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7 Grade Math Curriculum Map th Isaac School District No. 5Quarter 1Unit Name and Description: Rational Number OperationsCluster 1Big Ideas/Enduring Understandings Essential Question(s)Rational number skills are essential in solving real world problems What makes a number irrational or rational?Estimation helps to verify the reasonableness of a solution. How do you apply the four operations to integers?Rational numbers can be represented in various forms How many ways can you represent a single rational number? AZ Essential Learning TechnologyEIN Key Vocabulary Standard Knowledge Skills Resources E S1C2PO5 Order of operations; Simplify numerical expressions using the order of Irrational mathematical properties operations and appropriate mathematical properties. Integers Prime Factorization I S1C1PO2 Prime Factorization; Find factors and multiples within a set of numbers Absolute Value Factors; Standard Form Multiples [Apply] prime factorization to a number Scientific Notation E S1C1PO4 Absolute Value Model simple problems involving absolute value Exponents Consecutive Solve simple problems involving absolute value Square Roots Rational Numbers E S1C2PO1 Integers Add, subtract, multiply, and divide integers Compare Order * = 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 06-16-11Underlining = Cognitive rigor N= Nice to Know P.O. Isaac School District No. 5 E
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I S1C2PO4 Scientific Notation; Represent numbers in [standard form] and scientific notation Order of Positive (positive exponents only) Operations Exponents Factors Interpret numbers using [standard form] and Multiples scientific notation (positive exponents only) Estimate I S1C3PO1 Rational Numbers; Estimate rational numbers and common irrational numbers Common irrational numbers Apply benchmarks for rational numbers and common irrational numbers I S1C1PO3 Rational Numbers; Compare rational numbers using models and Models; representations Representations Order rational numbers using models and representations I S1C3PO2 Estimates [Justify] estimates appropriate to a give situation. E S1C3PO3 Square Roots Estimate square roots of numbers less than a thousand by locating them between two consecutive whole numbers * = 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 06-16-11Underlining = Cognitive rigor N= Nice to Know P.O. Isaac School District No. 5 E
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7 Grade Math Curriculum Map th Isaac School District No. 5Quarter 1Unit Name and Description: EquationsCluster 2Big Ideas/Enduring Understandings Essential Question(s)Proportional reasoning helps to solve day to day problems involving fractions, What is equivalency?percents, and ratios What types of daily situations involve proportional logic?Estimation simplifies daily mathematical computations. What are variables used for?Algebraic equations arerepresentative of real life situations How can we use equations to solve real life problems? AZ Essential Learning Key TechnologyEIN Standard Knowledge Skills Vocabulary Resources E S3C3PO5 Two-Step Equations; Inverse [Formulate] and solve two-step equations that Proportions Operations; Rational Numbers can be solved using inverse operations with Ratios rational numbers Discounts Tax I S1C1PO1 Positive and negative rational Recognize between expressions for positive and negative Convert Numbers rational numbers, including fractions, decimals, Tips percents, and ratios. Equivalent Extraneous Convert between expressions for positive and Relevant negative rational numbers, including fractions, Variables decimals, percents, and ratios Equations Inequalities * = 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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I S1C2PO2 Rational numbers; appropriate Solve problems with rational numbers and appropriate Fraction operations; exact answers or operations using exact answers or estimates. Decimal estimate Percent Inverse Operations E S1C2PO3 Percentages; ratios; proportions; Solve problems involving percentages, ratios and tax; discounts; tips; part-whole proportions, including tax, discounts, tips, and part-whole relationships relationships I S5C2PO10 Deductive Proof; Process of Demonstrate and explain that the process of solving Solving equations equations is a deductive proof. E S3C3PO3 Multi-Step Equations; Inverse Solve multi-step equations using inverse properties with Properties; Rational Numbers rational numbers E S3C3PO6 One-Step Inequalities; Whole Create and solve one-step inequalities with whole numbers Numbers * = 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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7 Grade Math Curriculum Map th Isaac School District No. 5 Quarter 2 Unit Name and Description: Algebraic Expressions Cluster 3 Big Ideas/Enduring