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Mathematics Pacing Guide Grade 8 (Algebra) Timing Content & Processes (MCF) Supporting Grade Level Content Expectations Vocabulary Integrated and Employability/Career Skills Assessable vocabulary = Ongoing regular font A-17 Careers Instructional vocabulary = Explore Professions and Related Salaries italicized font - Accountant box plot - Banker formula - Engineer graphing - Teacher histogram - Sales Internet - Artist LIST - Architect mean - Mathematician median mode A-18 Personal Management scatterplot Develop Personal Management Skills spread sheet - Budgeting (income, spending…) table - Calculate sports statistics trace window A-19 Teamwork Y= Develop Skills for Interacting with Others zoom - Negotiations analyze - Cooperative learning compare - Respect for others conjecture - Conflict resolution convey describe devise Technology discuss evaluate A-16 Use, Transfer, and Apply Appropriate Technology explain Investigate the Use of Calculators interpret - Determine key sequence algorithm add subtract divide multiply Grade 8 Mathematics Pacing Guide – Revised May 2008 1 Timing Content & Processes (MCF) Supporting Grade Level Content Expectations Vocabulary fraction percent decimal square roots exponents reciprocals Use Computer Spreadsheets to Solve Problems - Develop spreadsheet instructions Grade 8 Mathematics Pacing Guide – Revised May 2008 2 Mathematics Pacing Guide Grade 8 (Algebra) Timing Content & Processes (MCF) Supporting Grade Level Content Expectations Vocabulary Unit 1: Number Sense and Numeration additive identity property September of zero A-9 Concepts and Properties of Numbers associative property of Topic: Develop an understanding and investigate properties of addition numbers in measuring and counting activities. Understand Real Number Concepts associative property of Number Systems multiplication and Number commutative property of Sense Extend their understanding of numeration systems to N.ME.08.01 Understand the meaning of a square root of addition include decimal numeration, scientific numeration a number and its connection to the square whose area is commutative property of Timing: 2 weeks and non-decimal numeration systems. (IV.1.MS.2) the number; understand the meaning of a cube root and multiplication (IV.1.HS.2) its connection to the volume of a cube. consecutive cube root derived quantities A-10 Representation and Uses of Numbers distributive property Produce and translate among equivalent expressions. exponential growth integers Determine use of rational approximations. irrational number (IV.2.MS.3) (IV.2.HS.3) means and extremes multiplicative identify Apply estimation strategies. (IV.2.MS.4) (IV.2.HS.4) N.FL.08.05 Estimate and solve problems with square (property of one) roots and cube roots, using calculators. negative exponent prime property N.FL.08.06. Find square roots of perfect squares and proportion approximate the square roots of non-perfect squares by Pythagorean Theorem locating between consecutive integers, e.g., 13C is rational number between 11 and 12. real number Solve real-world problems. (IV.2.MS.5) (IV.2.HS.5) repeating decimal scaling A-11 Number Relationships scientific notation Explain the meaning of powers and roots of numbers square root and use calculators to compute powers and square squaring roots. (IV.3.MS.4) (IV.3.HS.4) terminating decimal truncate unit rate Grade 8 Mathematics Pacing Guide – Revised May 2008 3 Mathematics Pacing Guide Grade 8 (Algebra) Timing Content & Processes (MCF) Supporting Grade Level Content Expectations Vocabulary Unit 2: Number Sense and Numeration September and October A-9 Concepts and Properties of Numbers Develop an understanding and investigate properties of Topic: Number numbers in measuring and counting activities. Understand Real Number Concepts Systems and Number Sense Extend their understanding of numeration systems to N.ME.08.02 Understand meanings for zero and negative include decimal numeration, scientific numeration integer exponents. Timing: 3 