8 TH GRADE REV 9_24_14. 8th 2012 Outstanding Guides, LLC 245

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1 8 TH GRADE REV 9_24_14 8th 2012 Outstanding Guides, LLC 245

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3 Outstanding Math Guide Overview Vocabulary sheets allow terms and examples to be recorded as they are introduced in class. These reproducible graphic organizers can be used by your students to make an Outstanding Math Guide (OMG). The OMG is a work in progress; graphic organizers are constructed as an introduction or review of each topic. By the end of the year, your students will have an OMG that can be easily referenced for years to come. A standard 3 - prong pocket folder is folded in half. Holes are punched so OMG will store in the front of a notebook. 8th 2012 Outstanding Guides, LLC 247

4 Pockets in folder are cut down each side so they will open up. Outstanding Math Guide 8th 2012 Outstanding Guides, LLC 248

5 8.NS The Number System: Know that there are numbers that are not rational, and approximate them by rational numbers. 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. 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., p 2 ). 8.EE Expressions and Equations: Work with radicals and integer exponents. Organizer Rational Irrational Numbers Rat/ Irrational Numbers Radicals 1. Know and apply the properties of integer exponents to generate equivalent numerical expressions. Exponents 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 2 is irrational. 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. 4. Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology. 8.EE Expressions and Equations: Understand the connections between proportional relationships, lines, and linear equations. 5. Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. 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. Perfect Squares and Cubes Scientific Notation Scientific Notation Linear Functions 8.EE Expressions and Equations: Analyze and solve linear equations and pairs of simultaneous linear equations. 7. Solve linear equations in one variable. Systems of Equations 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. Slope Systems of Equations Solving Equations 8. Analyze and solve pairs of simultaneous linear equations. Systems of Equations a. Understand that solutions to a system of two linear equations in two variables correspond to points Systems of of intersection of their graphs, because points of intersection satisfy both equations simultaneously. Equations b. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. Linear Equations Systems of Equations 8th 2012 Outstanding Guides, LLC th Grade Common Core State Standards Graphic

6 c. Solve real-world and mathematical problems leading to two linear equations in two variables. Systems of Equations 8.F Functions: Define, evaluate, and compare functions. 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.) 2. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). 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. 8.F Functions: Use functions to model relationships between quantities. 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. 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. Functions Multiple Representations Linear Functions And Functions Linear Functions Functions Functional Relationship 8.G Geometry: Understand congruence and similarity using physical models, transparencies, or geometry software. 1. Verify experimentally the properties of rotations, reflections, and translations: Transformations a. Lines are taken to lines, and line segments to line segments of the same length. Similar and Congruent b. Angles are taken to angles of the same measure. Similar and Congruent c. Parallel lines are taken to parallel lines. 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. 3. Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. 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. 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. 8.G Geometry: Understand and apply the Pythagorean Theorem. Similar and Congruent Transformations Transformations Angles 6. Explain a proof of the Pythagorean Theorem and its converse. Pythagorean Theorem 7. Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world Pythagorean and mathematical problems in two and three dimensions. Theorem 8. Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. Pythagorean Theorem 8.G Geometry: Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres 9. Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. 8.SP Statistics and Probability: Investigate patterns of association in bivariate data. 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. Volume Scatter Plot 8th 2012 Outstanding Guides, LLC 250

7 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. 3. Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. 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. Scatter Plot Linear Functions Slope Scatter Plot 8th 2012 Outstanding Guides, LLC 251

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9 Change in x s & y s 8th 2012 Outstanding Guides, LLC 253 Systems of Equations Functions Slope Scientific Notation Rational & Irrational Transformations Linear Functions Perfect Squares & Cubes Linear Equations y = mx + b Exponents Solving Equations Folded Flap 8th Grade Graphic Organizers Suggested Layout Folded Flap Radicals Graphing Bivariate Data Congruent & Similar Volume Multiple Rep. Angles Pythag Back Cover Folded Flap

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11 8th 2012 Outstanding Guides, LLC Radicals Number Systems Estimate and simplify/perfect squares and cubes 8 Vocabulary estimate perfect cube perfect square radical radicand simplify