Understandings Essential Question(s)Algebraic expressions are representative of real life situations. How can we use expressions to solve real life problems?An algebraic expression is different from an equation. AZ Essential Learning Key EIN Technology Standard Knowledge Skills Vocabulary Resources E S3C3PO2 Expression; Variables; Evaluate an expression containing one or two variables by Inverse Operations Substitution substituting numbers for the variables Variables Substitute E S3C3PO1 Single variable algebraic [Generate] a single variable algebraic expression or one-step Evaluate expressions; one-step equation given a contextual situation Expressions equations Equation I S5C2PO1 Problem Situations Analyze a problem situation to determine the question(s) to Inequalities be answered Variable I S5C2PO2 Problem Solving Analyze mathematical strategies for efficient problem Strategies solving. Select and use one or more strategies to solve a problem N S5C2PO3 Information; Solution; [Discriminate] between relevant, missing, and extraneous Problem information related to the solution to a problem. * = 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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7 Grade Math Curriculum Map th Isaac School District No. 5Quarter 2Unit Name and Description: FunctionsCluster 4Big Ideas/Enduring Understandings Essential Question(s)Graphs, tables, and charts can be used to display and to analyze change How can we represent a function in various ways?Structures in the universe contain patterns and can be translated into functions. What processes are used to identify patterns?Functions can be efficiently displayed using visual representations. What constitutes a function? AZ Essential Learning Key TechnologyEIN Standard Vocabulary Resources Knowledge Skills E S3C3PO4 Graphs; Tables; Translate between graphs and tables that represent linear equations Inverse Operations Linear Equations Variables [Construct a function and table given a graph] Simplify Substitution E S3C4PO1 Analysis of Use graphs and tables to model and analyze change. Change Pattern Sequence [Formulate the rate of change in graphs, tables, and functions] Equation E S3C2PO1 Proportional Use a table of values to graph an equation or proportional relationship Evaluate Relationships; Substitute Table of values Describe the graph’s characteristics Graph Table E S3C1PO1 Numeric and Recognize, describe, create and analyze numerical and geometric Geometric sequences using tables or graphs Sequences; Tables; Graphs [Develop and defend] conjectures about these sequences. * = 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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7 Grade Math Curriculum Map th Isaac School District No. 5Quarter 2Unit Name and Description: Data AnalysisCluster 5Big Ideas/Enduring Understandings Essential Question(s)Data can be communicated using different representations and displays What are the different forms used to display data?Data can be efficiently interpreted and analyzed using specific representations Which representations most effectively and accurately communicate data? How do you develop solutions to problemsEffective data analysis yields constructive information based on data analysis? * = 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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AZ Essential Learning Key TechnologyEIN Standard Knowledge Skills Vocabulary Resources * = 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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E S2C1PO1 Displays of data; Multi-line Solve problems by selecting, constructing, Outlier graphs; Scatterplots and interpreting displays of data including Mode multi-line graphs and scatterplots. Mean Median Range I S2C1PO2 Trends; Data Set; Predicted or Interpret trends in a data set. Positive Estimated Value; Range Negative Estimate values for missing data Venn Diagram Predict and [defend] values for points beyond the range of Graph the data set E S2C1PO3 Outliers; Mean; Median; Identify outliers Mode: Range Determine the effect of outliers on the mean, median, mode, and range. I S2C3PO2 Counting Problems; Algebraic Solve counting problems using Venn diagrams Venn Diagrams Represent the answer algebraically I S2C4PO1 Vertex-Edged Graphs; Euler Use vertex-edge graphs and algorithmic thinking to Circuits represent and find solutions to practical problems related to Euler/Hamilton paths and circuits. [Detect the most effective path to achieve the specified goal] I S5C2PO4 Problem Situations; Multiple Represent a problem situation using multiple representations Representations; Reasonableness; Process Describe the process used to solve the problem Verify the reasonableness of the solution. I S5C2PO7 Mathematical Information; Isolate and organize mathematical information taken from Symbols; Diagrams; Graphs; symbols, diagrams, and