10th grade math special education course of study · 10th grade math special education course of...

10th Grade Math

Special Education Course of Study

Findlay City Schools

2006

Table of Contents

1. Findlay City Schools Mission Statement 2. 10th Grade Math Curriculum Map 3. 10th Grade Math Indicators

10th Grade Math Special Education Course of Study Writing Team

Laura Reinhart Kim Coffman

Karen Ouwenga Linda D’Angelo Donna Leonard

Sandy White

Mission Statement

The mission of the Findlay City Schools, a community partnership committed to educational excellence, is to instill in each student the knowledge, skills and virtues necessary to be lifelong learners who recognize their unique talents and purpose and use them in pursuit of their dreams and for service to a global society. This is accomplished through a passion for knowledge, discovery and vision shared by students, families, staff and community.

Beliefs Our beliefs form the ethical foundation of the Findlay City Schools. We believe….

• every person has worth • every individual can learn • family is the most important influence on the

development of personal values. • attitude is a choice and always affects performance • motivation and effort are necessary to achieve full

potential • honesty and integrity are essential for building

trust. • people are responsible for the choices they make. • performance is directly related to expectations. • educated citizens are essential for the survival of

the democratic process. • personal fulfillment requires the nurturing of mind,

body and spirit. • every individual has a moral and ethical obligation to

contribute to the well-being of society. • education is a responsibility shared by students,

family, staff and community. • the entire community benefits by investing its time,

resources and effort in educational excellence. • a consistent practice of shared morals and ethics is

essential for our community to thrive.

10th GRADE MATH Special Education

(Course # 362)

COURSE OF STUDY

November 2006

10th GRADE M MATH CURRICULUM MAP

Week Chapter Topic Indicator

1 1 Algebra: Integers 8N3, 8N4, 8N7, 8P7, 8P8, 9N4 2 1 Algebra: Integers 8N3, 8N4, 8N7, 8P7, 8P8, 9N4 3 1 Algebra: Integers 8N3, 8N4, 8N7, 8P7, 8P8, 9N4 4 2 Algebra: Rational Numbers 8N1, 8P7, 8N8, 8M9, 8M10, 9N4 5 2 Algebra: Rational Numbers 8N1, 8P7, 8N8, 8M9, 8M10, 9N4 6 2 Algebra: Rational Numbers 8N1, 8P7, 8N8, 8M9, 8M10, 9N4 7 3 Algebra: Real Numbers and

the Pythagorean Theorem 8N2, 8N3, 8N5, 8N7, 9N4, 9N5, 8P13, 9G2

8 3 Algebra: Real Numbers and the Pythagorean Theorem

8N2, 8N3, 8N5, 8N7, 9N4, 9N5, 8P13, 9G2

9 3 Algebra: Real Numbers and the Pythagorean Theorem

8N2, 8N3, 8N5, 8N7, 9N4, 9N5, 8P13, 9G2

10 4 Proportions, Algebra and Geometry

8M6, 8M7, 8G1, 8G3, 8G4, 9G3, 8P13, 8P14, 9P13


8M6, 8M7, 8G1, 8G3, 8G4, 9G3, 8P13, 8P14, 9P13


8M6, 8M7, 8G1, 8G3, 8G4, 9G3, 8P13, 8P14, 9P13

13 5 Percent 9N5, 8N6, 9N4, 8M7, 8P7, 9P6, 8P16

14 5 Percent 9N5, 8N6, 9N4, 8M7, 8P7, 9P6, 8P16

15 5 Percent 9N5, 8N6, 9N4, 8M7, 8P7, 9P6, 8P16

16 6 Geometry 8M8, 8G1, 8G2, 9G3, 8G4, 8G5, 10G8, 10G9

17 6 Geometry 8M8, 8G1, 8G2, 9G3, 8G4, 8G5, 10G8, 10G9

18 1 - 6 Exams See chapters 1-6 19 7 Geometry: Measuring Area

and Volume 8N5, 8M3, 8M4, 8M5, 8M7, 8M9, 8M10, 8G3, 8G6

20 7 Geometry: Measuring Area and Volume

8N5, 8M3, 8M4, 8M5, 8M7, 8M9, 8M10, 8G3, 8G6

21 7 Geometry: Measuring Area and Volume

8N5, 8M3, 8M4, 8M5, 8M7, 8M9, 8M10, 8G3, 8G6

22 8 Probability 8D7, 8D8, 9D5, 8D10, 9D7, 8D11, 9D9



25 9 Statistics and Matrices 8P7, 9P6, 9D2, 8D1, 10D2, 8D2, 8D3, 8D4, 10D1, 8D5, 8D9



28 10 Algebra: More equations and inequalities

8P7, 9P6


8P7, 9P6


8P7, 9P6

31 11 Algebra: Linear functions 8P7, 9P6, 8P1, 9P3, 9P2, 8P2, 8P3, 9P5, 8P4, 8P6, 9P14, 8P9, 8P10, 9P9, 8P11, 8P13, 8P15, 9P15, 9D2, 8D6



34 12 Algebra: Nonlinear Functions and Polynomials

8P1, 9P2, 9P3, 8P3, 9P5, 8P5, 9P11, 8P7, 9P6, 8P14, 9P13, 8P15, 9P15,

35 12 Algebra: Nonlinear Functions and Polynomials

8P1, 9P2, 9P3, 8P3, 9P5, 8P5, 9P11, 8P7, 9P6, 8P14, 9P13, 8P15, 9P15,

36 1 - 12 Review / Exams ALL Textbook: Glencoe Mathematics Applications and Concepts Course 3(Ohio Edition) ISBN: 0-07-865257-X Copyright © 2005

