Grade 11 Cluster I: Number Sense, Concepts, and Applications HSPA Corr.pdf · Grade 11 Cluster I:...

Grade 11 Cluster I: Number Sense, Concepts, and Applications

Macro Knowledge/Skills Interactive Mathematics Program

A: Understand types of numbers, our numeration system, and the ways they are used and applied in real-world situations.

KNOWLEDGE: The student should have a conceptual understanding of: 1. Real numbers

a. Rational numbers b. Irrational numbers

2. Powers, roots, and exponents 3. Absolute value 4. Scientific notation 5. Properties of equivalence relations (e.g., reflexive, symmetric, transitive) 6. Properties of arithmetic operations (e.g., associative, commutative) 7. Primes, factors, and multiples The student should be able to: 8. Extend understanding of the real number system to include rational and irrational numbers 9. Represent equivalent forms of the same number 10. Evaluate expressions containing powers, roots, and factorials

YEAR 1 Patterns

Getting Started: pp. 12 Investigating Sums: pp. 28-29,35 Both Positive & Negative: pp. 37-41

Game of Pig Flip, Flip: pp. 110-111, 113 In the Long Run: pp. 137-138

Overland T ailr Graph Tells a Story: pp. 227-228 How Fast Should You Go?: pp. 275-

280 Pit & the Pendulum

Statistics & the Pendulum: pp. 325, 328-329

Shadows Triangles Galore: pp. 435-436, 438-

439, 444-445

YEAR 2 Solve It!

What’s the Same?: pp. 54-55, 58-59 Do Bees Build it Best?

A Special Property of Right Triangles: p. 231

Corral Problem: pp. 245, 247 Cookies

Cookies & Inequalities: pp. 305-309 All About Alice

Extending Exponentiation: pp. 393-395, 397-399

“Curiouser & Curiouser!”: pp. 401-403, 406, 409-410

Turning Exponents Around: pp. 417-420

IMP (©1999, 2000, 2004) correlation to the NJ grade 11 High School Proficiency Exam 1 Key Curriculum Press September 2003


YEAR 3 Orchard Hideout!

All About Circles: pp. 90-96 Meadows or Malls?

Saved by the Matrices!: 223-226, 229-245

Small World, Isn’t It? Model for Populations Growth: pp.

313-321, 326, 328-331 Best Base: pp. 345-346, 348-349, 351,

354-355

YEAR 4 World of Functions

Tables: pp. 277-279 Going to the Limit: pp. 283-284, 288 Composing Functions: pp. 332-334

PROBLEM-SOLVING

SKILLS: In problem settings, using abilities that comprise the power base, the student should be able to: 11. Use primes, factors and multiples in real-world situations 12. Determine whether or not properties of equivalence relations and arithmetic operations apply to different relations and operations 13. Use absolute values, exponents, and approximations for roots of numbers in real-life

YEAR 1 Patterns

Getting Started: pp. 9, 12-13 Numbers to Functions: pp. 17-18 Investigating Sums: pp. 28-29, 35

Game of Pig Game of Chance & Strategy: pp. 99-

100 Overland T ailr

Journey Back in Time: pp. 198-199 Calculators on the Trail?: pp. 269-

271 Shadows

Triangles Galore: pp. 435-436, 444-445

YEAR 2 Solve It!

What’s the Same?: pp. 51-53 Is There Really a Difference?


Macro Knowledge/Skills Interactive Mathematics Program situations 14. Distinguish between rational and irrational numbers from their decimal representations 15. Distinguish between terminating and repeating decimal forms of rational numbers 16. Apply approximation techniques to situations involving initial portions of infinite decimal

Coins & Dice: pp. 126-127 Do Bees Build it Best?

Corral Problem: pp. 245 Cookies

Using the Feasible Region: pp. 332-333

Points of Intersection: pp. 340-346 Cookies & the University: pp. 348-

353 Creating Problems: pp. 355-363

All About Alice Who’s Alice?: pp. 380-381 Extending Exponentiation: pp. 388-

399 “Curiouser & Curiouser!”: pp. 401-

403, 406-410

YEAR 3 Fireworks

World of Quadratics: pp. 17 Orchard Hideout!

Orchards & Mini-Orchards: pp. 74-75

Coordinates & Distance: pp. 77-81 All About Circles: pp. 90-96, 99

Meadows or Malls? More Cookies: pp. 193-195 Saved by the Matrices!: 223-226, 229-

239, 242-243 Small World, Isn’t It?

All in a Row: pp. 306-307 Best Base: pp. 345-346, 349, 351, 354

Pennant Fever Play Ball!: pp. 394-396, 398 Pascal’s Triangle: pp. 450-457

YEAR 4 As the Cube Turns

Picture This!: pp. 115-118



Know How On Your Own: pp. 217-219

World of Functions What & Why of Functions: pp. 260-

261 Tables: pp. 266, 268, 271-279 Composing Functions: pp. 332-334

B: Apply ratios, proportions, and percents to a variety of situations.

KNOWLEDGE: The student should have a conceptual understanding of: 1. Equivalent and non-equivalent fractions 2. Ratio 3. Proportion 4. Percent (less than, greater than, or equal to 100%) The student should be able to: 5. Solve proportions 6. Change from a fraction or decimal to a percent and from a percent to a fraction or decimal

YEAR 1 Game of Pig

Flip, Flip: pp. 110-111, 113 Pictures of Probability: pp. 121 In the Long Run: pp. 128, 135-138,


Statistics & the Pendulum: pp. 333-334

Shadows Geometry of Shadows: pp. 415-419 Triangles Galore: pp. 4226-427, 430,

435-436, 438-439, 444-445 Lights & Shadows: pp. 450-454, 458 The Lamp & the Sun: pp. 461-463

YEAR 2 Solve It!

