Topic Solve real-world problems involving volume of ...



Glen Ridge Public Schools – Mathematics CurriculumCourse Title: Algebra 1 ConceptsSubject: MathematicsGrade Level: 8Duration: one yearPrerequisite: Pre-Algebra or Pre-Algebra AdvancedElective or Required: RequiredMathematics Mission StatementSince Mathematics and Computational thinking are an integral part of our lives and 21st Century learning, students must be actively involved in their mathematics education with problem solving being an essential part of the curriculum. The mathematics and computer science curricula will emphasize thinking skills through a balance of computation, intuition, common sense, logic, analysis and technologyStudents will be engaged and challenged in a developmentally appropriate, student –centered learning environment. Students will communicate mathematical ideas effectively and apply those ideas by using manipulative, computational skills, mathematical models and technology in order to solve practical problems. To achieve these goals, students will be taught a standards-based curriculum that is aligned with the National Common Core Standards in Mathematics and the New Jersey Core Curriculum Content Standards in Technology and 21st Century Life and Careers. Course Description:The ultimate goal of this course is to give the student a foundation for exploring and understanding algebra and geometry. Topics include the basic operations and properties of real numbers, measurement on a plane and in space, data analysis, linear equations, graphing, problem solving, functions and deductive reasoningAuthor: Darleen KennedyDate Submitted : Summer 2012Algebra 1 Concepts – 8th grade mathOutlineTopic Number System 2 weeks8 NS 1 - rational numbers, irrational numbers, real numbers8 NS 2 - identifying and graphing irrational numbersTopic Expressions and Equations3 weeks 8 EE 1 - exponents8 EE 2 - squares roots and cube roots8 EE 3 - scientific notation8 EE 4 - reading and calculating with scientific notationTopic Understand and apply the Pythagorean Theorem3 weeks8 G 6 \8 G 7 Pythagorean Theorem8 G 8 /Topic Proportional Relationships and connections to lines and linear equations 2 weeks8 EE 5 – converting unit measurements, solving linear equations by graphing, find slope of line8 EE 6 - triangles, slope, similar figures, slope interceptTopic Solving Linear Equations4.5 weeks8 EE 7 – simplifying multi-step variables on both sides and systems of equations Topic Understand congruence and similarity using physical models, transparencies, or geometry software3 weeks8 G 1 - transformations8 G2 - congruence8 G 3 - dilation8 G 4 - similar figures 8 G 5 - parallel lines perpendicular line, trianglesTopic Solve real-world problems involving volume of cylinders, cones, and spheres.2.5 weeks8 G 9 - volume of prisms, cylinders, cones, spheresTopic Analyze and solve pairs of simultaneous linear equations4 weeks8 EE 8 - slope, graphing linear equations, systems of linear equations, writing systems of equations, special systems of equations, solving equations by graphingTopic Investigate patterns of association in bivariate data2 weeks8.SP.1 - scatter plots8 SP 28 SP 3 - line of best fit8 SP 4 - patterns , 2 way tables 8 SP 5Topic Define, evaluate, and compare functions.4 weeks8.F.1 - linear functions8.F.2. compare functions8.F.3. slope-intercept formTopic Use functions to model relationships between quantities 4 weeks8.F.4. construct function to model linear relationships and determine rate of change8.F.5. functional relationshipsTopic Number System 8.NS.1 know that numbers that are not rational are called irrational Understand that every number has a decimal expansion - that for rational numbers show that the decimal expansion repeats eventually and converts to a decimal expansion which repeats eventually into a rational number8.NS.2 use rational approximations of irrational numbers to compare size of irrational numbers, locate them approximately on a number line and estimate the value of expressions. 