Grade 6 Advanced Math Guide for GT

Overview

This overview provides only the highlights of the new learning that should take place at the sixth-grade level. The specific skills and subject matter that sixth graders should be taught in each of the five mathematical strands are set forth in the formal standards and indicators for these strands. To alert educators as to when the progression in learning should occur for students in this grade, specific language is used with certain indicators: 16 An indicator beginning with the phrase “Generate strategies” addresses a concept that is being formally introduced for the first time, and students must therefore be given experiences that foster conceptual understanding. 17 An indicator beginning with the phrase “Apply an algorithm,” “Apply a procedure,” “Apply procedures,” or “Apply formulas” addresses a concept that has been introduced in a previous grade: students should already have the conceptual understanding, and the goal must now be fluency. 18 An indicator beginning with the phrase “Apply strategies and formulas” or “Apply strategies and procedures” addresses a concept that is being formally introduced for the first time, yet the goal must nonetheless be that students progress to fluency.

Highlights of the new learning for grade-six students are  understanding the concepts of percentages and integers,  comparing rational numbers and percentages,  applying an algorithm to add and subtract fractions,  generating strategies to multiply and divide fractions and decimals,  understanding the concepts of exponents and powers of ten,  applying order of operations,  using inverse operations to solve one-step equations,  representing location of points in all four quadrants,  constructing two-dimensional shapes with rotational symmetry,  classifying shapes as similar,  identifying pairs of angles that are complementary or supplementary,  applying strategies and formulas to approximate circumference and area of a circle,  applying strategies and procedures to estimate and determine perimeters and areas of irregular shapes,  using proportions to determine unit rates,  using a scale to determine distance, and  applying procedures to calculate the probability of complementary events. GRADE 6 ADVANCED MATH GUIDE FOR GT Mathematical Processes

The mathematical processes provide the framework for teaching, learning, and assessing in mathematics at all grade levels. Instructional programs should be built around these processes.

Standard 6-1: The student will understand and utilize the mathematical processes of problem solving, reasoning and proof, communication, connections, and representation.

The indicators for this standard, which are appropriate for grades six though eight, are adapted from Principles and Standards for School Mathematics (NCTM 2000). Classroom application should be based on the standard and its indicators; the mathematical goals for the class; and the skills, needs, and understandings of the particular students.

Indicators 6-1.1 Generate and solve complex abstract problems that involve modeling physical, social, and/or mathematical phenomena. 6-1.2 Evaluate conjectures and pose follow-up questions to prove or disprove conjectures. 6-1.3 Use inductive and deductive reasoning to formulate mathematical arguments. 6-1.4 Understand equivalent symbolic expressions as distinct symbolic forms that represent the same relationship. 6-1.5 Generalize mathematical statements based on inductive and deductive reasoning. 6-1.6 Use correct and clearly written or spoken words, variables, and notations to communicate about significant mathematical tasks. 6-1.7 Generalize connections among a variety of representational forms and real-world situations. 6-1.8 Use standard and nonstandard representations to convey and support mathematical relationships.

Unitedstreaming.com Grades 6 - 8 Search – math problem solving –14 lessons math reasoning—3 lessons math proofs—1 lesson math communications—6 lessons math connections—1 lesson math representation—7 lessons

GRADE 6 ADVANCED MATH GUIDE FOR GT Number and Operations

Standard 6-2: The student will demonstrate through the mathematical processes an understanding of the concepts of whole-number percentages, integers, and ratio and rate; the addition and subtraction of fractions; accurate, efficient, and generalizable methods of multiplying and dividing fractions and decimals; and the use of exponential notation to represent whole numbers.

Indicators  Lesson Plans Diagnostic Tests  Challenge the PACT Workbook Pages 1 – 11  Buckle Down PACT Form A 6-2.1 Understand whole-number  Fantastic Five percentages through 100.  Buckle Down PACT Pages 49 – 51  PACT Workbook Pages 5 – 6 6-2.2 Understand integers.  Fantastic Five  Buckle Down PACT Pages 9 – 10  PACT Workbook Pages 13 – 14  Challenge the PACT Workbook Pages 112 – 123  Glencoe Lesson 11-1  Lesson 11-1 Power Point  Subtracting Integers Power Point  Integers Power Point  Integers Power Point  Integers Power Point  Adding and Subtracting Integers Review Power Point  Integers Review Power Point  Integers Study Guide  Integers Test  Unitedstreaming.com Grade 6-8 (Page 1 – 9 lessons) 6-2.3 Compare rational numbers and  Fantastic Five whole-number percentages through 100 by  Buckle Down PACT Pages 30 – 32 using the symbols ≤, ≥, <, >, and =.  Buckle Down PACT Pages 41 – 42  PACT Workbook Pages 3 – 4  Challenge the PACT Workbook Page 39  Challenge the PACT Workbook Pages 116 – 117  Glencoe Lesson 3-3  Glencoe Lesson 5-8  Glencoe Lesson 11-2  Lesson 3-3 Power Point  Lesson 5-8 Power Point  Lesson 11-2 Power Point  Unitedstreaming.com Grade 6-8 Search – inequalities (6 lessons) 6-2.4 Apply an algorithm to add and  Fantastic Five subtract fractions.  Buckle Down PACT Pages 33 – 34  Challenge the PACT Workbook Pages 57 – 67  Glencoe Lesson 6-3  Glencoe Lesson 6-4  Glencoe Lesson 6-5  Glencoe Lesson 6-6  Lesson 6-4 Power Point  Lesson 6-5 Power Point  Lesson 6-6 Power Point  Simplifying Fractions Power Point  Mixed Numbers Power Point  Improper Fractions Power Point  Unitedstreaming.com Grade 6 - IIIA1(2 lessons) 6-2.5 Generate strategies to multiply and  Fantastic Five divide fractions and decimals.  Buckle Down PACT Pages 35 – 40  Buckle Down PACT 45 – 48  Challenge the PACT Workbook Pages 42 – 44  Challenge the PACT Workbook Pages 68 – 72  Glencoe Lesson 4-1  Glencoe Lesson 4-3  Glencoe Lesson 4-5  Glencoe Lesson 4-6  Glencoe Lesson 4-7  Glencoe Lesson 7-2  Glencoe Lesson 7-3  Glencoe Lesson 7-5  Glencoe Lesson 7-6  Lesson 4-1 Power Point  Lesson 4-3 Power Point  Lesson 4-5 Power Point  Lesson 4-6 Power Point  Lesson 4-7 Power Point  Lesson 7-2 Power Point  Lesson 7-3 Power Point  Lesson 7-5 Power Point  Lesson 7-6 Power Point  Unitedstreaming.com Grade 6-8 Search – * & / fractions (3 lessons) 6-2.6 Understand the relationship  Fantastic Five between ratio/rate and  PACT Workbook Pages 7 – 8 multiplication/division.  Challenge the PACT Workbook Pages 52 – 56  Glencoe Lesson 8-1  Lesson 8-1 Power Point  Ratio Power Point  Unitedstreaming.com Grade 6-8 Search – ratios :Page 1 (4 lessons) 6-2.7 Apply strategies and procedures to  Fantastic Five determine values of powers of 10, up to  Buckle Down PACT Pages 18 – 19 106.  PACT Workbook Pages 9 – 10  Exponents (Powers of Ten) Power Point  Unitedstreaming.com Grade 6-8 Search – exponents (First 7 lessons) 6.2.8 Represent the prime factorization of  Fantastic Five numbers by using exponents.  Buckle Down PACT Pages 20 – 23  Challenge the PACT Workbook Pages 152 – 154  Glencoe Lesson 5-2  Lesson 5-2 Power Point  Prime Factor Tree Power Point  Divisibility Rules Power Point  Exponents Power Point  Prime and Composite Numbers Power Point  Unitedstreaming.com Grade 6-8 Search – prime factorization (2 lessons) 6-2.9 Represent whole numbers in  Fantastic Five exponential form.  Glencoe Lesson 1-6 Additional Number and Operations  Fantastic Five Indicators  Challenge the PACT Workbook Pages 48 – 51  PACT Workbook Pages 1 – 2, 11 – 12,  15 – 16, 19 – 20, 25 – 26, 27 – 28 GRADE 6 ADVANCED MATH GUIDE FOR GT Algebra