Solving Equations & Understanding Situations: pp. 8, 16

What’s the Same?: pp. 61-62 Linear World: pp. 68-69

Do Bees Build it Best? Area, Geoboards, & Trigonometry:

pp. 221 Special Property of Right Triangles:

pp. 231 Corral Problem: pp. 245

PROBLEM-SOLVING YEAR 1


Macro Knowledge/Skills Interactive Mathematics Program SKILLS: In problem settings, using abilities that comprise the power base, the student should be able to: 7. Illustrate and model ratios, proportions, and percents in real-life situations 8. Compare effects of percent increase and percent decrease in price of objects where sales tax is applicable 9. Solve a variety of problems using proportions and percents

Game of Pig Flip, Flip: pp. 110-111, 113 Pictures of Probability: pp. 121 In the Long Run: pp. 128, 135-138,


Statistics & the Pendulum: pp. 333-334

Shadows Geometry of Shadows: pp. 415-419 Triangles Galore: pp. 4226-427, 430,

435-436, 438-439, 444-445 Lights & Shadows: pp. 450-454, 458 The Lamp & the Sun: pp. 461-463

YEAR 2 Solve It!

Solving Equations & Understanding Situations: pp. 8, 16

What’s the Same?: pp. 61-62 Linear World: pp. 68-69


pp. 221 Special Property of Right Triangles:

pp. 231 Corral Problem: pp. 245

All About Alice Who’s Alice?: pp. 386

YEAR 3 Small World, Isn’t It?

Model for Populations Growth: pp. 328-331, 335

Best Base: pp. 347-348, 350-351, 354

YEAR 4 High Dive

Components of Velocity: 81-87 World of Functions


Macro Knowledge/Skills Interactive Mathematics Program What & Why of Functions: pp. 259 Tables: pp. 267, 281


Grade 11 Cluster II: Spatial Sense and Geometry


A: Recognize, visualize, analyze, and apply geometric properties, relationships, and patterns in real-world and/or problem-solving contexts using models, manipulatives, or technology.

KNOWLEDGE: The student should have a conceptual understanding of: 1. Geometric terms (e.g. point, ray, line, angle, plane, side, vertices, polygon, face, polyhedron, circle, sphere) 2. Standard notations 3. Properties of geometric figures 4. Fundamental relationships between geometric figures (e.g., parallelism, perpendicularity, intersection, congruence, similarity) 5. Inductive and deductive reasoning 6. Spatial relationships (e.g., direction, orientation, and perspective of objects in space); The student should be able to: 7. Use properties, definitions, and relationships to identify, classify, and describe two-dimensional and three-dimensional

YEAR 1 Patterns

Angle on Patterns: pp. 43, 46, 53 Game of Pig

Pictures of Probability: pp. 115-118, 121, 124

In the Long Run: pp. 129-130, 134-138

Little Pig: pp. 153-155 Shadows

What is a Shadow?: pp. 409-410, 412 Geometry of Shadows: pp. 418 Triangles Galore: pp. 431-432, 435-

445 Lights & Shadows: pp. 449-454 The Lamp & the Sun: pp. 461-463,

468-472

YEAR 2 Solve It!

What’s the Same?: pp. 39-49 Do Bees Build it Best?

Area, Geoboards, & Trigonometry: pp. 213-216, 222-224

Special Property of Right Triangles: pp. 228-229, 233-236, 238-240

Corral Problem: pp. 242-244, 246 From Two Dimensions to Three: pp.

250-254, 262-263, 266 Back to Bees: pp. 271

Cookies Using the Feasible Region: pp. 326-

328, 330 All About Alice

Who’s Alice?: pp. 382-384 “Curiouser & Curiouser!”: pp. 404-


Macro Knowledge/Skills Interactive Mathematics Program geometric figures 8. Draw two-dimensional representations of three-dimensional objects by sketching shadows, projections, perspectives, and map views 9. Recognize, identify, and describe geometric relationships and properties as they exist in nature, art, and other real-world settings 10. Apply concepts of symmetry, similarity, and congruence to problem solving

405

YEAR 3 Fireworks

Factoring & Solving: pp. 22-26 Algebra of the Vertex: pp. 31-33

Orchard Hideout! Orchards & Mini-Orchards: pp. 68-

75 Coordinates & Distance: pp. 77-78,

81 Equidistant Points & Lines: pp. 84-

87 All About Circles: pp. 90-102 Cable Complications: pp. 104-108 Lines of Sight: pp. 117-120

Meadows or Malls? Equations, Points, Lines, & Planes:

pp. 188 More Cookies: pp. 196-197

Small World, Isn’t It? All in a Row: pp. 310

YEAR 4 High Dive

Going to the Circus: pp. 4-5, 11-13 Height & the Sine: pp. 15-18, 20-27 Moving Left & Right: pp. 42, 44-45 Finding the Release Time: pp. 49-50,

53 Trigonometric Interlude: pp. 59, 62-

67 Falling Start: pp. 70-72, 75 Components of Velocity: 79, 81-87,

89 High Dive Concluded: pp. 92-93

As the Cube Turns Projecting Pictures: pp. 161-164, 167-

169, 172-174, 176-178, 180, 182


Macro Knowledge/Skills Interactive Mathematics Program PROBLEM-SOLVING

SKILLS: In problem settings, using abilities that comprise the power base, the student should be able to: 11. Analyze properties of three-dimensional geometric figures by using models and by drawing and interpreting two-dimensional representations of them 12. Use inductive and deductive reasoning to solve real-life problems and justify solutions 13. Solve real-world and mathematical problems using geometric models

YEAR 1 Patterns

Investigating Sums: pp. 28-29, 35 Angle on Patterns: pp. 43, 46, 53

Game of Pig Pictures of Probability: pp. 115-118,

121, 124 In the Long Run: pp. 129-130, 134-

138 Little Pig: pp. 153-155

Shadows What is a Shadow?: pp. 409-410, 412 Geometry of Shadows: pp. 418, 422-

423 Triangles Galore: pp. 428-429, 431-

432, 435-445 Lights & Shadows: pp. 449-454 The Lamp & the Sun: pp. 461-463,

468-472

YEAR 2 Solve It!