2 weeks for UnitEssential QuestionsHow do you determine the difference between a rational and irrational number?Does a rational number have an expansion?What is a perfect square?How can you find decimal approximations of square roots that are irrational?How do you convert an irrational number to a decimal?How can you use a square root to describe the golden ratio?Upon Completion of the unit students will be able to :Write a rational number as the ratio of two integers. (8.NS.1)Identify irrational numbers (8.NS.1)Approximate the decimal value of an irrational number (8.NS.2)Understand and explain the relationship of rational, irrational, real, integers, and natural numbers (8.NS.1)Locate rational, irrational, real, integers and natural numbers on a number line. (8.NS.2)Create the decimal expansion of a rational number (8.NS.1)Define square root, cube root, perfect square, radical sign, radicand, irrational number, real numbers (8.NS.1)Review rules for computation of rational number (8.NS.2)Understand and apply the properties of addition, subtraction, division, and multiplication of square roots (8.NS.1)Interdisciplinary StandardsL.6.1 Language arts – learn that the prefix “it”- means not and other examples like dis-, il- , im-, in-, and un- 2.5 Physical Education - Sports – understand that a fours square court is 66 square feet and from this you can calculate the sides5.2 Physical Science – use and understand the formula for calculating the rate a object falls. 5-3 Life Science – understand and identify the golden ratio and the human bodyActivities – including 21st Century TechnologiesInstruction Holt McDougal chapters 1-1 Rational Numbers Lab - Use calculators to find approximate values of irrational numbersPractice from On Core Mathematics chapters 1-5 – how to write any rational number as a fractionInstruction Holt McDougal pg 128 Extension identifying and graphing irrational numbersInstruction Big Ideas lesson 6-3 irrational numbers – approximating square rootsInstruction Big Ideas 6-4 Simplifying square rootsActivity Big Ideas pg 244 Approximating square roots with scientific calculatorEnrichment ActivitiesReview of multiplying and dividing adding subtracting rational numbers with emphasis on integer rules – Holt McDougal chapter 1-2 Multiplying Rational Numbers & chapters 1-3 Dividing Rational Numbers & chapter 1-4 adding and subtracting with unlike denominators\Holt McDougal pg 25 Focusing on Problem Solving – make sense of problems and preserve to solving them.Instruction Holt McDougal chapters 3-7 Real NumbersInstruction Holt McDougal extension Identifying and graphing irrational numbersBig Ideas activity pg 252 constructing a golden ratioBig Ideas activity pg 253 The Golden ratio and the human bodyMethods of Assessment/Evaluation:Ticket out the doorInteractive Smart Board questOpen Ended QuestionsSmartboard Lessons (clickers)Study IslandThumbs Up/Thumbs DownPair/ShareDry Erase BoardsFind the MistakeMidterms/FinalsProjectObservation (Teacher/Small/Whole Group)Independent WorkClassworkHomeworkCalculatorsVerbal AssessmentGroup labsWarm up lesson checksFormal and informal tests and quizzesResources/Including Online Resources:Online Textbook- my. Userid and password to be determinedTeacher webpage Study IslandHolt McDougal Course 3 TextbookBig Ideas textbook Topic Expressions and Equations - exponents & scientific notation8.EE.1. Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 32?×?3–5 = 3–3 = 1/33 = 1/27.8.EE.2. Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.8.EE.3. Use numbers expressed in the form of a single digit times a whole-number power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 times 108 and the population of the world as 7 times 109, and determine that the world population is more than 20 times larger.8.EE.4. Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology. 