STANDARD: Number, Number Sense and Operations BENCHMARK: (B) Identify subsets of the real number system, (C) Apply properties of operations and the real number system, and justify when they hold for a set of numbers, (G) Estimate, compute and solve problems involving real numbers, including ratio, proportion and percent, and explain solutions, (H) Find the square root of perfect squares, and approximate the square root of non-perfect squares TOPIC/UNIT: Chapter 1 Time Line: 3 Weeks Indicators: (8N3) Apply order of operations to simplify expressions and perform computations involving integers exponents and radicals, (8N4) Explain and use the inverse and identify properties and use inverse relationships (addition/subtraction, multiplication/division, squaring/square roots) in problem solving situations, (8N7) Find the square root of perfect square root of perfect squares, and approximate the square root of non-perfect squares as consecutive integers between which the root lies; e.g., Square root of 130 is between 11 and 12, (8P7) Use symbolic algebra (equations and inequalities), graphs and tables to represent situations and solve problems, (8P8) Write, simplify and evaluate algebraic expressions (including formulas) to generalize situations and solve problems (9N4) Demonstrate fluency in computations using real numbers.

KNOW • The 4-step plan • The operational properties • Graph and perform

operations on a number line. • Translate words into math • The properties of equality

DO • Solve problems using the 4-step

plan • Evaluate expressions and

identify properties • Graph integers on a number line • Perform operations using

integers • Write algebraic expressions and

equations from verbal phrases and sentences.

• Solve equations using the properties of equality.

PRE-ASSESSMENT:

Prerequisite Skills pp 5, 27, 42, 49

ASSESSMENT: Study Guide pp 54-56 Practice test pp 57 Multiple-choice test: Forms 1, 2A, 2B Free-response test 2C, 2D, 3

GRAPHIC ORGANIZER & OR TECHNOLOGY: Foldable pp 5 Website with extra examples: Pgs 7, 13, 19, 25, 29, 35, 39, 47, 51

TESTING SKILL(S) & OR SAMPLE OGT TYPE QUESTIONS: OH 10, OH 11, OH12, OH13 Pg 10, #19, 20 Pg 15, #57-59 Pg 21, #62-67 Pg 27, #46-54 Pg 31, #48-53 Pg 32, #19-20 Pg 38, #65-72 Pg 42, #33-39 Pg 49, #47-51 Pg 53, #46-50

BEST PRACTICES: Cooperative Learning Manipulative Individual problem solving

RESOURCES: Parent and Student Study guide 5-Minute check transparencies Key Teaching Transparencies MathPASS: Tutorial Plus Teaching Mathematics with Manipulatives Study guide and Interventions pp1, 6, 11, 16, 21, 26, 31, 36, 41 Practice (Skills and Word Problems) Pgs 2, 7, 12, 17, 22, 27, 32, 37, 42 Reading to Learn Math Pg 4, 9, 14, 19, 24, 29, 34, 39, 44 Enrichment 5, 10, 15, 20, 25, 30, 35, 40, 45

TESTING VOCABULARY: Vocabulary and Concept Check pg 54 Vocabulary Quiz CRM pg 60

HISTORICAL/MODERN LINK: Weather 18 Card Games 36 Geography 40 Careers 51

STANDARD: Number and Number Sense BENCHMARK: (A) Use scientific notation to express large numbers and numbers less than one, (D) Connect physical, verbal, and symbolic representations of integers, rational numbers and irrational numbers, (G) Estimate, compute and solve problems involving real numbers, including ratio, proportion and percent, and explain solutions, (I) Estimate, compute and solve problems involving scientific notation, square roots and numbers with integer exponents. STANDARD: Measurement BENCHMARK: (C) Apply indirect measurement techniques, tools and formulas, as appropriate, to find perimeter, circumference and area of circles, triangle, quadrilaterals and composite shapes and to find volume of prisms, cylinders and pyramids. (E) Estimate and compute various attributes, including length, angle measure, area, surface area and volume, to a specified level of precision. TOPIC/UNIT: Chapter 2 Time Line: 3 Weeks Indicators: (8N1) Use scientific notations to express large numbers and small numbers between 0 and 1, (8P7) Use symbolic algebra (equations and inequalities), graphs and tables to represent situations and solve problems. (8N8) Add, subtract, multiply, divide and compare numbers written in scientific notation, (8M9) Demonstrate understanding of the concepts of perimeter, circumference and area by using established formulas for triangles, quadrilaterals, and circles to determine the surface area and volume of prisms, pyramids, cylinders, spheres, and cones. (Note: Only volume should be calculated for spheres and cones.), (8M10) Use conventional formulas to find the surface area and volume of prisms, pyramids and cylinders and the volume of spheres and cones to a specified level of precision. (9N4) Demonstrate fluency in computations using real numbers.

KNOW • Interpret decimals into

fractions and fractions into decimals and use in equations

• Understand powers and exponents

• Scientific notation

DO • Expression rational numbers as

decimals and decimals as fractions

• Compare and order rational numbers

• Compute and solve equations with fractions and mixed numbers

• Use powers and exponents in expressions

• Write numbers in scientific notation

PRE-ASSESSMENT:

Prerequisite Skills pp 61, 66, 70, 75, 80, 85, 91

ASSESSMENT: Study Guide pp 108-110 Practice test pp 111 Multiple-choice test: Forms 1, 2A, 2B CRM 113-118 Free-response test 2C, 2D, 3, CRM 119-124

GRAPHIC ORGANIZER & OR TECHNOLOGY: Foldable pp 61 Vocabulary Puzzle Maker (online) WebQuest Project (online)

TESTING SKILL(S) & OR SAMPLE OGT TYPE QUESTIONS: OH12, OH13, OH14, OH15, OH16 Pg 66, #48-54 Pg 70, #37-43 Pg 75, #35-41 Pg 80, #42-50 Pg 85, #38-44 Pg 86, #19-20 Pg 91, #42-47 Pg 95, #35-43 Pg 101, #46-52 Pg 107, #44-50 Pg 111, #25