weeks and non-decimal numeration systems. (IV.1.MS.2) (IV.1.HS.2) A-10 Representation and Uses of Numbers Produce and translate among equivalent expressions. Incorporate decimal representations of rational and N.ME.08.03 Understand that in decimal form, rational irrational numbers. (IV.2.MS.1) (IV.2.HS.1) numbers either terminate or eventually repeat, and that calculators truncate or round repeating decimals; locate Evaluate exponential expressions. (IV.2.MS.2) rational numbers on the number line; know fraction (IV.2.HS.2) forms of common repeating decimals, e.g. 1 1 0.1 ;0.3 Determine use of rational approximations. 9 3. (IV.2.MS.3) (IV.2.HS.3) Apply estimation strategies. (IV.2.MS.4) (IV.2.HS.4) N.ME.08.04 Understand that irrational numbers are those that cannot be expressed as the quotient of two integers, and cannot be represented by terminating or repeating decimals; approximate the position of familiar irrational numbers, (e.g., 2, 3, ) on the number line. Solve real-world problems. (IV.2.MS.5) (IV.2.HS.5) A-11 Number Relationships Investigate relationships, and represent and compare very large and small numbers. Grade 8 Mathematics Pacing Guide – Revised May 2008 4 Timing Content & Processes (MCF) Supporting Grade Level Content Expectations Vocabulary Compare and order integers and rational numbers using relations of equality and inequality. (IV.3.MS.1) (IV.3.HS.1) Explain the meaning of powers and roots of numbers and use calculators to compute powers and square roots. (IV.3.MS.4) (IV.3.HS.4) Grade 8 Mathematics Pacing Guide – Revised May 2008 5 Mathematics Pacing Guide Grade 8 (Algebra) Timing Content & Processes (MCF) Supporting Grade Level Content Expectations Vocabulary Unit 3: Number Sense and Numeration October A-10 Representation and Uses of Numbers Topic: Produce and translate among equivalent expressions. Solve Problems Calculations Using Real and Solve real-world problems. (IV.2.MS.5) (IV.2.HS.5) N.MR.08.08 Solve problems involving percent increases Complex and decreases. Numbers A-11 Number Relationships Investigate relationships, and represent and compare very N.FL.08.09 Solve problems involving compounded Timing: 3 weeks large and small numbers. interest or multiple discounts. Express numerical comparisons as ratios and rates. (IV.3.MS.2) (IV.3.HS.2) N.MR.08.07 Understand percent increase and percent decrease in both sum and product form, e.g. 3% increase of a quantity x is x + .03x = 1.03x. Understand the concept of non-linear functions using basic examples Apply their understanding of number relationships in solving problems. (IV.3.MS.5) (IV.3.HS.5) N.FL.08.09 Solve problems involving compounded interest or multiple discounts. Mathematics Pacing Guide Grade 8 (Algebra) Grade 8 Mathematics Pacing Guide – Revised May 2008 6 Timing Content & Processes (MCF) Supporting Grade Level Content Expectations Vocabulary Unit 4: Number Sense and Numeration November A-10 Representation and Uses of Numbers Topic: Produce and translate among equivalent expressions. Solve Problems Calculations using Real and Solve real-world problems. (IV.2.MS.5) (IV.2.HS.5) N.MR.08.10 Calculate weighted averages such as course Complex grades, consumer price indices, and sports ratings. Numbers A-11 Number Relationships Investigate relationships, and represent and compare very Timing: 2 weeks large and small numbers. Apply their understanding of number relationships in solving problems. (IV.3.MS.5) (IV.3.HS.5) N.FL.08.11 Solve problems involving ratio units, such as miles per hour, dollars per pound, or persons per square mile. Grade 8 Mathematics Pacing Guide – Revised May 2008 7 Mathematics Pacing Guide Grade 8 (Algebra) Timing Content & Processes (MCF) Supporting Grade Level Content Expectations Vocabulary Unit 5: Patterns, Relationships, and Functions binomial November and coefficient December A-1 Patterns Understand the Concept of Non-linear Functions constant Analyze, interpret, and predict patterns. using Basic Examples continuous Topic: Functions degree Use models to make predictions and