lessons that talks about finding surface area of three dimensional shapes: http://www.learner.org/interactives/geometry/area_surface.html Short online quiz: http://www.mrmaisonet.com/index.php?/area-quizzes/area-of- Uncommon-Shapes.html formula page for area http://www.mathsisfun.com/area.html quantitatively. 3. Construct viable arguments and critique the reasoning of others. 5. Use appropriate tools strategically. 8. Look for and express regularity in repeated reasoning. 33
Domain: Addendum: Volume of prism and pyramid Cluster: Addendum Unit 9: Measurement in Geometry Why do we need to find volume? This addendum to the unit is included to fill the void for the bridge assessment between Common Core and New Mexico State standards Students will be able to find the volume of prisms and pyramids and be able to apply formulas to find the volume, including to real world situations. Triangle Symmetry Area Two-dimensional Surface area Net Volume Prism Pyramid Cone Circle Chord Radius Diameter Rhombus Quadrilateral Parallelogram Symmetry // Online lesson that discusses finding the volume of a pyramid: http://www.mathopenref.com/pyramidvolume.html Short online quiz: http://www.proprofs.com/quiz-school/story.php?title=632-volumeprisms-pyramids-cones web page of problems dealing with volume http://www.shmoop.com/basic-geometry/volume-pyramidscones.html quantitatively. 5. use appropriate tools strategically. 6. Attend to precision 8. Look for and express regularity in repeated reasoning. 34
Domain: Geometry Cluster: Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres. Unit 9: Measurement in Geometry Why do we need to find volume? 8.G.C.9 Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve realworld and mathematical problems. Students know the formulas for finding the volume of cones, cylinders, and spheres and use them to solve realworld problems involving volume. Volume Formula Cone Cylinder Sphere Radical Rational Irrational Cube // 6 core lessons in PowerPoint format that deal with finding volume: ain%5d=g%3a+geometry&filters%5bstandard%5d=8.g.9%3a+know +the+formulas+for+the+volumes+of+... There is an extension at the end of the activity that may be used as a formative assessment. Ie Use measurement and geometrical shapes to demonstrate the relationship between the volume of a cone and volume of a similar cylinder. Record your measurements and calculate the percent error in your measurements assuming the actual relationship is 3Vcone = 1Vcylinder 6. Attend to precision webpage of various volume formulas http://www.science.co.il/formula.asp 35