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8th Grade Math Curriculum Map Isaac School District No. 5Quarter 1Unit Name and Description: Compare and Order Real NumbersCluster 1Big Ideas/Enduring Understandings Essential Question(s)Real numbers are classified as either rational or irrational numbers. Describe how multiplying or dividing a number by less than one affects the number?The value of all numbers is dependent on its place value. Why is checking the reasonableness of answer important? How do we use scientific notation to express equivalent forms of rational number? How do we compare and order real numbers? AZ Essential Learning Key TechnologyEIN Standard Knowledge Skills Vocabulary Resources E S1C1PO1 Real numbers; Large and Compare real numbers including very large and small Natural number small integers; Decimals; integers, and decimals, and fractions close to zero Counting number Fractions Whole Numbers I S1C1PO2 Rational numbers; Irrational Classify realnumbers including very large and small, and Order real numbers as rational or irrational Integers numbers; Real numbers Rational numbers Irrational number I S1C1PO3 Real number system; Model the relationship between the subsets of the real number Real number Relationship; Subsets system Standard notation Scientific notation Estimation * = POs previously introduced EIN= Level of Priority for P.O. Bold = Priority PO 1 E= Essential P.O. Italics = POs taught at earlier grade level I= Important P.O. [] = Increased skill rigor Revised 06-16-11 Underlining = Cognitive rigor N= Nice to Know P.O. Isaac School District No. 5 E
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E S1C2PO1 Prime number; Composite Solve problems with factors, multiples, divisibility or numbers; Multiples and remainders, prime numbers, and composite numbers Factors; Divisibility and RemaindersI S1C3PO2 Rational numbers; Estimate the location of rational and common irrational irrational numbers; numbers on a number line number lineI S1C2PO4 Standard notation; Convert standard notation to scientific notation and vice versa Scientific notation; (include positive and negative exponents) Positive and negative exponentsI S1C2PO2 Multiplying and dividing Describe the effect of multiplying and dividing a rational rational number by numbers a number less than zero a number between zero and one a number greater than oneI S1C3PO1 Estimation; Situation Make estimates appropriate to a given situation * = POs previously introduced EIN= Level of Priority for P.O. Bold = Priority PO 2 E= Essential P.O. Italics = POs taught at earlier grade level I= Important P.O. [] = Increased skill rigor Revised 06-16-11 Underlining = Cognitive rigor N= Nice to Know P.O. Isaac School District No. 5 E
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8th Grade Math Curriculum Map Isaac School District No. 5Quarter 1Unit Name and Description: Solving Algebraic Equations and InequalitiesCluster 2Big Ideas/Enduring Understandings Essential Question(s)Algebraic equations, inequalities, and graphs are representative of real life What is absolute value? Why do we have absolute value?situations. How do we use simple interest to track the growth of our money? How can we use equations to solve real life problems? AZ Essential Learning Key TechnologyEIN Standard Knowledge Skills Vocabulary Resources E S3C3PO3 Linear equations; Analyze situations involving linear equations and Linear equations Inequalities; Real inequalities using the properties of the real number system Inequalities number system Equations Simplify problems involving linear equations and Expression inequalities using the properties of the real number system Percent increase Percent decrease Solve problems involving linear equations and inequalities Absolute value using the properties of the real number system Solution E S3C3PO1 Algebraic expressions; Write algebraic expressions, equations, or inequalities that Principle Equations; represent a situation Interest rates Inequalities Identify algebraic expressions, equations, or inequalities that represent a situation * = POs previously introduced EIN= Level of Priority for P.O. Bold = Priority PO 3 E= Essential P.O.Italics = POs taught at earlier grade level I= Important P.O. [] = Increased skill rigor Revised 06-16-11Underlining = Cognitive rigor N= Nice to Know P.O. Isaac School District No. 5 E
