Scope & Sequence. Algebra. 16 IMPLEMENTATION GUIDE Scope & Sequence. Course 3. Course 2. Course 1

Transcription

1 Scope & Sequence Algebra Properties and Rules Patterns and Numeric orms Tables and Graphs oordinate Graphs Algebraic Representations Plotting and reading points Make predictions Relate to tables and written descriptions Relate to equations and expressions Solve equations, approximate solutions Graphing equations Direct, indirect, and inverse variation Slope and rates of change Distance and midpoint formulas oordinate models of transformations Analyze change vs. time data Making predictions and generalizations Modeling data patterns Relate to written descriptions Relate to equations and expressions Solve equations, approximate solutions What s My Rule? Algebraic Reasoning ind and describe patterns Extend and generalize patterns reate and verify patterns Express patterns as algebraic rules What s My Rule? Equivalent expressions actoring, expanding, simplifying Signed numbers and operations Absolute value and opposites Exponents, roots, and radicals Scientific notation Evaluating expressions lowcharts and backtracking Verify solutions by substitution Order of operations ombining like terms ormulas Distributive property Laws of exponents Additive and multiplicative inverse Additive and multiplicative identities Zero product rule Pythagorean Theorem Operations with Radicals ourse 1 ourse 2 ourse 3 16 IMPLEMENTATION GUIDE Scope & Sequence

2 Linear Expressions/Equations Quadratic Expressions/Equations Exponential Expressions/Equations Rational Expressions/ Equations unctions and Relations Recognize as equations, graphs, tables Relate equations, graphs, and tables Direct and indirect variation Slope and rates of change Slopes of parallel and perpendicular lines Intercepts Symbolic forms and effects of parameters Solve equations using backtracking Solve using guess-check-improve Solve equations symbolically Solve, approximate graphically Solve inequalities Solve systems of equations/inequalities Recognize as equations, graphs, tables Relate equations, graphs, and tables Intercepts Symbolic forms and effects of parameters Zero product rule Solve equations using backtracking Solve using guess-check-improve Solve, approximate graphically Solve factored equations Solve by factoring Solve by completing the square Solve using the quadratic formula Number of solutions Recognize as equations, graphs, tables Relate equations, graphs, and tables Ratio of consecutive y-values Rates of change and asymptotes Symbolic forms and effects of parameters Solve, approximate graphically Symbolic forms and effects of parameters Graphs, intercepts, and asymptotes Solving equations ourse 1 Expose ourse 2 ourse 3 = This topic is a ocus of Instruction in this chapter. = This topic is onnected to the content of the chapter and is either reviewed in this chapter or informally introduced. Expose: Ideas are introduced at an informal, concrete level and will be fully developed later in the program. : Ideas are formalized and fully developed. : Ideas are reviewed and used to extend understanding of related ideas. Scope & Sequence IMPLEMENTATION GUIDE 17

3 Scope & Sequence Geometry ourse 1 ourse 2 ourse 3 Polygons Quadrilaterals Triangles Angles Similarity ongruence Two-Dimensional Shapes Definitions and properties lassification and naming Reflectional symmetry Rotational symmetry Angle sums of polygons Area and perimeter On the coordinate plane Definitions and properties Determining uniqueness Interior angle sum Acute, right, obtuse Equilateral, isosceles, scalene Properties of special triangles Triangle inequality Triangle Sum Theorem Pythagorean Theorem Estimate and measure lassify acute, right, obtuse Geometric Relationships Definition and properties Identifies, determines congruence Identify corresponding parts As special case of similarity Represented by transformation Definition and properties Identifies, determines similarity Properties of similar figures Scale factors ongruence as scale factor of 1 Relation to area and perimeter Relation to surface area and volume Relation to ratio and rates Proportional reasoning AA Similarity Property Indirect measurement Scale drawings and maps Expose = This topic is a ocus of Instruction in this chapter. = This topic is onnected to the content of the chapter and is either reviewed in this chapter or informally introduced. Expose: Ideas are introduced at an informal, concrete level and will be fully developed later in the program. : Ideas are formalized and fully developed. : Ideas are reviewed and used to extend understanding of related ideas. 18 IMPLEMENTATION GUIDE Scope & Sequence

4 Spatial Visualization 3-D Solids Perimeter and Area Surface Area and Volume oordinate Representations Transformations Three-Dimensional igures Visualizing structures reating and drawing structures Types of 3-D drawings Determining unique structures Definitions and properties Prisms and pyramids ones and cylinders Nets Volume and surface area Measurement Approximation and estimation ormulas for squares and rectangles Areas of parallelograms Areas of triangles Areas of circles and circumference Relating perimeter and area hanges due to scale factor Maximizing and minimizing Pythagorean Theorem Approximation and estimation ormulas for prisms and cylinders ormulas for pyramids and cones Relating surface area and volume hanges due to scale factor Maximizing and minimizing oordinate Geometry Plotting and reading points Graphing equations Relating graphs, tables, equations Written descriptions of graphs Approximating and finding solutions Direct and indirect variation Slope of a line and rates of change Equations of lines Slopes of parallel lines Slopes of perpendicular lines Distance and midpoint formulas Reflectional symmetry Rotational symmetry Translations hanges of magnitude (dilations) Rotations ompound transformations ongruence and similarity Relating to equations ourse 1 Expose ourse 2 ourse 3 Scope & Sequence IMPLEMENTATION GUIDE 19

