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Curriculum and Pacing Guide (May 2007) Course # 1205080: 8th Grade Advanced Math Passport to Algebra and Geometry, McDougal Littell Correlated with Neufeld Learning Systems Inc. Understanding Math PLUS programs September 2007 General notes: 8th Grade Advanced Math #1205080 – Revised August 2007 Passport to Algebra and Geometry, McDougal Littel 1. At the beginning of the year, diagnose fluency in the Focal Points for 7 th grade. Be prepared to differentiate any instruction to help students that need reteaching. For entering 8th grade, Collier County teachers expect pre-requisite fluency in 1) Fractions, Proportions and Percents 2) Writing equations and translating English to Mathematical symbols (strategies for word problems) 3) Order of operations involving calculations with integers 4) Simple geometric perimeter/circumference, area, volume 5) Pythagorean Theorem 2. All tests after chapter 1 should be reasonably cumulative with an emphasis on the Focal Points for exiting 8th grade. For entering 9th grade, Collier County high school teachers expect fluency in 1) Applications of Rates, Ratios, Percents, Proportions with an emphasis on the principles of working with fractional expressions 2) High school level study skills, including reading texts for knowledge, taking useful notes, test preparation with emphasis on multi-level word problems. 3) High level order of operations involving all grouping symbols and exponents and working with real numbers. Simple integer calculations should be accomplished without calculator assistance. 4) Complex measurement of area and volume. 5) Algebraic skills involving multi-step problems. 3. FCAT preparation can be accomplished with startups. FCAT test question types can be included on tests. 4. Any textbook section that is omitted in the pacing can be considered an Extension exercise for that chapter. Note that section moved to be included in the Chapter 8 material. 5.8 is not omitted, but Curriculum and Pacing Guide Revised May 2007 Course # 1205080: 8th Grade Advanced Math PACING GUIDELINE for the 2007-2008 CCPS School Calendar Pre-FCAT TEXT SECTIONS Chapter 1.1 – 1.7 1ST QUARTER 2ND QUARTER 3RD QUARTER 4TH QUARTER Chapter 2.1 – 2.7; 2.9 Chapter 3.1 – 3.8 Chapter 4.1 – 4.6; 4.8 FCAT Benchmark Test and Review #1 FLEX DAYS Chapter 5.1 – 5.7; Chapter 14.1 – 14.3 Chapter 6.1 – 6.9 Chapter 7.1 – 7.9 Chapter 8.1 – 8.7; Chapter 5.8 FCAT Benchmark Test and Review #2 FLEX DAYS Chapter 9.3 & 9.4; Chapter 10.1 – 10.9 Chapter 11.1 – 11.7 Chapter 12.1 – 12.8 Chapter 13.1 – 13.4 FCAT Benchmark Test and Review #3 FLEX DAYS FLEX DAYS TOTAL DAYS DAYS 6 FCAT TESTING DAYS 10 9 8 9 TH 4 2 10 QUARTER Post-FCAT TEXT SECTIONS Chapter 13.5 – 13.8 Chapter 9.1 & 9.2; Chapter 9.5 – 9.8 Chapter 14.4 – 14.8 Chapter 11.8 & 11.9 FLEX DAYS TOTAL DAYS 9 9 8 DAYS 6 7 7 4 16 40 NOTES - Text Sections in bold text indicate 8th grade Focal Points - FLEX DAYS help to accommodate re-teaching, early release days, field trips, CBL lessons and other demands of your local school. - The day count in the following chapter guides will not exactly match this guide because chapters 9, 11, 13 and 14 are not split therein. This guide allows 2 additional days for testing and reviews in the 4th quarter study of these chapters. 8 2 6 10 9 8 5 - FCAT TESTING is scheduled from 3/12/08 to 3/25/08: 10 school days. Depending on your local school initiatives and incentives, some of these days might be available as FLEX days. 2 8 2 130 10 40 180 Curriculum and Pacing Guide Revised May 2007 Course # 1205080: 8th Grade Advanced Math Days Topic Benchmarks/SSS 1 Number patterns MA.A.5.3.1, MA.B.1.3.3 1 Number operations MA.A.1.3.1, MA.A.1.3.4, MA.A.2.3.1, MA.A.3.3.1, MA.A.3.3.3, MA.D.2.3.1 Chapter 1 – 8th Grade Advanced Math Section Vocabulary, Extensions Resources Understanding Math PLUS 1.1 Sequence Understanding Algebra Topic 3. Patterns, Patterns, Patterns Number Patterns Examples 1, 2, 3, 4, 5, 6 1.2 Sum, difference, product, factor, quotient, numerator, denominator, model DW Test Item(s) 34841,34844,3905 5451,11414,13974 13990,19700,20711 19685,577,19662 20733,614,615 80277,80278,80279 Understanding Math PLUS Understanding Whole Numbers and Integers Topic 2. Adding and Subtracting Whole Numbers All Sections Topic 3. Multiplying and Dividing Whole Numbers All Sections Powers and Square Roots 1.3 Power, base, exponent, square root, radical, square root symbol Understanding Math PLUS Understanding Exponents Topic 1. The Meaning of Exponents Exponents, Powers, Bases Powerful Explosions Introductory Examples Examples 1, 2, 3, 4, 5 Examples – Substitution Examples 1, 2, 3, 4 Examples – Order of Operation Examples 1, 2, 3 Practice Questions Topic 5. Square Root Squaring Numbers Square Roots Radical Signs Square Roots of Negative Numbers Example Questions 3921,14250 11749,34651 3465216808, 16840, 80339, 80340, 80353 11867,11899 17526,10885 11774,3881 Curriculum and Pacing Guide Revised May 2007 Course # 1205080: 8th Grade Advanced Math Days 1 Topic Order of Operations Variables in Expressions Benchmarks/SSS MA.A.1.3.4, MA.A.3.3.1, MA.A.3.3.3, MA.D.2.3.1, MA.D.2.3.1, MA.D.2.3.2 Chapter 1 – 8th Grade Advanced Math Section Vocabulary, Extensions Resources 1. Radicals First 2. The Four Equations 3. Lawn Question 4. Make a Square 1.4 Number expression, order of operations, Leftto-right Rule, grouping symbols 1.5 Variable, terms, values of the variable, substituting, algebraic expressions, verbal model, value of the expression, formulas, algebraic model SpringBoard, MSii: Squares and Cubes Understanding Math PLUS Understanding Whole Numbers and Integers Topic 9. Order of Operations Order in Addition Trials 1, 2 Conclusion Examples 1, 2 Order in Multiplication Trials 1, 2 Conclusion Examples 1, 2 Why use Order of Operations? BEDMAS Example Questions Examples 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 Word Problems Shipping Babysitting Garbage Understanding Math PLUS Understanding Algebra Topic 4. Patterns, Formulas, Substitution Expressions, Terms, Variables Definitions Summary Patterns to Formulas Example... Hockey Standings Example... Counting Money Example... Angles in a Polygon DW Test Item(s) 16052, 16761, 16797, 80264, 80265, 80266, 80341, 80342, 80357,19664 3648,3842 3885,3971 17625,19663 19664,20698 34671,34710 34716,34709 10894,10899,14153 631, 16049, 16053, 16587, 16757, 16826, 16836, 20691, 68536, 80267, 80268, 80350, 80351 17645,34850 11478,11449 34677,11402 Curriculum and Pacing Guide Revised May 2007 Course # 1205080: 8th Grade Advanced Math Days 1 Omit 2 Topic Exploring Data: Tables and Graphs Benchmarks/SSS MA.B.2.3.1, MA.C.1.3.1, MA.C.2.3.1, MA.C.3.3.1, MA.E.1.3.1, MA.E.1.3.2 Chapter 1 – 8th Grade Advanced Math Section Vocabulary, Extensions Resources SpringBoard, Alg I: Centipede & Bug, Part