Area, Geoboards, & Trigonometry: pp. 213-216, 222-224

Special Property of Right Triangles: pp. 228-229, 232-236, 238-240

Corral Problem: pp. 242-244, 246 From Two Dimensions to Three: pp.

250-254, 262-263, 266 Back to Bees: pp. 271



Who’s Alice?: pp. 382-384 “Curiouser & Curiouser!”: pp. 404-

405



YEAR 3 Fireworks



75 Coordinates & Distance: pp. 77-78,

81 Equidistant Points & Lines: pp. 83-

88 All About Circles: pp. 90-102 Cable Complications: pp. 104-108 Lines of Sight: pp. 113-114, 117-120

Meadows or Malls? Equations, Points, Lines, & Planes:

pp. 188 More Cookies: pp. 196-197

Small World, Isn’t It? All in a Row: pp. 310

YEAR 4 High Dive

Going to the Circus: pp. 4-5, 11-13 Height & the Sine: pp. 15-18, 20-27 Moving Left & Right: pp. 42, 44-45 Finding the Release Time: pp. 49-50,

53 Trigonometric Interlude: pp. 59, 60,

62-67 Falling Start: pp. 70-72, 75 Components of Velocity: 79, 81-87,


As the Cube Turns Translation in Two Dimensions: pp.

140-141 Rotating in Two Dimensions: pp.

144-146, 157


Macro Knowledge/Skills Interactive Mathematics Program Projecting Pictures: pp. 161-164, 167-

169, 172-174, 176-178, 180, 182

B: Use coordinate geometry in problem-solving situations and apply the principles of congruence, similarity, and transformations.

KNOWLEDGE: The student should have a conceptual understanding of: 1. Congruence 2. Similarity 3. Symmetry 4. Transformations

a. Rotations b. Reflections c. Translations d. Dilations

5. The rectangular coordinate system 6. Matrices 7. Tessellations 8. Vectors The student should be able to: 9. Use coordinates, maps, tables, and grids 10. Use transformations

a. Given the pre-image & transformation, find image b. Given the image and transformation, find the pre-image c. Given the pre-image & image, determine the transformation

11. Draw a figure & tessellate it 12. Perform scalar multiplication on

YEAR 1 Patterns

Angle on Patterns: pp. 43 Overland T ailr

Calculators on the Trail?: pp. 259-260

Pit & the Pendulum Measuring & Predicting: pp. 376

Shadows Geometry of Shadows: pp. 415-419 Triangles Galore: pp. 444-445 Lights & Shadows: pp. 450-454, 458 The Lamp & the Sun: pp. 461-463,

468-472

YEAR 2 Solve It!

Linear World: pp. 72-73 Do Bees Build it Best?

Area, Geoboards, & Trigonometry: pp. 222-224

Special Property of Right Triangles: pp. 233-236, 238-239

Corral Problem: pp. 242-244, 246, 248

From Two Dimensions to Three: pp. 264-265

Back to Bees: pp. 271 Cookies


Points of Intersection: pp. 340, 342

YEAR 3 Fireworks

World of Quadratics: pp. 11-12


Macro Knowledge/Skills Interactive Mathematics Program matrices 13. Use vectors to show the position of an object

Orchard Hideout! Coordinates & Distance: pp. 77-79,

81 All About Circles: pp. 94-96, 100-102 Cable Complications: pp. 104 Lines of Sight: pp. 117-119

Small World, Isn’t It? As the World Grows: pp. 285-287 Average Growth: pp. 289-297 All in a Row: pp. 308-310

YEAR 4 High Dive

Going to the Circus: pp. 12-13 Height & the Sine: pp. 15-18 Moving Left & Right: pp. 44-45 Finding the Release Time: pp. 49 Components of Velocity: 81-84 High Dive Concluded: pp. 92-93

As the Cube Turns Programming Loops: pp. 124-129,

131-132 Translation in Two Dimensions: pp.

134-136, 140-141 Rotating in Two Dimensions: pp.

143, 150-151 Projecting Pictures: pp. 170-171, 175,

178 Rotating in Three Dimensions: pp.

185-188

PROBLEM-SOLVING SKILLS: In problem settings, using abilities that comprise the power base, the student should be able to: 14. Determine the

YEAR 1 Overland T ailr


Pit & the Pendulum Measuring & Predicting: pp. 376

Shadows Geometry of Shadows: pp. 415-417


Macro Knowledge/Skills Interactive Mathematics Program sequence of transformations needed to map one figure onto another 15. Solve problems in geometry using transformations, coordinates, and vectors 16. Relate the concepts of symmetry, similarity, and congruence to transformations 17. Predict and represent resulting figures when combining, subdividing, and changing figure

YEAR 2 Cookies


YEAR 3 Fireworks

World of Quadratics: pp. 11-12

YEAR 4 As the Cube Turns

Programming Loops: pp. 124-129 Translation in Two Dimensions: pp.

134-136 Rotating in Two Dimensions: pp.

143, 150-151 Projecting Pictures: pp. 170-171, 175,

178 Rotating in Three Dimensions: pp.

185-188

C: Apply the principles of measurement and geometry to solve problems involving direct and indirect measurement.

KNOWLEDGE: The student should have a conceptual understanding of: 1. Measurable attributes (e.g., perimeter, circumference, area, surface area, volume, angle measure) 2. Standard and non-standard units of measure 3. Dimensions, shapes, and properties of figures and objects 4. Right triangle relationships

a. The Pythagorean Theorem

YEAR 1 Patterns

Angle on Patterns: pp. 46, 49, 51-54 Game of Pig

Pictures of Probability: pp. 115-118, 121

Pit & the Pendulum Poe – Master of Suspense: pp. 317-

321 Shadows

What is a Shadow?: pp. 404-406, 409-410

Geometry of Shadows: pp. 415-417 Triangles Galore: pp. 425, 428-434,

437 Lights & Shadows: pp. 452-454 The Lamp & the Sun: pp. 464-473

YEAR 2


Macro Knowledge/Skills Interactive Mathematics Program b. Basic trigonometric ratios

The student should be able to: 5. Utilize appropriate formulas and label answers with appropriate units of measure 6. Measure geometric objects and determine the degree of accuracy needed when measuring them 7. Choose the appropriate techniques, tools, and units to measure quantities to achieve the desired level of accuracy

Solve It! Keeping Things Balanced: pp. 37


pp. 202-206, 208, 210-214, 216, 221-224

Special Property of Right Triangles: pp. 226-231, 233, 240

Corral Problem: pp. 242-248 From Two Dimensions to Three: pp.