decisions. A.RP.08.01 Identify and represent linear functions, dependent variable Timing: 3 weeks (I.1.MS.3) (I.1.HS.3) quadratic functions, and other simple functions including direct variation inversely proportional relationships (y = k/x); cubics (y = domain Explore and describe visual and numeric patterns, ax3); roots (y = x ); and exponentials (y = ax, a > 0); equation including linear expressions, near-linear patterns and expression using tables, graphs, and equations. symmetric and spatial patterns. (I.1.MS.4) (I.1.HS.4) exponential function function A.PA.08.02 For basic functions, e.g. simple quadratics, A-2 Variability and Change function notation direct and indirect variation, and population growth, Explore variability and change. hyperbole describe how changes in one variable affect the others. independent variable Differentiate between functions and relationships A.PA.08.03 Recognize basic functions in problem indirect variation such as linear vs. not linear or continuous vs. non- inverse function context, e.g. area of a circle is r2, volume of a sphere is inversely proportional continuous. (I.2.MS.5) (I.2.HS.5) 4/3 r3, and represent them using tables, graphs, and relationship formulas linear Solve real-world problems. (I.2.MS.6) (I.2.HS.6) linear function A.RP.08.04 Use the vertical line test to determine if a linear equalities graph represents a function in one variable. linear inequalities Number Sense and Numeration monomial A-11 Number Relationships non-continuous Recognize, Represent, and Apply Common Formulas nonlinear function ordered pairs Express numerical comparisons as ratios and rates. A.FO.08.07 Recognize and apply the common formulas: perimeter area (IV.3.MS.2) (IV.3.HS.2) (a + b)2 = a2 + 2 ab + b2 polynomial relationship (a – b)2 = a2 – 2 ab + b2 proportional Explain the meaning of powers and roots of numbers (a + b) (a – b) = a2 – b2; represent geometrically. quadratic function and use calculators to compute powers and square range roots. (IV.3.MS.4) (IV.3.HS.4) rate of change root Probability and Discrete Mathematics scale factor Grade 8 Mathematics Pacing Guide – Revised May 2008 8 Timing Content & Processes (MCF) Supporting Grade Level Content Expectations Vocabulary A-14 Probability A.FO.08.08 Factor simple quadratic expressions with sequence simultaneous integer coefficients, e.g., x2 + 6x + 9, x2 + 2x – 3, and x2 linear equations Generate and interpret probability distributions. – 4; solve simple quadratic equations, e.g., x2 = 16 or x2 slope (VI.1.MS.2) (VI.1.HS.2) = 5 (by taking square roots); x2 – x – 6 = 0, x2 – 2x = 15 square root function (by factoring); verify solutions by evaluation. trinomial term vertical line test x-intercept y-intercept Grade 8 Mathematics Pacing Guide – Revised May 2008 9 Mathematics Pacing Guide Grade 8 (Algebra) Timing Content & Processes (MCF) Supporting Grade Level Content Expectations Vocabulary Unit 6: Patterns, Relationships, and Functions January A-1 Patterns Recognize, Represent, and Apply Common Formulas Topic: Binomials Analyze, interpret, and predict patterns. A.FO.08.07 Recognize and apply the common formulas: Timing: 3 weeks Analyze and generalize number sequences. (a + b)2 = a2 + 2 ab + b2 (I.1.MS.1) (I.1.HS.1) (a – b)2 = a2 – 2 ab + b2 (a + b) (a – b) = a2 – b2; represent geometrically. Solve real-world problems. (I.1.MS.5) (I.1.HS.5) A.FO.08.08 Factor simple quadratic expressions with integer coefficients, e.g., x2 + 6x + 9, x2 + 2x – 3, and x2 Number Sense and Numeration – 4; solve simple quadratic equations, e.g., x2 = 16 or x2 = 5 (by taking square roots); x2 – x – 6 = 0, x2 – 2x = 15 A-10 Representation and Uses of Numbers (by factoring); verify solutions by evaluation. Incorporate decimal representations of rational and irrational numbers. (IV.2.MS.1) (IV.2.HS.1) A-11 Number Relationships Explain the meaning of powers and roots of numbers and use calculators to compute powers and square roots. (IV.3.MS.4) (IV.3.HS.4) Numerical and Algebraic Operations and Analytical Thinking A-12 Operations and Their