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E S3C3PO5 Inequalities; Number line Graph an inequality on a number line E S1C1PO4 Absolute value Model problems involving absolute value Solve problems involving absolute value I S1C2PO3 Simple interest rates; Solve problems involving percent increase, percent decrease, Percent and simple interest rates increase/decrease; Ending balance E S3C3PO2 Expressions; Rational Evaluate an expression containing variables by substituting numbers; rational numbers for the variables Variables E S1C2PO5 Square roots; Cube roots; Simplify numerical expressions using the order of operations Grouping that include grouping symbols, square roots, cube roots, symbols; Positive absolute values, and positive exponents exponents; Absolute I S3C4PO2 value; Order of operations Simple rates Solve problems involving simple rates I S5C2PO6 Informal mathematical Communicate the answer(s) to the question(s) in a problem language; using appropriate representations, including symbols and Formal mathematical informal and formal mathematical language language; Symbols; Representations * = POs previously introduced EIN= Level of Priority for P.O. Bold = Priority PO 4 E= Essential P.O.Italics = POs taught at earlier grade level I= Important P.O. [] = Increased skill rigor Revised 06-16-11Underlining = Cognitive rigor N= Nice to Know P.O. Isaac School District No. 5 E
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8th Grade Math Curriculum Map Isaac School District No. 5Quarter 2Unit Name and Description: Ratios and ProportionsCluster 3Big Ideas/Enduring Understandings Essential Question(s)Ratios and proportions are used to determine the relationship between ideas. How do unit multipliers help me convert? How can we translate real-life situations into algorithms? How do we convert between customary and metric systems? AZ Essential Learning Key TechnologyEIN Standard Knowledge Skills Vocabulary Resources E S4C4PO2 Geometric problems; Solve geometric problems using ratios and proportions Ratios Ratios; Proportions Proportions Corresponding I S4C4PO1 Problems; Measurement Solve problems involving conversions within the same sides/angles system; Conversions measurement system Congruency I S4C1PO3 Proportional reasoning; Use proportional reasoning to determine congruence and Similarity Similar Triangles; similarity of triangles Geometric Congruence; Problems E S5C1PO1 Algorithm; Proportional Create an algorithm to solve problems involving indirect Algorithm reasoning; Density; measurements, using proportional reasoning, dimensional Density Dimensional analysis analysis, and the concepts of density and rate. Scale Factor I S5C2PO8 Problem solving; Describe when to use proportional reasoning to solve a Unit Rate Proportional problem. Density reasoning Dimensional * = POs previously introduced EIN= Level of Priority for P.O. Bold = Priority PO 5 E= Essential P.O.Italics = POs taught at earlier grade level I= Important P.O. [] = Increased skill rigor Revised 06-16-11Underlining = Cognitive rigor N= Nice to Know P.O. Isaac School District No. 5 E
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8th Grade Math Curriculum Map Isaac School District No. 5Quarter 2Unit Name and Description: Pythagorean TheoremCluster 4Big Ideas/Enduring Understandings Essential Question(s)The Pythagorean Theorem can be used to calculate the distance between two How the Pythagorean Theorem applies to right triangles?points. How do we apply the Pythagorean Theorem to calculate the distance of a line segment? AZ Essential Learning Key TechnologyEIN Standard Knowledge Skills Vocabulary Resources E S4C3PO2 Pythagorean Theorem; Use the Pythagorean Theorem to [calculate] the distance Pythagorean Coordinate between two points in the coordinate plane Theorem plane; Distance; Points Leg(s) Hypotenuse E S4C1PO4 Pythagorean Theorem Use the Pythagorean Theorem to solve problems Midpoint I S4C3PO1 Midpoint; Conjecture; Make a conjecture about how to [calculate] the midpoint Coordinate plane between any two points in the coordinate plane Test a conjecture about how to [calculate] the midpoint between any two points in the coordinate plane I S5C2PO13 Pythagorean Theorem; Verify the Pythagorean Theorem using a valid argument Valid argument * = POs previously introduced EIN= Level of Priority for P.O. Bold = Priority PO 6 E= Essential P.O.Italics = POs taught at earlier grade level I= Important P.O. [] = Increased skill rigor Revised 06-16-11Underlining = Cognitive rigor N= Nice to Know P.O. Isaac School District No. 5 E
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8th Grade Math Curriculum Map Isaac School District No. 5Quarter 2Unit Name and Description: Functions and Linear RelationshipsCluster 5Big Ideas/Enduring Understandings Essential Question(s)Functions represent given situations from real life. How do we determine if a graph is a function?Two variables are related. How do we determine if a graph is proportional? Explain how to determine if an equation is linear. How many output values are assigned to a function? How does changing the slope of a line affect its steepness? AZ Essential Learning Key TechnologyEIN Standard Vocabulary Resources Knowledge Skill E S3C4PO1 Linear equations; s Interpret, the relationship between a linear equation Slope-intercept Linear relationships; and its graph. form Slope; Intercept Standard form Identifying slope and intercepts Slope Y-intercept Computing slope and intercepts Proportionality Linear equations I S3C2PO5 Proportional relationships; Demonstrate that proportional relationships are linear using Linear functions Linear; Equations; equations, graphs, or tables Functions Graphs; Tables Function table * = POs previously introduced EIN= Level of Priority for P.O. Bold = Priority PO 7 E= Essential P.O.Italics = POs taught at earlier grade level I= Important P.O. [] = Increased skill rigor Revised 06-16-11Underlining = Cognitive rigor N= Nice to Know P.O. Isaac School District No. 5 E