Standard 6-3: The student will demonstrate through the mathematical processes an understanding of writing, interpreting, and using mathematical expressions, equations, and inequalities.

Indicators Lesson Plans 6-3.1 Analyze numeric and algebraic  Fantastic Five patterns and pattern relationships.  Buckle Down PACT Pages 93 – 98  PACT Workbook Pages 29 – 30  Glencoe Lesson 1-2  Glencoe Lesson 7-8  Lesson 7-8 Power Point  Unitedstreaming.com Grade 6 – Search patterns—3 choices 6-3.2 Apply order of operations to  Fantastic Five simplify whole-number expressions.  Buckle Down PACT Pages 24 – 25  PACT Workbook Pages 31 – 32  Challenge the PACT Workbook Pages 98 – 100  Glencoe Lesson 1-4  Unitedstreaming.com Grade 6 – Search order of operations—1 choice 6-3.3 Represent algebraic relationships  Fantastic Five with variables in expressions, simple  Buckle Down PACT Pages 82 – 85 equations, and simple inequalities.  Glencoe Lesson 1-5  Unitedstreaming.com Grade 6 – Search equations—1 choice 6-3.4 Use the commutative, associative,  Fantastic Five and distributive properties to show that two  Buckle Down PACT Pages 78 – 81 expressions are equivalent.  Glencoe Lesson 4-2  PACT Workbook Pages 17 – 18  PACT Workbook Pages 35 – 36  Challenge the PACT Workbook Pages 107 – 111  Lesson 4-2 Power Point  Properties Power Point  Properties Power Point  Properties Review Power Point  Properties Study Guide  Properties Practice Test  Properties Test  Unitedstreaming.com Grade 6 – Search order of operations—1 choice 6-3.5 Use inverse operations to solve  Fantastic Five one-step equations that have whole-number  Glencoe Lesson 12-1 solutions and variables with whole-number  Glencoe Lesson 12-2 coefficients.  Glencoe Lesson 12-3  Lesson 12-1 Power Point  Lesson 12-2 Power Point  Lesson 12-3 Power Point  Unitedstreaming.com Grade 6 – Search equations—1 choice Additional Algebra Indicators  Fantastic Five  Challenge the PACT Workbook Pages 124 – 130, 131, 132 – 139  PACT Workbook Pages 33 – 34, 37 – 38 GRADE 6 ADVANCED MATH GUIDE FOR GT Geometry

Standard 6-4: The student will demonstrate through the mathematical processes an understanding of shape, location, and movement within a coordinate system; similarity, complementary, and supplementary angles; and the relationship between line and rotational symmetry.

Indicators Lesson Plans 6-4.1 Represent with ordered pairs of  Fantastic Five integers the location of points in a  Challenge the PACT Workbook coordinate grid. Pages 247 – 256  Glencoe Lesson 2-9  Glencoe Lesson 11-7  Lesson 2-9 Power Point  Lesson 11-7 Power Point  Battlegraph Power Point 6-4.2 Apply strategies and procedures to  Fantastic Five find the coordinates of the missing vertex  Buckle Down PACT Pages 126 – of a square, rectangle, or right triangle 128 when given the coordinates of the  PACT Workbook Pages 47 – 48 polygon’s other vertices. 6-4.3 Generalize the relationship between  Fantastic Five line symmetry and rotational symmetry for  Buckle Down PACT Pages 120 – two-dimensional shapes. 122  Symmetry Power Point 6.4.4 Construct two-dimensional shapes  Fantastic Five with line or rotational symmetry.  PACT Workbook Pages 43 – 44 6-4.5 Identify the transformation(s) used  Fantastic Five to move a polygon from one location to  Buckle Down PACT Pages 117 – another in the coordinate plane. 119 6-4.6 Explain how transformations affect  Fantastic Five the location of the original polygon in the  Buckle Down PACT Pages 129 – coordinate plane. 133  PACT Workbook Pages 51 – 52 6-4.7 Compare the angles, side lengths,  Fantastic Five and perimeters of similar shapes.  Buckle Down PACT Pages 113 – 114  PACT Workbook Pages 41 – 42 6-4.8 Classify shapes as similar.  Fantastic Five  Buckle Down PACT Pages 111 – 112  PACT Workbook Pages 45 – 46  Glencoe Lesson 9-6  Lesson 9-6 Power Point 6-4.9 Classify pairs of angles as either  Fantastic Five complementary or supplementary.  Glencoe Lesson 9-1  Lesson 9-1 Power Point Additional Geometry Indicators  Fantastic Five  Challenge the PACT Workbook Pages 172 – 174  PACT Pages 39 – 40, 49 – 50, 53 – 54, 55 – 56, 57 – 58, 59 – 60 GRADE 6 ADVANCED MATH GUIDE FOR GT Measurement

Standard 6-5: The student will demonstrate through the mathematical processes an understanding of surface area; the perimeter and area of irregular shapes; the relationships among the circumference, diameter, and radius of a circle; the use of proportions to determine unit rates; and the use of scale to determine distance.

Indicators Lesson Plans 6-5.1 Explain the relationships among the  Fantastic Five circumference, diameter, and radius of a  Glencoe Lesson 7-4 circle.  Unitedstreaming.com Grade 6 – Search circumference—1 choice 6-5.2 Apply strategies and formulas with  Fantastic Five 22  Challenge the PACT Workbook an approximation of pi (3.14, or 7 ) to Pages 235 – 240 find the circumference and area of a circle.  Glencoe Lesson 7-4  Glencoe Lesson 10-3  Lesson 10-3 Power Point  Circle Study Guide  Circle Test 6-5.3 Generate strategies to determine the  Fantastic Five surface area of a rectangular prism and a  Challenge the PACT Workbook cylinder. Pages 212 – 219  Glencoe Lesson 10-6  Lesson 10-6 Power Point 6-5.4 Apply strategies and procedures to  Fantastic Five estimate the perimeters and areas of  PACT Workbook Pages 67 - 68 irregular shapes. 6.5.5 Apply strategies and procedures of  Fantastic Five combining and subdividing to find the  Buckle Down PACT Pages 163 – perimeters and areas of irregular shapes. 165  Buckle Down PACT Pages 169 – 171 6.5.6 Use proportions to determine unit  Fantastic Five rates. 6-5.7 Use a scale to determine distance.  Fantastic Five  Buckle Down PACT Pages 152 – 153 6-5.7 Use a scale to determine distance.  Fantastic Five  PACT Workbook Pages 75 - 76  Challenge the PACT Workbook Pages 196 – 198  Glencoe Lesson 8-3  Lesson 8-3 Power Point Additional Measurement Indicators  Fantastic Five  PACT Workbook Pages 61 - 62, 62 – 63, 65 – 66, 69 – 70, 71 – 72, 73 - 74 GRADE 6 ADVANCED MATH GUIDE FOR GT Data Analysis and Probability

Standard 6-6: The student will demonstrate through the mathematical processes an understanding of the relationships within one population or sample.