One Understanding Math PLUS Understanding Graphing Topic 2. Statistics Data... What is it? Examples of Data Example 1... Fast Food Earnings Example 2... Infant’s Walk Example 3... Canada and U.S.A. Forecast Example 4... King of the Strike Out Example 5... U.S.A. Stake in India Example 6... Allergy Troubles A Summary: Examples Statistics... What is it? Collecting Data Throw a Die Throw 2 Dice Voting Primary Data - Gathering Methods Secondary Data - Gathering Methods 1.6 Exploring Patterns in Geometry 1.7 Polygon, sides, vertex, diagonal Exploring Patterns with Technology Review and Assessment 1.8 Whole numbers, natural numbers Understanding Math PLUS Understanding Algebra Topic 3. Patterns, Patterns, Patterns Geometric Patterns Examples 1, 2, 3, 4, 5, 6, 7, 8 DW Test Item(s) 34852,11484 14159,34156 34708,34669 34670,34711 616, 19698, 68452, 68476 17516 Curriculum and Pacing Guide Revised May 2007 Course # 1205080: 8th Grade Advanced Math Days Total 6 Topic Benchmarks/SSS Chapter 1 – 8th Grade Advanced Math Section Vocabulary, Resources Extensions DW Test Item(s) Curriculum and Pacing Guide Revised May 2007 Course # 1205080: 8th Grade Advanced Math Days Topic 1 The Distributive Property Simplifying by Adding Like Terms Benchmarks /SSS MA.A.1.3.4, MA.A.3.3.1, MA.D.2.3.1, MA.D.2.3.2 Chapter 2 – 8th Grade Advanced Math Section Vocabulary, Extensions Resources Understanding Math PLUS 2.1 Equivalent Understanding Whole Numbers expressions, and Integers distributive Topic 3. Multiplying and Dividing property, Whole Numbers commutative property of Commutative Property multiplication 5x1=1x5 5x2=2x5 5x3=3x5 4x3=3x4 Distributive Method Distributive Method - Examples 1, 2, 3 Distributive Method - Questions 1, 2, 3 2.2 Like terms, add like terms, collect like terms, simplify, commutative property of addition Understanding Math PLUS Understanding Algebra Topic 5. Adding Expressions Our Problem Adding Expressions with X and Y Tiles Examples 1, 2, 3 Adding Expressions with X-Squared Tiles Examples 1, 2, 3 Adding Expressions without Tiles Examples 1, 2 Practice Questions with Tiles Practice Questions without Tile DW Test Item(s) 16063, 80290 34699,17522 67865,67804 34842,16606 61636 80293, 80295 34842,17522 Curriculum and Pacing Guide Revised May 2007 Course # 1205080: 8th Grade Advanced Math Days 1 Topic Solving Equations with mental math Benchmarks /SSS MA.A.1.3.4, MA.A.3.3.2, MA.A.3.3.3, MA.D.1.3.1, MA.D.1.3.2, MA.D.2.3.1, MA.D.2.3.2 Solving Equations: Addition or Subtraction 1 Solving Equations: Multiplication or Division 1 Modeling Verbal Expressions Real-Life Modeling with Equations MA.A.3.3.2, MA.D.1.3.1, MA.D.1.3.2, MA.D.2.3.1, MA.D.2.3.2 MA.A.3.3.2, MA.D.1.3.1, MA.D.1.3.2, MA.D.2.3.1 A Problem Solving Plan MA.A.3.3.2, 1 1 Chapter 2 – 8th Grade Advanced Math Section Vocabulary, Extensions Resources 2.3 Equation, identities, Understanding Math PLUS Understanding Equations conditional Topic 2. Solving One-Step equations, solving Equations the equation, solutions (of an equation), Our Problem equivalent Concepts – Examples with Tiles equations Examples 1, 2, 3, 4 Concepts – Examples without Tiles Practice Questions 2.4 Addition property of equality, subtraction property of equality, commutative properties of addition and multiplication, associative property of addition and associative property of multiplication 2.5 Multiplication property of equality, division property of equality 2.8 Understanding Math PLUS Understanding Whole Numbers and Integers Topic 3. Multiplying and Dividing Whole Numbers Commutative Property 5x1=1x5 5x2=2x5 5x3=3x5 4x3=3x4 The 12 x 12 Multiplication Table Associative Property Examples 1, 2 3824,3953 34807,68527 16805, 16811, 80288, 80296, 80297, 80325, 80326, 80328, 80380 564,575, 16837, 80299, 80300, 80301, 80302, 80329, 80330, 80331 34706 16610,1628,8026 2.6 2.7 DW Test Item(s) SpringBoard, MSii: Melody’s Music Solution 562,628,572 11480,13994 762,761 1255,20689 Curriculum and Pacing Guide Revised May 2007 Course # 1205080: 8th Grade Advanced Math Days Topic 1 Exploring Variables and Inequalities 2 Review and Assessment Ch. 1, 2 Total 9 Benchmarks /SSS MA.A.4.3.1 MA.D.1.3.2, MA.D.2.3.1, MA.D.2.3.2 Chapter 2 – 8th Grade Advanced Math Section Vocabulary, Resources 2.9 Inequalities, Inequality symbol, solution (of an inequality), solving the inequality Extensions Understanding Math PLUS Understanding Equations Topic 7. Solving Inequalities Comparing Integers The Integer Line Example 1... Greater Than; Example 2... Less Than Explanation Example 3... Greater Than; Example 4... Less Than Greater Than or Less Than Inequalities What Are They? Inequality vs. Equation Summary of Relationships Inequality on the Number Line Examples 1, 2, 3, 4 Solving Inequalities Examples 1, 2, 3, 4, 5, 6 DW Test Item(s) 16779, 68543, 68544, 80308, 34877,34868,34875,34876 34325,34862,34864,20734, 20735, 34315,14762,19580 3862,11467,11468,3473,34 75, 3819,3948,3991 20734,20735,19690 80309, Curriculum and Pacing Guide Revised May 2007 Course # 1205080: 8th Grade Advanced Math Days Topic 1 Integers and Absolute Value 1 Adding two integers Adding three or more integers Benchmarks /SSS MA.A.1.3.1, MA.A.1.3.2, MA.A.1.3.4, MA.A.3.3.2 MA.A.1.3.4, MA.A.3.3.1, MA.A.3.3.2, MA.D.2.3.1 Chapter 3 – 8th Grade Advanced Math Section Vocabulary, Extensions Resources Understanding Math PLUS 3.1 Integers, absolute Understanding Whole Numbers and Integers value, absolute Topic 4. The Meaning of Integers value signs, opposites Absolute Values Examples 1, 2 Comparing Integers Examples 1, 2, 3, 4 Example Questions Examples 1, 2, 3, 4, 5, 6 3.2 3.3 Coefficients DW Test Item(s) 634,34649, 34654,11737 11756,14022 3792, ,11734, 16057, 16058, 16798, 16799, 80269, 80270, 80271, 80272, 80352 Understanding Math PLUS Understanding Whole Numbers and Integers Topic 5. Adding Integers Going for a Walk... An Introduction to Addition Examples 1, 2, 3 Number Line... An Introduction to Addition Examples 1, 2, 3 Summary... Using a Number Line Writing Positive Integers Examples 1, 2, 3 20713,80273, 80274 Understanding Math PLUS Understanding Whole Numbers and Integers Topic 5. Adding Integers Word Problems Temperature Money Car 16059, 68527 Curriculum and Pacing Guide Revised May 2007 Course # 1205080: 8th Grade Advanced Math Days Topic 1 Subtracting integers 1 Multiplying Integers Benchmarks /SSS MA.A.1.3.4, MA.A.3.3.1, MA.A.3.3.2, MA.D.2.3.1 Chapter 3 – 8th Grade Advanced Math Section Vocabulary, Extensions Resources Understanding Math PLUS 3.4 Difference Understanding Whole Numbers and Integers Topic 6. Subtracting Integers Elevators... An Introduction to Subtraction Examples 1, 2, 3, 4 Summary... Using Elevators Summary... Add the Opposite Example Questions Example 1 – With Brackets Example 2 – With Brackets Example 3 – Meaning of... 2 – 5 Example 4 – Meaning of... -7 – 3 