graphs to make inferences, Inferences; Conclusions; draw conclusions, and justify reasoning. * Reasoning = POs previously introduced EIN= Level of Priority for P.O. E= Essential P.O. Bold = Priority PO 9Italics = 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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7 Grade Math Curriculum Map th Isaac School District No. 5Quarter 2Unit Name and Description: ProbabilityCluster 6Big Ideas/Enduring Understandings Essential Question(s) What is the difference between theoretical and experimentalProbability can be used to predict the outcome of an event. probability?The total number of outcomes affects the probability. What is the difference between dependent and independentProbability has a range from impossible (0) to certainty (1). events? AZ Essential Learning Key Technology EIN Standard Knowledge Skills Vocabulary Resources E S2C2PO2 Independent Events; Experiment with two different events to determine Counting Dependent Events whether the two events are dependent or independent of principal each other Tree diagram Probability E S2C2PO1 Conditional Probabilities; Determine conditional probabilities (experimental) in Dependent Compound Probabilities compound probability Independent Compound E S2C3PO1 Tree Diagrams; Relationships; Analyze relationships among the tree diagrams where Theoretical Numerical Connections; items repeat and do not repeat Experimental Multiplication Principal of Random Counting Make numerical connections to the multiplication principle Non Random of counting * = 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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I S2C2PO4 Fairness; Probability; Compare probabilities to determine fairness in experimental Experimental situations Situations E S2C2PO3 Probability Experiments; Compare the results of multiple repetitions of the same Results; Repetitions; probability experiment to the theoretical probability Theoretical Probability N S5C2PO5 Problem-solving strategy Apply a previous used problem-solving strategy in a new context I S2C1PO4 Simple Random and Non Distinguish between a simple random and non-random Random sample Samples * = 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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7 Grade Math Curriculum Map th Isaac School District No. 5Quarter 3Unit Name and Description: Geometry and MeasurementCluster 7Big Ideas/Enduring Understandings Essential Question(s)Geometric properties and principles exist and provide solutions in everyday life How do geometric properties and principals solve and apply to real world scenarios?Geometry is based on rules and relationships that exist on a micro to macrocontinuum What is the relationship between angles and intercepted arcs? * = 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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AZ Essential Learning KeyEIN Technology Standard Knowledge Skills Vocabulary Resources * = 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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E S4C4PO1 Circumference; Area; Circle Solve problems involving the circumference and area Circumference of a circle by calculating and estimating Area Parallel Perpendicular I S4C1PO3 3-Dimensional Figures; Labels; Draw and classify 3-dimensional figures with the Arc Attributes; Parallelism; appropriate labels showing specified attributes of Central angle Congruence; Perpendicularity; parallelism, congruence, perpendicularity, and Interior Symmetry symmetry Exterior Angles I S4C1PO1 Central Angles; Intercepted Arcs; Explain the relationship between central angles and Corresponding Chords; Circle intercepted arc Pi Chord Identify arcs and chords of a circle Diameter I S4C1PO4 Regular Polygons; Describe the relationship between the number of sides in Interior Angles; a regular polygon and the sum of its interior angles Sum; Relationship; Sides E S4C1PO5 Congruent Figures; Identify corresponding parts of congruent figures Corresponding Parts N S5C2PO6 Answers; Questions; Problem; Communicate the answer(s) to the question(s) in a Symbols; Representations; problem using appropriate representations, Informal and Formal including symbols and informal and formal Mathematical mathematical language Language; I S5C2PO11 Pi; Circumference; Diameter; Use manipulatives and other modeling techniques to Manipulatives; Modeling defend (Pi) π as a ratio of circumference to diameter Techniques * = 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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* = 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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7 Grade Math Curriculum Map th Isaac School District No. 5Quarter 3Unit Name and Description: Geometry and MeasurementCluster 8Big Ideas/Enduring Understandings Essential Question(s)It is necessary to use