Indicators Lesson Plans 6.6.1 Predict the characteristics of one  Fantastic Five population based on the analysis of sample  Navigating through Data Analysis data. Chapter 4  Navigating through Probability Chapter 3  Unitedstreaming.com Grade 6 – IVB2 Page 10 of 10 (1 lesson) 6-6.2 Organize data in frequency tables,  Fantastic Five histograms, or stem-and-leaf plots as  Navigating through Data Analysis appropriate. Chapters 1 and 2  Buckle Down PACT Pages 193 – 196  Glencoe Lesson 2-1  Glencoe Lesson 2-2  Glencoe Lesson 2-6  Lesson 2-2 Power Point  Unitedstreaming.com Grade 6 – IB1 Page 9 of 10 (5 lessons) 6-6.3 Analyze which measure of central  Fantastic Five tendency (mean, median, or mode) is the  Navigating through Data Analysis most appropriate for a given purpose. Chapter 2  Buckle Down PACT Pages 185 – 190  Challenge the PACT Workbook Pages257 – 268  Glencoe Lesson 2-7 (teacher integrate own questions)  Lesson 2-7 Power Point  Mean, Median, Mode Power Point  Unitedstreaming.com Grade 6 – IIA1 Page 9 of 10 (2 lessons) 6-6.4 Use theoretical probability to  Fantastic Five determine the sample space and probability  Navigating through Probability for one- and two-stage events such as tree Chapters 1, 2, 3, and 4 diagrams, models, lists, charts, and  Buckle Down PACT Pages 199 – pictures. 201  Buckle Down PACT Pages 204 – 207  Challenge the PACT Workbook Pages 269 - 277  Glencoe Lesson 13-1  Glencoe Lesson 13-4  Lesson 13-1 Power Point  Lesson 13-4 Power Point  Unitedstreaming.com Grade 6 – IIIB Page 9 of 10 (2 lessons)  Unitedstreaming.com Grade 6 – IVB1 Page 10 of 10 (1 lesson) 6-6.5 Apply procedures to calculate the  Fantastic Five probability of complementary events.  Navigating through Probability Chapter 4  Buckle Down PACT Pages 202 - 203

Unitedstreaming.com Grade 6 – Data Analysis and Probability Standard 6-6 Search statistics and data analysis—1 choice BrainPop

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Overview

This overview provides only the highlights of the new learning that should take place at the seventh-grade level. The specific skills and subject matter that seventh graders should be taught in each of the five mathematical strands are set forth in the formal standards and indicators for these strands. To alert educators as to when the progression in learning should occur for students in this grade, specific language is used with certain indicators: 19 An indicator beginning with the phrase “Generate strategies” addresses a concept that is being formally introduced for the first time, and students must therefore be given experiences that foster conceptual understanding. 20 An indicator beginning with the phrase “Apply an algorithm,” “Apply a procedure,” “Apply procedures,” or “Apply formulas” addresses a concept that has been introduced in a previous grade: students should already have the conceptual understanding, and the goal must now be fluency. 21 An indicator beginning with the phrase “Apply strategies and formulas” or “Apply strategies and procedures” addresses a concept that is being formally introduced for the first time, yet the goal must nonetheless be that students progress to fluency.

Highlights of the new learning for grade-seven students are  understanding fractional percentages and percentages greater than 100;  understanding the concept of square roots and the inverse relationship between squaring and finding square roots of perfect squares;  understanding the meaning of absolute value;  generating strategies to add, subtract, multiply, and divide integers;  applying an algorithm to multiply and divide fractions and decimals;  using inverse operations to solve two-step equations and inequalities;  classifying and explaining proportional relationships;  translating between two- and three-dimensional representations of compound figures;  creating tessellations with transformations and explaining the angle-measure relationships among shapes that tessellate;  applying strategies and formulas to determine the surface area and volume of three- dimensional shapes;  using one-step unit analysis to convert between and within U.S. Customary System and the metric system; and  applying procedures to calculate the interquartile range and the probability of mutually exclusive events. GRADE 7 ADVANCED MATH GUIDE FOR GT

Mathematical Processes

The mathematical processes provide the framework for teaching, learning, and assessing in mathematics at all grade levels. Instructional programs should be built around these processes.

Standard 7-1: The student will understand and utilize the mathematical processes of problem solving, reasoning and proof, communication, connections, and representation.

Indicators 7-1.1 Generate and solve complex abstract problems that involve modeling physical, social, or mathematical phenomena. 7-1.2 Evaluate conjectures and pose follow-up questions to prove or disprove conjectures. 7-1.3 Use inductive and deductive reasoning to formulate mathematical arguments. 7-1.4 Understand equivalent symbolic expressions as distinct symbolic forms that represent the same relationship. 7-1.5 Generalize mathematical statements based on inductive and deductive reasoning. 7-1.6 Use correct and clearly written or spoken words, variables, and notation to communicate about significant mathematical tasks. 7-1.7 Generalize connections among a variety of representational forms and real-world situations. 7-1.8 Use standard and nonstandard representations to convey and support mathematical relationships. GRADE 7 ADVANCED MATH GUIDE FOR GT Number and Operations

Standard 7-2: The student will demonstrate through the mathematical processes an understanding of the representation of rational numbers, percentages, and square roots of perfect squares; the application of ratios, rates, and proportions to solve problems; accurate, efficient, and generalizable methods for operations with integers; the multiplication and division of fractions and decimals; and the inverse relationship between squaring and finding the square roots of perfect squares.