Example 5 – Meaning of... -7 + 9 – 18 Example 6 – Meaning of... -4 – 9 + 2 – 8 Summary from Examples 3 to 6 3.5 Understanding Math PLUS Understanding Whole Numbers and Integers Topic 7. Multiplying Integers Order in Multiplication The Multiplication Table Examples 1, 2, 3 Summary #1... Signs Negative X Negative... Note Patterns Patterns 1, 2 Summary #2... Signs Example Questions Examples 1, 2, 3, 4, 5 DW Test Item(s) 11902,80276 3798,3841 16060, 16061, 3743,3927,1762 8 19661,16772,80 282 Curriculum and Pacing Guide Revised May 2007 Course # 1205080: 8th Grade Advanced Math Days Topic Benchmarks /SSS Dividing Integers 1 Problem Solving Using Integers MA.A.3.3.2, MA.D.1.3.1, MA.D.1.3.2, MA.D.2.3.1 Chapter 3 – 8th Grade Advanced Math Section Vocabulary, Extensions Resources Understanding Math PLUS 3.6 Understanding Whole Numbers and Integers Topic 8. Dividing Integers Division to Multiplication The Division Table Instructions Patterns Practice The Inverse of Multiplication Examples 1, 2 Summary #1... Signs Summary #2... Signs Example Questions Examples 1, 2, 3, 4 3.7 Inverse operation Understanding Math PLUS Understanding Whole Numbers and Integers Topic 5. Adding Integers Word Problems Temperature Money Car Topic 6. Subtracting Integers Going for a Walk Preliminary The Walk David’s Trip Part 1, Part 2 Summary Word Problems The Sailboat The Bank DW Test Item(s) 3647,16773, 80284 Curriculum and Pacing Guide Revised May 2007 Course # 1205080: 8th Grade Advanced Math Days Topic Benchmarks /SSS Chapter 3 – 8th Grade Advanced Math Section Vocabulary, Extensions Resources Topic 7. Multiplying Integers Word Problems Washing Cars The Helicopter Construction DW Test Item(s) Topic 8. Dividing Integers Word Problems Casino Plant Graham’s Walk 1 Exploring Patterns in the Coordinate Plane MA.A.1.3.4, MA.B.1.3.2, MA.B.3.3.1 3.8 Coordinate plane, axes, quadrants, ordered pair, xcoordinate, ycoordinate, solution Understanding Math PLUS Understanding Graphing Topic 3. Points on a Grid Ordered Pairs Axis Quadrants and Cartesian Plane Find a Point Order is Important Examples Shapes Battleship Topic Test CBL, MS Science w/Calculators: Lab #27, Mapping a Magnetic Field 2 Total 8 Review and Assessment Ch. 1-3 16774, 16775, 16780, Curriculum and Pacing Guide Revised May 2007 Course # 1205080: 8th Grade Advanced Math Days Topic 1 Solving Two-Step Equations 1 Solving Multi-Step Equations 1 Two-Step Equations and Problem Solving 1 Solving Equations: The Distributive Property Benchm arks/SS S MA.D.1.3 .1, MA.D.1.3 .2, MA.D.2.3 .1, MA.D.2.3 .2 Chapter 4 – 8th Grade Advanced Math Section Vocabulary, Resources Extensions DW Test Item(s) 4.1 Understanding Math PLUS Understanding Equations Topic 3. Solving Two-Step Equations Our Problem Concepts – Examples with Tiles Examples 1, 2, 3, 4 Concepts – Examples without Tiles Examples 1, 2, 3, 4, 5, 6 16801, 20690,20729, 34871,5683 14161,14167, 17552,17555 MA.D.1.3 .1, MA.D.1.3 .2, MA.D.2.3 .1, MA.D.2.3 .2 4.2 Understanding Math PLUS Understanding Equations Topic 4. Solving Multi-Step Equations Our Problem Concepts – Examples with Tiles Concepts – Examples without Tiles Examples 1, 2, 3, 4, 5 Summary Literal Equations What Are They? How do you solve them? Why Solve the Literal Equations? A Perimeter Example A Temperature Example Practice Questions Topic Test 16064, 16308, 16766 MA.D.1.3 .2, MA.D.2.3 .1, MA.D.2.3 .2 MA.D.1.3 .1, MA.D.2.3 4.3 Understanding Math PLUS Understanding Equations Topic 3. Solving Two-Step Equations Practice Questions Topic Test 16765 4.4 Reciprocal 16762, 16764, 16767, 80289 Curriculum and Pacing Guide Revised May 2007 Course # 1205080: 8th Grade Advanced Math Days Topic 1 Solving Equations: Variables on Both Sides 1 Problem Solving Strategies Omit Solving Equations Using Technology Benchm arks/SS S .1, MA.D.2.3 .2 MA.D.1.3 .1, MA.D.2.3 .1, MA.D.2.3 .2 MA.A.3.3 .2, MA.A.4.3 .1 Chapter 4 – 8th Grade Advanced Math Section Vocabulary, Resources 4.5 Extensions Equilateral triangle DW Test Item(s) 16066, 16609 16768 4.6 Understanding Math PLUS Understanding Equations Topic 5. Problem Solving Words and Symbols The Translation Machine Examples 1, 2, 3, 4 The Trick Machine Instructions The Machine Explanation with Pictures Explanation with Symbols Area of Walls Chemistry Pool Puzzler – The First Problem Perimeter Problem with Diagram Money Problem with Chart Age Problem with Chart 4.7 Understanding Math PLUS Understanding Equations Topic 5. Problem Solving Words and Symbols The Translation Machine Examples 1, 2, 3, 4 The Trick Machine Instructions The Machine Curriculum and Pacing Guide Revised May 2007 Course # 1205080: 8th Grade Advanced Math Days Topic Benchm arks/SS S Chapter 4 – 8th Grade Advanced Math Section Vocabulary, Resources Extensions DW Test Item(s) Explanation with Pictures Explanation with Symbols Area of Walls Chemistry Pool Puzzler – The First Problem Perimeter Problem with Diagram Money Problem with Chart Age Problem with Chart 1 Formulas and Variables in Geometry MA.B.1.3 .1, MA.B.1.3 .3, MA.C.1.3 .1 4.8 Understanding Math PLUS Understanding Algebra Topic 4. Patterns, Formulas, Substitution Patterns to Formulas Example... Angles in a Polygon SpringBoard, MSii: Putting Back the Pieces 2 Total 9 Review and Assessment Ch. 1-4 752, 16834 Curriculum and Pacing Guide Revised May 2007 Course # 1205080: 8th Grade Advanced Math Days 1 Topic Exploring Pictographs and Time Lines Benchm arks/SS S MA.E.1.3 .1 Exploring Bar Graphs and Histograms Chapter 5 – 8th Grade Advanced Math Section Vocabulary, Resources Extensions 5.1 Pictograph, time line Understanding Math PLUS Understanding Graphing Topic 2. Statistics An Introduction Tally Chart Pictograph #1 Pictograph #2 5.2 Bar graph, histogram, frequency distribution Understanding Math PLUS Understanding Graphing Topic 2. Statistics Bar Graph #1 Bar Graph #2 Histogram Example 1... Heights of Students Example 2... Roll a Die DW Test Item(s) 5464 11545,34927,11537 34897,14259,11397 SpringBoard, Alg i: Olympic Hoops 1 Exploring Line Graphs MA.E.1.3 .1 5.3 1 Problem Solving: Choosing an Appropriate Graph MA.E.1.3 .1 5.4 Line graph Understanding Math PLUS Understanding Graphing Topic 2. Statistics Line Graph Example 1... Life Expectancy Example 2... Software Profits 34882,34879,14178 34922,5681,34922 14151,14177,20686,2 0727 Understanding Math PLUS Understanding Graphing Topic 2. Statistics Presenting Data – All sections 3827,19799,34883,34 886, 34887,34888, 34928 http://score.kings.k12.ca.us/lessons/score. html (Gifted) Curriculum and Pacing Guide Revised May 2007 Course # 1205080: 8th Grade Advanced Math Days Topic Benchm arks/SS S Problem Solving: Misleading Graphs 1 Statistics: Line Plots Statistics: Scatter Plots Chapter 5 – 8th Grade Advanced Math Section Vocabulary, Resources Understanding Math PLUS Understanding Graphing Topic 2. Statistics Presenting