253-269


Orchards & Mini-Orchards: pp. 75 All About Circles: pp. 90-96, 102 Cable Complications: pp. 104-107 Lines of Sight: pp. 113-116, 118-120

PROBLEM-SOLVING SKILLS: In problem settings, using abilities that comprise the power base, the student should be able to: 8. Use basic trigonometric ratios to solve problems involving indirect measurement 9. Develop and apply a variety of strategies for determining perimeter, circumference, area, surface area, volume, and angle measure

YEAR 1 Patterns

Angle on Patterns: pp. 43, 46 Game of Pig

Pictures of Probability: pp. 115-118, 121, 124

In the Long Run: pp. 129-130, 134-138, 144


What is a Shadow?: pp. 409-410, 412 Geometry of Shadows: pp. 418-419 Triangles Galore: pp. 444-445 Lights & Shadows: pp. 449-454, 458 The Lamp & the Sun: pp. 461-463,

468-472

YEAR 2


Macro Knowledge/Skills Interactive Mathematics Program 10. Solve problems using the Pythagorean Theorem 11. Develop informal ways of approximating the measures of familiar objects 12. Express mathematically and explain the impact of change in an object's dimensions on its surface area, volume, and/or perimeter

Solve It! Keeping Things Balanced: pp. 37 What’s the Same?: pp. 39-49


pp. 202-208, 210, 213-216, 222-224 Special Property of Right Triangles:

pp. 233, 238-240 Corral Problem: pp. 242-244, 246,

248 From Two Dimensions to Three: pp.

251-252, 254, 257, 258-259, 262-269

Back to Bees: pp. 271 Cookies

Using the Feasible Region: pp. 326-328, 330

YEAR 3 Fireworks



71, 73-75 Coordinates & Distance: pp. 77-78,

81 Equidistant Points & Lines: pp. 84,

86-87 All About Circles: pp. 90-102 Cable Complications: pp. 104-108 Lines of Sight: pp. 115-120

Meadows or Malls? More Cookies: pp. 196-197

YEAR 4 High Dive

Going to the Circus: pp. 4-5, 11-13 Height & the Sine: pp. 15-18, 20-27 Moving Left & Right: pp. 42, 44-45


Macro Knowledge/Skills Interactive Mathematics Program Finding the Release Time: pp. 49-50,

53 Trigonometric Interlude: pp. 59, 62-

67 Falling Start: pp. 70-72, 75 Components of Velocity: 79, 81-87,


As the Cube Turns Programming Loops: pp. 131-132 Translation in Two Dimensions: pp.

140-141 Projecting Pictures: pp. 161-164, 167-

169, 172-174


Grade 11 Cluster III: Data Analysis, Probability, Statistics, and Discrete Mathematics


A: Determine, interpret, and use probabilities of simple and compound events

KNOWLEDGE: The student should have a conceptual understanding of: 1. Probability

a. Experimental b. Theoretical c. Range of values (0 through 1) d. Notation [e.g. P(A) is read “probability of A”]

2. Events/Outcomes a. Simple b. Compound c. Equally likely d. Dependent e. Independent

3. Simulations 4. Law of large numbers [that experimental results tend to approach theoretical probabilities after a large number of trials] The student should be able to: 5. Model situations using simulations 6. Compare a simulation model to the theoretical model 7. Find probabilities of simple and compound

YEAR 1 Game of Pig

Game of Chance & Strategy: pp. 102-103

Flip, Flip: pp. 105-107, 110-111, 113 Pictures of Probability: pp. 115-121,

124-126 In the Long Run: pp. 128-131, 134-

140, 142-149 Little Pig: pp. 151-156 Back to Pig: pp. 158-160

YEAR 3 Pennant Fever

Play Ball!: pp. 392-393, 397 Trees & Baseball: pp. 400-405 Birthday Problem: pp. 407-414 Baseball & Counting: pp. 416-417,

427-428 Combinatorial Reasoning: pp. 439

YEAR 4 Pollster’s Dilemma

What’s a Pollster to Think?: pp. 371-375

Polls & Pennant Fever: pp. 378-385


Macro Knowledge/Skills Interactive Mathematics Program events 8. Find theoretical and experimental probabilities 9. Recognize probabilities as ratios and percents

PROBLEM-SOLVING SKILLS: In problem settings, using abilities that comprise the power base, the student should be able to: 10. Solve problems involving

a. Compound events b. Uncertainty c. Independent events

11. Create an experiment and communicate the outcomes

YEAR 1 Game of Pig

Pictures of Probability: pp. 119-120, 124-126

In the Long Run: pp. 135-138, 144-146, 149

Little Pig: pp. 151-156 Back to Pig: pp. 158-160

Pit & the Pendulum Poe – Master of Suspense: pp. 312,

315, 317-321 Standard Pendulum: pp. 353-356

Shadows What is a Shadow?: pp. 404-406,

409-410

YEAR 2 Is There Really a Difference?

Tool for Measuring Differences: pp. 138


Trees & Baseball: pp. 400-401, 403-404

Birthday Problem: pp. 407-408, 410-414

Baseball & Counting: pp. 416-417, 427-428

Combinatorial Reasoning: pp. 439 Baseball Finale: pp. 459, 461

YEAR 4



Pollster’s Dilemma What’s a Pollster to Think?: pp. 373-

375 Polls & Pennant Fever: pp. 378-385

B: Understand and interpret statistical distributions and apply to real-world situations.