12 8th 2012 Outstanding Guides, LLC 256 PERFECT SQUARE 8 A = = STEPS ESTIMATE NUMBER LINE Radicals Find the perfect square below and above 72. Estimate the 72 by determining the decimal value of where it falls on a number line between the two perfect squares PERFECT CUBE 8 V = =

13 8th 2012 Outstanding Guides, LLC 257 PERFECT SQUARE 8 A = = 64 STEPS ESTIMATE NUMBER LINE Radicals Find the below and above 72. Estimate the 72 by determining the decimal value of where it falls on a between the two perfect squares PERFECT CUBE 8 V = = 512

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15 8th 2012 Outstanding Guides, LLC Rational and Irrational Numbers Number Systems 8 Vocabulary irrational numbers perfect square rational numbers real numbers square root terminating decimal whole number

16 IRRATIONAL 8th 2012 Outstanding Guides, LLC 260 Numbers that can be written as a fraction (ratio) are rational. RATIONAL Rational Numbers 4-9 1/2-3/ All repeating and terminating decimals, whole numbers, fractions and square roots of perfect squares. Irrational Numbers 72 π 2π 42 1/3π Numbers that cannot be expressed as terminating or repeating decimals. The two types of irrational numbers are non-perfect squares and expressions containing pi, (π).

17 IRRATIONAL 8th 2012 Outstanding Guides, LLC 261 Numbers that can be written as a (ratio) are rational. RATIONAL Rational Numbers 4-9 1/2-3/ All repeating and terminating, whole, and of perfect squares. Irrational Numbers 72 π 2π 42 1/3π Numbers that cannot be expressed as terminating or repeating. The two types of irrational numbers are non-perfect and expressions containing, (π).

18 IRRATIONAL 8th 2012 Outstanding Guides, LLC 262 RATIONAL

19 8th 2012 Outstanding Guides, LLC Exponents Expressions and Equations Adding/Subtracting/Multiplying/Dividing 8 Vocabulary base coefficient exponent order of operation power

20 8th 2012 Outstanding Guides, LLC 264 Multiplying with Exponents Dividing with Exponents Exponents X 2 Adding & Subtracting Exponents Power of an Exponent Negative Powers Zero Power

21 8th 2012 Outstanding Guides, LLC 265 If the base is the same, add the exponents. 1) m 3 m 5 = m 8 2) 3x 4 y 5 2x 5 y 2 = 6x 9 y 7 1) m 7 = m 2 m 5 2) 3x 4 y 5 = x 2 6x 2 y 7 2y 2 If the base is the same, subtract the exponents. Follow the order of operations. 1) = = 57 1) (2 3 ) 5 = ) (3x 4 ) 2 = 9x 8 Keep the base and multiply the exponent by the power. Multiply coefficient if necessary. If base and exponent are not zero, rewrite as a fraction and that base now has a positive exponent. 1) 2-3 = 1 = ) 3m -2 n 4 = 3n 4 m 2 1) 2 0 = 1 2) 3x 2 y 0 = 3x 2 Any base raised to the zero power has a value of 1.

22 8th 2012 Outstanding Guides, LLC 266 If the base is the same, the exponents! 1) m 3 m 5 = 2) 3x 4 y 5 2x 5 y 2 = 1) m 7 = m 5 2) 3x 4 y 5 = 6x 2 y 7 If the base is the same, the exponents. Follow the of operations! 1) = 1) (2 3 ) 5 = 2) (3x 4 ) 2 = Keep the and the exponent by the power. Multiply coefficient if necessary. If base and exponent are not zero, as a fraction and that base now has a exponent. 1) 2-3 = 2) 3m -2 n 4 = 1) 2 0 = 2) 3x 2 y 0 = Any base raised to the zero power has a value of.