Data – All sections 5.5 MA.E.1.3 .2 5.6 5.7 Extensions Line Plot Scatter plot, positive correlation, no correlation, negative correlation Understanding Math PLUS Understanding Graphing Topic 2. Statistics Scatter Plot Example 1... The T-Shirt Tailor Example 2... Matching SpringBoard, MSii: Much Ado About Candy Later Exploring Probability 5.8 Probability of an event Understanding Math PLUS Understanding Probability Topic 2. What’s the Chance? Probability What is it? Introduction 1 Introduction 2 Probability Examples 1. Coin Toss 2. Picking One Ball 3. Picking Two Balls 4. Travel Example 5. Number Example 6. Rabbit Example 7. Mailing Letters 8. Forest 9. Ahmed’s Maze The Probability Scale Examples Summary DW Test Item(s) 3877,19798,3920 4006,20707,20727 68476 20687,14183 11490,14187 Curriculum and Pacing Guide Revised May 2007 Course # 1205080: 8th Grade Advanced Math Days Topic Benchm arks/SS S Chapter 5 – 8th Grade Advanced Math Section Vocabulary, Resources Extensions DW Test Item(s) Follow Up Soccer Example present as part of chapter 8 2 Total 6 Review and Assessment Ch. 1-5 Interpreting Graphs: 14189,20707,14191 11593 Curriculum and Pacing Guide Revised May 2007 Course # 1205080: 8th Grade Advanced Math Days 1 Topic Divisibility Tests Factors and Primes 1 Greatest Common Factor 1 Least Common Multiple 1 Simplifying and Comparing Fractions Benchm arks/SSS MA.A.1.3. 4, MA.A.3.3. 1, MA.A.3.3. 3, MA.D.2.3 .1 MA.A.1.3. 4, MA.A.3.3. 1, MA.A.3.3. 3, MA.D.2.3 .1 MA.A.1.3. 4, MA.A.3.3. 1, MA.A.3.3. 3, MA.D.2.3 .1 MA.A.3.3. 1, MA.A.3.3. 2, MA.A.4.3. 1 Chapter 6 – 8th Grade Advanced Math Section Vocabulary, Extensions Resources 6.1 Divisible, factored, factors Understanding Math PLUS 6.2 Prime, composite, Understanding Algebra tree diagrams Topic 3. Patterns, Patterns, Patterns Factor Pairs in Arrays Factors of 8, 12, 16, 20, 5, 15, 18 Prime and Composite Prime Numbers Composite Numbers 6.3 Common factor, relatively prime, greatest common factor 6.4 Common multiple, least common multiple 6.5 Equivalent, simplest form, simplifying Understanding Math PLUS Understanding Algebra Topic 3. Patterns, Patterns, Patterns Common Factors/GCF Examples 1, 2 DW Test Item(s) 80337 80338, 80343, 80344 80345, 80346 80362, 80363 Understanding Math PLUS Understanding Fraction Topic 3. Equivalent Fractions Equivalent Fractions on a Number Line Comparison of Fractions Equivalent Fractions in a Multiplication Table One Equivalent Fractions... The Pattern 550, 80347, 80348, 546,548,3835 547,3878 549,11746,1186 0 34656,34657 Curriculum and Pacing Guide Revised May 2007 Course # 1205080: 8th Grade Advanced Math Days 1 Topic Rational Numbers and Decimals Benchm arks/SSS MA.A.1.3. 3, MA.A.1.3. 4, MA.A.3.3. 2, MA.D.2.3 .1 Chapter 6 – 8th Grade Advanced Math Section Vocabulary, Extensions Resources Example Questions Examples 1, 2, 3 Greatest Common Factor 12 and 18 30 and 40 70 and 42 Simplifying Fractions to Simplest Form Method 1, 2 6.6 Rational numbers, rational, irrational Understanding Math PLUS Understanding Fraction Topic 5. Introduction to Decimals Introduction to Decimals Tenths and Decimals Examples 1, 2, 3, 4 Ones and Tenths Examples 1, 2, 3, 4 Decimals on a Number Line Examples 1, 2, 3, 4, 5 Place Value Ones and Tenths 1 Ones and Tenths 2 Tens, Ones and Tenths Decimals on a Number Line Hundreds and Tenths Greater and Less Than Ones, Tenths, Hundreds, Thousandths Decimals to Tenths Examples 1, 2, Decimals to Hundredths Examples 1, 2, 3, 4, 5 Decimals to Thousandths Examples 1, 2, 3, 4, 5 Understanding Place Value Examples 1, 2, 3, 4 Equivalent Decimals Examples 1, 2, 3, 4 DW Test Item(s) 16803, 20703, 80312, 80313, 80361, 80364, 80365, 80366 550,10890 551,34661 552,558 553 Curriculum and Pacing Guide Revised May 2007 Course # 1205080: 8th Grade Advanced Math Days 1 Topic Powers and Exponents Scientific Notation Benchm arks/SSS MA.A.1.3. 1, MA.A.1.3. 2, MA.A.1.3. 4, MA.A.2.3. 1, MA.A.3.3. 1, MA.D.2.3 .1 Chapter 6 – 8th Grade Advanced Math Section Vocabulary, Extensions Resources Comparing Decimals Examples 1, 2, 3, 4 Understanding Math PLUS Understanding Exponents Topic 1. The Meaning of Exponents Exponents, Powers, Bases Powerful Explosions Introductory Examples Examples 1, 2, 3, 4, 5 Examples – Substitution Examples 1, 2, 3, 4 Examples – Order of Operation Examples 1, 2, 3 Practice Questions 6.7 6.8 Scientific Notation Understanding Math PLUS Understanding Exponents Topic 4. Scientific Notation Why Use Scientific Notation? Scientific Notation for Large Numbers Introduction Chart The Rule The Steps Scientific Notation for Small Numbers Introduction Chart The Steps Examples 1. Number Question 2. Park Question 3. Sun Question 4. Kitchen Question Practice Questions DW Test Item(s) 16781, 16787, 80356,11867,11 899 17526,10885 11774,3881 559,554,560, 561,3795,3838 3924,3967,1088 3, 1089,11763, 17656,13983, 17623,19659 19655,19656, 19657, 19660 20699,34678 34673,34674 34676,20700 34655,34672 34723,596,1677 7 16783,16809 80359,80360 Curriculum and Pacing Guide Revised May 2007 Course # 1205080: 8th Grade Advanced Math Days Topic 1 Exploring Patterns 2 Review and Assessment Ch. 1-6 Total 9 Benchm arks/SSS MA.A.5.3. 1, MA.B.1.3. 3 Chapter 6 – 8th Grade Advanced Math Section Vocabulary, Extensions Resources Understanding Math PLUS 6.9 Understanding Algebra Topic 3. Patterns, Patterns, Patterns Introduction... Math is Patterns Geometric Patterns Examples 1, 2, 3, 4, 5, 6, 7, 8 Number Patterns Examples 1, 2, 3, 4, 5, 6 Number and Geometric Patterns Examples 1, 2 Patterns to Formulas Examples 1, 2, 3 DW Test Item(s) 20711, 80303 Curriculum and Pacing Guide Revised May 2007 Course # 1205080: 8th Grade Advanced Math Days 1 Topic Addition and Subtraction of Like Fractions Benchm arks/SS S MA.A.3.3 .1, MA.A.3.3 .2, MA.A.3.3 .3, MA.D.2.3 .1 Chapter 7 – 8th Grade Advanced Marth Section Vocabulary, Resources 7.1 Vocabulary Extensions Understanding Math PLUS Understanding Fractions Topic 7. Adding Fractions Pattern Blocks Hexagon 1, 2, 3 Summary Fraction Strips Concepts 1, 2 Percent Strips Examples 1, 2 Decimal Strips Examples 1, 2 The Clock Examples 1, 2 Adding Fractions on a Number Line Examples 1, 2, 3 Topic 8. Subtracting Fractions Pattern Blocks Hexagons 1, 2, 3 Summary The Clock Examples 1, 2 Fraction Strips Concepts 1, 2 Percent Strips Examples 1, 2 Decimal Strips Examples 1, 2 Subtracting Fractions on a Number Line Examples 1, 2, 3 DW Test Item(s) 80367, 80368, 80369, 80370 Curriculum and Pacing Guide Revised May 2007 Course # 1205080: 8th Grade Advanced Math Days 1 Topic Benchm arks/SS S Addition and Subtraction of Unlike Fractions Chapter 7 – 8th Grade Advanced Marth Section Vocabulary, Resources 7.2 Like Fractions Extensions Understanding Math PLUS Understanding Fractions Topic 7. Adding Fractions The Lowest Common Denominator Examples 1, 2 Word Problems Alexander’s