KNOWLEDGE: The student should have a conceptual understanding of: 1. Scatter plot 2. Line of best fit 3. Outlier 4. Correlation 5. Curve fitting 6. Normal curve distribution 7. Direct and inverse variation 8. Probability distributions

a. Discrete b. Continuous

The student should be able to: 9. Draw a scatter plot 10. Draw a line of best fit 11. Model situations using probability distributions 12. Identify any outliers in a set of data


Making Predictions With Graphs: pp. 239-241, 244-251, 259-260

Pit & the Pendulum Statistics & the Pendulum: pp. 325,

339-347, 350-351 Standard Pendulum: pp. 353-356 Graphs & Equations: pp. 367 Measuring & Predicting: pp. 374,

376


Tool for Measuring Differences: pp. 136-137, 142-17, 153-157

Comparing Populations: pp. 159-174


All in a Row: pp. 304-305 Best Base: pp. 348, 355 Back to the Data: pp. 357, 359-360


What & Why of Functions: pp. 258 Tables: pp. 280 Who’s Who?: pp. 298-299 Tight Fit: pp. 301-303 Back to Arithmetic: pp. 314 Back to the Beginning: pp. 342

Pollster’s Dilemma Normal Distributions Revisited: pp.

400-403


Macro Knowledge/Skills Interactive Mathematics Program Means & Standard Deviations: pp.

412-413 Matter of Confidence: pp. 424-426,

432-434 Putting it Together; pp. 437-440

PROBLEM-SOLVING

SKILLS: In problem settings, using abilities that comprise the power base, the student should be able to: 13. Make predictions from data using

a. A line of best fit b. Correlation techniques c. Graphical symmetry (Normal Curve distribution) d. Curve fitting

14. Solve problems related to real-world situations




339-347, 350-351 Standard Pendulum: pp. 353-356 Graphs & Equations: pp. 367 Measuring & Predicting: pp. 374,

376










Macro Knowledge/Skills Interactive Mathematics Program 400-403

Means & Standard Deviations: pp. 412-413

Matter of Confidence: pp. 424-426, 432-434

Putting it Together; pp. 437-440

C: Collect, organize, represent, analyze, and interpret data.

KNOWLEDGE: The student should have a conceptual understanding of: 1. Population 2. Sample

a. Biased b. Unbiased

3. Measures of central tendency

a. Mean b. Median c. Mode

4. Other statistical measures

a. Range b. Rank c. Frequency

5. Data displays a. Histograms b. Pictographs c. Bar graphs d. Circle graphs e. Line graphs f. Tables g. Lists h. Charts i. Matrices j. Spreadsheets k. Line plots

The student should be able to:

YEAR 1 Patterns

Angle on Patterns: pp. 51-52 Game of Pig

Game of Chance & Strategy: pp. 96-98

Pictures of Probability: pp. 119-120, 122

In the Long Run: pp. 136, 145-148 Overland T ailr

Making Predictions With Graphs: pp. 239-241, 244-251



321 Statistics & the Pendulum: pp. 328-

332 Standard Pendulum: pp. 353-360 Measuring & Predicting: pp. 374-376

Shadows What is a Shadow?: pp. 405-406,

409-410


Data, Data, Data: pp. 110-111, 113-115

Coins & Dice: pp. 117-120 Tool for Measuring Differences: pp.

138, 141, 147, 154-157


Macro Knowledge/Skills Interactive Mathematics Program 7. Determine why a sample is biased or unbiased 8. Determine the size of a sample 9. Determine a method of gathering data 10. Use chance devices (e.g., spinners, number cubes, coins, and cards) to generate data 11. Display data 12. Use addition of matrices to manipulate data 13. Determine mean, median, mode, and range of a set of data

Comparing Populations: pp. 159-171, 173-174

POW Studies: pp. 176

YEAR 3 Meadows or Malls?

Saved by the Matrices!: 224-226 Small World, Isn’t It?

As the World Grows: pp. 282, 285-286

Average Growth: pp. 294 Back to the Data: pp. 359-360


What’s a Pollster to Think?: pp. 366-368, 371-372, 374-375

Normal Distributions Revisited: pp. 402-403

Matter of Confidence: pp. 425-427, 435

Putting it Together; pp. 437-438, 440

PROBLEM-SOLVING SKILLS: In problem settings, using abilities that comprise the power base, the student should be able to: 14. Design an experiment

a. Formulate a question b. Choose a population c. Select an unbiased sample d. Formulate an hypothesis

15. Collect, organize, and analyze data and




339-347, 350-351 Standard Pendulum: pp. 353-356,

362-363 Graphs & Equations: pp. 367 Measuring & Predicting: pp. 374,

376




Macro Knowledge/Skills Interactive Mathematics Program make predictions 16. Select and use appropriate data displays 17. Select an appropriate measure of central tendency or other statistical measure to describe data 18. Make inferences and evaluate arguments based on an analysis of data







400-403 Means & Standard Deviations: pp.

412-413 Matter of Confidence: pp. 424-426,

432-434 Putting it Together; pp. 437-440

D: Apply the concepts and methods of discrete mathematics to model and explore a variety of practical situations.