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25 8th 2012 Outstanding Guides, LLC Linear Equations Expressions and Equations Slope intercept form/standard form/slope of parallel and perpendicular lines 8 Vocabulary coefficient parallel perpendicular reciprocal slope intercept standard form y-intercept

26 8th 2012 Outstanding Guides, LLC 270 Linear Equations Y = mx + b slope y intercept Slope Intercept Form y = mx + b Slopes of and Standard Form Ax + By = C Lines

27 8th 2012 Outstanding Guides, LLC 271 Slope Intercept Standard Form The slopes of parallel lines ( are the same. y = -3x x +3x 3x + y = 4 In Standard form, the leading coefficient cannot be negative nor a fraction. y = 2x + 7 and y = 2x - 4 Slopes are the same Standard Form 3x + y = 4-3x -3x Slope Intercept y = -3x + 4 In Slope Intercept form, the coefficient of y must be positive one. The slopes of perpendicular lines ( are opposite reciprocals. y = 2x + 7 and y = -½x - 4 Slopes are opposite reciprocals

28 8th 2012 Outstanding Guides, LLC 272 Slope Intercept Standard Form The slopes of parallel lines ( are the. y = -3x + 4 y = 2x + 7 and y = 2x - 4 In Standard form, the leading coefficient cannot be negative nor a fraction. Slopes are the Standard Form 3x + y = 4 Slope Intercept The slopes of perpendicular lines ( are. y = 2x + 7 and y = -½x - 4 In Slope Intercept form, the coefficient of y must be positive one. Slopes are

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31 8th 2012 Outstanding Guides, LLC Linear Functions Expressions and Equations Graphs/Tables/Equations 8 Vocabulary constant rate of change denominator exponent function linear linear functions slope intercept form

32 8th 2012 Outstanding Guides, LLC 276 Graphs Equations What is a Linear Function? Tables Linear Functions

33 8th 2012 Outstanding Guides, LLC 277 Any function that forms a straight line when it is graphed. Draw a single straight line. Have a constant rate of change. x y Examples: y = 2x + 7 y = 4 Non examples: y = x 2 y = 8/x Can be written in slope intercept form. Exponents are not greater than 1. Can not have a variable in the denominator.

34 8th 2012 Outstanding Guides, LLC 278 Any function that forms a when it is graphed. Draw a single line. Have a rate of change. x y _ Examples: y = 2x + 7 y = 4 Non examples: y = x 2 y = 8/x Can be written in form. Exponents are greater than 1. Can not have a variable in the.

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37 8th 2012 Outstanding Guides, LLC Perfect Squares and Cubes Expressions and Equations 8 Glue this chart on the back of the OMG so it can be accessed easily. Vocabulary cube cube root perfect cube perfect square square square root

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39 8th 2012 Outstanding Guides, LLC Scientific Notation Expressions and Equations Writing/Multiplying/Dividing 8 Vocabulary base ten coefficient exponent scientific notation standard form

40 8th 2012 Outstanding Guides, LLC 284 What is Scientific Notation? Numbers larger than one Numbers smaller than one Multiplication Division Steps a. Multiply coefficients. Steps a. Divide coefficients. Scientific notation is used to represent very large and very small numbers. Exponent is Positive! Exponent is Negative! b. Add exponents. c. Check to see if new coefficient is between 1 and 10, and rewrite in Scientific Notation if needed. b. Subtract exponents. c. Check to see if new coefficient is between 1 and 10, and rewrite in Scientific Notation if needed. Scientific Notation always has a coefficient that is between 1 and 10 multiplied by a power of ten! Standard Form 123,547,000 Standard Form (4.6 x 10 4 )(3.5 x 10 2 ) = a = b = x x 10 2 a = 3.2 b = 10 6 coefficient 4.6 x 10 4 Exponent Scientific Notation x 10 8 Scientific Notation 5.78 x 10-4 c x 10 6 NOT in Scientific Notation, so must be rewritten as x 10 7 c. 3.2 x 10 6 IS in Scientific Notation, so does not need to be rewritten. Scientific Notation

41 8th 2012 Outstanding Guides, LLC 285 What is Scientific Notation? Numbers larger than one Numbers smaller than one Multiplication Division Steps a. coefficients. Steps a. coefficients. Scientific notation is used to represent very and very numbers. Exponent is! Exponent is! b. exponents. c. to see if new coefficient is between 1 and 10, and rewrite in Scientific Notation if needed. b. exponents. c. to see if new coefficient is between 1 and 10, and rewrite in Scientific Notation if needed. Scientific Notation always has a is between 1 and 10 multiplied by a power of ten! Standard Form 123,547,000 Standard Form (4.6 x 10 4 )(3.5 x 10 2 ) = a = b = 6.72 x x 10 2 a = b = coefficient 4.6 x 10 4 Exponent Scientific Notation Scientific Notation c. NOT in Scientific Notation, so must be rewritten as c. IS in Scientific Notation, so does not need to be rewritten. Scientific Notation