Friends Eating Candy Goal Scoring Taking a Walk Topic 8. Subtracting Fractions The Lowest Common Denominator Examples 1, 2 Word Problems Pedro and Alex Race Washing the Cars Planting a Garden 1 Exploring Fractions and Decimals MA.A.1.3 .3, MA.A.1.3 .4, MA.A.3.3 .2 7.3 Least common denominator Understanding Math PLUS Understanding Fractions Topic 6. Percents…Fractions…Decimals Expressing a Percent as a Decimal Introduction Examples 1, 2, 3 Number Line #1 Decimal Strips Concepts 1, 2, 3 Expressing a Decimal as a Percent Examples 1, 2, 3 Summary and Pattern % Nitrogen in the Air Batting Averages Expressing a Fraction as a Percent An Example Method 1 DW Test Item(s) 34721,3930, 14144,14265, 3801,14032 Curriculum and Pacing Guide Revised May 2007 Course # 1205080: 8th Grade Advanced Math Days Topic Benchm arks/SS S Chapter 7 – 8th Grade Advanced Marth Section Vocabulary, Resources Extensions DW Test Item(s) Examples 1, 2 Method 2 Examples 1, 2 Lightning Example Number Line #2 Chart Practice Questions 1 Multiplication of Rational Numbers MA.A.3.3 .1, MA.A.3.3 .2, MA.D.2.3 .1 7.4 Understanding Math PLUS Understanding Fractions Topic 9. Multiplying Fractions Pattern Blocks Hexagons 1, 2, 3 Fraction Strips Concepts 1, 2 Word Problems Boris’ Money Maria’s Trip Developing the Rule Example 1 Example 2 A Summary The Meaning of “OF” Order in Multiplying Examples 1, 2 Multiplying Fractions with Large Numbers Examples 1, 2 Practice Questions 571, 80371, 80372,573, 11879,11889 5466,3884 3969,13985 14006,34700 34703,34705 20703 Curriculum and Pacing Guide Revised May 2007 Course # 1205080: 8th Grade Advanced Math Days Topic Benchm arks/SS S Chapter 7 – 8th Grade Advanced Marth Section Vocabulary, Resources Division of Rational Numbers 1 Exploring Percents 7.5 MA.A.1.3 .1, MA.A.1.3 .2, MA.A.1.3 .3, MA.A.1.3 .4, MA.A.3.3 .1, MA.A.3.3 .2, MA.A.3.3 .3, MA.E.1.3 .1 7.6 Extensions Understanding Math PLUS Understanding Fractions Topic 10. Dividing Fractions Understanding Division Recall from Whole Numbers Introduction Examples with Diagrams Soda Pop Ice Cream Shape 1 Shape 2 Patterns from Examples Another Explanation Examples 1, 2 Examples without Diagrams Numerical Examples 1, 2 Central High School Practice Questions Understanding Math PLUS Understanding Percent Topic 5. Percent of a Number In This Topic The Concept Examples 1. Money Example 2. Service Charge 3. Bird Example 4. Marathon Race 5. Freezing 6. Pie Chart The Bouncing Ball Grades What if? Calculate Pass or Fail? Practice Questions DW Test Item(s) 16784, 16806, 80373, 80374 3970,5688 11900,11901 20730,34701 34707 547 Curriculum and Pacing Guide Revised May 2007 Course # 1205080: 8th Grade Advanced Math Days Topic Percents, Decimals, and Fractions Benchm arks/SS S Chapter 7 – 8th Grade Advanced Marth Section Vocabulary, Resources 7.7 Portion, percent Extensions Understanding Math PLUS Understanding Fractions Topic 6. Percents…Fractions…Decimals Expressing a Percent as a Decimal Introduction Examples 1, 2, 3 Number Line #1 Decimal Strips Concepts 1, 2, 3 Expressing a Decimal as a Percent Examples 1, 2, 3 Summary and Pattern % Nitrogen in the Air Batting Averages Expressing a Fraction as a Percent An Example Method 1 Examples 1, 2 Method 2 Examples 1, 2 Lightning Example Number Line #2 Chart Practice Questions DW Test Item(s) 558,551,10886,11 946, 14016,17627,206 88 34650,34659,346 62, 34665,3466, 16819, Curriculum and Pacing Guide Revised May 2007 Course # 1205080: 8th Grade Advanced Math Days 1 Topic Finding a Percent of a Number Problem Solving with Percents Benchm arks/SS S MA.A.1.3 .1, MA.A.1.3 .4, MA.A.3.3 .1, MA.A.3.3 .2, MA.A.3.3 .3, MA.A.3.4 .1, MA.D.1.3 .2, MA.D.2.3 .1, MA.D.2.3 .2 Chapter 7 – 8th Grade Advanced Marth Section Vocabulary, Resources Extensions 7.8 Understanding Math PLUS Understanding Percent Topic 5. Percent of a Number In This Topic The Concept Examples 1. Money Example 2. Service Charge 3. Bird Example 4. Marathon Race 5. Freezing 6. Pie Chart The Bouncing Ball Grades What if? Calculate Pass or Fail? Practice Questions 7.9 Understanding Math PLUS Understanding Percent Topic 6. Problems Involving Percent In This Topic Steps in Solving Problems Finding the Whole Recall Proportion School Population: Method 1... Using Proportions School Population: Method 2 Grades Problem: Method 1... Using Proportions Grades Problem: Method 2 Bike Sale: Method 1... Using Proportions Bike Sale: Method 2 Finding the Percent Theatre Problem DW Test Item(s) 705, 16786, 16816, 16817, 19699, 68452 20693 Curriculum and Pacing Guide Revised May 2007 Course # 1205080: 8th Grade Advanced Math Days Topic Benchm arks/SS S Chapter 7 – 8th Grade Advanced Marth Section Vocabulary, Resources Extensions Car Problem Percent of a Number Earnings Problem Nickel Ore SpringBoard, MSii: Nothing But Net 2 Total 8 Review and Assessment Ch. 1-7 DW Test Item(s) Curriculum and Pacing Guide Revised May 2007 Course # 1205080: 8th Grade Advanced Math Days Topic 2 Exploring Rates and Ratios Solving Proportions Benchm arks/SS S MA.A.1.3 .1, MA.A.1.3 .2, MA.A.3.3 .2, MA.A.3.3 .3, MA.B.1.3 .2, MA.D.1.3 .1 Chapter 8 – 8th Grade Advanced Math Section Vocabulary, Resources Extensions DW Test Item(s) 8.1 Rate, ratio Understanding Math PLUS Understanding Percent Topic 4. Ratios and Proportions Ratios in the News What is a Ratio? Examples 1.Fraction Strip 2.Balls 3.Students 4.Gears Writing Ratios Concept Examples 1, 2, 3, 4 548,556,586 3799,3928,16810 11947,14018 17626,17655,14147 586,13992,5462,347 53 34754,34755,34782 11483,19691 8.2 Proportion, cross, product property, similar, similar triangles, corresponding sides Understanding Math PLUS Understanding Percent Topic 4. Ratios and Proportions What is a Proportion? Proportions Example 1 Example 2 – Lemonade Example 3 – Marbles Example 4 – Trout Example 5 – Tree Height Example 6 – Map Example 7 – Scale Drawing 556, 80294 CBL, Real World Math: Lab #7, Mix It Up Curriculum and Pacing Guide Revised May 2007 Course # 1205080: 8th Grade Advanced Math Days Topic Benchm arks/SS S Chapter 8 – 8th Grade Advanced Math Section Vocabulary, Resources Problem Solving Using Proportions 2 Solving Percent Equations Problem Solving Using Percents Understanding Math PLUS Understanding Percent Topic 4. Ratios and Proportions What is a Proportion? Proportions Example 1 Example 2 – Lemonade Example 3 – Marbles Example 4 – Trout Example 5 – Tree Height Example 6 – Map Example 7 – Scale Drawing 8.3 MA.A.1.3 .4, MA.A.3.3 .1, MA.A.3.3 .2, MA.A.3.3 .3, MA.A.4.3 .1, MA.D.1.3 .2, MA.D.2.3 .1, MA.D.2.3 .2 8.4 8.5 Extensions Base of a Percent Discount, discount percent Understanding Math PLUS Understanding Percent Topic 6. Problems Involving Percent In This Topic Steps in Solving Problems Finding the Whole Recall Proportion School Population: Method 1... Using Proportions School Population: Method 2 