North Carolina Standard Course of Study, 2003, grade 8 [NC] PH Course 3 Lesson

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1 [NC] North Carolina Standard Course of Study, 2003, grade 8 PH Course 3 Lesson COMPETENCY GOAL 1: The learner will understand and compute with real 1.01 Develop number sense for the real numbers. 1-2, 2-3, 3-1, 3-2, 3-3, 3-4, 7-7, 8-4, 8-5, 8-6, 8-7, a Define and use irrational numbers. 3-1, 3-2, 3-3, 3-4, 7-7, 8-4, 8-5, 8-6, 8-7, b Compare, order and classify real numbers. 1-2, 2-3, 3-1, c Use estimates of irrational numbers in appropriate 3-1, situations Develop flexibility in solving problems by selecting strategies and using mental computation, estimation, calculators or computers, and paper and pencil. throughout the program COMPETENCY GOAL 2: The learner will understand and use measurement 2.01 Determine the effect on perimeter/circumference, area, 8-9, 4-4b, 4-5b, 8-9a surface area, or volume when one or more dimensions of two- and threedimensional figures are changed Apply and use concepts of indirect measurement. 3-2, 3-3, 4-7 COMPETENCY GOAL 3: The learner will understand and use properties and 3.01 Represent problem situations with geometric models. 4-5a, 4-5b 3.02 Apply geometric properties and relationships, including 2-6, 3-2, 3-3, 3-4, 3-7, 3- the Pythagorean Theorem, to solve problems. 8, 4-4, 4-5, 4-7, 8-4, 8-5, 8-6, 8-7, Identify, predict, and describe dilations on a rectangular 4-5, coordinate plane. COMPETENCY GOAL 4: The learner will understand and use graphs and data 4.01 Collect, organize, analyze, and display data (including scatterplots) to solve problems. 9-2, 9-5, 9-6, 9-7, 9-8, 9-9, 9-1, 9-7a, 11-2b 4.02 Approximate a line of best fit for a given scatterplot; explain the meaning of the line as it relates to the problem and make predictions Identify misuses of statistical and numerical data. 9-4 COMPETENCY GOAL 5: The learner will understand and use linear relations and 5.01 Develop an understanding of function 5.01a Translate among verbal, tabular, graphic, and algebraic 11-3, 11-5, 11-6, 3-5a, representations of functions. 11-7b 5.01b Identify relations and functions as linear or nonlinear 11-6, 4-3a among verbal, tabular, graphic, and algebraic representations. 5.01c Find, identify, and interpret the slope (rate of change) 11-4, 11-5, 11-6, 11-4a and intercepts of a linear relation. 5.01d Interpret and compare properties of linear functions 3-5, 11-4, 11-5, 11-6 from tables, graphs, or equations Write an equation of a linear relationship given: two 3-5, points, the slope and one point on the line, or the slope and y-intercept Solve problems using linear inequalities; justify 6-5, 6-6 symbolically and graphically Solve equations using the inverse relationships of addition and subtraction, multiplication and division, squares and square roots, and cubes and cube roots. 1-6, 1-7, 3-5, 4-3, 4-4, 4-7, 5-3, 5-4, 6-1, 6-3, 6-4, 6-5, 6-6,

2 Course 3 Stnd 1 Stnd 2 Stnd 3 Stnd Algebraic Expressions and the Order of 1-2 Integers and Absolute Value 1.01b 1-3 Adding and Subtracting Integers 1-4 Multiplying and Dividing Integers 1-5 Properties of Numbers 1-6 Solving Equations by Adding and Solving Equations by Multiplying and Factors 2-2 Equivalent Forms of Rational Numbers 2-3 Comparing and Ordering Rational 1.01b 2-4 Adding and Subtracting Rational 2-5 Multiplying and Dividing Rational Formulas Powers and Exponents 2-8 Scientific Notation 3-1 Exloring Square Roots and Irrational 1.01a 1.01b 1.01c 1.01d 3-2 The Pythagorean Theorem 1.01a Using the Pythagorean Theorem 1.01a Graphing in the coordinate Plane 1.01a Equations, Tables, and Graphs 5.01d Translations 3-7 Reflections and Symmetry Rotations Ratios and Rates 4-2 Converting Units 4-3 Solving Proportions Similar Figures and Proportions Similarity Transformations Scale Models and Maps 4-7 Similarity and Indirect measurement Fractions, Decimals, and Percents 1.01b 5-2 Estimating with Percents 5-3 Percents and Proportions Percents and Equations Percent of Change 5-6 Markup and Discount 5-7 Simple Interest 5-8 Ratios and Probability 6-1 Solving Two-Step Equations Simplifying Algebraic Expressions 6-3 Solving Multi-Step Equations Solving Equations with Variables in Both Solving Inequalities by Adding or Solving Inequalities by Multiplying or Pairs of Angles 3.02