3 weeks for UnitEssential QuestionsHow can you use exponents to write numbers?How can you multiply two powers that have the same base?How can you divide two powers that have the same base?How can you define zero and negative exponents?How can you use scientific numbers to express very large or very small numbers?What are the properties of integer exponents for multiplication and division?How do you multiply or divide numbers in scientific format?Upon Completion of the unit students will be able to :Write numbers with exponents (8.EE.1)Convert numbers to and from exponential form (8.EE.1)Define power, exponent, and base (8.EE.1)Apply exponents in real life problems (8.EE.2)Multiply and divide two powers with the same base (8.EE.2)Distribute exponential powers correctly (8.EE.2)Write numbers in scientific notation and standard notation (8.EE.3)Understand and write numbers as powers of 10 (8.EE.3)Create and calculate scientific notations on calculator (8.EE.4)Do calculations with scientific notation (8.EE.4)Identify and use correct units of measure with scientific notation (8.EE.4)Interdisciplinary StandardsL.6.2 Language Arts – exponents expressed in poetryS.5.4 Science – uses in astronomy and micro-biology and chemistry2.1 Health – nutrition measurementsActivities – including 21st Century TechnologiesInstruction Holt McDougal chapters 3-1 review positive and negative exponents & powers of 10Instruction Holt McDougal chapters 3-2 properties of exponents Instruction Holt McDougal chapters 3-3 scientific notationInstruction Holt McDougal chapters 3-4 operations with scientific notation Instruction from Big Ideas, chapter 6-1 Finding Square RootsInstruction from Big Ideas chapter 6-3 approximating square rootsInstruction Holt McDougal chapters 3-5 Squares and Square roots Instruction Holt McDougal chapters 3-6 Estimating Square rootsInstruction Big Ideas, chapter 9-3 quotient of powers propertyInstruction Big Ideas, chapter 9-4 zero and negative exponentsInstruction Big Ideas, chapter 9-5 Reading scientific notationInstruction Big Ideas, chapter 9-6 Writing Scientific NotationPractice On Core 1-2 scientific notationPractice on Core 1-3 operations of scientific notationPractice On Core 1-4 square roots and cube rootsLab – Prentice Hall - pg 61 Repeating decimals Lab – Holt McDougal chapters 3-4 multiplying scientific notationProblem solving Holt McDougal chapters 3-1 to 3-4 (real life examples)Enrichment ActivitiesReview from Big Ideas, chapter 6-3Challenge worksheets accompanying the textbook Practice level C worksheets Methods of Assessment/Evaluation:Open notebook quizTicket out the doorInteractive Smart Board questOpen Ended QuestionsSmartboard Lessons (clickers)Study IslandThumbs Up/Thumbs DownPair/ShareDry Erase BoardsFind the MistakeMidterms/FinalsProjectObservation (Teacher/Small/Whole Group)Independent WorkClassworkHomeworkCalculatorsVerbal AssessmentGroup labsWarm up lesson checksFormal and informal tests and quizzesResources/Including Online Resources:Online Textbook- my. Userid and password to be determinedTeacher webpage Study IslandHolt McDougal Course 3 TextbookBig Ideas textbook Topic Understand and apply the Pythagorean Theorem8.G.6. Explain a proof of the Pythagorean Theorem and its converse.8.G.7. Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.8.G.8. Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. 3 weeks for UnitEssential QuestionsHow can you use the Pythagorean Theorem to solve real life problems?How can you find the distance between two points on a coordinate plane using Pythagorean Theorem?How can you find the side lengths of a right triangle if you are given two other sides?How are the lengths of the sides of a right triangle related?What is the name of the longest side in a right triangle?If the equation a2 + b2 = c2 is true, then what type of triangle is formed?Upon Completion of the unit students will be able to :Solve real life problems using the Pythagorean Theorem. (8.G.6)Identify a right triangle by using Pythagorean Theorem and the length of the 3 sides.(8.G.6)Determine if three side lengths form a right triangle (8.G.7)Find the measurement of missing side in right triangle. (8.G.7)Define theorem, legs, hypotenuse, Pythagorean Theorem, Pythagorean triple (8.G.6)Find the distance between two points on a coordinate plane. (8.G.8)Interdisciplinary Standards2.5 Sports - finding distance across the baseball diamondActivities – including 21st Century TechnologiesActivity Big Ideas pg 236-237 Discovering the Pythagorean TheoremInstruction Big Ideas 6-2 The Pythagorean TheoremInstruction Big Ideas 6-5 Using the Pythagorean TheoremActivity Big Ideas pg 258-259 Using the Pythagorean TheoremFind perimeter of right triangles, trapezoids and parallelograms where hypotenuse side is missing.Have students work in pairs to solve