Grades Problem: Method 1... Using Proportions Grades Problem: Method 2 Bike Sale: Method 1... Using Proportions Bike Sale: Method 2 Finding the Percent Theatre Problem Car Problem Percent of a Number Earnings Problem Nickel Ore DW Test Item(s) 600,16812, 80333,80334,80335 80376,68504 19674,34712 14257,11949 14165, 68504,34900 17525 19686,11951,11948 568,19665,570 34719,3887,19666, 19546,10943,5516 Curriculum and Pacing Guide Revised May 2007 Course # 1205080: 8th Grade Advanced Math Days Topic Benchm arks/SS S Exploring Percent of Increase or Decrease 1 Exploring Probability MA.A.1.3 .4, MA.A.3.3 .2, MA.E.2.3 .1, MA.E.2.3 .2 Chapter 8 – 8th Grade Advanced Math Section Vocabulary, Resources Extensions DW Test Item(s) 8.6 Percent of increase, Percent of decrease Understanding Math PLUS Understanding Percent Topic 3. Fraction/Decimal to Percent Percent Change Percent Increase Percent Decrease Percent Increase or Decrease 565, 16778,34727 10942,17658,34714 5463,17624 5.8 Probability of an event Understanding Math PLUS Understanding Probability Topic 2. What’s the Chance? Probability Examples 1. Coin Toss 2. Picking One Ball 3. Picking Two Balls 4. Travel Example 5. Number Example 6. Rabbit Example 7. Mailing Letters 8. Forest 9. Ahmed’s Maze 701, 68495, 68505, 34905,17682,701,38 73 3916,14146,14169,1 7681 13971,13998 3490,3588 This section is from chapter 5 SpringBoard, MSii: Toss Up 1 Omit The Counting Principle Probability and Simulations MA.A.1.3 .4, MA.E.2.3 .2 MA.A.3.3 .2, MA.A.4.3 .1, MA.E.2.3 .1, MA.E.3.3 8.7 Counting Principle 68495, 80280,3588 16241 8.8 68503 SpringBoard, MSii: Double the Fun Curriculum and Pacing Guide Revised May 2007 Course # 1205080: 8th Grade Advanced Math Days Topic 2 Review and Assessment Ch. 1-8 Total 8 Benchm arks/SS S .1 Chapter 8 – 8th Grade Advanced Math Section Vocabulary, Resources Extensions DW Test Item(s) Curriculum and Pacing Guide Revised May 2007 Course # 1205080: 8th Grade Advanced Math Day s 1 Topic Exploring Square Roots Benchmark s/SSS MA.A.1.3.1, MA.A.1.3.2, MA.A.1.3.3, MA.A.1.3.4, MA.A.4.3.1 The Real Number System Chapter 9 – 8th Grade Advanced Math Section Vocabulary, Extensions Resources Understanding Math PLUS 9.1 Understanding Exponents Topic 5. Square Root Squaring Numbers Square Roots Radical Signs Square Roots of Negative Numbers Example Questions 1. Radicals First 2. The Four Equations 3. Lawn Question 4. Make a Square Practice Questions 9.2 Real Numbers SpringBoard, Alg I: Sorting it All Out 2 The Pythagorean Theorem Problem Solving Using the Pythagorean Theorem MA.A.1.3.4, MA.B.3.3.1, MA.C.1.3.1, MA.C.3.3.1, MA.D.1.3.1, MA.D.1.3.2, MA.D.2.3.1 9.3 9.4 Right angle, legs, hypotenuse, isosceles triangle, Pythagorean theorem, Pythagorean triple, solving a right triangle Understanding Math PLUS Understanding Exponents Topic 6. Pythagorean Theorem The Right Triangle Math or Magic? Introduction Omar’s Rope Trick #1, #2 Our Rope Trick Squares on a Grid Examples 1, 2, 3, 4 Squares on the Sides of a Right Triangle Triangles 1, 2, 3 The Pythagorean Theorem The Pattern In General Theorem Example Questions DW Test Item(s) 3921,14250 11749,34651 34652,34737 16841,17483,34658 546 610 20717,34825 763,34827 764,5450 610,17666 34794,34805 34806,14139 14223,17635,610 11315,11339 Curriculum and Pacing Guide Revised May 2007 Course # 1205080: 8th Grade Advanced Math Day s Topic Benchmark s/SSS Chapter 9 – 8th Grade Advanced Math Section Vocabulary, Extensions Resources Example 1... Pole Example Example 2... Tower Example Example 3... Walking Example Example 4... Lake Example Example 5... Geometric Example DW Test Item(s) Sections 9.3 and 9.4 should be covered before FCAT SpringBoard, MSii Stop the Presses 1 Graphing Inequalities MA.D.1.3.2, MA.D.2.3.1, MA.D.2.3.2 9.5 1 Solving Inequalities: Multiplying and Dividing MA.D.2.3.1, MA.D.2.3.2 9.6 1 Solving Multi-Step Inequalities MA.D.1.3.1, MA.D.1.3.2, MA.D.2.3.1, MA.D.2.3.2 9.7 http://score.kings.k12.ca.us/lessons/ pytha.html (Gifted) Understanding Math PLUS Understanding Equations Topic 7. Solving Inequalities Graphing Linear Inequalities in Two Variables Concepts 1, 2 Examples 1, 2, 3 Understanding Math PLUS Understanding Equations Topic 7. Solving Inequalities Solving Inequalities Examples 1, 2, 3, 4, 5, 6 Understanding Math PLUS Understanding Equations Topic 7. Solving Inequalities Solving Inequalities Examples 1, 2, 3, 4, 5, 6 80304, 80305, 6854,3910 34877,34868,34875,34876 34325,34862,34864,20734, 20735, 34315,14762,19580 3862,11467,11468,3473,34 75, 3819,3948,3991 20734,20735,19690 80310, 19690,34878,68543 16769, 16770 Curriculum and Pacing Guide Revised May 2007 Course # 1205080: 8th Grade Advanced Math Day s 1 2 Tota l 9 Topic The Triangle Inequality Review and Assessment Ch. 1-9 Benchmark s/SSS MA.C.1.3.1 Chapter 9 – 8th Grade Advanced Math Section Vocabulary, Resources 9.8 Triangle inequality Extensions DW Test Item(s) 16468 Curriculum and Pacing Guide Revised May 2007 Course # 1205080: 8th Grade Advanced Math Days Topic 1 Exploring Points, Lines, and Planes Benchmarks /SSS MA.C.1.3.1, MA.C.2.3.1 Naming, Measuring, and Drawing Angles 1 Exploring Parallel Lines Symmetry MA.C.1.3.1, MA.C.2.3.1 Chapter 10 – 8th Grade Advanced Math Section Vocabulary, Extensions Resources Understanding Math PLUS 10.1 Points, line, plane, Understanding Measurement and Geometry ray, line segment, Topic 5. Angles and their Measure congruent segments, parallel, In This Topic intersection Lines and Rays DW Test Item(s) 10.2 vertex, angle measure, congruent angles, acute angle, right angle, obtuse angle, straight angle, perpendicular, complementary, supplementary Understanding Math PLUS Understanding Measurement and Geometry Topic 5. Angles and their Measure Angles... An Introduction The Degree Classifying Angles Classifications Memory Game Measuring Angles Practice Questions 17668,19679,54 44 34750,19697,19 677 5543,19679,141 24, 34798,17605,11 285, 14173,34749,11 287 11337,14135,13 988 14148 10.3 Vertical angles, corresponding angles Understanding Measurement and Geometry Topic 6. Angles and Polygons In This Topic Parallel Lines Example with Parallel Lines Examples 1, 2 10.4 Line symmetry, rotational symmetry Understanding Math PLUS Understanding Graphing Line of Symmetry - An Introduction Introduction Examples 1, 2, 3, 4 Symmetry Match Puzzle 1, 2 16462, 17512 17634,19688,38 13 3856,19559,389 9 3985,11286,196 81 3943,3986 Curriculum and Pacing Guide Revised May 2007 Course # 1205080: 8th Grade Advanced Math Days Topic Benchmarks /SSS Chapter 10 – 8th Grade Advanced Math Section Vocabulary, Resources Extensions DW Test Item(s) 19677,5959 19680,13911, 758,14170,1955 5 14255,17606,17 665 17669,34789,75 8 627, 16684 20695,17640,17 670, 1 Exploring Triangles MA.C.1.3.1 10.5 Scalene, right, isosceles, acute, equilateral, obtuse, and equiangular triangles Understanding