RESOURCES: Parent and Student Study guide 5-Minute check transparencies Key Teaching Transparencies MathPASS: Tutorial Plus Teaching Mathematics with Manipulatives Study guide and Interventions pp 67, 72, 77, 82, 87, 92, 97, 102, 107 Practice (Skills and Word Problems) Pgs 68, 73, 78, 83, 88, 93, 98, 103, 108 Reading to Learn Math Pg 70, 75, 80, 85, 90, 95, 100, 105, 110 Enrichment 71, 76, 81, 86, 91, 96, 101, 106, 111


HISTORICAL/MODERN LINK: Careers 64 Roller Coasters 68 Aircraft 73 Holidays 78 Basketball 93 Travel 105

STANDARD: NUMBER AND NUMBER SENSE BENCHMARK: (B) Identify subsets of the real number system., (F) Explain the effects of operations on the magnitude of quantities., (G) Estimate, compute and solve problems involving real numbers, including ratio, proportion and percent, and explain solutions., (H) Find the square root of perfect squares, and approximate the square root of non-perfect squares., (I) Estimate, compute and solve problems involving scientific notation, square roots and numbers with integer exponents. STANDARD: PATTERNS, FUNCTIONS AND ALGEBRA BENCHMARK: (J) Describe and interpret rates of change from graphical and numerical data. STANDARD: GEOMETRY AND SPATIAL SENSE BENCHMARK: (I) Use right triangle trigonometric relationships to determine lengths and angle measures. TOPIC/UNIT: Chapter 3 Time Line: 3 Weeks Indicators: (8N2) Recognize that natural numbers, whole numbers, integers, rational numbers and irrational numbers are subsets of the real number system. (8N3) Apply order of operations to simplify expressions and perform computations involving integer exponents and radicals. (8N5) Determine when an estimate is sufficient and when an exact answer is needed in problem situations, and evaluate estimates in relation to actual answers; e.g., very close, less than, greater than. (8N7) Find the square root of perfect squares, and approximate the square root of non-perfect squares as consecutive integers between which the root lies. (9N4) Demonstrate fluency in computations using real numbers. (9N5) Estimate the solutions for problem situations involving square and cube roots. (8P13) Compute and interpret slope, midpoint and distance given a set of ordered pairs. (9G2) Apply proportions and right triangle trigonometric ratios to solve problems involving missing lengths and angle measures in similar figures.

KNOW • Square roots • Pythagorean Theorem • Coordinate planes • Distance formula •

DO • Find square roots of perfect

squares and estimate square roots

• Use the Pythagorean Theorem and solve problems using it.

• Find the distance between points on the coordinate plane

PRE-ASSESSMENT:

Prerequisite Skills pp 115, 119, 122, 129, 136, 140

ASSESSMENT: Study Guide pp 146-148 Practice test pp 149 Multiple-choice test: Forms 1, 2A, 2B, CRM 163-168 Free-response test 2C, 2D, 3, CRM pgs 169-174

GRAPHIC ORGANIZER & OR TECHNOLOGY: Foldable pp 115 Vocabulary Puzzlemaker (online) WebQuest (online)

TESTING SKILL(S) & OR SAMPLE OGT TYPE QUESTIONS: OH 14, OH 15, OH16, OH17 Pg 119, #49-56 Pg 122, #37-40 Pg 129, #52-58 Pg 136, #36-42 Pg 140, #22-29 Pg 145, #26-30 Pg 149, #20


RESOURCES: Parent and Student Study guide 5-Minute check transparencies Key Teaching Transparencies MathPASS: Tutorial Plus Teaching Mathematics with Manipulatives Study guide and Interventions pp133, 138, 143, 148, 153, 158 Practice (Skills and Word Problems)

Pgs 134, 139, 144, 149, 154, 159 Reading to Learn Math Pg 136, 141, 146, 151, 156, 161 Enrichment 137, 142, 147, 152, 157, 162


HISTORICAL/MODERN LINK: History 117 Careers 127 Kites 133 Travel 143

STANDARD: Measurement BENCHMARK: (A) Solve increasingly complex non-routine measurement problems and check for reasonableness of results., (D) Use proportional reasoning and apply indirect measurement techniques, including right triangle trigonometry and properties of similar triangles, to solve problems involving measurements and rates. STANDARD: Geometry BENCHMARK: (B) Describe and apply the properties of similar and congruent figures; and justify conjectures involving similarity and congruence. (D) Use coordinate geometry to represent and examine the properties of geometric figures. (G) Prove or disprove conjectures and solve problems involving two- and three-dimensional objects represented within a coordinate system. STANDARD: Patterns, Functions and Algebra BENCHMARK: (I) Model and solve problem situations involving direct and inverse variation. (J) Describe and interpret rates of change from graphical and numerical data. TOPIC/UNIT: Chapter 4 Time Line: 3 Weeks Indicators: (8M6) 3 Solve and determine the reasonableness of the results for problems involving rates and derived measurements, such as velocity and density, using formulas, models and graphs., (8M7) Apply proportional reasoning to solve problems involving indirect measurements or rates., (8G1) Make and test conjectures about characteristics and properties (e.g., sides, angles, symmetry) of two-dimensional figures and three- dimensional objects., (8G3) Use proportions in several forms to solve problems involving similar figures (part-between figures)., (8G4) Represent and analyze shapes using coordinate geometry; e.g., given three vertices and the type of quadrilateral, find the coordinates of the fourth vertex., (9G3) Analyze two-dimensional figures in a coordinate plane; e.g., use slope and distance formulas to show that a quadrilateral is a parallelogram., (8P13) Compute and interpret slope, midpoint and distance given a set of ordered pairs., (8P14) Differentiate and explain types of changes in mathematical relationships, such as linear vs. nonlinear, continuous vs. noncontinuous, direct variation vs. inverse variation., (9P13) 2Model and solve problems involving direct and inverse variation using proportional reasoning.