real life problems using Pythagorean Theorem.Using graph paper have the student create the 3 squares and then compare area sLAB Holt McDougal pg 131 Exploring Right TrianglesInstruction Holt McDougal chapters 3-8 Pythagorean TheoremHolt McDougal chapters 3-8 problem solving Practice On Core 5-5 Using Pythagorean Theorem Practice On Core 5-6 Proving Pythagorean Theorem LAB Holt McDougal pg 136 Exploring the Converse of the Pythagorean TheoremInstruction Holt McDougal chapters 3-9 Applying the Pythagorean Theorem and its ConverseHolt McDougal chapters 3-9 problem solving Lab Prentice Hall Pythagorean Proofs pg CC8Enrichment ActivitiesHolt McDougal pg 143 Real World Connections – reasoning abstractly and quantitatively problem solvingBig Ideas pg T263 taking the Math DeeperLab Prentice Hall Using the Pythagorean Theorem with three-dimensional figures pg CC16Methods of Assessment/Evaluation:Open notebook quizTicket out the doorInteractive Smart Board questOpen Ended QuestionsSmartboard Lessons (clickers)Study IslandThumbs Up/Thumbs DownPair/ShareDry Erase BoardsFind the MistakeMidterms/FinalsProjectObservation (Teacher/Small/Whole Group)Independent WorkClassworkHomeworkCalculatorsVerbal AssessmentGroup labsWarm up lesson checksFormal and informal tests and quizzesResources/Including Online Resources:Online Textbook- my. Userid and password to be determinedTeacher webpage Study IslandMathematics grade 8 by Holt McDougal Course 3 TextbookBig Ideas textbook Topic Proportional Relationships and connections to lines and linear equations 8.EE.5. Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.8.EE.6. Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.2 weeks for UnitEssential QuestionsHow can you convert one measurement system to another?How do you describe the graph of the equation y = mx + b?How can students find the slope of a line and use the slope to understand and draw graphs?How can you use rates and ratios in real life problems?How can you determine whether figures are similar?How can you find the missing dimension in similar figures?How can you use slopes and intercepts to graph linear equations?Upon Completion of the unit students will be able to :Use similar right triangles to find slope of a line (8.EE.6)Compare proportional relationships and functions.(8.EE.5)Interpret rates as lope of graph (8.EE.5) Make a graph to model a situation. (8.EE.5)Find the missing measurements in similar figures (8.EE.6)Find the slope of a line and use the slope to understand and draw graphs (8.EE.6)Interdisciplinary Standards5.2 Science – study of density5.2 Science – energy for light patternsActivities – including 21st Century TechnologiesInstruction Holt McDougal chapters 2-3 Interpreting GraphsLab Holt McDougal pg 58 graphing points on graphing calculatorInstruction Holt McDougal chapters 4-1 ratios, rates and unit ratesLAB Holt McDougal pg 168-169 Explore SimilarityInstruction Holt McDougal chapters 4-3 Similar FiguresInstruction Holt McDougal 8-1 Graphing Linear EquationsLAB Holt McDougal pg 343 Explore SlopeInstruction Holt McDougal chapters 8-2 Slope of LineInstruction Holt McDougal chapters 8-3 Using Slopes and Intercepts LAB Holt McDougal pg 355 Graph Equations in Slope Intercept Form on Graphing CalculatorInstruction Holt McDougal chapters 8-4 Point Slope Form Instruction Big Ideas 1-5 Converting Units of MeasureActivity Big Ideas pg 30 Converting Units of MeasureInstruction Big Ideas 2-2 Slope of a LineInstruction Big Ideas 2-2b Triangles and Slope Instruction Big Ideas 3-3 Writing equations using two points Instruction Big Ideas 4-4b Comparing RatesActivity Big Ideas pg 173 Comparing Proportional RelationshipsInstruction Big Ideas 2-3 Graphing Linear Equations in Slope Intercept form Slope of a LineInstruction Big Ideas 2-4 Graphing Linear Equations in Standard FormInstruction Big Ideas 3-1 Writing Equations in Slope Intercept formInstruction Big Ideas 3-2 Writing Equations using a Slope and a pointInstruction Big Ideas 3-4 Solving Real Life ProblemsPractice On Core 2-3 Rate of ChangePractice On Core 2-4 Slope Intercept formPractice On Core 5-4 similar Triangles and SlopeEnrichment ActivitiesReview Holt McDougal chapters 1-5 solving equations with rational numbersReview