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43 8th 2012 Outstanding Guides, LLC Slope Expressions and Equations Four types of slope/finding slope from a graph and two points/slopes of similar triangles 8 Vocabulary adjacent ratio horizontal similar slope vertical

44 8th 2012 Outstanding Guides, LLC 288 Rise Positive Slope Negative Slope Zero Slope Undefined Slope How do you find slope from a graph? Rise Run How do you find slope from two points? y x 2 2 y x 1 1 How do the adjacent side ratios of similar triangles, on the same line, relate to the slope of that line? 4 Large Small 2 1 Run (2, 1) and (5, 3) 3-1 = The adjacent sides ratios of these similar triangles are EQUAL. Vertical Horizontal Rise Run SLOPE

45 8th 2012 Outstanding Guides, LLC 289 Rise Positive Slope Negative Slope Zero Slope Undefined Slope How do you find slope from a graph? How do you find slope from two points? How do the adjacent side ratios of similar triangles, on the same line, relate to the slope of that line? Rise Run y x 2 2 y x 1 1 Large Small Run (2, 1) and (5, 3) The adjacent sides ratios of these similar triangles are EQUAL. Vertical Horizontal Rise Run SLOPE

46 8th 2012 Outstanding Guides, LLC 290 Positive Slope Negative Slope Zero Slope Undefined Slope SLOPE

47 8th 2012 Outstanding Guides, LLC Solving Equations Expressions and Equations Two Step Equations/Combine Like Terms/Distributive Property 8 Vocabulary coefficient distributive property expressions isolate like terms variable

48 292 EQUATIONS Two Step 2x + 5 = -11 MATH STEPS VERBAL STEPS CHECK 2x + 5 = x = x = -8 To isolate variable: Subtract 5 from both sides Divide both sides by 2 2x + 5 = -11 2(-8) + 5 = = = -11 EQUATIONS Combine Like Terms 7x - 4 = 5x x - 4 = 5x x -5x 2x - 4 = x = x = -9 To combine like terms: Subtract 5x from both sides Add 4 to both sides Divide both sides by 2 7x - 4 = 5x (-9) - 4 = 5(-9) = = -67 EQUATIONS Distributive Property 4(3x - 2) = 52 4(3x - 2) = 52 12x - 8 = x = x = 5 Distributive 4 Add 8 to both sides Divide both sides by 12 4(3x - 2) = 52 4(3 5-2) = 52 4(15-2) = 52 4(13) = = 52 8th 2012 Outstanding Guides, LLC

49 293 EQUATIONS Two Step 2x + 5 = -11 MATH STEPS VERBAL STEPS CHECK 2x + 5 = -11 To isolate variable: Subtract 5 from both sides Divide both sides by 2 2x + 5 = -11 EQUATIONS Combine Like Terms 7x - 4 = 5x - 22 To combine like terms: Subtract 5x from both sides Add 4 to both sides 7x - 4 = 5x x - 4 = 5x - 22 Divide both sides by 2 EQUATIONS Distributive Property 4(3x - 2) = 52 Distributive 4 Add 8 to both sides 4(3x - 2) = 52 4(3x - 2) = 52 Divide both sides by 12 8th 2012 Outstanding Guides, LLC

50 294 EQUATIONS Two Step MATH STEPS VERBAL STEPS CHECK EQUATIONS Combine Like Terms EQUATIONS Distributive Property 8th 2012 Outstanding Guides, LLC

51 8th 2012 Outstanding Guides, LLC Systems of Equations Expressions and Equations Graph/Set Equal to Each Other/Elimination/Substitution 8 Vocabulary elimination or linear combination standard form substitution variable

52 8th 2012 Outstanding Guides, LLC 296 Elimination or Linear Combination Substitution Graphing Setting Equal to each other Systems of Equations