Indicators Lesson Plans 7.2.1 Understand fractional percentages Fantastic Five And percentages greater than one hundred. Pre-algebra Lesson 9-7 Group Activity Card 9-7 PACT wkbk pages 1 & 2 and 7 & 8 7.2.2 Represent the location of rational Fantastic Five numbers and square roots of perfect squares Pre-algebra Lesson 13-1 on a number line. Group Activity Card 13-1 Pre-algebra Enrichment Workbook page 108 PACT wkbk pages 3 & 4 7.2.3 Compare rational numbers, Fantastic Five percentages, and square roots of perfect Glencoe Lesson 5-1 squares by using the symbols ≤, ≥, <, >, and Pre-algebra Lesson 13-3 =. Group Activity Card 13-3 Glencoe Lesson 4-10 Pre-algebra Enrichment Workbook, page 110 PACT workbook, pages 5 & 6 7-2.4 Understand the meaning of absolute Fantastic Five value. Glencoe Lesson 5-1 Pre-algebra Lesson 2-1 Group Activity Card 2-1 7-2.5 Apply ratios, rates, and proportions Fantastic Five to discounts, taxes, tips, interest, unit costs, Glencoe Lesson 8-1 and similar shapes. Pre-algebra Lesson 9-1 Group Activity Card 9-1 Glencoe Lesson 8-2 Pre-algebra Lesson 9-9 Group Activity Card 9-9 Glencoe Lesson 8-2 Pre-algebra Lesson 9-9 Group Activity Card 9-9 Glencoe Lesson 8-3 Pre-algebra Lesson 11-6 Group Activity Card 11-6 Glencoe Lesson 11-6 Glencoe Lesson 11-7 PACT workbook, pages 9 & 10 , 31 & 32, 51, and 52

7-2.6 Translate between standard form and Fantastic Five exponential form. Glencoe Lesson 1-4 Pre-algebra Lesson 4-2 Graphing Calculator Activity – pre- algebra Lesson4-2B Glencoe Lesson 2-5 Group Activity Card 4-2 PACT workbook, pages 11 & 12 7-2.7 Translate between standard form and Fantastic Five scientific notation. Glencoe Lesson 2-9 Pre-algebra Lesson 6-9 PACT workbook (8th), pages 7 & 8 7-2.8 Generate strategies to add, subtract, Fantastic Five multiply, and divide integers Glencoe Lesson 5-1 Pre-algebra Lesson 2-4 Group Activity Card 2-4 Pre-algebra Enrichment Workbook, page 14 Glencoe Lesson 5-4 Pre-algebra Lesson 2-5 Pre-algebra Hands-on Activity Lesson2- 5A Group Activity Card 2-5 Glencoe Lesson 5-5 Pre-algebra Lesson 2-7 Pre-algebra Enrichment Workbook page 17 Group Activity Card 2-7 Glencoe Lesson 5-6 Pre-algebra Lesson 2-8 Group Activity Card 2-8 Glencoe Lesson 5-7 PACT workbook, pages 23 & 24, 25 & 26, 27, and 28 7-2.9 Apply an algorithm to multiply and Fantastic Five divide fractions and decimals. Glencoe Lesson 2-4 Pre-algebra Lesson 6-3 Pre-algebra Enrichment Workbook Page 47 Group Activity Card 6-3 Glencoe Lesson 2-6 Pre-algebra Lesson 6-4 Pre-algebra Enrichment Workbook Page 48 Group Activity Card 6-4 Glencoe Lesson 7-4 Pre-algebra Lesson 6-5 Pre-algebra Enrichment Workbook Page 49 Group Activity Card 6-5 Glencoe Lesson 7-9 PACT workbook (8th) pages 1 & 2 , 13 & 14 7-2.10 Understand the inverse relationship Fantastic Five between squaring and finding the square Glencoe Lesson 10-1 roots of perfect squares. Pre-algebra Lesson 13-1 GRADE 7 ADVANCED MATH GUIDE FOR GT Algebra

Standard 7-3: The student will demonstrate through the mathematical processes an understanding of proportional relationships.

Indicators Lesson Plans 7-3.1 Analyze geometric patterns and Fantastic Five pattern relationships. Pre-algebra Lesson 5-9 and 6-8 PACT workbook, pages 33 & 34 7-3.2 Analyze tables and graphs to Fantastic Five describe the rate of change between and Pre-algebra Lesson 8-5 among quantities. Activity: Chapter 3 (pages 41-43) of Navigating Through Algebra PACT workbook pages 35 & 36, 37 & 38, 41 & 42 7-3.3 Understand slope as a constant rate Fantastic Five of change. Pre-algebra Lesson 8-6 Activity: Chapter 2 (pages 25-26) and Chapter 3 (44-58) of Navigating Through Algebra Pre-algebra Lesson 8-3, Problem # 6 Graphing Calculator Activity PACT workbook pages 43 & 44 7-3.4 Use inverse operations to solve two- Fantastic Five step equations and two-step inequalities. Glencoe Lesson 6-1 (review) Pre-algebra Lesson 7-2 Activity: Chapter 4 (63-64) of Navigating Through Algebra Glencoe Lesson 6-2 (review) Pre-algebra Lesson 7-6 Activity: Chapter 4 (65-70) of Navigating Through Algebra Glencoe Lesson 6-5 (review) Pre-algebra Lesson 8-9A Graphing Calculator Activity PACT workbook (8th) pages 35 & 36 7-3.5 Represent on a number line the Fantastic Five solution of a two-step inequality. Glencoe Lesson 6-5 (review) Pre-algebra Lesson 7-7 (review) 7-3.6 Represent proportional relationships Fantastic Five with graphs, tables, and equations. Glencoe Lesson 6-7 Pre-algebra Lesson 8-1 2 Activities: Chapter 1 of Navigating Through Algebra Glencoe Lesson 8-9 Pre-algebra Lesson 9-9 Activity: Chapter 2 (pages 21-23) of Navigating Through Algebra 7.3.7 Classify relationships as either Fantastic Five directly proportional, inversely proportional, Algebra Lesson 5-2 or nonproportional. Algebra Lesson 12-1 PACT wkbk (8th) pages 21 & 22 GRADE 7 ADVANCED MATH GUIDE FOR GT Geometry

Standard 7-4: The student will demonstrate through the mathematical processes an understanding of proportional reasoning, tessellations, the use of geometric properties to make deductive arguments. the results of the intersection of geometric shapes in a plane, and the relationships among angles formed when a transversal intersects two parallel lines.

Indicators Lesson Plans 7-4.1 Analyze geometric properties and the Fantastic Five relationships among the properties of Glencoe Lesson 5-8 triangles, congruence, similarity, and Pre-algebra Lesson 11-9 transformations to make deductive Activity: Chapter 4 page 77 Navigating arguments. Through Geometry PACT workbook pages 65 & 66 PACT workbook pages 67 & 68

7.4.2 Explain the results of the Fantastic Five intersection of two or more geometric shapes www.euclideanspace.com/threed/animati in a plane. on/collisiondetect/index.htm

7-4.3 Illustrate the cross section of a Fantastic Five solid. Activity: Chapter 4 (67-68) Navigating Through Geometry

7.4.4 Translate between two- and three- Fantastic Five dimensional representations of compound Activity: Chapter 4 (69-72) Navigating figures. Through Geometry PACT workbook (8th) pages 59 & 60 7.4.5 Analyze the congruent and Fantastic Five supplementary relationships—specifically, Pre-algebra Lesson 11-3 alternate interior, alternate exterior, PACT workbook (8th) pages 57 & 58 corresponding, and adjacent—of the angles formed by parallel lines and a transversal. 7.4.6 Compare the areas of similar shapes Fantastic Five And the areas of congruent shapes. PACT workbook (8th) pages 43 & 44 Power point: www.worldofteaching.com/

7.4.7 Explain the proportional Fantastic Five relationship among attributes of similar Glencoe Lesson 9-3 shapes. 7.4.8 Apply proportional reasoning to Fantastic Five find missing attributes of similar shapes. Pre-algebra Lesson 11-6 PACT workbook pages 59 & 60 7-4.9 Create tessellations with Fantastic Five transformations. Glencoe Lesson 9-5 Activity: Chapter 3 Navigating Through Geometry PACT workbook pages 77 & 78

7.4.10 Explain the relationship of the angle Fantastic Five measurements among shapes that tessellate. See Chapter 3 of Navigating Through Geometry GRADE 7 ADVANCED MATH GUIDE FOR GT Measurement

Standard 7-5: The student will demonstrate through the mathematical processes an understanding of how to use ratio and proportion to solve problems involving scale factors and rates and how to use one-step unit analysis to convert between and within the U.S. Customary System and the metric system.