KNOWLEDGE: The student should have a conceptual understanding of: 1. Counting and sorting techniques 2. Combinations 3. Game strategies 4. Trees 5. Networks

a. vertices b. paths/edges c. traversability

The student should be

YEAR 1 Game of Pig

Flip, Flip: pp. 112 Pictures of Probability: pp. 124-125 In the Long Run: pp. 128-131, 134-

140, 142-149 Little Pig: pp. 151-156 Back to Pig: pp. 159


Trees & Baseball: pp. 400, 402, 404 Baseball & Counting: pp. 416-417,

419-434 Combinatorial Reasoning: pp. 436-

439, 442-444, 447-448


Macro Knowledge/Skills Interactive Mathematics Program able to: 6. Represent information using discrete methods such as networks and tree diagrams 7. Use tree diagrams to create a systematic list of all possible outcomes 8. Use formulas that efficiently count ways to group items 9. Use systematic listing, counting, and reasoning in a variety of contexts 10. Use various methods to arrange, organize, analyze, store, transform and communicate information

Baseball Finale: pp. 459



PROBLEM-SOLVING SKILLS: In problem settings, using abilities that comprise the power base, the student should be able to: 11. Find the shortest path 12. Find optimal schedules for components of complex tasks 13. Determine which of two players has a winning strategy in a game 14. Find the number of possible combinations (e.g., the number of

YEAR 1 Game of Pig

Flip, Flip: pp. 112 Pictures of Probability: pp. 124-125 In the Long Run: pp. 128-131, 134-

140, 142-149 Little Pig: pp. 151-156 Back to Pig: pp. 159

YEAR 3 Meadows or Malls?

Equations & More Variables in Linear Programming: pp. 213-215

Pennant Fever Trees & Baseball: pp. 400, 402, 404 Baseball & Counting: pp. 416-417,

419-434 Combinatorial Reasoning: pp. 436-

439, 442-444, 447-448


Macro Knowledge/Skills Interactive Mathematics Program possible pizzas with three toppings) 15. Use codes in a variety of contexts to transform information (e.g., ISBN numbers, ZIP codes, and UPC codes) 16. Apply discrete methods to problems of voting, apportionment, and allocation.

Baseball Finale: pp. 459



E: Use iterative and recursive patterns and processes to model a variety of practical situations and solve problems.

KNOWLEDGE: The student should have a conceptual understanding of: 1. Basic principles of iteration and recursion 2. Fractals 3. Algorithms and flow charts The student should be able to: 4. Recognize and use iterative and recursive processes 5. Recognize patterns produced by geometric change related to iteration, approximation, and fractals

YEAR 1 Patterns

Getting Started: pp. 9 Numbers to Functions: pp. 15-21


All in a Row: pp. 306-307 Model for Populations Growth: pp.

328-331 Best Base: pp. 351, 354

YEAR 4 High Dive

Going to the Circus: pp. 8-10

PROBLEM-SOLVING SKILLS: In problem settings, using abilities that comprise the power base, the student should be able to:

YEAR 1 Patterns

Getting Started: pp. 9 Numbers to Functions: pp. 15-18 Angle on Patterns: pp. 50-52

Game of Pig In the Long Run: pp. 147-148


Macro Knowledge/Skills Interactive Mathematics Program 6. Analyze and apply iterative and recursive processes to solve problems (e.g., pattern recognition, compound interest, and fractals). 7. Develop and use an algorithm to perform a given task 8. Analyze patterns produced by processes of geometric change, using iteration, approximation, and fractals


What is a Shadow?: pp. 400-402


Beyond Linearity: pp. 324-325 Best Base: pp. 351, 355

YEAR 4 High Dive

Going to the Circus: pp. 8-10


Grade 11 Cluster IV: Patterns, Functions, and Algebra


A: Recognize, create, and extend a variety of patterns and use inductive reasoning to understand and represent mathematical and other real-world phenomena.

KNOWLEDGE: The student should have a conceptual understanding of: 1. Patterns 2. Sequences and series 3. Limits 4. Tables, rules, variables, open sentences and graphs to describe patterns and other relationships The student should be able to: 5. Construct, recognize, and extend patterns 6. Use tables and graphs to identify patterns and relationships 7. Use appropriate graphing techniques to represent patterns and real-world phenomena 8. Recognize and describe patterns in both finite and infinite number sequences, and informally evaluate the limit of an infinite sequence 9. Find the sum of finite arithmetic series and of finite and infinite geometric series

YEAR 1 Patterns

Numbers to Functions: pp. 17-18 Investigating Sums: pp. 28-29, 32-35 Angle on Patterns: pp. 50 Putting It Together: pp. 56


321 Statistics & the Pendulum: pp. 325,

327, 333-334


Coins & Dice: pp. 130 Tool for Measuring Differences: pp.

148-150, 152 Do Bees Build it Best?

Special Property of Right Triangles: pp. 240

Corral Problem: pp. 242-244. 246 Cookies



All About Circles: pp. 90-96 Small World, Isn’t It?

All in a Row: pp. 306-307, 311 Beyond Linearity: pp. 313-323 Model for Populations Growth: pp.

335 Best Base: pp. 349, 351, 354

YEAR 4



High Dive Going to the Circus: pp. 8-10 Falling, Falling, Falling: pp. 31-33

World of Functions Going to the Limit: pp. 283-290

Pollster’s Dilemma Polls & Pennant Fever: pp. 380-385 Normal Distributions Revisited: pp.

387-391

PROBLEM-SOLVING SKILLS: In problem settings, using abilities that comprise the power base, the student should be able to: 10. Analyze and describe sequences and patterns found in the real world 11. Use patterns and inductive reasoning to solve problems arising from mathematical situations, everyday experiences, and other disciplines

YEAR 1 Patterns

Getting Started: pp. 9, 12 Investigating Sums: pp. 28-29, 35 Angle on Patterns: pp. 50-52 Putting It Together: pp. 61-62

Overland T ailr Setting Out With Variables: pp. 220-

221 Making Predictions With Graphs:

pp. 242-243 Calculators on the Trail?: pp. 253-

273 How Fast Should You Go?: pp. 275-

280 California at Last!: pp. 282-287

Pit & the Pendulum Graphs & Equations: pp. 367 Measuring & Predicting: pp. 374,

376

YEAR 2 Solve It!


Special Property of Right Triangles: pp. 240

Corral Problem: pp. 242-244, 246




333 Points of Intersection: pp. 340-346 Cookies & the University: pp. 348-

353 Creating Problems: pp. 355-363

All About Alice Extending Exponentiation: pp. 397-

399


All About Circles: pp. 90-96 Small World, Isn’t It?