KNOW

• Slope • Proportions • Similar triangle

DO • Find rates of change • Find slope of a line • Use proportions to solve

problems • Solve problems involving similar

triangles

PRE-ASSESSMENT: Prerequisite Skills pp 155, 159, 164, 169, 182, 187, 191



TESTING SKILL(S) & OR SAMPLE OGT TYPE QUESTIONS: OH 16, OH 17, OH19 Pg 159, #36-42 Pg 164, #20-24 Pg 169, #21-24 Pg 173, #45-48 Pg 174, #15-16 Pg 182, #20-25 Pg 187, #23-26 Pg 191, #19-33 Pg 197, #26-29 Pg 201, #15-16


RESOURCES: Parent and Student Study guide 5-Minute check transparencies Key Teaching Transparencies MathPASS: Tutorial Plus Teaching Mathematics with Manipulatives

Study guide and Interventions pp 185, 190, 195, 200, 205, 210, 215, 220 Practice (Skills and Word Problems) Pgs 186, 191, 196, 201, 206, 211, 216, 221 Reading to Learn Math Pg 188, 193, 198, 203, 208, 213, 218, 223 Enrichment 189, 194, 199, 204, 209, 214, 219, 224


HISTORICAL/MODERN LINK: Civics 157 Mail 162 Libraries 167 Careers 171 Model Trains 185

STANDARD: Number, Number Sense and Operations BENCHMARK: (I) Estimate, compute, and solve problems involving scientific notation, square roots and numbers with integer exponents. (G) Estimate, compute and solve problems involving real numbers, including ratio, proportion and percent, and explain solutions. STANDARD: Measurement BENCHMARK: (D) Use proportional reasoning and apply indirect measurement techniques, including right triangle trigonometry and properties of similar triangles, to solve problems involving measurements and rates. STANDARD: Patterns, Functions and Algebra BENCHMARK: (D) Use algebraic representations, such as tables, graphs, expressions, functions and inequalities, to model and solve problem situations. (F) Solve and graph linear equations and inequalities. (J) Describe and interpret rates of change from graphical and numerical data. TOPIC/UNIT: Chapter 5 Time Line: 3 weeks Indicators: (8N6) Estimate, compute and solve problems involving rational numbers, including ratio, proportion and percent, and judge the reasonableness of solutions. (9N4) Demonstrate fluency in computations using real numbers. (9N5) Estimate the solutions for problem situations involving square and cube roots. (8M7) Apply proportional reasoning to solve problems involving indirect measurements or rates. (8P7) Use symbolic algebra (equations and inequalities), graphs and tables to represent situations and solve problems. (8P16) Use graphing calculators or computers to analyze change; e.g., interest compounded over time as a nonlinear growth pattern. (9P6) Write and use equivalent forms of equations and inequalities in problem situations; e.g., changing a linear equation to the slope- intercept form.

KNOW • Fractions, percents, decimals • Simple interest formula

DO • Write percents as fractions and

decimals and vice versa. • Solve problems and compute

percents mentally • Find and use the percent of

increase and decrease • Solve problems involving simple

interest.

PRE-ASSESSMENT: Prerequisite Skills pp 205, 209, 214, 231, 235, 240

ASSESSMENT: Study Guide pp 246-248 Practice test pp 249 Multiple-choice test: Forms 1, 2A, 2B, CRM pgs 285-290 Free-response test 2C, 2D, 3, CRM pgs 291-296


TESTING SKILL(S) & OR SAMPLE OGT TYPE QUESTIONS: OH 18, OH19 Pg 209, #48-52 Pg 214, #72-81 Pg 219, #40-45 Pg 223, #43-49 Pg 224, #19, 20 Pg 231, #44-49 Pg 235, #31-37 Pg 240, #35-41 Pg 244, #28-32 Pg 249, #20

BEST PRACTICES: Cooperative Learning Manipulatives Individual problem solving

RESOURCES: Parent and Student Study guide 5-Minute check transparencies Key Teaching Transparencies MathPASS: Tutorial Plus Teaching Mathematics with

Manipulatives Study guide and Interventions pp 245, 250, 255, 260, 265, 270, 275, 280 Practice (Skills and Word Problems) Pgs 246, 251, 256, 261, 266, 271, 276, 281 Reading to Learn Math Pg 248, 253, 258, 263, 268, 273, 278, 283 Enrichment 249, 254, 259, 264, 269, 274, 279, 284


HISTORICAL/MODERN LINK: Cars pg 207 History pg 217 Car Sales pg 242

STANDARD: Measurement BENCHMARK: (E) Estimate and compute various attributes, including length, angle measure, area, surface area and volume, to a specified level of precision. STANDARD: Geometry BENCHMARK: (B) Describe and apply the properties of similar and congruent figures; and justify conjectures involving similarity and congruence. (C) Recognize and apply angle relationships in situations involving intersecting lines, perpendicular lines, and parallel lines. (D) Use coordinate geometry to represent and examine the properties of geometric figures. (F) Represent and model transformations in a coordinate plane and describe the results. (G) Prove or disprove conjectures and solve problems involving two- and three-dimensional objects represented within a coordinate system. TOPIC/UNIT: Chapter 6 Time Line: 2 Weeks Indicators: (8M8) Find the sum of the interior and exterior angles of regular convex polygons with and without measuring the angles with a protractor. (8G1) Make and test conjectures about characteristics and properties (e.g., sides, angles, symmetry) of two-dimensional figures and three- dimensional objects. (8G2) Recognize the angles formed and the relationship between the angles when two lines intersect and when parallel lines are cut by a transversal. (8G4) Represent and analyze shapes using coordinate geometry; e.g., given three vertices and the type of quadrilateral, find the coordinates of the fourth vertex. (8G5) Draw the results of translations, reflections, rotations and dilations of objects in the coordinate plane, and determine properties that remain fixed; e.g., lengths of sides remain the same under translations. (9G3) Analyze two-dimensional figures in a coordinate plane; e.g., use slope and distance formulas to show that a quadrilateral is a parallelogram. (10G8) Derive coordinate rules for translations, reflections and rotations of geometric figures in the coordinate plane. (10G9) Show and describe the results of combinations of translations, reflections and rotations (compositions); e.g., perform compositions and specify the result of a composition as the outcome of a single motion, when applicable.