Holt McDougal chapter 4-2 Solving ProblemsReview ordered pairs and graphing on coordinate plane Holt McDougal chapters 2-1 and 2-2Holt McDougal pg 65 Focusing on Problem Solving – make sense of problems and preserve to solving them.Holt McDougal pg 361 Focusing on Problem Solving – make sense of problems and preserve to solving them.Methods of Assessment/Evaluation:Open notebook quizTicket out the doorInteractive Smart Board questOpen Ended QuestionsSmartboard Lessons (clickers)Study IslandThumbs Up/Thumbs DownPair/ShareDry Erase BoardsFind the MistakeMidterms/FinalsProjectObservation (Teacher/Small/Whole Group)Independent WorkClassworkHomeworkCalculatorsVerbal AssessmentGroup labsWarm up lesson checksFormal and informal tests and quizzesProjectStudent Reflective Focus WritingResources/Including Online Resources:Online Textbook- my. Userid and password to be determinedTeacher webpage Study IslandHolt McDougal Course 3 TextbookBig Ideas textbook by Holt McDougalTopic Solving Linear Equations 8.EE.7. Solve linear equations in one variable. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.3 weeks for UnitEssential QuestionsHow can you use inductive reason to discover rules in mathematics?How can you test rules you discover inductively?How can you solve a multi-step equation?How can you check the reasonableness of a solution?How can you solve an equation that has variables on both sides?How can you use a formula for one measurement to write a formula for a different measurement?How can you write, solve and graph one-step linear inequalities?How can you write, solve and graph multi-step linear inequalities?How can you use and inequality to describe a real-life statement?How can you use addition or subtraction to solve an inequality?How can you use multiplication and division to solve an inequality?How can you use an inequality to describe the area and perimeter of a composite figure?Upon Completion of the unit students will be able to :Use the Properties of Equality to solve one-step equations. (8.EE.7)Solve multi-step equations using the inverse operation. (8.EE.7)Solve equations using the distributive property. (8.EE.7)Solve multi-step equation by combining like terms. (8.EE.7)Solve equations with variables on both sides using properties of equalities. (8.EE.7)Solve equations that have no solution, one solution or infinitely many solutions. (8.EE.7)Rewrite common geometric formulas. (8.EE.7)Translate inequalities from words to symbols and check to see if a value is a solution of the inequality. (8.EE.7)Solve inequalities and equations using addition and subtraction properties of inequality. (8.EE.7)Solve inequalities and equations using multiplication and division properties of inequality. (8.EE.7)Solve and graph multi-step inequalities. (8.EE.7)Interdisciplinary Standards2.1 Health Nutrition5.2 Physical ScienceActivities – including 21st Century TechnologiesLAB Holt McDougal pg 30 Model Two Step Equations Instruction Holt McDougal chapters 1-6 Solving two-step Equations Instruction Holt McDougal chapters 7-2 Solving Multi-step Equations LAB Holt McDougal pg 308 Model Equations with variables on Both SidesHolt McDougal Extension pg 314 Possible Solutions of One-variable Equations Instruction Holt McDougal chapter 7-3 solving equations with variables on both sides Instruction Big Ideas 1-1 Solving Simple equationsActivity Big Ideas pg 2-3 Sum of the angles of a triangleInstruction Big Ideas 1-2 Solving Multi-step equationsActivity Big Ideas pg 10-11 Solving the angles of a triangleInstruction Big Ideas 1-3 Solving Equations with variables on both sidesActivity Big Ideas pg 16-17 Perimeter and Area equationsInstruction Big Ideas 1-3b Solutions of linear equationsInstruction Big Ideas 1-4 Rewriting equations and FormulasActivity Big Ideas pg 24-25 Using Perimeter and area formulasInstruction Big Ideas 8-1 Writing and graphing InequalitiesActivity Big Ideas pg 312-313 Writing and graphing inequalitiesInstruction Big Ideas 8-2 Solving Inequalities Using Addition or SubtractionActivity Big Ideas pg 318-319 Quarterback Passing efficiencyInstruction Big Ideas 8-3 Solving Inequalities Using Multiplication or DivisionActivity Big Ideas pg 326-327 Using a table to solve and