Math PLUS Understanding Measurement and Geometry Topic 6. Angles and Polygons Angles in Triangles Exploration An Explanation Exterior Angles – Example 1 Exploring Quadrilaterals MA.C.1.3.1 10.6 Convex Understanding Math PLUS Understanding Measurement and Geometry Topic 2. Perimeter and Area of Polygons A Quadrilateral is Polygons and Congruence MA.B.2.3.1, MA.C.1.3.1, MA.C.2.3.1, MA.C.3.3.1 MA.C.1.3.1, MA.C.2.3.1 10.7 Regular Polygons 10.8 Interior angles, exterior angles MA.C.1.3.1, MA.C.2.3.1 10.9 1 Angles of Polygons 1 Angle and Side Relationships 2 Review and Assessment Ch. 1-10 Total 8 Understanding Math PLUS Understanding Measurement and Geometry Topic 6. Angles and Polygons Angles in Polygons Methods 1, 2 Exterior Angles in a Polygon Understanding Math PLUS Understanding Measurement and Geometry Topic 6. Angles and Polygons Angles in Polygons Methods 1, 2 Exterior Angles in a Polygon 605, 16427 Curriculum and Pacing Guide Revised May 2007 Course # 1205080: 8th Grade Advanced Math Days Topic Benchmarks/SSS Chapter 11 – 8th Grade Advanced Math Section Vocabulary, Extensions Resources Understanding Math PLUS 11.1 Height of a Understanding Measurement parallelogram, and Geometry base of a Topic 2. Perimeter and Area of parallelogram, Polygons height of a trapezoid, bases of Relationship – Area and Perimeter a trapezoid The Information The Graph Given Area and Perimeter – Create Shape Example 1 Example 2 Example 3 Example 4 Problems Section Length of Fence Area of a Wall The Tablecloth 1 Area and Perimeter MA.B.1.3.3, MA.C.1.3.1 1 1 Exploring Congruence Line Reflections MA.C.2.3.1 MA.C.2.3.1 11.2 11.3 1 Rotations MA.C.2.3.1 11.4 Transformation, rotation 1 Translations MA.C.2.3.1 11.5 Translation Reflection, reflection line Understanding Math PLUS Understanding Graphing Topic 4. Transformations Reflections - An Introduction Flip #1, #2, #3 Translations Object to Image We Say We Write Reflection Mapping Rule Examples Examples 1, 2, 3 DW Test Item(s) 16788, 16789, 16790, 16791, 16832, 16833, 16838, 80323, 80324, 80332, 80349 13993,34726,20723 34722,34762,34766,34675 34156,34708,19668,19673 17633,17654,34759 14009,14129,14162,14264 34760,591,592,752 3797,13937,13962,13993 11253,3840,3883,3926,20723 19668,582, (perimeter 34747, 34748 13968,3516) 14126,34803 3857,3900,11324,3814 3816,3462,17518,34800,13335 19683,3323,3376 11277,17637,34269 13586,17667,34802 34809 14061,34799,3432,14005 SpringBoard, MSii: One, Two, Three… Red Light 1 Exploring Similarity MA.A.3.3.2, 11.6 Similar, scale 592, 16825 Curriculum and Pacing Guide Revised May 2007 Course # 1205080: 8th Grade Advanced Math Days Topic 1 Problem Solving Using Similar Figures 1 Trigonometric Ratios 1 Problem Solving Using Trigonometric Ratios 2 Review and Assessment Ch. 1-11 Total 11 Benchmarks/SSS MA.A.3.3.3, MA.B.1.3.4, MA.B.2.3.1, MA.B.3.3.1, MA.C.2.3.1 MA.A.3.3.2, MA.B.2.3.1, MA.C.1.3.1, MA.C.2.3.1, MA.C.3.3.1 MA.A.1.3.4, MA.B.3.3.1, MA.C.1.3.1, MA.C.3.3.1 MA.A.1.3.4, MA.B.3.3.1, MA.C.1.3.1, MA.C.3.3.1 Chapter 11 – 8th Grade Advanced Math Section Vocabulary, Extensions Resources factor, dilation 11.7 11.8 DW Test Item(s) (see lesson 11.7 DW questions) 11258,11341 3989,5558 3860,3903 34808,34882 14276,17638 13976,14123 17659,20728 Trigonometric ratio, sine, cosine, tangent Sections 11.8 and 11.9 can be delayed until after FCAT 11.9 Area of complex figures: 34742,19670,34739 13591,17660,17662 17663,34743,34745 Curriculum and Pacing Guide Revised May 2007 Course # 1205080: 8th Grade Advanced Math Days Topic 1 Circle Relationships 1 Polyhedrons and Other Solids Exploring Surface Area of Prisms and Cylinders Benchmarks/S SS MA.B.1.3.3, MA.C.1.3.1 MA.B.1.3.1, MA.B.1.3.3, MA.C.1.3.1 Chapter 12 – 8th Grade Advanced Math Section Vocabulary, Resources 12.1 Diameter, radius, center, circumference 12.2 12.3 Polyhedron, prisms, faces, pyramids, edges, net, vertices Surface area Extensions Understanding Math PLUS Understanding Measurement and Geometry Topic 4. Solids…Volume and Surface Area Classifying Solids A Solid is... Recall Polygons A Polyhedron is... A Prism is... Some Special Pyramids A Cylinder is... A Cone is... Platonic Solids http://www.beaconlearningcenter.com/Les sons/11510.htm (Gifted) Understanding Math PLUS Understanding Measurement and Geometry Topic 4. Solids…Volume and Surface Area Surface Area of a Solid The Concept Surface Area of a Pyramid Surface Area of a Cylinder SpringBoard, MSii: All Boxed Up DW Test Item(s) 34765,34256,17629, 14157,34764,14134, 13997,10899,10941, 11192,589,16469 20704,34793,34797, 34796,14140 14252,20705 594, 16611, 16792 34795,17630,19671,3 4740 3946, Curriculum and Pacing Guide Revised May 2007 Course # 1205080: 8th Grade Advanced Math Days 1 Topic Exploring Volumes of Prisms Benchmarks/S SS MA.B.1.3.1, MA.B.1.3.3, MA.C.1.3.1 Exploring Volumes of Cylinders Chapter 12 – 8th Grade Advanced Math Section Vocabulary, Extensions Resources 12.4 Volume, cubic units Understanding Math PLUS Understanding Measurement and Geometry Topic 4. Solids…Volume and Surface Area Volume of a Solid The Concept Volume of a Prism: Examples 1, 2 12.5 DW Test Item(s) 16050,3891,3848, 13970,34767,34768, 34746,34763,11196 34741,13943,20704 34669 Understanding Math PLUS Understanding Measurement and Geometry Topic 4. Solids…Volume and Surface Area Volume of a Cylinder 16839,34761,34744 3977,17661,3934, 3805,10963 1 Exploring Volumes of Pyramids and Cones MA.B.1.3.1, MA.B.1.3.3, MA.C.1.3.1 12.6 Tetrahedron Understanding Math PLUS Understanding Measurement and Geometry Topic 4. Solids…Volume and Surface Area Volume of a Pyramid Volume of a Cone 16604, 16794, 16835 17632 1 Exploring Volumes of Spheres MA.B.1.3.1, MA.B.1.3.3, MA.C.1.3.1 12.7 Hemispheres Understanding Math PLUS Understanding Measurement and Geometry Topic 4. Solids…Volume and Surface Area Volume of a Sphere 16795 1 Exploring Similar Solids MA.B.2.3.1, MA.C.1.3.1, MA.C.2.3.1, MA.C.3.3.1 12.8 2 Review and Assessment Ch. 1-12 Total Curriculum and Pacing Guide Revised May 2007 Course # 1205080: 8th Grade Advanced Math Days 8 Topic Benchmarks/S SS Chapter 12 – 8th Grade Advanced Math Section Vocabulary, Resources Extensions DW Test Item(s) Curriculum and Pacing Guide Revised May 2007 Course # 1205080: 8th Grade Advanced Math Days Topic 1 Linear Equations in Two Variables Benchmarks/S SS MA.C.3.3.2, MA.D.1.3.1, MA.D.1.3.2, MA.D.2.3.1 Exploring Graphs of Linear Equations 1 1 Exploring Intercepts of Graphs Exploring Slope Section 13.1 Chapter 13 – 8th Grade Advanced Math Vocabulary, Extensions Resources Understanding Math PLUS Linear Equation Understanding Graphing Topic 8. Equation on a Straight Line Graph y = mx + b Examples 1, 2, 3, 4 Patterns to Summary Examples 5, 6, 7 Slope y - intercept Equation Concept Examples 1, 2, 3, 4 Section 13.1 CBL, Real World Math: Lab #2, Making Sense with Math SpringBoard, MSii: The