Properties Investigate algebraic operations and their properties. Present and explain geometric and symbolic models for operations with real numbers and algebraic expressions. (V.1.MS.1) (V.1.HS.1) Grade 8 Mathematics Pacing Guide – Revised May 2008 10 Timing Content & Processes (MCF) Supporting Grade Level Content Expectations Vocabulary Compute with real numbers and algebraic expressions. (V.1.MS.2) (V.1.HS.2) Describe the properties of operations and generalize about their properties. (V.1.MS.3) (V.1.HS.3) A-13 Algebraic And Analytic Thinking Represent algebraic concepts with matrices, diagrams, graphs, etc. (V.2.MS.2) (V.2.HS.2) Grade 8 Mathematics Pacing Guide – Revised May 2008 11 Mathematics Pacing Guide Grade 8 (Algebra) Timing Content & Processes (MCF) Supporting Grade Level Content Expectations Vocabulary Unit 7: Patterns, Relationships, and Functions January & February A-1 Patterns Understand and Represent Quadratic Functions Analyze, interpret, and predict patterns. Topic: A.RP.08.05 Relate quadratic functions in factored form Understand and Analyze and generalize number sequences. and vertex form to their graphs, and vice versa; in Represent (I.1.MS.1) (I.1.HS.1) particular, note that solutions of a quadratic equation are Quadratic the x-intercepts of the corresponding quadratic function. Functions Analyze, interpret, and translate among representations such as tables and graphs. (I.1.MS.2) A.RP.08.06 Graph factorable quadratic functions, Timing: 3 weeks (I.1.HS.2) finding where the graph intersects the x-axis and the coordinates of the vertex; use words “parabola” and Use models to make predictions and decisions. “roots”; include functions in vertex form and those with (I.1.MS.3) (I.1.HS.3) leading coefficient –1, e.g., y = x2 – 36, y = (x – 2)2 – 9; y = – x2; y = – (x – 3)2. Explore and describe visual and numeric patterns, including linear expressions, near-linear patterns and symmetric and spatial patterns. (I.1.MS.4) (I.1.HS.4) Recognize, Represent, and Apply Common Formulas Solve real-world problems. (I.1.MS.5) (I.1.HS.5) A.FO.08.08 Factor simple quadratic expressions with integer coefficients, e.g., x2 + 6x + 9, x2 + 2x – 3, and x2 – 4; solve simple quadratic equations, e.g., x2 = 16 or Number Sense and Numeration x2 = 5 (by taking square roots); x2 – x – 6 = 0, x2 – 2x = 15 (by factoring); verify solutions by evaluation. A-11 Number Relationships A.FO.08.09 Solve applied problems involving simple Distinguish between prime and composite numbers; quadratic equations. identify factors, multiples, common factors and multiples, and relatively prime numbers; and apply divisibility tests to numbers. (IV.3.MS.3) (IV.3.HS.3) Grade 8 Mathematics Pacing Guide – Revised May 2008 12 Mathematics Pacing Guide Grade 8 (Algebra) Timing Content & Processes (MCF) Supporting Grade Level Content Expectations Vocabulary Unit 8: Numerical and Algebraic Operations February and Analytical Thinking Understand Solutions and Solve Equations, Simultaneous Equations, and Linear Inequalities Topic: A-13 Algebraic and Analytic Thinking Recognize, Analyze and model problems using algebraic notation. A.FO.08.10 Understand that to solve the equation f(x) = Represent, and g(x) means to find all values of x for which the equation is Apply Common Identify variables and express their relationships true; e.g., determine whether a given value, or values from Formulas algebraically. (V.2.MS.1) (V.2.HS.1) a given set, is a solution of an equation (0 is a solution of 3x2 + 2 = 4x + 2, but 1 is not a solution). Timing: 3 weeks Represent algebraic concepts with matrices, diagrams, graphs, etc. (V.2.MS.2) (V.2.HS.2) A.FO.08.11 Solve simultaneous linear equations in two variables, by graphing, by substitution and by linear Solve equations and inequalities. (V.2.MS.3) combination; estimate solutions using graphs; include (V.2.HS.3) examples with no solutions and infinitely many solutions. Solve linear systems. (V.2.MS.3) (V.2.HS.3) A.FO.08.12 Solve linear inequalities in one and two variables, and graph the solution