KNOW • Angle measurements • Polygons • Symmetry • Coordinate plane

DO • Find missing angles in triangles

and quadrilaterals and classify them by their angles and sides

• Identify congruent polygons • Identify line symmetry and

rotational symmetry • Graph reflections, rotations and

translations on a coordinate plane.

PRE-ASSESSMENT:

Prerequisite Skills pp 255, 260, 265, 270, 275, 289, 294, 299

ASSESSMENT: Study Guide pp 306-308 Practice test pp 309 Multiple-choice test: Forms 1, 2A, 2B, CRM pgs 353-358 Free-response test 2C, 2D, 3, CRM pgs 359, 364


TESTING SKILL(S) & OR SAMPLE OGT TYPE QUESTIONS: OH 20, OH21 , OH Pg 260, #40-46 Pg 265, #34-39 Pg 270, #21-30 Pg 275, #35-41 Pg 282, #25-30 Pg 284, #9-10 Pg 289, #23-26 Pg 294, #30-37 Pg 299, #16-20 Pg 309, #20


RESOURCES: Parent and Student Study guide 5-Minute check transparencies Key Teaching Transparencies MathPASS: Tutorial Plus

Teaching Mathematics with Manipulatives Study guide and Interventions pp 307, 312, 317, 322, 327, 332, 337, 342, 347 Practice (Skills and Word Problems) Pgs 308, 313, 318, 323, 328, 333, 338, 343, 348 Reading to Learn Math Pg 310, 315, 320, 325, 330, 335, 340, 345, 350 Enrichment 311, 316, 321, 326, 331, 336, 341, 346, 351


HISTORICAL/MODERN LINK: Art pg 268 Folk Art pg 301 Carpenter pg 258

STANDARD: Number, Number Sense and Operations BENCHMARK: (G) Estimate, compute, and solve problems involving real numbers, including ratio, proportion and percent, and explain solutions. STANDARD: Measurement BENCHMARK: (A) Solve increasingly complex non-routine measurement problems and check for reasonableness of results., (B) Use formulas to find surface area and volume for specified three-dimensional objects accurate to a specified level of precision. (C) Apply indirect measurement techniques, tools and formulas, as appropriate, to find perimeter, circumference and area of circles, triangle, quadrilaterals and composite shapes and to find volume of prisms, cylinders and pyramids. (D) Use proportional reasoning and apply indirect measurement techniques, including right triangle trigonometry and properties of similar triangles, to solve problems involving measurements and rates. (E) Estimate and compute various attributes, including length, angle measure, area, surface area and volume, to a specified level of precision. STANDARD: Geometry BENCHMARK: (B) Describe and apply the properties of similar and congruent figures; and justify conjectures involving similarity and congruence. (E) Draw and construct representations of two-and three-dimensional geometric objects using a variety of tools, such as straightedge, compass and technology. TOPIC/UNIT: Chapter 7 Time Line: 3 Weeks Indicators: (8N5) Determine when an estimate is sufficient and when an exact answer is needed in problem situations, and evaluate estimates in relation to actual answers; e.g., very close, less than, greater than. (8M3) Use appropriate levels of precision when calculating with measurements. (8M4) Derive formulas for surface area and volume and justify them using geometric models and common materials. For example, find: a. the surface area of a cylinder as a function of its height and radius; b. that the volume of a pyramid (or cone) is one-third of the volume of a prism (or cylinder) with the same base area and height. (8M5) Determine surface area for pyramids by analyzing their parts. (8M7) Apply proportional reasoning to solve problems involving indirect measurements or rates. (8M9) Demonstrate

understanding of the concepts of perimeter, circumference and area by using established formulas for triangles, quadrilaterals, and circles to determine the surface area and volume of prisms, pyramids, cylinders, spheres and cones. (Note: Only volume should be calculated for spheres and cones.) (8M10) Use conventional formulas to find the surface area and volume of prisms, pyramids and cylinders and the volume of spheres and cones to a specified level of precision. (8G3) Use proportions in several forms to solve problems involving similar figures (part-to-part, part-to-whole, corresponding sides between figures). (8G6) Draw nets for a variety of prisms, pyramids, cylinders and cones. KNOW

• Area, volume, surface area • 2D and 3D figures

DO • Find the areas of

parallelograms, trapezoids, triangles and complex figures

• Identify and draw three-dimensional figures

• Find the volumes and surface area of pyramids and cones

• Analyze measurements

PRE-ASSESSMENT: Prerequisite Skills pp 313, 334, 339, 345, 351



TESTING SKILL(S) & OR SAMPLE OGT TYPE QUESTIONS: OH22 , OH23 Pg 318, #29-33 Pg 323, #33-37 Pg 329, #21-25 Pg 334, #23-28 Pg 339, #37-44

Pg 340, #11-12 Pg 345, #30-33 Pg 351, #33-37 Pg 355, #25-28 Pg 362, #45-52 Pg 367, #16