5 Scope & Sequence Number and Operation ourse 1 ourse 2 ourse 3 raction and Decimal oncepts Exponents and Roots Signed Numbers Whole Numbers Numbers and Number Sense Magnitude of large, small numbers Operations on odd and even numbers actors and multiples ommon factors and multiples actor pairs and area models Greatest common factor Least common multiple Prime and composite Relatively prime Prime factorization undamental Theorem of Arithmetic actor trees Meaning and basic concepts oncrete and number line models our quadrant coordinate model omparison Order Absolute value and opposites Addition and subtraction Multiplication and division Meaning in exponential notation Negative slope Meaning and basic concepts Positive and negative exponents Scientific notation Laws of exponents Used in expressions and equations Geometric interpretation of square Geometric interpretation of cube Rationals and Irrationals Rational and irrational numbers Geometric and number line models ractional relationships to a whole omparison Benchmarks for comparison Order Naming equivalent fractions Naming equivalent decimals raction and decimal equivalencies raction and decimal approximations ractions as indicated division Repeating decimals Relating fractions and decimals onverting fractions to decimals onverting decimals to fractions 20 IMPLEMENTATION GUIDE Scope & Sequence

6 Meaning and Representations Meaning and Representations Proportions ractions Decimals Signed Numbers Percents Definition and basic concepts Greater than 100 or less than 1 ommon scale comparisons Relating to fractions and decimals Relating to ratios and proportions onverting to a decimal onverting to a fraction Estimate percent using benchmarks alculate percent Solve percent problems (all cases) Relating to proportional reasoning Percent increase and decrease Ratios and Rates Basic concepts omparison statements Part-to-part comparisons Part-to-whole comparisons Relating unlike quantities or units Types and uses of ratio notation Equivalent ratios and ratio tables omparing ratios Equivalent rates Rate tables and rate graphs Slope and rates of change Definition and basic concepts Proportions as equations hecking if a proportion exists Methods of solving proportions Proportional relationships Proportional reasoning Algorithms and Operations Generating equivalent fractions raction, mixed number conversions Percent, decimal conversion Addition and subtraction Multiplication and division raction, percent conversions Addition and subtraction Multiplication and division Addition and subtraction Multiplication and division ourse 1 Expose ourse 2 ourse 3 = This topic is a ocus of Instruction in this chapter. = This topic is onnected to the content of the chapter and is either reviewed in this chapter or informally introduced. Expose: Ideas are introduced at an informal concrete level and will be fully developed later in the program. : Ideas are formalized and fully developed. : Ideas are reviewed and used to extend understanding of related ideas. Scope & Sequence IMPLEMENTATION GUIDE 21

7 Scope & Sequence Probability and Statistics ourse 1 ourse 2 ourse 3 Surveys and Sampling Statistical Measures Modeling and Analysis Graphs and Displays Data Analysis Line plots Stem-and-leaf plots Box plots ircle graphs requency tables Histograms Scatter plots hoose appropriate displays Skewness and symmetry Identify patterns and trends Identify clusters, gaps, and outliers Describe shape and scatter ompare data sets it a line by eyeballing Make predictions and generalizations Misleading graphs Law of large numbers Outlier affect on measurers of center ompare measures of center hoose appropriate measure of center requency Range Mode Median Mean Quartiles Sample survey vs. census Randomization Simple random sample Sample size Law of large numbers Bias in survey methods Population and sample identification 22 IMPLEMENTATION GUIDE Scope & Sequence

8 ourse 1 ourse 2 ourse 3 Basic oncepts and Rules ounting Methods Experiments and Simulations Probability Measure between 0 and 1 Empirical and theoretical probabilities Equally likely ompound events Mutually exclusive events Independent events Dependent events onfidence Expected value ounting trees ombinations Permutations Estimate likelihood Relate to theoretical probabilities Analyze fairness = This topic is a ocus of Instruction in this chapter. = This topic is onnected to the content of the chapter and is either reviewed in this chapter or informally introduced. Expose: Ideas are introduced at an informal, concrete level and will be fully developed later in the program. : Ideas are formalized and fully developed. : Ideas are reviewed and used to extend understanding of related ideas. Scope & Sequence IMPLEMENTATION GUIDE 23