Media Center 13.2 MA.B.1.3.2, MA.D.1.3.1, MA.D.1.3.2, MA.D.2.3.1 MA.A.3.3.2, MA.B.1.3.2, MA.C.3.3.2, MA.D.1.3.1, MA.D.1.3.2, MA.D.2.3.1 13.3 x-intercept, yintercept Section 13.4 CBL, Real World Math: Lab #13, Velocity Test DW Test Item(s) 34848,34856,34 857, 131194,5514,14 001, 14258,14263,17 551, 17672,19685,34 839, 34845,14258,20 711 616 17671,34843,34 847 34853,34854 760,3818,3904 Sections 13.1 -13.4 should be covered before FCAT 13.4 Slope http://score.kings.k12.ca.us/lessons/growth.html (Gifted) 16346, 16785, 16796, 16814, 16823, 16831 20718,756 17641,11331,11 349 11366,34831,34 833 34835,34836,34 855 34838,17674,34 858 Curriculum and Pacing Guide Revised May 2007 Course # 1205080: 8th Grade Advanced Math Days Topic 1 The SlopeIntercept Form Benchmarks/S SS MA.B.1.3.2, MA.D.1.3.1, MA.D.1.3.2, MA.D.2.3.1 1 Problem Solving with Linear Equations MA.B.1.3.2, MA.C.3.3.2, MA.D.1.3.2 Section 13.5 13.6 Chapter 13 – 8th Grade Advanced Math Vocabulary, Extensions Resources Understanding Math PLUS Slope-Intercept Understanding Graphing Topic 8. Equation on a Straight Line Graph y = mx + b Examples 1, 2, 3, 4 Patterns to Summary Examples 5, 6, 7 Slope y - intercept Equation Concept Examples 1, 2, 3, 4 Linear Relationship Understanding Math PLUS Understanding Graphing Topic 8. Equation on a Straight Line Slope – Point Form of the Equation Example 1: Solutions 1, 2 Example 2: Solutions 1, 2, 3, 4 Special Cases Example 1 – Zero Slope Example 2 – Undefined Example to Summarize Word Problems/ Applications The Taxi Cases 1, 2 Find Equation Graph Equation Interpret Equation Summary The Walker Basketball Food Point of Intersection of Two Lines Examples 1, 2 CBL, Real World Math: Lab #9, Stretch It to the Limit DW Test Item(s) 16830, 17520 756, 757, 16824 Curriculum and Pacing Guide Revised May 2007 Course # 1205080: 8th Grade Advanced Math Days Topic 1 Graphs of Linear Inequalities 1 The Distance and Midpoint Formulas 2 Review and Assessment Ch. 1-13 Benchmarks/S SS MA.D.1.3.2 Section 13.7 Chapter 13 – 8th Grade Advanced Math Vocabulary, Extensions Resources Understanding Math PLUS Linear Inequality, Understanding Equations solution of a linear Topic 7. Solving Inequalities inequality, half plane Graphing Linear Inequalities in Two Variables Concepts 1, 2 Examples 1, 2, 3 Solving Systems of Linear Inequalities by Graphing Examples 1, 2 DW Test Item(s) 16688 SpringBoard, Alg I: A Tale of a Trucker Total 9 MA.A.1.3.4, MA.B.1.3.2, MA.B.3.3.1, MA.C.3.3.1 13.8 Distance formula, midpoint 16815, 16306 Curriculum and Pacing Guide Revised May 2007 Course # 1205080: 8th Grade Advanced Math Days 1 Topic Measures of Central Tendency Benchmarks/SSS MA.A.1.3.2, MA.E.1.3.2 Chapter 14 – 8th Grade Vocabulary, Resources 14.1 Mean (average), median, mode, measure of central tendency Section Advanced Math Extensions Understanding Math PLUS Understanding Graphing Topic 2. Statistics Presenting Data Stem-and-Leaf Diagram Example 1... Ages of Fans Example 2... Heights of Students Measures of Central Tendency Introduction The Mean Average The Median average The Mode Summary Another Example Adding Data Points Box and Whisker Plots Concepts Examples 1, 2 Sections 14.1 through 14.3 should be covered before FCAT 1 1 Stem-and-Leaf Plots Box-andWhisker Plots Exploring Data and Matrices MA.E.1.3.2 14.2 Stem-and-Leaf plot 14.3 Quartile, box-andwhisker plot 14.4 Matrix, add matrices, entries, subtract matrices, equal matrices DW Test Item(s) 34898,34921,34 923,34891,1764 8 34889,34890,34 893,34895,3489 6 17649,17680,19 695,19701,1970 2 20726,14253,17 647,17648 11531,11549,11 552,13969 14145,645,3828 3871,3914,3957 ,4000 5541,639,640 641,19701,8031 8 80319,80320 17649 17677,34924,18 83 34892,14011,34 894 80244,80738 Curriculum and Pacing Guide Revised May 2007 Course # 1205080: 8th Grade Advanced Math Days Topic Benchmarks/SSS 1 Exploring Polynomials MA.D.2.3.1, MA.D.2.3.2 1 Adding and Subtracting Polynomials MA.D.2.3.1, MA.D.2.3.2 Chapter 14 – 8th Grade Advanced Math Vocabulary, Extensions Resources Understanding Math PLUS 14.5 Polynomial, Understanding Algebra standard form Topic 4. Patterns, Formulas, Substitution Substitution is... Math Scrabble Scrabble 1, 2, 3 Challenge Substitution Examples Examples 1, 2, 3, 4 Practice Questions Section 14.6 Sum of polynomials, add polynomials, degree of a polynomial Understanding Math PLUS Understanding Algebra Topic 5. Adding Expressions Our Problem Adding Expressions with X and Y Tiles Examples 1, 2, 3 Adding Expressions with X-Squared Tiles Examples 1, 2, 3 Adding Expressions without Tiles Examples 1, 2 Practice Questions with Tiles Practice Questions without Tiles Topic Test Topic 6. Subtracting Expressions Our Problem Subtracting Expressions with X and Y Tiles Concept Examples 1, 2 Subtracting Expressions with X-Squared Tiles Examples 1, 2 Subtracting Expressions without Tiles Practice Questions with Tiles Practice Questions without Tiles DW Test Item(s) 16068, 16069, 1046, 1051, 1177, 1178, 1179 Curriculum and Pacing Guide Revised May 2007 Course # 1205080: 8th Grade Advanced Math Days 1 Topic Multiplying Polynomials 1 More About Multiplying Polynomials 2 Review and Assessment Ch. 1-14 Total 9 Benchmarks/SSS MA.A.2.3.1 MA.A.2.3.1 Chapter 14 – 8th Grade Advanced Math Vocabulary, Extensions Resources Understanding Math PLUS 14.7 Understanding Algebra Topic 7. Multiplying Expressions Our Problem Recall Tile Concepts Multiplying Monomials Like Terms With Tiles Without Tiles Multiplying Monomials and Polynomials With Tiles... Examples 1, 2, 3, 4 Without Tiles Section 14.8 SpringBoard, Alg I: Tri-Com computers Understanding Math PLUS Understanding Algebra Topic 7. Multiplying Expressions Our Problem Recall Tile Concepts Multiplying Monomials Like Terms With Tiles Without Tiles Multiplying Monomials and Polynomials With Tiles... Examples 1, 2, 3, 4 Without Tiles DW Test Item(s) 16062, 16071 1937, 1968, 96671 16072, 16074 Curriculum and Pacing Guide Revised May 2007 Course # 1205080: 8th Grade Advanced Math Days Topic Graphing Quadratic Functions Benchmarks/SSS MA.D.1.3.1, MA.D.1.3.2, MA.D.2.3.1, MA.D.2.3.2 Section None Chapter 14 – 8th Grade Advanced Math Vocabulary, Extensions Resources Understanding Math PLUS Non-linear, Quadratic functions Understanding Graphing Topic 9. Quadratic Equations Introductory Examples Examples 1, 2 Summary Examples 1, 2 Definitions Parabolas Quadratic Functions The Role of a The Plan: a = 1, 2, 3 a = -1, -2, -3 Parabolas with the Same Width Summary The Role of c The Plan: Increase c Summary The Role of b Examples 1, 2, 3, 4 Summary and Pattern In General Intercepts of a Quadratic Function Method 1: Graphing... Examples 1, 2 Method 2: Factoring (If Possible)... Examples 1, 2 Method 3: Using the Quadratic Formula... Examples 1, 2 CBL, Real World Math: Lab #11, That’s the Way the Ball Bounces DW Test Item(s)