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E S3C3PO4 Representations; Translate between different representations of linear Linear equations; equations using symbols, graphs, tables, or written Graphs, Tables, Written descriptions descriptions I S3C2PO3 Rule; Algebraic notation; Write the rule for a simple function using algebraic notation Simple functions I S3C2PO2 Relationship; Graph; Determine if a relationship represented by a graph or table is Table; a function Function I S3C2PO4 Linear and nonlinear Identify functions as linear or nonlinear and contrast functions; graphs, distinguishing properties of functions using equations, or tables graphs, or tables I S3C1PO1 Numerical and geometric Recognize and describe numerical and geometric sequences sequences; Tables, using tables, graphs, words, or symbols. Graphs, Words, Symbols; Conjectures Create and analyze numerical and geometric sequences using tables, graphs, words, or symbols. I S5C2PO12 Conclusions; Make conjectures about these sequences conclusions and generalizations about linear Generalizations; relationships Linear relationships Validate conclusions and generalizations about linear relationships * = POs previously introduced EIN= Level of Priority for P.O. Bold = Priority PO 8 E= Essential P.O.Italics = POs taught at earlier grade level I= Important P.O. [] = Increased skill rigor Revised 06-16-11Underlining = Cognitive rigor N= Nice to Know P.O. Isaac School District No. 5 E
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8th Grade Math Curriculum Map Isaac School District No. 5Quarter 2Unit Name and Description: Geometric ShapesCluster 6Big Ideas/Enduring Understandings Essential Question(s)Geometric shapes are evident in everyday life. How does the area of the base affect an objects volume?Geometric formulas can be manipulated to solve for the unknown attribute of How do you use a rectangle to calculate the surface area of a cylinder?a shape. Will a given transformations affect an objects size or shape? How does doubling the diameter of a circle affect its area? AZ Essential Learning Key TechnologyEIN Standard Knowledge Skills Vocabulary Resources E S4C1PO2 Geometric planes and Predict results of combining, subdividing, and changing Rectangular prism solids shapes of plane figures and solids Triangular prism Cylinder Surface area E S4C4PO3 Rectangular prisms; Calculate the surface area and volume of rectangular prisms, Volume Cylinders; right triangular prisms, and cylinders Radius Right triangular prisms Diameter Chords * = POs previously introduced EIN= Level of Priority for P.O. Bold = Priority PO 9 E= Essential P.O.Italics = POs taught at earlier grade level I= Important P.O. [] = Increased skill rigor Revised 06-16-11Underlining = Cognitive rigor N= Nice to Know P.O. Isaac School District No. 5 E
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E S4C1PO1 Radius; Diameter; Chords; Identify for the attributes of circles: radius, diameter, chords, Tangent Tangents; Secants; tangents, secants, inscribed angles, central angles, intercepted Secants Inscribed angles; Central; arcs, circumference, and area Inscribed angles angles; Intercepted arcs; Central [Solve for the circumference and the area of a circle] anglesIntercepted arcs Circumference N S4C2PO2 Transformations; Describe the transformations that create a given tessellation Rotations (turn) Tessellations Origin Rotational symmetry Reflective N S4C2PO1 Rotations; Origin; 45 Model the result of rotations in multiples of 45 degrees of a 2- symmetry degrees, 2- dimensional figure about the origin Tessellations Dimensional figure Midpoint Pi ( ) Parallelogram Trapezoid N S4C2PO3 Lines of symmetry; Identify lines of symmetry in plane figures Rhombus Plane figures; Quadrilateral 2-Dimensional figures [Determine] lines of symmetry in plane figures Prism Complex polygon Classify types of symmetries of 2-dimensional figures Composite figure Polyhedron * = POs previously introduced EIN= Level of Priority for P.O. Bold = Priority PO 10 E= Essential P.O.Italics = POs taught at earlier grade level I= Important P.O. [] = Increased skill rigor Revised 06-16-11Underlining = Cognitive rigor N= Nice to Know P.O. Isaac School District No. 5 E