appropriate units of measure depending on the situation How do you measure the appropriate dimension of a shape or solid?Algebraic formulas represent relationships between geometric figures and How do you construct an algebraic formula to find the measure of atheir dimensions figure?Measurement can be applied to solve practical problems AZ Essential Learning Key TechnologyEIN Standard Knowledge Skills Vocabulary Resources E S5C1PO1 Composite Figures; [Develop] an algorithm to determine the area of a given Area Algorithm; Area composite figure Perimeter Algorithm I S1C3PO4 System of Units; Conversion Estimate the measure of an object in one system of units given Composite Figures Factor; Measure of an Object; the measure of that object in another system and the Conversion Factors approximate conversion factor Semi-circle Conversion [Generate a process to estimate a measure of an object in one Polygon system of units] Scale Estimation [Translate the measurement of an object from one system of units to another using estimation] * = 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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I S4C4PO2 Polygons; Perimeter; Area [Compare] polygons having the same perimeter or area E S4C4PO3 Area; Perimeter; Composite Calculate the area and perimeter of composite 2 dimensional 2-Dimensional Figures figures E S4C4PO4 Lengths; Scale Drawings; Maps Determine actual lengths based on scale drawings or maps * = 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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7 Grade Math Curriculum Map th Isaac School District No. 5Quarter 3Unit Name and Description: Geometry and MeasurementCluster 9Big Ideas/Enduring Understandings Essential Question(s)Geometric properties and principles exist and provide solutions in everyday How do geometric properties and principals solve and apply to reallife world scenarios?Geometry is based on rules and relationships that exist on a micro to macro How are we able to create new images based on transformationscontinuum AZ Essential Learning Key TechnologyEIN Standard Knowledge Skills Vocabulary Resources E S4C4PO5 Net; Surface Area; Solid Create a net to calculate the surface area of a given solid Net Volume I S4C4PO6 Volume; Unit of Measure; Identify the appropriate unit of measure to compute the Transversal Reasoning volume of an object and justify reasoning Coordinate Plane N S4C4PO7 Degree of Accuracy Measure to the appropriate degree of accuracy and justify Transformation reasoning Reflection E S4C2PO1 Double Transformation; Model the result of a double transformation (translations or Corresponding Reflections; 2- Dimensional reflections) of a 2-dimensional figure on a coordinate Supplementary Figure; Coordinate Plane; plane using all four quadrants Accurate E S4C1PO2 Angles; Parallel Lines; Analyze and determine relationships between angles created Surface Area Transversals by parallel lines cut by a transversal Parallel Relationships Coordinate Plan [Defend] the stated relationships between angles created Angle by parallel lines cut by a transversal * = POs previously introduced EIN= Level of Priority for P.O. Bold = Priority PO 18 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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7 Grade Math Curriculum Map th Isaac School District No. 5Quarter 4Unit Name and Description: Expressions, Inequalities, and Absolute ValueCluster 10Big Ideas/Enduring Understandings Essential Question(s)Expressions and equations can be represented graphically and numerically Why do certain operations have to be performed in a specific order?Algebra is a language of numbers, letters, and symbols used to solve problems What is the purpose of a variable in an expression, inequality, or equation? AZ Essential Learning Key TechnologyEIN Standard Knowledge Skills Vocabulary Resources E M08-S3C3PO3 Linear equations; Analyze, simplify, and solve situations problems involving Linear equations Inequalities; Real linear equation and inequalities using the properties of Inequalities number system; the real number system Exponents Coefficients Variables I M08-S3C3PO5 Inequalities; Number line Graph an inequality on a number line Expressions Equations Inverse property E M08-S1C1PO4 Absolute value; Problems Model and solve problems involving absolute value. Number line Square roots E M08-S1C2PO5 Square roots; Cube roots; Simplify numerical expressions using the order of operations Cube roots Grouping symbols; that include grouping symbols, square roots, cube roots, Grouping Symbols Positive exponents; absolute values, and positive exponents Absolute value; E M08-S4C4PO2 Geometric problems; Solve geometric problems using ratios and proportions Ratios; Proportions * = POs previously introduced EIN= Level of Priority for P.O. Bold = Priority PO 19 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