sets. Solve problems using equations and inequalities. (V.2.MS.5) (V.2.HS.5) A.FO.08.13 Set up and solve applied problems involving simultaneous linear equations and linear inequalities. Number Sense and Numeration A-10 Representation and Uses of Numbers Solve real-world problems. (IV.2.MS.5) (IV.2.HS.5) Grade 8 Mathematics Pacing Guide – Revised May 2008 13 Mathematics Pacing Guide Grade 8 (Algebra) Timing Content & Processes (MCF) Supporting Grade Level Content Expectations Vocabulary Unit 9: Geometry and Measurement bisector March Understand and Use the Pythagorean Theorem circle A-3 Shape and Shape Relationships complimentary angles Identify properties and describe relationships among G.GS.08.01 Understand at least one proof of the corresponding angles Topic: cones Understand and shapes. Pythagorean Theorem; use the Pythagorean Theorem and congruent Use the its converse to solve applied problems, including cube Pythagorean Use shape properties and relationships to solve perimeter, area, and volume problems. cylinder Theorem problems. (II.1.MS.7) (II.1.HS.7) dilation G.LO.08.02 Find the distance between two points on the edge Timing: 2 weeks A-4 Position coordinate plane, using the distance formula; recognize face that the distance formula is an application of the horizontal stretch Locate the position of points or objects described by Pythagorean Theorem. image two or more conditions; locate all the points (locus) isometric view net that satisfy a given condition. (II.2.MS.4) (II.2.HS.4) orthogonal view parabola perpendicular bisector plane figure prism projective view pyramid quadrilateral reflection reflectional symmetry rotational symmetry scale factor similarity slide solid figure sphere supplementary angles transformation translate vertex vertical stretch Grade 8 Mathematics Pacing Guide – Revised May 2008 14 Mathematics Pacing Guide Grade 8 (Algebra) Timing Content & Processes (MCF) Supporting Grade Level Content Expectations Vocabulary Unit 10: March A-3 Shape and Shape Relationships Solve Problems About Geometric Figures area Identify properties and describe relationships among circumference shapes. G.SR.08.03 Understand the definition of a circle; know perimeter Topic: Solve radius Problems About and use the formulas for circumference and area of a surface area Geometric Generalize the characteristics of shapes and apply circle to solve problems. volume Figures their generalizations to classes of shapes. (II.1.MS.2) (II.1.HS.2) G.SR.08.04 Find area and perimeter of complex figures Timing: 3 weeks by sub-dividing them into basic shapes (quadrilaterals, Construct familiar shapes using coordinates, triangles, circles). appropriate tools (including technology), sketching and drawing two- and three dimensional shapes. G.SR.08.05 Solve applied problems involving areas of (II.1.MS.4) (II.1.HS.4) triangles, quadrilaterals, and circles. Combine, dissect, and transform shapes. (II.1.MS.5) (II.1.HS.5) Use shape properties and relationships to solve problems. (II.1.MS.7) (II.1.HS.7) A-5 Measurement Use proportional reasoning and indirect measurements to draw inferences. (II.3.MS.5) (II.3.HS.5) Grade 8 Mathematics Pacing Guide – Revised May 2008 15 Mathematics Pacing Guide Grade 8 (Algebra) Timing Content & Processes (MCF) Supporting Grade Level Content Expectations Vocabulary Unit 11: Geometry and Measurement April Understand Concepts of Volume and Surface Area, A-5 Measurement and Apply Formulas Topic: Volume Compare and analyze objects with a standard unit. and Surface Area G.SR.08.06 Know the volume formulas for generalized Interpret measurements and explain how changes in cylinders ((area of base) x height),generalized cones and Timing: 2 weeks one measurement affects another. (II.3.MS.4) pyramids ( (area of base) x height) and spheres ( (II.3.HS.4) (radius)3), and apply them to solve problems. Use proportional reasoning and indirect G.SR.08.07 Understand the concept of surface area and measurements to draw inferences. (II.3.MS.5) find the surface area of prisms, cones, spheres, pyramids, (II.3.HS.5) and