53 8th 2012 Outstanding Guides, LLC 297 Use when the system is presented on a graph. A A B -4x - 2y = -12 4x + 8y = -24 6y = -36 y = -6 Use when both equations are presented in standard form. A. The solution is the coordinates of the point at which two lines cross. Solution is (-3, -1) C 4x + 8(-6) = -24 4x - 48 = x = 24 x = 6 Solution is (6,-6) A. Set equations up like an addition problem. B. Solve for one variable. C. Plug that solution into an equation to solve for the other variable. Use when both equations are set equal to the same variable. A. Set equations equal to each other. B. Solve for one variable. C. Plug that solution into an equation to solve for the other variable. A B C y = 2x + 16 y = 4x x + 16 = 4x x -2x 16 = 2x = 2x 3 = x y = 2(3) + 16 y = y = 22 Solution is (3, 22) A B C 2x - 3y = -1 y = x - 1 2x - 3(x - 1) = -1 2x - 3x + 3 = -1-1x + 3 = x = -4 x = 4 y = x - 1 y = 4-1 y = 3 Solution is (4, 3) Use when one equation is set equal to a variable. A. Substitute isolated variable into the other equation. B. Solve for one variable. C. Plug that solution into the other equation to solve for the other variable.

54 8th 2012 Outstanding Guides, LLC 298 Use when the system is presented on a. A A B -4x - 2y = -12 4x + 8y = -24 6y = -36 y = -6 Use when both equations are presented in. A. The solution is the coordinates of the point at which two lines cross. Solution is C 4x + 8(-6) = -24 4x - 48 = x = 24 x = 6 Solution is A. Set equations up like an addition problem. B. Solve for one variable. C. Plug that solution into an equation to solve for the other variable. Use when both equations are set to the. A. Set equations equal to each other. B. Solve for one variable. C. Plug that solution into an equation to solve for the other variable. A B C y = 2x + 16 y = 4x x + 16 = 4x x -2x 16 = 2x = 2x 3 = x y = 2(3) + 16 y = y = 22 Solution is A B C 2x - 3y = -1 y = x - 1 2x - 3(x - 1) = -1 2x - 3x + 3 = -1-1x + 3 = x = -4 x = 4 y = x - 1 y = 4-1 y = 3 Solution is Use when one equation is set equal to a. A. Substitute isolated variable into the other equation. B. Solve for one variable. C. Plug that solution into the other equation to solve for the other variable.

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57 8th 2012 Outstanding Guides, LLC Functions Functions Sets/Ordered pairs/tables/graphs 8 Vocabulary domain function input output range vertical line test x-axis y-axis

58 8th 2012 Outstanding Guides, LLC 302 Sets Ordered Pairs Tables Graphs Narrative Context To be a function, each input can have one and only one output. To be a function, the x value cannot be repeated. To be a function, the x value cannot be repeated. Vertical Line Test If a vertical line through the image only touches in one place, it is a function. A context in which at least two values vary jointly, with one being dependent on or related to the other is a function. Input output (1, 2), (3, 4), (5, 6), (7, 9), (8, 0), (9, 1) x y Joey is paid $7 an hour to deliver papers. If he works 5 hours, he gets $35. If he works 10 hours, he earns $70. FUNCTIONS

59 8th 2012 Outstanding Guides, LLC 303 Sets Ordered Pairs Tables Graphs Narrative Context To be a function, each can have one and only one. To be a function, the value cannot be. To be a function, the x value cannot be. Vertical Line Test If a vertical line through the image only touches in place, it is a function. A context in which at least two values vary jointly, with one being on or related to the other is a function. Input output (1, 2), (3, 4), (5, 6), (7, 9), (8, 0), (9, 1) x y Joey is paid $7 an hour to deliver papers. If he works 5 hours, he gets $35. If he works 10 hours, he earns $70. FUNCTIONS

60 8th 2012 Outstanding Guides, LLC 304 Sets Ordered Pairs Tables Graphs Narrative Context FUNCTIONS

61 8th 2012 Outstanding Guides, LLC Functional Relationships Functions Identifying the constant rate of change 8 Vocabulary constant rate of change function linear nonlinear

62 x y Analysis As x increases by 1, y increases by 2. Constant rate of change = 2 x y Analysis As x increases by 2, y decreases by 10. Constant rate of change = -10 = -5 2 Change in x s and y s 8th 2012 Outstanding Guides, LLC 306 Going Up Going Down

63 x y Analysis As increases by, y increases by. Constant rate of change = x y Analysis As increases by, y decreases by. Constant rate of change = Change in x s and y s 8th 2012 Outstanding Guides, LLC 307 Going Up Going Down