Indicators Lesson Plans 7.5.1 Use ratio and proportion to solve Fantastic Five problems involving scale factors Pre-algebra Lesson 12-8B and rates. Pre-algebra Lesson 11-7 Activity: Chapter 3 (48-49) Navigating Through Geometry Activity: Pre-algebra page 605 7-5.2 Apply strategies and formulas to Fantastic Five determine the surface area and Glencoe Lesson 12-2 volume of the three-dimensional Pre-algebra Lesson 12-5 shapes prism, pyramid, and Glencoe Lesson 12-3 cylinder. Pre-algebra Lesson 12-6 Glencoe Lesson 12-4 Pre-algebra Lesson 12-7 Glencoe Lesson 12-5 Pre-algebra Lesson 12-8 PACT workbook pages 87 & 88, 91 & 92, 97 & 98 7-5.3 Generate strategies to determine Fantastic Five the perimeters and areas of Glencoe Lesson 10-5 trapezoids. Pre-algebra Lesson 12-1 Activity: Chapter 4 (73-76) Navigating Through Geometry Pre-algebra Lesson 3-5B Graphing Calculator Activity PACT workbook (8th) pages 73 & 74 7-5.4 Recall equivalencies associated Fantastic Five with length, mass and weight, and Pre-algebra Lesson 7-8 liquid volume: Glencoe Lesson 7-5 1 square yard = 9 square feet, 1 Glencoe Course 3 Lesson 11-7 cubic meter = 1 million cubic www.regentsprep.org/REgents/math/meten centimeters, g/MetEng.htm 5 www.thefarm.org/charities/ 1 kilometer = 8 mile, 1 inch = www.gillespie.macoupin.k12.il.us/metricco 2.54 centimeters; 2.2 kilograms = nversions.htm 1 pound; and PACT workbook pages 81 & 82, 83 & 84 1.06 quarts = 1 liter. 7-5.5 Use one-step unit analysis to Fantastic Five convert between and within the Glencoe Lesson 2-8 U.S. Customary System and the Glencoe Lesson 7-5 metric system. PACT wkbk (8th) pages 69 & 70 GRADE 7 ADVANCED MATH GUIDE FOR GT Data Analysis and Probability

Standard 7-6: The student will demonstrate through the mathematical processes an understanding of the relationships between two populations or samples.

Indicators Lesson Plans 7-6.1 Predict the characteristics of two Fantastic Five populations based on the analysis Pre-algebra Lesson 9-6 of sample data. PACT workbook pages 103 & 104 7-6.2 Organize data in box plots or circle Fantastic Five graphs as appropriate. Glencoe Lesson 3-6A Pre-algebra Lesson 10-3 Glencoe Lesson 3-6 Pre-algebra Lesson 11-2 Glencoe Lesson 11-3 PACT workbook pages 105 & 106, 107 & 108 7-6.3 Apply procedures to calculate the Fantastic Five interquartile range. Glencoe Lesson 3-6 Pre-algebra Lesson 10-2 PACT workbook page 109 7-6.4 Interpret the interquartile range for Fantastic Five data. Glencoe Lesson 3-6 PACT workbook page 110 7-6.5 Apply procedures to calculate the Fantastic Five probability of mutually exclusive Pre-algebra Lesson 10-10 simple or compound events. PACT workbook pages 115 & 116 7-6.6 Interpret the probability of mutually Fantastic Five exclusive simple or compound Glencoe Lesson 13-4 events. PACT workbook pages 121 & 122 PACT workbook (8th)pages 99 & 100 7-6.7 Differentiate between experimental Fantastic Five and theoretical probability of the Glencoe Lesson 13-1 same event. Pre-algebra Lesson 10-8 PACT workbook pages 117 & 118 PACT workbook (8th) pages 97 & 98 7-6.8 Use the fundamental counting Fantastic Five principle to determine the number Glencoe Lesson 13-3 of possible outcomes for a Pre-algebra Lesson 10-6 multistage event. Pre-algebra Lesson 10-9 Technology Activity PACT workbook pages 119 & 120 Grade 8 Advanced Math Guide for GT

Overview

This overview provides only the highlights of the new learning that should take place at the seventh-grade level. The specific skills and subject matter that seventh graders should be taught in each of the five mathematical strands are set forth in the formal standards and indicators for these strands. To alert educators as to when the progression in learning should occur for students in this grade, specific language is used with certain indicators: 22 An indicator beginning with the phrase “Generate strategies” addresses a concept that is being formally introduced for the first time, and students must therefore be given experiences that foster conceptual understanding. 23 An indicator beginning with the phrase “Apply an algorithm,” “Apply a procedure,” “Apply procedures,” or “Apply formulas” addresses a concept that has been introduced in a previous grade: students should already have the conceptual understanding, and the goal must now be fluency. 24 An indicator beginning with the phrase “Apply strategies and formulas” or “Apply strategies and procedures” addresses a concept that is being formally introduced for the first time, yet the goal must nonetheless be that students progress to fluency.

Highlights of the new learning for grade-eight students are  applying an algorithm to add, subtract, multiply, and divide integers;  understanding the concept of irrational numbers;  applying procedures to approximate square and cube roots;  applying procedures to solve multistep equations;  classifying relationships between two variables as either linear or nonlinear;  identifying the coordinates of the x- and y-intercepts of a linear equation;  understanding slope as a constant rate of change;  applying the Pythagorean theorem;  using ordered pairs, equations, intercepts, and intersections to locate points and lines in a coordinate plane;  applying a dilation on a square, rectangle, or right triangle in a coordinate plane and analyzing the effect;  applying strategies and formulas to determine volume of three-dimensional shapes;  using multistep unit analysis to convert between and with the U.S. Customary System and the metric system; and applying procedures to compute the odds of a given event. GRADE 8 ADVANCED MATH GUIDE FOR GT Mathematical Processes

The mathematical processes provide the framework for teaching, learning, and assessing in mathematics at all grade levels. Instructional programs should be built around these processes.

Standard 8-1: The student will understand and utilize the mathematical processes of problem solving, reasoning and proof, communication, connections, and representation.