RESOURCES: Parent and Student Study guide 5-Minute check transparencies Key Teaching Transparencies MathPASS: Tutorial Plus Teaching Mathematics with Manipulatives Study guide and Interventions pp 377, 382, 387, 392, 397, 4402, 407, 412, 417 Practice (Skills and Word Problems) Pgs 378, 383, 388, 393, 398, 403, 408, 413, 418 Reading to Learn Math Pg 380, 385, 390, 395, 400, 405, 410, 415, 420 Enrichment 381, 386, 391, 396, 401, 406, 411, 416, 421


HISTORICAL/MODERN LINK: Landscape Architecture 316 Architecture 322 Pyramids 343 Skateboarding 348

STANDARD: Data Analysis and Probability BENCHMARK: (E) Evaluate the validity of claims and predictions that are based on data by examining the appropriateness of the data collection and analysis. (G) Describe sampling methods and analyze the effects of method chosen on how well the resulting sample represents the population. (H) Use counting techniques, such as permutations and combinations, to determine the total number of options and possible outcomes. (J) Compute probabilities of compound events, independent events, and simple dependent events. TOPIC/UNIT: Chapter 8 Time Line: 3 Weeks Indicators: (8D7) Identify different ways of selecting samples, such as survey response, random sample, representative sample and convenience sample. (8D8) Describe how the relative size of a sample compared to the target population affects the validity of predictions. (8D10) Calculate the number of possible outcomes for a situation, recognizing and accounting for when items may occur more than once or when order is important. (8D11) Demonstrate an understanding that the probability of either of two disjoint events occurring can be found by adding the probabilities for each and that the probability of one independent event following another can be found by multiplying the probabilities. (9D5) Describe characteristics and limitations of sampling methods, and analyze the effects of random versus biased sampling; e.g., determine and justify whether the sample is likely to be representative of the population. (9D7) Use counting techniques and the Fundamental Counting principle to determine the total number of possible outcomes for mathematical situations. (9D9) Identify situations involving independent and dependent events, and explain differences between, and common misconceptions about, probabilities associated with those events.

KNOW • Probability • Permutations, Combinations • Dependent and independent

events • Samples

DO • Find the probability of a simple

event • Find number of permutations

and combinations of objects • Find probability of independent

and dependent events • Predict actions of large group

by using a sample

PRE-ASSESSMENT: Prerequisite Skills pp 373, 383, 387, 391, 399, 403



TESTING SKILL(S) & OR SAMPLE OGT TYPE QUESTIONS: OH24 , OH25 Pg 377, #31-37 Pg 383, #25-31 Pg 387, #35-42 Pg 391, #34-40 Pg 394, #19-20 Pg 399, #28-34 Pg 403, #24-28 Pg 409, #22-24 Pg 413, #20


RESOURCES: Parent and Student Study guide 5-Minute check transparencies Key Teaching Transparencies MathPASS: Tutorial Plus Teaching Mathematics with Manipulatives

Study guide and Interventions pp 445, 450, 455, 460, 465, 470, 475 Practice (Skills and Word Problems) Pgs 446, 451, 456, 461, 466, 471, 476 Reading to Learn Math Pg 448, 453, 458, 463, 468, 473, 478 Enrichment 449, 454, 459,464, 469, 474, 479


HISTORICAL/MODERN LINK: Communications 381 Music 389 Populations 397 Marketing 401

STANDARD: Patterns, Functions and Algebra BENCHMARK: (D) Use algebraic representation, such as tables, graphs, expressions, functions and inequalities, to model and solve problem situations. (F) Solve and graph linear equations and inequalities. STANDARD: Data Analysis and Probability BENCHMARK: (A) Create, interpret and use graphical displays and statistical measures to describe data; e.g., box-and-whisker plots, histograms, scatter plots, measures of center and variability. (B) Evaluate different graphical representations of the same data to determine which is the most appropriate representation for an identified purpose (C) Compare the characteristics of the mean, median, and mode for a given set of data, and explain which measure of center best represents the data (D) Find, use and interpret measures of center and spread, such as mean and quartiles, and use those measures to compare and draw conclusions about sets of data. TOPIC/UNIT: Chapter 9 Time Line: 3 Weeks Indicators: (8P7) Use symbolic algebra (equations and inequalities), graphs and tables to represent situations and solve problems. (9P6) Write and use equivalent forms of equations and inequalities in problem situations; e.g., changing a linear equation to the slope- intercept form. (8D1) Use, create and interpret scatterplots and other types of graphs as appropriate. (8D2) Evaluate different graphical representations of the same data to determine which is the most appropriate representation for an identified purpose; e.g., line graph for change over time, circle graph for part-to-whole comparison, scatterplot for relationship between two variants. (8D3) Differentiate between discrete and continuous data and appropriate ways to represent each. (8D4) Compare two sets of data using measures of center (mean, mode, median) and measures of spread (range, quartiles, interquartile range, percentiles). (8D5) Explain the mean's sensitivity to extremes and its use in comparison with the median and mode. (8D9) Construct convincing arguments based on analysis of data and interpretation of graphs. (9D2) Create a scatterplot for a set of bivariate data, sketch the line of best fit, and interpret the slope of the line of best fit. (10D1) Describe measures of center and the range verbally, graphically and algebraically. (10D2)

Represent and analyze bivariate data using appropriate graphical displays (scatterplots, parallel box-and-whisker plots, histograms with more than one set of data, tables, charts, spreadsheets) with and without technology. KNOW