cylinders. A-3 Shape and Shape Relationships Visualize Solids Identify properties and describe relationships among shapes. G.SR.08.08 Sketch a variety of two-dimensional representations of three-dimensional solids, including: Generalize the characteristics of shapes and apply orthogonal views (top, front, and side), picture views their generalizations to classes of shapes. (II.1.MS.2) (projective or isometric) and nets, and use such two- (II.1.HS.2) dimensional representations to help solve problems. Construct familiar shapes using coordinates, appropriate tools (including technology), sketching and drawing two- and three dimensional shapes. (II.1.MS.4) (II.1.HS.4) Use shape properties and relationships to solve problems. (II.1.MS.7) (II.1.HS.7) Grade 8 Mathematics Pacing Guide – Revised May 2008 16 Mathematics Pacing Guide Grade 8 (Algebra) Timing Content & Processes (MCF) Supporting Grade Level Content Expectations Vocabulary Unit 12: Geometry and Measurement April & May Understand and Apply Concepts of A-3 Shape and Shape Relationships Transformation and Symmetry Topic: Identify properties and describe relationships among Transformations shapes. G.TR.08.09 Understand the definition of a dilation from a point in the plane and relate it to the definition of Timing: 2 weeks Generalize the characteristics of shapes and apply similar polygons. their generalizations to classes of shapes. (II.1.MS.2) (II.1.HS.2) G.TR.08.10 Understand and use reflective and rotational symmetries of two-dimensional shapes and Combine, dissect, and transform shapes. (II.1.MS.5) relate them to transformations to solve problems. (II.1.HS.5) Generalize about the common properties of similar, congruent, parallel and perpendicular shapes and verify their generalizations informally. (II.1.MS.6) (II.1.HS.6) A-4 Position Identify location of objects, location relative to other objects, and the effects of transformations. Locate and describe objects in terms of their orientation and relative position. (II.2.MS.2) (II.2.HS.2) Describe translations, reflections, rotations and dilations using the language of transformations and employ transformations to verify congruence of figures. (II.2.MS.3) (II.2.HS.3) Data Analysis and Statistics Grade 8 Mathematics Pacing Guide – Revised May 2008 17 Timing Content & Processes (MCF) Supporting Grade Level Content Expectations Vocabulary A-6 Collection, Organization, and Presentation of Data Explain how data can be skewed/biased. (III.1.MS.3) (III.1.HS.3) Implement strategies to obtain, organize, and present data. (III.1.MS.4) (III.1.HS.4) Number Sense and Numeration A-10 Representation and Uses of Numbers Solve real-world problems. (IV.2.MS.5) (IV.2.HS.5) Grade 8 Mathematics Pacing Guide – Revised May 2008 18 Mathematics Pacing Guide Grade 8 (Algebra) Timing Content & Processes (MCF) Supporting Grade Level Content Expectations Vocabulary Unit 13: May Data Analysis and Statistics basic counting principal Draw, Explain, and Justify Conclusions Based on biased sample Topic: Bias A-6 Collection, Organization and Presentation of Data Data box plots Collect, organize, and analyze data. coordinate graph Timing: 2 weeks D.AN.08.01 Determine which measure of central counting tree Collect data through survey and observation. tendency (mean, median, mode) best represents a data cumulative frequency (III.1.MS.1) (III.1.HS.1) set, e.g. salaries, home prices for answering certain dependent event questions, and justify the choice made. experimental probability Organize data in various forms such as tables, charts, extrapolations and graphs. (III.1.MS.2) (III.1.HS.2) D.AN.08.02 Recognize practices of collecting and five number summary displaying data that may bias the presentation or analysis. frequency table Explain how data can be skewed/biased. (III.1.MS.3) histogram (III.1.HS.3) independent event interpolations Implement strategies to obtain, organize, and present intersection data. (III.1.MS.4) (III.1.HS.4) IQR (inter-quartile) range line graph A-7 Description and Interpretation