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8th Grade Math Curriculum Map Isaac School District No. 5Quarter 3Unit Name and Description: Data DisplayCluster 7Big Ideas / Enduring Understandings Essential Question(s)Data allows us to analyze the past and make predictions about the future. How do we determine which graph is the most appropriate representation of a given data set?There are multiple ways to represent data. How do we determine which measure of central tendency is most representative of a given data set? How do outliers affect the mean of a data set? Will each measure of central tendency be representative of your data set? AZ Essential Learning Key TechnologyEIN Standard Knowledge Skills Vocabulary Resources E S2C1PO3 Summary statistics; Describe how summary statistics relate to the shape of the Box and whisker Shape of distribution distribution plot First quartile Median Third quartile I S2C1PO2 Summary statistics; Data Make inferences by comparing the same summary statistic for Lower extreme sets; Inferences two or more data sets Upper extreme Inter-quartile range Random sampling * = POs previously introduced EIN= Level of Priority for P.O. Bold = Priority PO 11 E= Essential P.O.Italics = POs taught at earlier grade level I= Important P.O. [] = Increased skill rigor Revised 06-16-11Underlining = Cognitive rigor N= Nice to Know P.O. Isaac School District No. 5 E
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I S2C1PO1 Displays of data; Box and Solve problems by selecting and constructing, displays of Sample whisker plots; Scatterplots data, including box and whisker plots and scatterplots Biased surveys Circle graphs Solve problems by interpreting and calculating displays of Time-distance data, including box and whisker plots and scatterplots graph Directed graph N S2C1PO4 Information; Sources of Determine whether information is represented effectively and Experiment bias; Representations of appropriately given a graph or a set of data by identifying Experimental data; Graphs; (Histograms; sources of bias and compare and contrast the effectiveness of design Circle graphs; Stem- different representations of data Scatterplots and-leaf plot; Scatterplots; Line) graph; Double line graph; Venn diagram N S3C2PO1 Graph; Context; Sketch a graph that models a given context Interpret a graph that models a given context Describe a context that is modeled by a given graph I S5C2PO7 Information; Symbols; Isolate mathematical information taken from symbols, Diagrams; diagrams, and graphs to make inferences, draw conclusions, Graphs; Inferences; and justify reasoning Conclusions; Reasoning (Frequency tables; Venn Organize mathematical information taken from symbols, diagrams; Bar graphs; diagrams, and graphs to make inferences, draw conclusions, Circle and justify reasoning I S2C4PO1 graphs; Vertex-edge Directed graphs; Problems Use directed graphs to solve problems N S5C2PO1 Problem situation; Analyze a problem situation to determine the question(s) to be Questions answered N S2C1PO5 Experimental design Evaluate the design of an experiment * = POs previously introduced EIN= Level of Priority for P.O. Bold = Priority PO 12 E= Essential P.O.Italics = POs taught at earlier grade level I= Important P.O. [] = Increased skill rigor Revised 06-16-11Underlining = Cognitive rigor N= Nice to Know P.O. Isaac School District No. 5 E
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8th Grade Math Curriculum Map Isaac School District No. 5Quarter 3Unit Name and Description: ProbabilityCluster 8Big Ideas/Enduring Understandings Essential Question(s)Probability can be used to predict the outcome of an event. How does changing the total outcome of an event affect the probability?The total number of outcomes affects the probability of an event. How do dependent events affect the probability of a compound event? What is the difference between theoretical and experimental probability? What is the difference between combinations and permutations? AZ Essential Learning Key TechnologyEIN Standard Knowledge Skills Vocabulary Resources E S2C2PO1 Theoretical probability; Determine theoretical and experimental conditional Theoretical Experimental probabilities in compound probability experiments probability probability; Compound Experimental probability; probability Compound events Independent events Dependent events I S2C2PO2 Probability; Outcome; Interpret probabilities within a given context Mutually exclusive Experiment; Predictions; Fundamental Context Experiments Compare the outcome of an experiment to predictions made counting principle prior to performing the experiment * = POs previously introduced EIN= Level of Priority for P.O. Bold = Priority PO 13 E= Essential P.O.Italics = POs taught at earlier grade level I= Important P.O. [] = Increased skill rigor Revised 06-16-11Underlining = Cognitive rigor N= Nice to Know P.O. Isaac School District No. 5 E