Indicators

8-1.1 Generate and solve complex abstract problems that involve modeling physical, social, or mathematical phenomena. 8-1.2 Evaluate conjectures and pose follow-up questions to prove or disprove conjectures. 8-1.3 Use inductive and deductive reasoning to formulate mathematical arguments. 8-1.4 Understand equivalent symbolic expressions as distinct symbolic forms that represent the same relationship. 8-1.5 Generalize mathematical statements based on inductive and deductive reasoning. 8-1.6 Use correct and clearly written or spoken words, variables, and notations to communicate about significant mathematical tasks. 8-1.7 Generalize connections among a variety of representational forms and real-world situations. 8-1.8 Use standard and nonstandard representations to convey and support mathematical relationships. GRADE 8 ADVANCED MATH GUIDE FOR GT Number and Operations

Standard 8-2: The student will demonstrate through the mathematical processes an understanding of operations with integers, the effects of multiplying and dividing with rational numbers, the comparative magnitude of rational and irrational numbers, the approximation of cube and square roots, and the application of proportional reasoning.

Indicators Lesson Plans 8-2.1 Apply an algorithm to add, Fantastic Five subtract, multiply, and divide Integer Bingo Activity integers. United Streaming, Power of Algebra: Positive and Negative Numbers Glencoe Pre-Algebra 2-4, 2-5, 2-7, and 2-8 Magic Squares Activity Integers Bingo Pact Workbook, p.1-2 Challenge the Pact, p.104-113 8-2.2 Understand the effect of Fantastic Five multiplying and dividing a rational United Streaming, Discovering Math: number by another rational Rational Numbers Concepts number. Glencoe Pre-Algebra 6-3, 6-4, and 6-5 Menu Activity Challenge the Pact, p.26-36, 41-47 and 63- 66 8-2.3 Represent the approximate Fantastic Five location of irrational numbers on a Transparencies number line. Pact Workbook, p.3-4 Challenge the Pact, p.94-96 8-2.4 Compare rational and irrational Fantastic Five numbers by using the symbols ≤, Birthday Post-it Note Activity ≥, <, >, and =. Glencoe Pre-Algebra, Lesson 2-3 (Powerpoint) Glencoe Pre-Algebra, Lesson 5-1 Buckle Down Pact, Lesson 1 p.9-18 Fraction and Decimal Bingo Pact Workbook, p.3-4 Challenge the Pact, p.39 8-2.5 Apply the concept of absolute Fantastic Five value. Name Value Activity Challenge the Pact, p.101-103 8-2.6 Apply strategies and procedures to Fantastic Five approximate between two whole Glencoe Pre-Algebra, Lesson 13-1 and 13- numbers the square roots or cube 1 Enrichment roots of numbers less than 1,000. Pact Workbook, p.11-12 Pact Coach, Lesson 7 Challenge the Pact, p.154-155 8-2.7 Apply ratios, rates, and Fantastic Five proportions. Glencoe Pre-Algebra 9-5 Pact Workbook, p.19-20 Pact Workbook,p.21-22 Pact Coach, Lesson 3 Challenge the Pact, p.134-138 Buckle Down Pact, p.39-50 GRADE 8 ADVANCED MATH GUIDE FOR GT Algebra

Standard 8-3: The student will demonstrate through the mathematical processes an understanding of equations, inequalities, and linear functions.

* See Attached list of United Streaming Videos for Algebra

Indicators Lesson Plans 8-3.1 Translate among verbal, graphic, Fantastic Five tabular, and algebraic Linear Circle Activity representations of linear functions.

8-3.2 Represent algebraic relationships Fantastic Five with equations and inequalities. Glencoe Pre-Algebra, Lesson 7-3 Glencoe Pre-Algebra, Lesson 7-7 Challenge the Pact, p.129-133 Buckle Down Pact, p.62-64 8-3.3 Use commutative, associative, and Fantastic Five distributive properties to examine Make a Foldable the equivalence of a variety of Glencoe Pre-Algebra, Lesson 1-5 algebraic expressions. Glencoe Pre-Algebra, Lesson 1-6 Property Concentration Game Pact Workbook, p.9-10 Pact Coach, Lesson 2 Challenge the Pact, p.97-100 8-3.4 Apply procedures to solve multistep Fantastic Five equations. Glencoe Pre-Algebra, Lesson 7-2 Glencoe Pre-Algebra, Lesson 7-3 Glencoe Pre-Algebra, Lesson 7-5 Pact Coach, Lesson 13 Challenge the Pact, p.114-128 Buckle Down Pact, p.56-61 8-3.4 Apply procedures to solve multistep Fantastic Five equations. Math Jeopardy Magic Square Activity 8-3.5 Classify relationships between two Fantastic Five variables in graphs, tables, and/or Glencoe Pre-Algebra, Lesson 8-3 equations as either linear or Pact Workbook, p.25-26, 37-38, and 39-40 nonlinear. Buckle Down Pact, p.80-84

8-3.6 Identify the coordinates of the x- Fantastic Five and y-intercepts of a linear equation Glencoe Pre-Algebra, Lesson 8-7 from a graph, equation, and/or Buckle Down Pact, p.85-92 table.

8-3.7 Identify the slope of a linear Fantastic Five equation from a graph, equation, I Have…Who Has? Activity and/or table. Rolling Race Cars Activity Barbie Bungee Activity Buckle Down Pact, p.71-79 GRADE 8 ADVANCED MATH GUIDE FOR GT Geometry

Standard 8-4: The student will demonstrate through the mathematical processes an understanding of the Pythagorean theorem; the use of ordered pairs, equations, intercepts, and intersections to locate points and lines in a coordinate plane; and the effect of a dilation in a coordinate plane.

Indicators Lesson Plans 8-4.1 Apply the Pythagorean Theorem. Fantastic Five Safari Montage, The Pythagorean Theorem Kite Flying Activity Pact Coach, Lesson 20 Challenge the Pact, p.158-163 Buckle Down Pact, p.100-107 Pact Workbook, p.47-50 8-4.2 Use ordered pairs, equations, Fantastic Five intercepts, and intersections to Glencoe Pre-Algebra, Lesson 1-7 locate points and lines in a Glencoe Pre-Algebra, Lesson 2-2 coordinate plane. Pact Workbook, p.51-52

8-4.3 Apply a dilation to a square, Fantastic Five rectangle, or right triangle in a United Streaming: Discovery Math, coordinate plane. Geometry Grades 6 – 8 ( section on Geometric Transformations) Comic Strip Poster Drawing Activity Pact Workbook, p.53-54 8-4.4 Analyze the effect of a dilation on Fantastic Five a square, rectangle, or right Glencoe Pre-Algebra, Lesson 11-6 (Hands- triangle in a coordinate plane. On Activity only) GRADE 8 ADVANCED MATH GUIDE FOR GT Measurement

Standard 8-5: The student will demonstrate through the mathematical processes an understanding of the proportionality of similar figures; the necessary levels of accuracy and precision in measurement; the use of formulas to determine circumference, perimeter, area, and volume; and the use of conversions within and between the U.S. Customary System and the metric system.

Indicators Lesson Plans 8-5.1 Use proportional reasoning and the Fantastic Five properties of similar shapes to Glencoe Pre-Algebra, Lesson 11-6 determine the length of a missing Shadows Measure Height Activity side. Pact Coach, Lesson 24 Challenge the Pact, p.138-140 Buckle Down Pact, p.123-124 Pact workbook, p.77-78 8-5.2 Explain the effect on the area of Fantastic Five two-dimensional shapes and on the Pact Coach, Lesson 19 volume of three-dimensional Challenge the Pact, p.195-209 and 218-228 shapes when one or more of the Buckle Down Pact, p.154-160 dimensions are changed. Pact workbook, p.61-62 Cord Bridges, p.299-301 (worksheet) 8-5.3 Apply strategies and formulas to Fantastic Five determine the volume of the three- Christmas Greeting Card Box Activity dimensional shapes cone and Pact Coach, Lesson 21 sphere.