64 Change in x s and y s 8th 2012 Outstanding Guides, LLC 308 x y x y Going Down Going Up

65 8th 2012 Outstanding Guides, LLC Multiple Representations of Linear Relations Functions Representation of Linear Relations 8 Vocabulary independent dependent horizontal axis vertical axis linear

66 8th 2012 Outstanding Guides, LLC 310 Table x weeks y total $ Multiple Representations of Linear Relations Narrative David has $10 and started saving $3 a week. Reminders x - value independent horizontal axis first value in table y - value dependent vertical axis second value in table Graph Equation x = the number of weeks y = the total amount David has saved y = 3x + 10

67 8th 2012 Outstanding Guides, LLC 311 Table x weeks y total $ Multiple Representations of Linear Relations Narrative David has $10 and started saving $3 a week. Reminders x - value independent axis first value in table y - value dependent axis second value in table Graph Equation x = the number of weeks y = the total amount David has saved y =

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69 8th 2012 Outstanding Guides, LLC Angles Geometry Alternate Exterior/Alternate Interior/Corresponding/Complementary/Supplementary/Vertical 8 Vocabulary adjacent alternate exterior angles alternate interior angles complementary angles corresponding angles parallel lines supplementary angles transversal vertex

70 8th 2012 Outstanding Guides, LLC 314 Alternate Exterior Angles Alternate Exterior Angles are angles that are outside the parallel lines and on opposite sides of the transversal. 1 and 8 2 and 7 Alternate Interior Angles Alternate Interior Angles are angles that are inside the parallel lines and on opposite sides of the transversal. 3 and 6 4 and 5 Supplementary Angles Complementary Angles Supplementary Angles are angles whose outer rays form a straight line. The sum of their measure is and 4 5 and 6 Complementary Angles are angles whose outer rays form a right angle. The sum of their measure is 90. Opposite or Vertical Angles Corresponding Angles Angles formed by a Transversal crossing a set of parallel lines: Vertical angles are formed when two lines intersect. They share a vertex, but are not adjacent. Corresponding angles are in the same position. They are on the same side of the transversal, but not side by side. 2 and 3 5 and 8 2 and 6 3 and 7

71 8th 2012 Outstanding Guides, LLC 315 Length of Segment Proportion The segments formed by two non parallel transversals cutting through parallel lines can be written as a proportion and solved. Interior and Exterior Angles of a Triangle The interior angles of a triangle total 180. The interior angle, its adjacent exterior angles and its vertical angle total 360. The exterior angle adjacent to an interior angle is equal to the sum of the other two interior angles. The sum of the exterior angles adjacent to each of the interior angles totals 360.

72 8th 2012 Outstanding Guides, LLC 316 Alternate Exterior Angles Alternate Exterior Angles are angles that are the parallel lines and on opposite sides of the transversal. 1 and 8 2 and 7 Alternate Interior Angles Alternate Interior Angles are angles that are the parallel lines and on opposite sides of the transversal. 3 and 6 4 and 5 Supplementary Angles Complementary Angles Supplementary Angles are angles whose outer rays form a The sum of their measure is. 2 and 4 5 and 6 Complementary Angles are angles whose outer rays form a. The sum of their measure is. Opposite or Vertical Angles Corresponding Angles Angles formed by a Transversal crossing a set of parallel lines: Vertical angles are formed when two lines. They share a vertex, but are not adjacent. Corresponding angles are in the position. They are on the side of the transversal, but not side by side. 2 and 3 5 and 8 2 and 6 3 and 7

73 8th 2012 Outstanding Guides, LLC 317 Length of Segment Proportion The segments formed by two non parallel transversals cutting through parallel lines can be written as a and solved. Interior and Exterior Angles of a Triangle The angles of a triangle total. The interior angle, its adjacent exterior angles and its vertical angle total. The exterior angle adjacent to an interior angle is to the sum of the other two interior angles. The sum of the exterior angles adjacent to each of the interior angles totals.