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I S2C2PO3 Possible outcomes; Sample Use all possible outcomes (sample space) to determine the Possible outcomes space; Probability; probability of dependent and independent events Tree diagram. Dependent events; Permutations Independents events Combinations Factorial notation E S2C3PO2 Problems; Factorial Solve counting problems algebraically including factorial Sample space notation; notation Counting principal Represent counting principles algebraically including factorial notation I S2C3PO1 Counting problems Represent, analyze, and solve counting problems with or without ordering repetitions N S5C2PO9 Conjectures; Information; Make conjectures based on information collected from Explorations; Experiments explorations and experiments Test conjectures based on information collected from explorations and experiments N S5C2PO10 Logical conclusions; Solve logic problems involving multiple variables, conditional Conditional statements; statements, conjectures, and negation using words, Conjectures; Negation; charts, and pictures Charts; Pictures I S5C2PO11 Simple valid arguments; Identify simple valid arguments using If then statements. If then statements * = POs previously introduced EIN= Level of Priority for P.O. Bold = Priority PO 14 E= Essential P.O.Italics = POs taught at earlier grade level I= Important P.O. [] = Increased skill rigor Revised 06-16-11Underlining = Cognitive rigor N= Nice to Know P.O. Isaac School District No. 5 E
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8th Grade Math Curriculum Map Isaac School District No. 5Quarter 3Unit Name and Description: Logical EvaluationsCluster 9Big Ideas/Enduring Understandings Essential Question(s)There are various strategies for problem solving. Why do we use different mathematical strategies to solve a problem?Logical processes help them to eliminate unreasonable solutions. How do we identify pertinent and extraneous information from a question? AZ Essential Learning Key TechnologyEIN Standard Resources Knowledge Skill Vocabulary E S5C2PO2 s Mathematical strategies; Analyze and compare mathematical strategies for efficient Expressions Problem solving problem solving Guess and check Substitute Select and use one or more strategies to solve a problem Extraneous information I S5C2PO3 Relevant, missing, and Identify relevant, missing, and extraneous information related Pertinent extraneous information; to the solution to a problem information Relevant I S5C2PO4 Problem situation; Represent a problem situation using multiple representations information Representations; Conditional Process; Reasonableness; Describe the process used to solve the problem statement Verify the reasonableness of the solution I S5C2PO5 Problem solving strategy; Apply a previously used problem-solving strategy in a new context * = POs previously introduced EIN= Level of Priority for P.O. Bold = Priority PO 15 E= Essential P.O.Italics = POs taught at earlier grade level I= Important P.O. [] = Increased skill rigor Revised 06-16-11Underlining = Cognitive rigor N= Nice to Know P.O. Isaac School District No. 5 E
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8th Grade Math Curriculum Map Isaac School District No. 5Quarter 4Unit Name and Description: Algebra and EquationsCluster 10Big Ideas/Enduring Understandings Essential Question(s)Functions model real life situations. How are inequalities represented on the coordinate plane?Algebra is essential in using functional notation. Why do problems involving absolute value have two answers?Absolute value represents the distance from zero. What is the relationship between rate of change and slope? What is the relationship between tables, functions, and graphs? AZ Essential Learning Key TechnologyEIN Standard Knowledge Skills Vocabulary Resources E MHS-S4C3PO5 Linear equation; Graph a linear equation or linear inequality in two Slope-intercept Linear inequalities; variables form Two variables Linear inequalities Standard form I MHS-S3C3PO5 Linear equations; absolute Solve linear equations and equations involving absolute value System of value; Variable with one variable equations Absolute value Constant rate of change Functional notation Domain * = POs previously introduced EIN= Level of Priority for P.O. Bold = Priority PO 16 E= Essential P.O.Italics = POs taught at earlier grade level I= Important P.O. [] = Increased skill rigor Revised 06-16-11Underlining = Cognitive rigor N= Nice to Know P.O. Isaac School District No. 5 E
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E MHS-S3C4PO1 Slope; Intercepts; Graph; Determine the slope and intercepts of the graph of a linear Slope; Constant rate function, interpreting slope as a constant rate of change of change; Linear functions I MHS-S3C2PO3 Functions notation; Use function notation; evaluate a function at a specified value Functions; Value; Domain in its domain I MHS-S3C3PO3 Equations; Table of values; Write an equation given a table of values, two points on the Points; Line; Slope; Graph line, the slope and a point on the line, or the graph of the line I MHS-S3C3PO6 Linear inequalities; Solve linear inequalities in one variable Variable * = POs previously introduced EIN= Level of Priority for P.O. Bold = Priority PO 17 E= Essential P.O.Italics = POs taught at earlier grade level I= Important P.O. [] = Increased skill rigor Revised 06-16-11Underlining = Cognitive rigor N= Nice to Know P.O. Isaac School District No. 5 E
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