8-5.4 Apply formulas to determine the Fantastic Five exact (pi) circumference and area of Christmas Ornament Activity a circle. Challenge the Pact, p.229-234 8-5.5 Apply formulas to determine the Fantastic Five perimeters and areas of trapezoids. Glencoe Pre-Algebra, Lesson 12-1 Challenge the Pact, p.195-209 and 218-228 Buckle Down Pact, p.144-145 Pact workbook, p.73-74 8-5.6 Analyze a variety of measurement Fantastic Five situations to determine the United Streamline, Discovery Math necessary level of accuracy and Measurement precision. 8-5.7 Use multistep unit analysis to Fantastic Five convert between and within U.S. Dimensional Analysis Powerpoint Customary System and the metric Pact workbook, p.69-70 system. Pact Coach, Lesson 23 Buckle Down Pact, p.135-139 Pact workbook, p.69-70 GRADE 8 ADVANCED MATH GUIDE FOR GT Data Analysis and Probability

Standard 8-6: The student will demonstrate through the mathematical processes an understanding of the relationships between two variables within one population or sample.

Indicators Lesson Plans 8-6.1 Generalize the relationship Fantastic Five between two sets of data by using Glencoe Pre-Algebra, Lesson 8-2 scatterplots and lines of best fit. Challenge the Pact, p.312-316 Pact workbook, p.91-92 8-6.2 Organize data in matrices or Fantastic Five scatterplots as appropriate. Powerpoint Pact Coach, Lesson 26 Challenge the Pact, p.312-316 Buckle Down Pact, p.168-172 Pact workbook, p.81-84 8-6.3 Use theoretical and experimental Fantastic Five probability to make inferences and Mother’s Day Card Project convincing arguments about an Probability Simulation Activities event or events. Pact Coach, Lesson 29 Buckle Down Pact, p.184-185 and 188-190 Pact workbook, p.97-98 8-6.4 Apply procedures to calculate the Fantastic Five probability of two dependent Powerpoint events. Pact Coach, Lesson 30 Buckle Down Pact, p.186-187 Pact workbook, p.99-100 8-6.5 Interpret the probability for two Fantastic Five dependent events. Glencoe Pre-Algebra, Lesson 10-9 Challenge the Pact, p.283-291 Pact workbook, p.99-100 8-6.6 Apply procedures to compute the Fantastic Five odds of a given event. Glencoe Pre-Algebra, Lesson 10-7 Pact Coach, Lesson 32 Buckle Down Pact, p.182-183 Pact workbook, p.101-102 8-6.7 Analyze probability using area Fantastic Five models. Glencoe Pre-Algebra 12-3 Chalk and Pennies Activity Pact Coach, Lesson 31 Buckle Down Pact, p.191-192 Pact workbook, p.65-66 8-6.8 Interpret graphic and tabular data Fantastic Five representations by using range and Glencoe Pre-Algebra, Lesson 6-6 the measures of central tendency 2-D Model of an Average Student (mean, median, and mode). Pact Coach, Lessons 25 and 27 Challenge the Pact, p.269-282 Buckle Down Pact, p.164-167

* United Streaming Algebra Titles: Adventurous World of Algebra Program 3: Linear Equations Pumped up World of Pre Algebra Program 4 Pumped up World of Pre-Algebra Program 5 Math Mastery: Equations Linear Equating : y=mx + b Operation Algebra : Linear Equations: AX + BY = C Discovering Math:Algebra (Grades 6 – 8) Operation Algebra: Introduction to Linear Relations Elementary Algebra

Overview

The academic standards for the elementary algebra core area establish the process skills and core content for Algebra 1, Mathematics for the Technologies 1, and Mathematics for the Technologies 2, which should provide students with the mathematics skills and conceptual understanding necessary for them to further their mathematical education or to pursue mathematics-related technical careers. These standards will be the basis for the development of the items on the state-required end-of-course examination for Algebra 1 and Mathematics for the Technologies 2.

The content of the elementary algebra standards encompasses the real number system; operations involving exponents, matrices, and algebraic expressions; relations and functions; writing and solving linear equations; graphs and characteristics of linear equations; and quadratic relationships and functions. Teachers, schools, and districts should use the elementary algebra standards to make decisions concerning the structure and content of Algebra 1, Mathematics for the Technologies 1, and Mathematics for the Technologies 2. Content in these three courses may go beyond the elementary algebra standards.

All courses based on the academic standards for elementary algebra must include instruction using the mathematics process standards, allowing students to engage in problem solving, decision making, critical thinking, and applied learning. Educators must determine the extent to which such courses or individual classes may go beyond these standards. Such decisions will involve choices regarding additional content, activities, and learning strategies and will depend on the objectives of the particular courses or individual classes.

In all courses based on the elementary algebra standards, hand-held graphing calculators are required for instruction and assessment. Students should learn to use a variety of ways to represent data, to use a variety of mathematical tools such as graph paper, and to use technologies such as graphing calculators to solve problems.

Note: The term including appears in parenthetical statements in the high school mathematics indicators to introduce a list of specifics that are intended to clarify and focus the teaching and learning of the particular concept. That is, within these parenthetical including statements are specified the components of the indicator that are critical for the particular core area with regard both to the state assessments and to the management of time in the classroom. While instruction must focus on the entire indicator, educators must be certain to cover the components specified in the parenthetical including statements. HIGH SCHOOL CORE AREA Elementary Algebra

The mathematical processes provide the framework for teaching, learning, and assessing in all high school mathematics core courses. Instructional programs should be built around these processes.

Standard EA-1: The student will understand and utilize the mathematical processes of problem solving, reasoning and proof, communication, connections, and representation.

Indicators EA-1.1 Communicate a knowledge of algebraic relationships by using mathematical terminology appropriately. EA-1.2 Connect algebra with other branches of mathematics. EA-1.3 Apply algebraic methods to solve problems in real-world contexts. EA-1.4 Judge the reasonableness of mathematical solutions. EA-1.5 Demonstrate an understanding of algebraic relationships by using a variety of representations (including verbal, graphic, numerical, and symbolic). EA-1.6 Understand how algebraic relationships can be represented in concrete models, pictorial models, and diagrams. EA-1.7 Understand how to represent algebraic relationships by using tools such as handheld computing devices, spreadsheets, and computer algebra systems (CASs). HIGH SCHOOL CORE AREA Elementary Algebra

Standard EA-2: The student will demonstrate through the mathematical processes an understanding of the real number system and operations involving exponents, matrices, and algebraic expressions.

Indicators Lesson Plans EA-2.1 Exemplify elements of the real Glencoe Algebra I, Lesson 2-7 number system (including integers, rational numbers, and irrational numbers).