3 7-2 Angles and Parallel Lines Congruent Polygons Classifying Triangles and Quadrilaterals 7-5 Angles and Polygons Areas of Polygons Circumference and Area of a Circle 1.01a Constructions 8-1 Solids 8-2 Drawing Views of Three-Dimensional 8-3 Nets and Three-Dimensional Figures 8-4 Surface Areas of Prisms and Cylinders 1.01a Surface Areas of Pyramids and Cones 1.01a Volume of Prisms and cylinders 1.01a Volumes of Pyramids and Cones 1.01a Spheres 1.01a Exploring Similar Solids Finding Mean, Median, and Mode 9-2 Displaying Frequency Venn Diagrams 9-4 Reading Graphs Critically Stem-and-Leaf Plots Box-and-Whisker Plots Mnaking Predictions from Scatter Plots Circle Graphs Choosing an Appropriate Graph Theoretical and Experimental Probability 10-2 Making Predictions 10-3 Conducting a Survey 10-4 Independent and Dependent Events 10-5 Permutations 10-6 Combinations 11-1 Sequences 11-2 Relating Graphs to Events 11-3 Functions 5.01a 11-4 Understanding Slope 5.01c 5.01d 11-5 Graphing Linear Equations 5.01a 5.01c 5.01d 11-6 Writing Rules for Linear Functions 5.01a 5.01b 5.01c 5.01d 11-7 Quadratic and Other Nonlinear 12-1 Exploring Polynomials 12-2 Adding and Subtracting Polynomials 12-3 Exponents and Multiplications 12-4 Multiplying Polynomials 12-5 Exponents and Division

4 Course 3 NC Stand ard 1 NC Standar d 2 FEATURE PAGES 14 After 1-2: AL Data Analysis: Integers and Differences 15 Before 1-3: AL: Adding Integers 32 Before 1-6: AL Hands On: Modeling Equations 37 After 1-6: AL: Number Squares 42 After 1-7: AL Algebra Thinking: The Cover-up Method 61 After 2-2: AL: Repeating Decimals 71 Before 2-5: AL Hands On: Modeling Fraction 80 Before 2-6: AL Algebra Thinking: Estimating Solutions 85 After 2-6: AL Technology: Using Formulas 90 After 2-7: AL Technology: Evaluating Expressions 91 Before 2-8: AL: Multiplying by Powers of Ten 96 After 2-8: AL Data Analysis: Writing Measurements 111 Before 3-2: AL Hands On: Exploring the Pythagorean Theorem 122 After 3-3: Extension: Analyzing Triangles 128 After 3-4: AL: Finding the Midpoint 129 Before 3-5: AL Data Analysis: Tables and Graphs 5.01a 135 After 3-5: AL AlgebraThinking: Matching Graphs 140 Before 3-7: AL Hands On: Exploring Reflections 145 Before 3-8: AL Hands On: Exploring Rotations 150 After 3-8: Extension: Tessellations 164 After 4-1: AL: Finding Rates 165 Before 4-2: AL: Choosing Units 171 Before 4-3: AL: Proportional and Non-Proportional Relationships 5.01b 185 After 4-4: AL: Ratios of Similar Figures Before 4-5: AL: Exploring Dilations After 4-5: AL: Geometry Software and Dilations Before 4-7: AL Hands-On: Using Similar Figures 223 After 5-3: AL Data Analysis: Percents and Graphs 229 Before 5-5: AL Data Analysis: Describing Change 239 After 5-6: AL Hands On: Using Percents 245 Before 5-8: AL Hands On: Exploring Probability 260 Before 6-1: AL Hands On: Modeling Multi-Step Equations 265 Before 6-2: AL Hands On: Modelling Expressions 281 Before 6-5: AL: Graphing Inequalities 287 Before 6-6: AL: Inequalities and Negative Numbers 302 Before 7-1: AL Hands On: Exploring Pairs of Angles 311 After 7-2: AL Algebra Thinking: Solving Angle 323 Before 7-5: AL: Angle Sums 335 Before 7-7: AL Hands-On: Estimating Area 340 After 7-7: Extension: Arcs, Chords, and Semicircles 344 After 7-8: AL Technolgy: Geometry Software and Constructions 362 After 8-2: AL: Sketching Solids 363 Before 8-3: AL Hands On: Making Solids From Nets 367 Before 8-4: AL Hands On: Modeling Surface Area 373 Before 8-5: AL Hands On: Surface Area of a Pyramid

5 379 Before 8-6: AL Hands On: Modeling Volume 387 Before 8-7: AL Hands-On: Finding Volume Using 397 Before 8-9: AL: Changing Dimensions After 8-9: AL Data Analysis: Precision and Significant Digits 417 After 9-1: AL Data Collection: Comparing Mean and Median After 9-2: AL Technology: Making Histograms 427 Before 9-4: AL Data Analysis: Reading Graphical Displays 432 After 9-4: AL Data Analysis: Making Graphs to Tell a Story 442 After 9-6: AL Technology: Making Box-and-Whisker 443 Before 9-7: AL Data Collection: Scatter Plots After 9-7: AL Algebra Thinking: Plotting a Strategy 460 After 9-9: Al Technology: Graphing Data Using Spreadsheets 474 Before 10-2: AL Hands On: Fair Games 479 After 10-2: Extension: Complements and Probability 484 After 10-3: AL Technology: Simulations With Random Numbers 485 Before 10-4: AL Hands On: Comparing Types of Events 517 After 11-1: AL Technology: Exploring Sequences 522 After 11-2: AL Data Collection: Line Graphs Before 11-4: AL: Rate of Change 5.01c 532 After 11-4: Extension: Parallel and Perpendicular Lines 533 Before 11-5: AL Technology: Graphing Equations 550 After 11-7: AL Data Analysis: Changing Representations 5.01a 560 Before 12-1: AL: Writing Expressions 570 Before 12-3: AL: Exploring Exponents 575 After 12-3: AL Technology: Scientific Notation 586 After 12-5: Extension: Power Rules