All in a Row: pp. 306-307, 311 Beyond Linearity: pp. 313-315 Model for Populations Growth: pp.

328-331 Best Base: pp. 347, 351, 354

YEAR 4 High Dive

Going to the Circus: pp. 8-10 Height & the Sine: pp. 28-29

As the Cube Turns Picture This!: pp. 115-118

B: Use various types of functions to represent mathematical or real-world situations.

KNOWLEDGE: The student should have a conceptual understanding of: 1. Relations 2. Functions (linear and non-linear) 3. Independent and dependent variables 4. Domain and range 5. Rectangular coordinate system


Graph Tells a Story: pp. 223-226, 230-232, 233-235


Calculators on the Trail?: pp. 258-262, 272-273

How Fast Should You Go?: pp. 275-280

California at Last!: pp. 284 Pit & the Pendulum


Macro Knowledge/Skills Interactive Mathematics Program 6. Slope 7. Basic transformations (translations, reflections, and dilations) The student should be able to: 8. Use linear and nonlinear functions to model mathematical situations and real-world phenomena 9. Recognize that a variety of phenomena can be modeled by the same type function 10. Explain how change in one physical quantity can produce a corresponding change in another quantity 11. Differentiate between linear and exponential growth 12. Use appropriate graphing technologies to represent functions and real-world phenomena 13. Find the slope of a line 14. Apply basic transformations to graphs of relations

Standard Pendulum: pp. 362-363 Graphs & Equations: pp. 367-372 Measuring & Predicting: pp. 374-376

Shadows What is a Shadow?: pp. 409-410 Lights & Shadows: pp. 458 The Lamp & the Sun: pp. 462-463,

472

YEAR 2 Solve It!

Keeping Things Balanced: pp. 26, 29-32

Linear World: pp. 72-73 Beyond Linearity: pp. 82, 83-87

Cookies Cookies & Inequalities: pp. 302-303 Using the Feasible Region: pp. 326-

331, 334-336, 338 Points of Intersection: pp. 340, 342-

343 Cookies & the University: pp. 352 Creating Problems: pp. 357

All About Alice Who’s Alice?: pp. 380-381, 385, 386

YEAR 3 Fireworks

World of Quadratics: pp. 8-15, 17 Factoring & Solving: pp. 19-21 Algebra of the Vertex: pp. 28-35

Meadows or Malls? Recreations Versus Development: A

Complex Problem: pp. 156-160, 163-164

Strategy for Linear Programming: pp. 169-172, 174-175

Equations, Points, Lines, & Planes: pp. 186-187

More Cookies: pp. 196-197


Macro Knowledge/Skills Interactive Mathematics Program Equations, Equations, Equations:

pp. 203-204 Equations & More Variables in

Linear Programming: pp. 208, 217-218

Solving “Meadows or Malls?”: pp. 248-250

Small World, Isn’t It? As the World Grows: pp. 282, 285-

287 Average Growth: pp. 289-297 All in a Row: pp. 299-305, 308-309,

311 Beyond Linearity: pp. 313-316, 318-

320, 324-326 Model for Populations Growth: pp.

334-338, 341-343 Best Base: pp. 347-348, 355 Back to the Data: pp. 357, 359-360

YEAR 4 High Dive

Going to the Circus: pp. 4-5, 8-10, 11-13

Height & the Sine: pp. 16, 20-27 Falling, Falling, Falling: pp. 31-35 Finding the Release Time: pp. 49-50 Falling Start: pp. 69-72, 76 High Dive Concluded: pp. 92-93

As the Cube Turns Rotating in Two Dimensions: pp.

148-149 World of Functions

What & Why of Functions: pp. 258-259, 262-265

Tables: pp. 266-276, 280-281 Who’s Who?: pp. 283-287, 289-290,

292-299 Tight Fit: pp. 301-305 Back to Arithmetic: pp. 313-314


Macro Knowledge/Skills Interactive Mathematics Program Composing Functions: pp. 316, 320-

321 Transforming Functions: pp. 336-

340 Back to the Beginning: pp. 342

PROBLEM-SOLVING

SKILLS: In problem settings, using abilities that comprise the power base, the student should be able to: 15. Use relations, and functions to solve problems arising from mathematical situations, everyday experiences, and other disciplines 16. Analyze and represent functional relationships to explain how a change in one quantity results in a change in another quantity 17. Express change in related quantities as a linear, quadratic, exponential, or periodic relationship in order to predict relations between quantities that change over time 18. Recognize that real-world phenomena can be modeled using simple polynomial, rational, trigonometric, and exponential

YEAR 1 Patterns

Angle on Patterns: pp. 47-48, 50-52 Putting It Together: pp. 56

Overland T ailr Graph Tells a Story: pp. 223-226,

230-235 Making Predictions With Graphs:

pp. 239-241, 244-251 Calculators on the Trail?: pp. 258,

261-262, 272-273 How Fast Should You Go?: pp. 275-


Standard Pendulum: pp. 362-363 Graphs & Equations: pp. 367-369 Measuring & Predicting: pp. 374,

376 Shadows

What is a Shadow?: pp. 404-406, 409-410, 412

Lights & Shadows: pp. 458 The Lamp & the Sun: pp. 462-463,

472

YEAR 2 Solve It!