EA-2.2 Apply the laws of exponents Glencoe Algebra I, Lesson 2-7 and Chapter and roots to solve problems. 8

EA-2.3 Carry out a procedure to Glencoe Algebra I, Lesson 8-3 perform operations (including multiplication and division) with numbers written in scientific notation.

EA-2.4 Use dimensional analysis to Glencoe Algebra I, Lesson 3-8 convert units of measure within a system. EA-2.5 Carry out a procedure using the Glencoe Algebra I, Lesson 1-5 and 1-6 properties of real numbers (including commutative, associative, and distributive) to simplify expressions.

EA-2.6 Carry out a procedure to Glencoe Algebra I, Lesson 1-1, 1-2 evaluate an expression by substituting a value for the variable.

EA-2.7 Carry out a procedure Glencoe Algebra I, Chapter 8 (including addition, subtraction, multiplication, and division by a monomial) to simplify polynomial expressions. EA-2.8 Carry out a procedure to factor Glencoe Algebra I, Chapter 9 binomials, trinomials, and polynomials by using various techniques (including the greatest common factor, the difference between two squares, and quadratic trinomials).

EA-2.9 Carry out a procedure to Glencoe Algebra I, Lesson 13-2 perform operations with matrices (including addition, subtraction, and scalar multiplication).

EA-2.10 Represent applied problems by Glencoe Algebra I, Lesson 13-2 using matrices. HIGH SCHOOL CORE AREA Elementary Algebra

Standard EA-3: The student will demonstrate through the mathematical processes an understanding of relationships and functions.

Indicators Indicators Lesson Plans EA-3.1 Classify a relationship as being Glencoe Algebra I, Lesson 1-8, 4-6 either a function or not a function when given data as a table, set of ordered pairs, or graph.

EA-3.2 Use function notation to represent Glencoe Algebra I, Lesson 4-6 functional relationships.

EA-3.3 Carry out a procedure to evaluate Glencoe Algebra I, Lesson 4-6 a function for a given element in the domain.

EA-3.4 Analyze the graph of a continuous Glencoe Algebra I, Lesson 4-6 function to determine the domain and range of the function.

EA-3.5 Carry out a procedure to graph Graphing Calculator Activity parent functions (including 1 y  x, y  x2 , y  x, y  x , and y  x .

EA-3.6 Classify a variation as either Glencoe Algebra I, Lesson 5-2 and 12-1 direct or inverse.

EA-3.7 Carry out a procedure to solve Glencoe Algebra I, Lesson 3-8 literal equations for a specified variable.

EA-3.8 Apply proportional reasoning to Glencoe Algebra I, Lesson 3-6 solve problems.

HIGH SCHOOL CORE AREA Elementary Algebra

Standard EA-4: The student will demonstrate through the mathematical processes an understanding of the procedures for writing and solving linear equations and inequalities.

Indicators Lesson Plans EA-4.1 Carry out a procedure to write an Glencoe Algebra I, Lesson 5-4 equation of a line with a given slope and a y-intercept.

EA-4.2 Carry out a procedure to write an Glencoe Algebra I, Lesson 5-4, 5-5 equation of a line with a given slope passing through a given point.

EA-4.3 Carry out a procedure to write an Glencoe Algebra I, Lesson 5-4 equation of a line passing through two given points.

EA-4.4 Use a procedure to write an Glencoe Algebra I, Lesson 5-7 equation of a trend line from a given scatterplot.

EA-4.5 Analyze a scatterplot to make Glencoe Algebra I, Lesson 5-7 predictions. EA-4.6 Represent linear equations in Glencoe Algebra I, Lesson 4-5, 5-4 and 5-5 multiple forms (including point- slope, slope-intercept, and standard).

EA-4.7 Carry out procedures to solve Glencoe Algebra I, Chapter 3 linear equations for one variable algebraically.

EA-4.8 Carry out procedures to solve Glencoe Algebra I, Chapter 6 linear inequalities for one variable algebraically and then to graph the solution.

EA-4.9 Carry out a procedure to solve Glencoe Algebra I, Lesson 7-1 systems of two linear equations graphically.

EA-4.10 Carry out a procedure to solve Glencoe Algebra I, Lesson 7-2, 7-3, and 7- systems of two linear equations 4 algebraically. HIGH SCHOOL CORE AREA Elementary Algebra

Standard EA-5: The student will demonstrate through the mathematical processes an understanding of the graphs and characteristics of linear equations and inequalities.

Indicators Lesson Plans EA-5.1 Carry out a procedure to graph a Glencoe Algebra I, Lesson 4-5 line when given the equation of the line.

EA-5.2 Analyze the effects of changes in Glencoe Algebra I, Lesson 5-3GCI the slope, m, and the y-intercept, b, on the graph of y = mx + b.

EA-5.3 Carry out a procedure to graph Glencoe Algebra I, Lesson 5-4 the line with a given slope and a y-intercept.

EA-5.4 Carry out a procedure to graph Glencoe Algebra I, Lesson 5-4 the line with a given slope passing through a given point.

EA-5.5 Carry out a procedure to Glencoe Algebra I, Lesson 4-5 determine the x-intercept and y- intercept of lines from data given tabularly, graphically, symbolically, and verbally.

EA-5.6 Carry out a procedure to Glencoe Algebra I, Lesson 5-1 determine the slope of a line from data given tabularly, graphically, symbolically, and verbally.

EA-5.7 Apply the concept of slope as a Glencoe Algebra I, Lesson 5-1 rate of change to solve problems.

EA-5.8 Analyze the equations of two Glencoe Algebra I, Lesson 5-6 lines to determine whether the lines are perpendicular or parallel. EA-5.9 Analyze given information to Glencoe Algebra I, Lesson 5-3 write a linear function that models a given problem situation.

EA-5.10 Analyze given information to Glencoe Algebra I, Lesson 4-3 and 4-4 determine the domain and range of a linear function in a problem situation.

EA-5.11 Analyze given information to Glencoe Algebra I, Chapter 7 write a system of linear equations that models a given problem situation.

EA-5.12 Analyze given information to Glencoe Algebra I, Lesson 7-5 write a linear inequality in one variable that models a given problem situation. HIGH SCHOOL CORE AREA Elementary Algebra

Standard EA-6: The student will demonstrate through the mathematical processes an understanding of quadratic relationships and functions.

Indicators Lesson Plans EA-6.1 Analyze the effects of changing Glencoe Algebra I, Lesson 10-1, 10-1 GCI, the leading coefficient a on the 10-2, and 10-3 GCI graph of y  ax2 .

EA-6.2 Analyze the effects of changing Glencoe Algebra I, Lesson 10-1, 10-1 GCI, the constant c on the graph of 10-2, and 10-3 GCI y  x 2  c .

EA-6.3 Analyze the graph of a quadratic Glencoe Algebra I, Lesson 10-3 GCI function to determine its  equation.

EA-6.4 Carry out a procedure to solve Glencoe Algebra I, Chapter 9 quadratic equations by factoring.

EA-6.5 Carry out a graphic procedure to Glencoe Algebra I, Lesson 10-2 approximate the solutions of quadratic equations.

EA-6.6 Analyze given information to Glencoe Algebra I, Chapter 9, Lesson 10-1, determine the domain of a 10-2, 10-3, and 10-4 quadratic function in a problem situation.