• Histograms • Circle graphs • Measures of Center • Matrices •

DO • Construct and interpret

histograms and circle graphs • Find the mean, median, mode,

range and quartiles of a set of data

• Recognize when graphs and statistics are misleading

• Use matrices to organize data

PRE-ASSESSMENT: Prerequisite Skills pp 417, 424, 429, 433, 438, 445, 449, 453



TESTING SKILL(S) & OR SAMPLE OGT TYPE QUESTIONS: OH26 , OH27 Pg 424, #24-35 Pg 429, #13-16 Pg 433, #16-18 Pg 438, #20-24 Pg 440, #9-10 Pg 445, #26-30 Pg 449, #20-26 Pg 453, #14-22 Pg 457, #21-26 Pg 461, #16


RESOURCES: Parent and Student Study guide 5-Minute check transparencies Key Teaching Transparencies MathPASS: Tutorial Plus Teaching Mathematics with Manipulatives Study guide and Interventions pp 501, 506, 511, 516, 521, 526, 531, 536 Practice (Skills and Word Problems) Pgs 502, 507, 512, 517, 522, 527, 532, 537 Reading to Learn Math Pg 504, 509, 514, 519, 524, 529, 534, 539 Enrichment 505, 10, 515, 520, 525, 530, 535, 540


HISTORICAL/MODERN LINK: History 421 History 427 Cell Phones 431 Dietician 437 Geography 436 Roller Coasters 451

STANDARD: Patterns, Functions and Algebra BENCHMARK: (D) Use algebraic representation, such as tables, graphs, expressions, functions and inequalities, to model and solve problem situations. (F) Solve and graph linear equations and inequalities. TOPIC/UNIT: Chapter 10 Time Line: 3 Weeks Indicators: (8P7) Use symbolic algebra (equations and inequalities), graphs and tables to represent situations and solve problems. (9P6) Write and use equivalent forms of equations and inequalities in problem situations; e.g., changing a linear equation to the slope- intercept form. KNOW

• Solve equations • Graph equations • Solve inequalities • Graph inequalities

DO • Solve two-step equations • Solve equations with variables

on both sides • Write and graph inequalities • Solve inequalities by using the

addition, subtraction, multiplication or division properties of inequality

PRE-ASSESSMENT:

Prerequisite Skills pp 467, 473, 477, 481, 487, 495, 499



TESTING SKILL(S) & OR SAMPLE OGT TYPE QUESTIONS: OH28 , OH29 Pg 473, #55-62 Pg 477, #46-52 Pg 481, #22-33 Pg 487, #37-44 Pg 490, #19-20

Pg 495, #45-51 Pg 499, #52-59 Pg 504, #47-54 Pg 507, #20


RESOURCES: Parent and Student Study guide 5-Minute check transparencies Key Teaching Transparencies MathPASS: Tutorial Plus Teaching Mathematics with Manipulatives Study guide and Interventions pp 563, 568, 573, 578, 583, 588, 593 Practice (Skills and Word Problems) Pgs 564, 569, 574, 579, 584 589, 594 Reading to Learn Math Pg 566, 571, 576, 581, 586, 591, 596 Enrichment 567, 572, 577, 582, 587, 592, 597


HISTORICAL/MODERN LINK: Food 471 Fundraising 479 Animals 497 Work 502

STANDARD: Patterns, Functions and Algebra BENCHMARK: (A) Generalize and explain patterns and sequences in order to find the next term and the nth term., (B) Identify and classify functions as linear or nonlinear, and contrast their properties using tables, graphs or equations., (C) Translate information from one representation (words, table, graph or equation) to another representation of a relation or function., (D) Use algebraic representations, such as tables, graphs, expressions, functions and inequalities, to model and solve problem situations., (E) Analyze and compare functions and their graphs using attributes, such as rates of change, intercepts and zeros., (F) Solve and graph linear equations and inequalities., (H) Solve systems of linear equations involving two variables graphically and symbolically., (I) Model and solve problem situations involving direct and inverse variation., (J) Describe and interpret rates of change from graphical and numerical data. STANDARD: Data Analysis and Probability BENCHMARK: (A) Create, interpret and use graphical displays and statistical measures to describe data; e.g., box-and-whisker plots, histograms, scatter plots, measures of center and variability. (F) Construct convincing arguments based on analysis of data and interpretation of graphs. TOPIC/UNIT: Chapter 11 Time Line: 3 weeks Indicators: (8P7) Use symbolic algebra (equations and inequalities), graphs and tables to represent situations and solve problems. (8P1) Relate the various representations of a relationship; i.e., relate a table to graph, description and symbolic. (8P2) Generalize patterns and sequences by describing how to find the nth term. (8P3) Identify functions as linear or nonlinear based on information given in a table, graph or equation. (8P4) Extend the uses of variables to include covariants where y depends on x. (8P6) Describe the relationship between the graph of a line and its equation, including being able to explain the meaning of slope as a constant rate of change and y-intercept in real-world problems. (8P9) Solve linear equations and inequalities graphically, symbolically and using technology. (8P10) Solve 2 by 2 systems of linear equations graphically and by simple substitution. (8P11) Interpret the meaning of the solution of a 2 by 2 system of equations; i.e., point, line, no solution. (8P13) Compute and interpret slope, midpoint and distance given a set of ordered pairs. (8P15) Describe and

compare how changes in an equation affects the related graphs; e.g., for a linear equation changing the coefficient of x affects the slope and changing the constant affects the intercepts. (8D6) Make conjectures about possible relationship in a scatterplot and approximate line of best fit. (9P6) Write and use equivalent forms of equations and inequalities in problem situations; e.g., changing a linear equation to the slope- intercept form. (9P2) Generalize patterns using functions or relationships (linear, quadratic and exponential), and freely translate among tabular, graphical and symbolic representations. (9P3) Describe problem situations (linear, quadratic and exponential) by using tabular, graphical and symbolic representations. (9P5) Describe and compare characteristics of the following families of functions: linear, quadratic and exponential functions; e.g., general shape, number of roots, domain, range, rate of change, maximum or minimum. (9P9) Solve and interpret the meaning of 2 by 2 systems of linear equations graphically, by substitution and by elimination, with and without technology. (9P14) Describe the relationship between slope and the graph of a direct variation and inverse variation. (9P15) Describe how a change in the value of a constant in a linear or quadratic equation affects the related graphs. (9D2) Create a scatterplot for a set of bivariate data, sketch the line of best fit, and interpret the slope of the line of best fit. KNOW