Beyond Linearity: pp. 83, 85-87 Cookies

Cookies & Inequalities: pp. 302-303 Using the Feasible Region: pp. 331,


Macro Knowledge/Skills Interactive Mathematics Program functions 19. Extend the concept of a slope of a line to slope of a curve and use the concept of slope to interpret a graph representing a real-world situation 20. Analyze the effect of change in parameters on functions and the resulting basic transformations to their graphs

334-336 Cookies & the University: pp. 352 Creating Problems: pp. 357

All About Alice Who’s Alice?: pp. 380-381, 385, 386 Extending Exponentiation: pp. 397-

399 “Curiouser & Curiouser!”: pp. 401-

403

YEAR 3 Fireworks

World of Quadratics: pp. 8-10 Algebra of the Vertex: pp. 31-33





More Cookies: pp. 196-197 Equations, Equations, Equations:





287 Average Growth: pp. 289-291, 294-

297 All in a Row: pp. 299-305, 311 Beyond Linearity: pp. 313-318, 324-

325 Model for Populations Growth: pp.

328-331, 334-337, 341-343


Macro Knowledge/Skills Interactive Mathematics Program Best Base: pp. 347, 355 Back to the Data: pp. 359-360

YEAR 4 High Dive


Height & the Sine: pp. 16, 20-22, 24-27

Falling, Falling, Falling: pp. 31-35 Finding the Release Time: pp. 49-50 Falling Start: pp. 69-72, 76 High Dive Concluded: pp. 92-93


259, 262-265 Tables: pp. 266-276, 280-281 Going to the Limit: pp. 283-287, 289-

290 Who’s Who?: pp. 292-299 Tight Fit: pp. 301-305 Back to Arithmetic: pp. 314 Composing Functions: pp. 316, 320-


C: Use algebraic concepts and processes to concisely express, analyze, and model real-world situations.

KNOWLEDGE: The student should have a conceptual understanding of: 1. Variables, expressions, number sentences, and open sentences 2. Linear equations and inequalities 3. Algebraic order of operations The student should be able to:


Journey Back in Time: pp. 203-204 Making Predictions With Graphs:

pp. 239-251 Calculators on the Trail?: pp. 253-

273 How Fast Should You Go?: pp. 275-

280 California at Last!: pp. 284

Pit & the Pendulum Standard Pendulum: pp. 362-363 Measuring & Predicting: pp. 376

Shadows


Macro Knowledge/Skills Interactive Mathematics Program 4. Use algebraic methods to model real-life situations 5. Evaluate algebraic expressions 6. Interpret algebraic equations and inequalities geometrically, and describe geometric objects algebraically 7. Solve equations and inequalities using a variety of methods (e.g., intuitive methods, paper-and-pencil techniques, tables and graphs, graphing calculators, and computers) 8. Develop, explain, use, and analyze operations and algebraic procedures on real numbers and algebraic expressions

Triangles Galore: pp. 426-427, 435-436

Lights & Shadows: pp. 458 The Lamp & the Sun: pp. 461-476

YEAR 2 Solve It!

Keeping Things Balanced: pp. 20-28, 36

What’s the Same?: pp. 39-49, 54-66 Linear World: pp. 71, 75-78 Beyond Linearity: pp. 80-82, 84-90

Cookies Cookies & Inequalities: pp. 305-310 Picturing Cookies: pp. 312-314, 323-

324 Using the Feasible Region: pp. 326-

331, 334-338 Points of Intersection: pp. 340, 342-


Who’s Alice?: pp. 385-386

YEAR 3 Fireworks

Factoring & Solving: pp. 22-26 Algebra of the Vertex: pp. 28, 30-34



Strategy for Linear Programming: pp. 166-176

Equations, Points, Lines, & Planes: pp. 179-180, 186-187, 189-191





Macro Knowledge/Skills Interactive Mathematics Program Saved by the Matrices!: 246 Solving “Meadows or Malls?”: pp.

250 Small World, Isn’t It?

As the World Grows: pp. 282, 284-286

Model for Populations Growth: pp. 328-333, 335-337, 339-340

Best Base: pp. 345-348, 350-351, 354-355

Back to the Data: pp. 357, 359-360

YEAR 4 High Dive

Finding the Release Time: pp. 49 Falling Start: pp. 73-74 High Dive Concluded: pp. 92-93

Know How On Your Own: pp. 226-230, 234-235

PROBLEM-SOLVING

SKILLS: In problem settings, using abilities that comprise the power base, the student should be able to: 9. Apply fundamental mathematical models to problems arising from mathematical situations and everyday experiences 10. Use algebraic methods to solve problems arising from mathematical situations, everyday experiences, and other disciplines


Graph Tells a Story: pp. 223-226, 233-235


Calculators on the Trail?: pp. 258, 261-262, 272-273

How Fast Should You Go?: pp. 275-280

Pit & the Pendulum Standard Pendulum: pp. 362-363 Graphs & Equations: pp. 367-369 Measuring & Predicting: pp. 374,

376 Shadows

What is a Shadow?: pp. 409-410 Lights & Shadows: pp. 458 The Lamp & the Sun: pp. 462-463,


Macro Knowledge/Skills Interactive Mathematics Program 472

YEAR 2 Solve It!


Linear World: pp. 68-69 Beyond Linearity: pp. 83

Cookies Cookies & Inequalities: pp. 302-303 Using the Feasible Region: pp. 331,

334-336 Cookies & the University: pp. 352 Creating Problems: pp. 357

All About Alice Who’s Alice?: pp. 380-381, 385, 386

YEAR 3 Fireworks

World of Quadratics: pp. 8-10 Algebra of the Vertex: pp. 31-33










287


Macro Knowledge/Skills Interactive Mathematics Program Average Growth: pp. 291, 294 All in a Row: pp. 299-301, 302-305,

311 Beyond Linearity: pp. 313-316, 318,

324-325 Model for Populations Growth: pp.

334, 335, 336-337, 341-343 Best Base: pp. 347, 355 Back to the Data: pp. 359-360

YEAR 4 High Dive


Height & the Sine: pp. 16, 20-22, 24-27

Falling, Falling, Falling: pp. 31-35 Finding the Release Time: pp. 49-50 Falling Start: pp. 69-72, 76 High Dive Concluded: pp. 92-93


259, 262-265 Tables: pp. 266-276, 280-281 Going to the Limit: pp. 283-287, 289-

290 Who’s Who?: pp. 292-299 Tight Fit: pp. 301-305 Back to Arithmetic: pp. 314 Composing Functions: pp. 316, 320-



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