inequalityInstruction Big Ideas 8-4 Solving Multi-step inequalitiesActivity Big Ideas pg 334-335 Areas and perimeters of Composite figuresPractice On Core 3-1 Solving equations Practice On Core 3-2 Analyzing SolutionsEnrichment ActivitiesHolt McDougal pg 37 Real World Connections – reasoning abstractly and quantitatively problem solvingReview Simplifying Algebraic Equations Holt McDougal 7-1 Holt McDougal pg 317 Focusing on Problem Solving – make sense of problems and preserve to solving them.Big Ideas pg T15 Taking Math Deeper – problem solving algebraically in sportsBig Ideas pg T29 Taking Math Deeper – circles and percentsMethods of Assessment/Evaluation:Open notebook quizTicket out the doorInteractive Smart Board questOpen Ended QuestionsSmartboard Lessons (clickers)Study IslandThumbs Up/Thumbs DownPair/ShareDry Erase BoardsFind the MistakeMidterms/FinalsProjectObservation (Teacher/Small/Whole Group)Independent WorkClassworkHomeworkCalculatorsVerbal AssessmentGroup labsWarm up lesson checksFormal and informal tests and quizzesResources/Including Online Resources:Online Textbook- my. Userid and password to be determinedTeacher webpage Holt McDougal Course 3 TextbookBig Ideas textbook by Holt McDougalTopic Understand congruence and similarity using physical models, transparencies, or geometry software8.G.1. Verify experimentally the properties of rotations, reflections, and translations: a. Lines are taken to lines, and line segments to line segments of the same length.b. Angles are taken to angles of the same measure.c. Parallel lines are taken to parallel lines.8.G.2. Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.8.G.3. Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.8.G.4. Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.8.G.5. Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.3 weeks for UnitEssential QuestionsWhat are transformations?How do you identify rotation, reflection and translation of 2 dimensional figures?How can you classify two angles as complementary or supplementary?How do you calculate the sum of interior angles in a polygon?How do you calculate the exterior angles of a triangle and other polygons?How can you determine congruence by a sequence of rotations, reflections, or translations?How can you identify similar figures on a coordinate plane using dilations, rotations, reflections or translations?How do you classify triangles by their angles?How can you find a formula for the sum of the angle measures in any polygon?Which properties of triangles make them special among all other types of polygons?How can you use similar triangles to find a missing measurement?How can you use the properties of parallel lines to solve real life problems?How do parallel lines and a transversal create corresponding angles?Upon Completion of the unit students will be able to :Identify the 4 different types of transformation. (8.G.3)Identify complementary or supplementary angles. (8.G.1)Differentiate between interior and exterior angles. (8.G.5)Understand and draw transformation on a coordinate plane (8.G.1)Understand that two dimensional figure is congruent to another (8.G.4)Identify and describe dilation, translation, rotation and reflection and their effects on two dimensional figures on coordinate plane. (8.G.3)Determine congruency between transformed figures. (8.G.2)Understand and calculate sum of interior angles in a triangle.(8.G.5)Understand and calculate exterior angles of triangles (8.G.5)Understand relationship of angles formed by parallel lines and a transversal. (8.G.5)Interdisciplinary Standards9.3 Art – design9.4 Building – design and construction5.2 Physics – angle reflectionsActivities – including 21st Century TechnologiesInstruction holt McDougal chapters 4-4 DilationsLAB Holt McDougal pg 174 Explore Dilations LAB Holt McDougal pg 201 Bisect FiguresInstruction Holt McDougal chapters 5-1 Angle RelationshipsInstruction Holt McDougal chapters 5-2 Parallel and Perpendicular LinesInstruction Holt McDougal chapters 5-3 TrianglesLAB Holt McDougal pg 212 Exterior Angles of PolygonsInstruction Holt McDougal chapters 5-4 Coordinate GeometryLAB Holt McDougal pg 220 Explore CongruenceInstruction Holt McDougal chapters 5-5 CongruenceInstruction Holt