74 8th 2012 Outstanding Guides, LLC 318 Alternate Exterior Angles Alternate Interior Angles Supplementary Angles Complementary Angles Opposite or Vertical Angles Corresponding Angles Angles formed by a Transversal crossing a set of parallel lines:

75 8th 2012 Outstanding Guides, LLC Pythagorean Theorem Geometry 8 Vocabulary hypotenuse leg Pythagorean Theorem Pythagorean triplets right angle right triangle

76 8th 2012 Outstanding Guides, LLC ft 6 ft Leg Some Special Triangles form right triangles: by Angle Measures 30, 60, 90 45, 90, 45 by Side Measures 3, 4, 5 5, 12, 13 a 2 + b 2 = c = c = c = c 2 Hypotenuse Pythagorean Theorem a 2 + b 2 = c 2 10 = c Leg

77 8th 2012 Outstanding Guides, LLC ft 6 ft Some Special Triangles form right triangles: by Measures 30, 60, 90 45, 90, 45 by Measures 3, 4, 5 5, 12, 13 a 2 + b 2 = c = c = c = c 2 Pythagorean Theorem a 2 + b 2 = c 2 = c

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79 8th 2012 Outstanding Guides, LLC Similar / Congruent Geometry Identifying Congruent and Similar Figures 8 Front Cover Bottom congruent tab Top similar tab Vocabulary congruent parallel perpendicular similar

80 Congruent Congruent Figures Same Shape Same Angles Same Size Inside Front Cover Similar Similar Figures Same Shape Same Angles Different Size Inside 8th 2012 Outstanding Guides, LLC 324

81 c a b These four squares are Congruent. z This square is similar to the larger square that makes this graphic organizer. x y Symbols parallel perpendicular congruent similar In congruent and similar figures, corresponding angles are congruent. In congruent figures, corresponding sides are congruent. 8th 2012 Outstanding Guides, LLC 325 acb cab xyz yzx ac ab xy xz This triangle is congruent to the triangle below.

82 c a b These four squares are. z This square is to the larger square that makes this graphic organizer. x y Symbols parallel perpendicular congruent similar In and figures, corresponding are. In figures, corresponding are. 8th 2012 Outstanding Guides, LLC 326 acb cab xyz yxz ac ab xy xz This triangle is to the triangle below.

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85 8th 2012 Outstanding Guides, LLC Transformations Geometry Rotations/Reflections/Translations/Dilations 8 Vocabulary coordinates dilations reflections rotations transformations translations

86 8th 2012 Outstanding Guides, LLC 330 Transformations Rotation Rotation TURN FLIP SLIDE ENLARGE/REDUCE Rotation Reflection Translations Translations Dilations Dilations

87 8th 2012 Outstanding Guides, LLC 331 Translation Rotation Clockwise around origin Degree Rule 90º (y, -x) 180º (-x, -y) 270º (-y, x) Reflection Axis Rule over x (x, -y) over y (-x, y) Direction Rule Up (x, y+c) Down (x, y-c) Right (x+c, y) Left (x-c, y) c = vertical or horizontal change Dilation Enlargement sf > 1 Reduction sf < 1 sf = scale factor

88 8th 2012 Outstanding Guides, LLC 332 Translation Rotation Clockwise around origin Degree Rule 90º 180º 270º Reflection Axis Rule over x over y Direction Rule Up Down Right Left c = vertical or horizontal change Dilation Enlargement Reduction sf = scale factor

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90 8th 2012 Outstanding Guides, LLC 334

91 8th 2012 Outstanding Guides, LLC Volume Geometry Calculating volume of solid figures 8 Vocabulary calculate cone cubed cylinder formula sphere substitute volume

92 4 cm 8th 2012 Outstanding Guides, LLC 336 Volume Cone Sphere Cylinder 6 cm 3 cm 4 cm 2 cm 4 cm 6 cm Step 1 Formula Step 2 Substitute Step 3 Calculate Express answers with units! V = (.33)(3.14)(3²)(6) V = (.33)(3.14)(9)(6) V = (4)(6) V = (54) V = cm 3 V = (1.33)(3.14)(4 3 ) V = (1.33)(3.14)(64) V = (64) V = cm 3 V = 3.14(2²)(6) V = 3.14(4)(6) V = 3.14(24) V = cm 3

93 4 cm 8th 2012 Outstanding Guides, LLC 337 Volume Cone Sphere Cylinder 6 cm 3 cm 4 cm 2 cm 4 cm 6 cm Step 1 Formula Step 2 Substitute Step 3 Calculate V = (.33)(3.14)(3²)(6) V = (1.33)(3.14)(4 3 ) V = 3.14(2²)(6) Express answers with units!