line of best fit Examine, describe, and relate data. line plot lower quartile mean Present and critically examine data from tables, measures of central graphs, and charts. (III.2.MS.1) (III.2.HS.1) tendency median Calculate measures of central tendency. (III.2.MS.2) mode (III.2.HS.2) organized list outcomes Utilize data and their characteristics to draw and population support conclusions. (III.2.MS.3) (III.2.HS.3) probability proportion Question sources of data and collection techniques. quartile (III.2.MS.4) (III.2.HS.4) random range Formulate problems to gather and interpret data. relative frequency (III.2.MS.5) (III.2.HS.5) repeated events Grade 8 Mathematics Pacing Guide – Revised May 2008 19 Timing Content & Processes (MCF) Supporting Grade Level Content Expectations Vocabulary sample A-8 Inference and Prediction sampling Develop and justify inferences and predictions. scatter plot stem-and-leaf plot Develop and test hypothesis. (III.3.MS.1) theoretical probability (III.3.HS.1) trend union upper quartile Employ confidence intervals and curve fitting in Venn Diagram analyzing data. (III.3.MS.2) (III.3.HS.2) Formulate, communicate, and evaluate arguments. (III.3.MS.3) (III.3.HS.3) Make predictions and decisions based on data. (III.3.MS.4) (III.3.HS.4) Solve real-world problems. (III.3.MS.5) (III.3.HS.5 Grade 8 Mathematics Pacing Guide – Revised May 2008 20 Mathematics Pacing Guide Grade 8 (Algebra) Timing Content & Processes (MCF) Supporting Grade Level Content Expectations Vocabulary Unit 14: Data Analysis and Statistics May & June A-6 Collection, Organization and Presentation of Data Topic: Collect, organize, and analyze data. Frequency Collect data through survey and observation. Timing: 3 weeks (III.1.MS.1) (III.1.HS.1) Organize data in various forms such as tables, charts, and graphs. (III.1.MS.2) (III.1.HS.2) Explain how data can be skewed/biased. (III.1.MS.3) (III.1.HS.3) Implement strategies to obtain, organize, and present data. (III.1.MS.4) (III.1.HS.4) A-7 Description and Interpretation Examine, describe, and relate data. Present and critically examine data from tables, graphs, and charts. (III.2.MS.1) (III.2.HS.1) A-8 Inference and Prediction Develop and justify inferences and predictions. Develop and test hypothesis. (III.3.MS.1) (III.3.HS.1) Employ confidence intervals and curve fitting in analyzing data. (III.3.MS.2) (III.3.HS.2) Formulate, communicate, and evaluate arguments. (III.3.MS.3) (III.3.HS.3) Grade 8 Mathematics Pacing Guide – Revised May 2008 21 Timing Content & Processes (MCF) Supporting Grade Level Content Expectations Vocabulary Make predictions and decisions based on data. (III.3.MS.4) (III.3.HS.4) Solve real-world problems. (III.3.MS.5) (III.3.HS.5) Understand Probability Concepts for Simple Probability and Discrete Mathematics and Compound Events A-14 Probability D.PR.08.05 Find and/or compare the theoretical Utilize knowledge of probability to make critical probability, the experimental probability, and/or the judgments of various situations. relative frequency of a given event. Generate and interpret probability distributions. D.PR.08.04 Apply the Basic Counting Principle to find (VI.1.MS.2) (VI.1.HS.2) total number of outcomes possible for independent and dependent events, and calculate the probabilities using Identify probability of compound or multiple events. organized lists or tree diagrams. (VI.1.MS.3) (VI.1.HS.3) D.PR.08.06 Understand the difference between Utilize simulations and samplings to determine independent and dependent events, and recognize probability. (VI.1.MS.4) (VI.1.HS.4) common misconceptions involving probability, e.g. Alice rolls a 6 on a die three times in a row; she is just as likely to roll a 6 on the 4th roll as she was on any previous roll. D.PR.08.03 Compute relative frequencies from a table of experimental results for a repeated event. Interpret the results using relationship of probability to relative frequency. Grade 8 Mathematics Pacing Guide – Revised May 2008 22

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