• Functions • Graph functions • Slope and y-intercept • Graph inequalities

DO • Complete function tables • Graph linear functions by using

function tables • Graph linear equations using the

slope and y-intercept • Graph linear inequalities

PRE-ASSESSMENT: Prerequisite Skills pp 511, 515, 520, 525, 529, 536, 542, 547



TESTING SKILL(S) & OR SAMPLE OGT TYPE QUESTIONS: OH30 , OH31 , OH Pg 515, #34-40 Pg 520, #27-33 Pg 525, #27-32 Pg 529, #30-36 Pg 530, #14-15 Pg 536, #40-45 Pg 538, #5-9 Pg 542, #23-28 Pg 547, #36-42 Pg 551, #27-37 Pg 555, #20


RESOURCES: Parent and Student Study guide 5-Minute check transparencies Key Teaching Transparencies MathPASS: Tutorial Plus Teaching Mathematics with Manipulatives Study guide and Interventions pp 619, 624, 629, 634, 639, 644, 649, 654 Practice (Skills and Word Problems) Pgs 620, 625, 630, 635, 640, 645, 650, 655 Reading to Learn Math Pg 622, 627, 632, 637, 642, 647, 652, 657 Enrichment 623, 628, 633, 638, 643, 648, 653, 658


HISTORICAL/MODERN LINK: Zoo Keeper 518 Advertising 534 Lakes 540 Money matters 545 Fairs 549

STANDARD: Patterns, Functions and Algebra BENCHMARK: (A) Generalize and explain patterns and sequences in order to find the next term and the nth term., (B) Identify and classify functions as linear or nonlinear, and contrast their properties using tables, graphs or equations., (C) Translate information from one representation (words, table, graph or equation) to another representation of a relation or function., (D) Use algebraic representations, such as tables, graphs, expressions, functions and inequalities, to model and solve problem situations., (E) Analyze and compare functions and their graphs using attributes, such as rates of change, intercepts and zeros., (F) Solve and graph linear equations and inequalities., (I) Model and solve problem situations involving direct and inverse variation., (J) Describe and interpret rates of change from graphical and numerical data. TOPIC/UNIT: Chapter 12 Time Line: 3 weeks Indicators: (8P1) Relate the various representations of a relationship; i.e., relate a table to graph, description and symbolic form. (9P2) Generalize patterns using functions or relationships (linear, quadratic and exponential), and freely translate among tabular, graphical and symbolic representations. (9P3) Describe problem situations (linear, quadratic and exponential) by using tabular, graphical and symbolic representations. (8P3) Identify functions as linear or nonlinear based on information given in a table, graph or equation. (9P5) Describe and compare characteristics of the following families of functions: linear, quadratic and exponential functions; e.g., general shape, number of roots, domain, range, rate of change, maximum or minimum. (8P5) 8 Use physical models to add and subtract monomials and polynomials, and to multiply a polynomial by a monomial. (9P11) Add, subtract, multiply and divide monomials and polynomials (division of polynomials by monomials only). (8P7) Use symbolic algebra (equations and inequalities), graphs and tables to represent situations and solve problems. (9P6) Write and use equivalent forms of equations and inequalities in problem situations; e.g., changing a linear equation to the slope- intercept form. (8P14) Differentiate and explain types of changes in mathematical relationships, such as linear vs. nonlinear, continuous vs. noncontinuous, direct variation vs. inverse variation. (9P13) Model and solve problems involving direct and inverse variation using proportional reasoning. (8P15)

Describe and compare how changes in an equation affects the related graphs; e.g., for a linear equation changing the coefficient of affects the slope and changing the constant affects the intercepts. (9P15) Describe how a change in the value of a constant in a linear or quadratic equation affects the related graphs. KNOW

• Linear and nonlinear functions • Polynomials

DO • Determine whether a function

is linear or nonlinear • Graph quadratic functions • Add and subtract polynomials • Multiply monomials and

polynomials

PRE-ASSESSMENT: Prerequisite Skills pp 559, 563, 568, 573, 577, 583, 587

ASSESSMENT: Study Guide pp 593,-594 Practice test pp 595 Multiple-choice test: Forms 1, 2A, 2B, CRM pgs 715-720 Free-response test 2C, 2D, 3, CRM pgs 721-726


TESTING SKILL(S) & OR SAMPLE OGT TYPE QUESTIONS: OH32 Pg 563, #33-40 Pg 568, #39-48 Pg 573, #39-45 Pg 577, #42-52 Pg 578, #19-20 Pg 583, #42-48 Pg 587, #50-58 Pg 592, #28-34 Pg 595, #25


RESOURCES: Parent and Student Study guide 5-Minute check transparencies Key Teaching Transparencies MathPASS: Tutorial Plus Teaching Mathematics with Manipulatives Study guide and Interventions pp 679, 684, 689, 694, 699, 704, 709 Practice (Skills and Word Problems) Pgs 680, 685, 690, 695, 700, 705, 710 Reading to Learn Math Pg 682, 687, 692, 697, 702, 707, 712 Enrichment 683, 688, 693, 698, 703, 708, 713


HISTORICAL/MODERN LINK: Basketball 561 Monuments 566 Automotive Engineer 581 Sound 585

10th grade math special education course of study · 10th grade math special education course of...

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