94 4 cm 8th 2012 Outstanding Guides, LLC 338 Volume Cone Sphere Cylinder 6 cm 3 cm 4 cm 2 cm 4 cm 6 cm

95 8th 2012 Outstanding Guides, LLC Scatter Plots Statistics and Probability Graphing Bivariate Data 8 Vocabulary bivariate data line of best fit scatter plot slope y-intercept Copy this graphic organizer front to back.

96 340 Graphing Bivariate Data Strong Positive Weak Positive Strong Negative Weak Negative No Correlation Bivariate Data - two variables or quantities changing. Bivariate Data is represented with two column tables and a coordinate graph. Graphing Bivariate Data Bivariate Data Associations 8th 2012 Outstanding Guides, LLC

97 341 Gap - A section of a table or graph with no data points. Linear Model of Bivariate Relationships Steps 1. Draw a line through the data points to the y axis. 2. Determine Constant Rate of Change or Slope. 3. Determine y-intercept or starting point. 4. Use y = mx + b to write equation. Bivariate Data Distribution Cluster - Data points which tend to crowd around a particular point in a set of values. Outlier - A number that is significantly out of range of other data. 8th 2012 Outstanding Guides, LLC

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99 Appendices 8th 2012 Outstanding Guides, LLC 343

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101 VOCABULARY Definition Definition Definition VOCABULARY Definition Definition Definition Example Example Example Example Example Example VOCABULARY Definition Definition Definition VOCABULARY Definition Definition Definition Example Example Example Example Example Example 8th 2012 Outstanding Guides, LLC 345

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103 Vocabulary Rubric Owner of OMG: Student Grader: Date: Vocabulary Grade: Vocabulary Definition is Given Example is Given Yes No Yes No 8th 2012 Outstanding Guides, LLC 347

104 8th 2012 Outstanding Guides, LLC 348

105 Proportions Order of Operation Rate and Ratios Properties Decimal Computation Solving Equations Divisibility Rules Variables and Expressions Division Variable Relationships and Equations Factor Slide Formulas Fraction Computation Surface Area Multiplication Table Volume Positive and Negative Numbers Graphs Prime Factorization Mean Absolute Deviation Inequalities Statistics 8th 2012 Outstanding Guides, LLC 349 6th Grade Graphic Organizer Labels for File Box

106 7th Grade Graphic Organizer Labels for File Box Ratios and Proportions Writing Inequalities Unit Rate Angle Relationships Decimals Cross Sections Fractions, Decimals, Percents Formulas Integer Rules Scale Properties Triangles Linear Expressions Central Tendencies Multiple Representations of Linear Relations Outcomes Solving Equations Probability: Experimental/Theoretical Verbal Expressions Probability: Compound/Simple Sample Distribution 8th 2012 Outstanding Guides, LLC 350

107 Radicals Multiple Representations Rational/Irrational Numbers Angles Exponents Pythagorean Theorem Linear Equations Similar /Congruent Linear Functions Transformations Perfect Squares and Cubes Volume Scientific Notation Scatter Plots Slope Solving Equations Systems of Equations Functions Functional Relationships 8th Grade Graphic Organizer Labels for File Box 8th 2012 Outstanding Guides, LLC 351

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109 Dear Parents/Guardian: This letter is to inform you about a quick reference that students create and use to review math concepts we have covered in class - an Outstanding Math Guide (OMG). The OMG consists of brightly colored graphic organizers for each unit of study that are kept in a standard, 3-prong pocket folder that s been transformed into a compact math resource. Each graphic organizer contains notes and examples of key concepts. Your student can use the OMG as a visual reference as they work on homework and review material. The OMG also contains vocabulary terms. As the terms are introduced in class, students are required to record a definition and example. The OMG s will be collected and vocabulary assignments will be graded periodically. The OMG is a valuable asset for your student. It should be in their notebook at all times. You are encouraged to look through it now and watch it take shape with each unit of study. Sincerely, Math Team 8th 2012 Outstanding Guides, LLC 353