McDougal chapters 5-6 Transformations Instruction Holt McDougal chapters 5-7 Similarity and Congruence TransformationsLAB Holt McDougal pg 237 Combine TransformationsInstruction Holt McDougal chapters 5-8 Identifying Combined TransformationsInstruction Big Ideas Topic 1 pg 398-401 Transformation on coordinate planeInstruction Big Ideas 5-1 Classifying AnglesActivity Big Ideas pg 184 Identifying complementary and supplementary anglesInstruction Big Ideas 5-2 Angles and Sides of TrianglesActivity Big Ideas pg 190 Exploring the angles of a TriangleInstruction Big Ideas 5-3 Angles of PolygonsActivity Big Ideas pg 196 The sum of the angle measure of a polygonInstruction Big Ideas 5-4 Using Similar TrianglesActivity Big Ideas pg 206 Angles of Similar trianglesInstruction Big Ideas 5-5 Parallel Lines and TransversalsActivity Big Ideas pg 212 A property of Parallel lines and Creating Parallel linesPractice On Core 5-1Parallel lines cut by transversalsPractice On Core 5-2 Triangle angle theoremPractice On Core 5-3 Similar trianglesEnrichment ActivitiesHolt McDougal pg 181 Real World Connections – reasoning abstractly and quantitatively problem solvingHolt McDougal pg 219 Focusing on Problem Solving – make sense of problems and preserve to solving them.Holt McDougal pg 245 Real World Connections – reasoning abstractly and quantitatively problem solvingBig Ideas pg T189 Taking Math Deeper – vertical anglesActivity Big Ideas pg T195 Taking Math Deeper – exploring anglesBig Ideas pg T203 Taking Math Deeper – comparison of linear and non-linear functionsBig Ideas pg T219 Taking Math Deeper – use reflective propertyMethods of Assessment/Evaluation:Open notebook quizTicket out the doorInteractive Smart Board questOpen Ended QuestionsSmartboard Lessons (clickers)Study IslandThumbs Up/Thumbs DownPair/ShareDry Erase BoardsFind the MistakeMidterms/FinalsProjectObservation (Teacher/Small/Whole Group)Independent WorkClassworkHomeworkCalculatorsVerbal AssessmentGroup labsWarm up lesson checksFormal and informal tests and quizzesResources/Including Online Resources:Online Textbook- my. Userid and password to be determinedTeacher webpage Holt McDougal Course 3 TextbookBig Ideas textbook by Holt McDougalTopic Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.8.G.9. Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. 2 weeks for UnitEssential QuestionsHow can students find volume of cylinders, cones and spheres using given formulas?How can students apply finding volume to real life problems?Upon Completion of the unit students will be able to :Find Volume of cylinders.(8.G.9)Find Volume of cones.(8.G.9)Find Volume of spheres.(8.G.9)Find volume of compound figures.(8.G.9)Apply formulas for finding volume to real life problems.(8.G.9)Interdisciplinary Standards5.2 Physical Science 5.2 Earth Systems Science Activities – including 21st Century TechnologiesLAB Holt McDougal pg 266 Find Volume of Prisms and Cylinders Instruction Holt McDougal chapters 6-2 Volume of Prisms and CylindersLAB Holt McDougal pg 274 Find Volume of Pyramids and Cones Practice On Core 5-7 Instruction Holt McDougal chapters 6-3 Volume of Pyramids and ConesInstruction Holt McDougal chapters 6-4 SpheresInstruction Big Ideas Topic 2 Volume pg 402 Enrichment ActivitiesReview of Circles Holt McDougal 6-1 circlesHolt McDougal pg 273 Focusing on Problem Solving – make sense of problems and preserve to solving them.Holt McDougal pg 287 Real World Connections – reasoning abstractly and quantitatively problem solvingMethods of Assessment/Evaluation:Open notebook quizTicket out the doorInteractive Smart Board questOpen Ended QuestionsSmartboard Lessons (clickers)Study IslandThumbs Up/Thumbs DownPair/ShareDry Erase BoardsFind the MistakeMidterms/FinalsProjectObservation (Teacher/Small/Whole Group)Independent WorkClassworkHomeworkCalculatorsVerbal AssessmentGroup labsWarm up lesson checksFormal and informal tests and quizzesResources/Including Online Resources:Online Textbook- my. Userid and password to be determinedTeacher webpage Holt McDougal Course 3 TextbookBig Ideas textbook by Holt McDougalTopic Analyze and solve pairs of simultaneous linear equations8.EE.8. Analyze and solve pairs of simultaneous linear equations. Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6.Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair.2 weeks for UnitEssential QuestionsHow can you recognize a linear equation?How can you draw a graph of a linear equation?How can you solve a system of linear equations?Can a system of linear equations have no solution?Can a system of linear equations have many solutions?How can you use a system of linear equations to solve an equation that has variable on both sides?How can you use a system of linear equations to model and solve a real-life problem?Upon Completion of the unit students will be able to :Graph Linear equations using a table of values. (8.EE.8.)Solving systems of linear equations using three different techniques. (8.EE.8.)Identify the 3 types of solutions for systems of linear equations (no solution, one solution, and infinitely many solutions). (8.EE.8.)Solve equations with variables on both sides by using two techniques.(graphing or solving algebraically) (8.EE.8.)Interdisciplinary Standards2.5 Sports 5.2 Physical ScienceActivities – including 21st Century TechnologiesInstruction Holt McDougal chapters 7-4 Systems of Equations Instruction Holt McDougal chapters 8-6 Solving Systems of Linear Equations by graphing Instruction Big Ideas 2-1 Graphing Linear equations Activity Big Ideas pg 48 Graphing a linear equationInstruction Big Ideas 2-5 Systems of Linear equations Activity Big Ideas pg 76 Writing a System of Linear EquationsInstruction Big Ideas 2-6 Special Systems of Linear equations Activity Big Ideas pg 82-83 Writing a System of Linear Equations using a table Instruction Big Ideas 2-7 Solving equations by graphingActivity Big Ideas pg 88-89 Solving a system of linear equations using a graphing calculatorInstruction Big Ideas 3-5 Writing Systems of Linear equations Enrichment ActivitiesHolt McDougal pg 323 Real World Connections – reasoning abstractly and quantitatively problem solvingHolt McDougal pg 373 Real World Connections – reasoning abstractly and quantitatively problem solvingBig Ideas pg T81 Taking Math Deeper – using 3 methods to solve systems of linear equationsBig Ideas pg T87 Taking Math Deeper – comparisons of systems of linear equationsMethods of Assessment/Evaluation:Open notebook quizTicket out the doorInteractive Smart Board questOpen Ended QuestionsSmartboard Lessons (clickers)Study IslandThumbs Up/Thumbs DownPair/ShareDry Erase BoardsFind the MistakeMidterms/FinalsProjectObservation (Teacher/Small/Whole Group)Independent WorkClassworkHomeworkCalculatorsVerbal AssessmentGroup labsWarm up lesson checksFormal and informal tests and quizzesResources/Including Online Resources:Online Textbook- my. Userid and password to be determinedTeacher webpage Holt McDougal Course 3 TextbookBig Ideas textbook by Holt McDougalTopic Investigate patterns of association in bivariate data.8.SP.1. Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.8.SP.2. Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.8.SP.3. Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height.8.SP.4. Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores?2 weeks for UnitEssential QuestionsDetermine and describe how changes in data values impact measures of central tendency.How can you use the measures of central tendency to distribute an amount evenly among a group of people?What is the impact of removing an outlier on the measures of central tendency?How can you use a box-and-whisker plot to describe a population?How can you use data to predict an event?Upon Completion of the unit students will be able to :Construct, read, and interpret a box-and-whisker plot. (8.SP.1)Write an equation of the line of best fit. (8.SP.2)Draw line of best fit (8.SP.2)Understand the purpose of the line of best fit and the resulting equation. (8.SP.3)Interdisciplinary Standards5.3 Science - Biology – animal studiesActivities – including 21st Century TechnologiesInstruction Holt McDougal chapters 9-1 Scatter Plots Instruction Holt McDougal chapters 9-2 Linear Best Fit Models LAB Holt McDougal pg 394 Create a Scatter Plot on graphing calculatorInstruction Big Ideas 7-1 Measures of Central TendencyBig Ideas Activity pg 274-275 Exploring Mean, Median, Mode and Line PlotsInstruction Big Ideas 7-2 Box and Whiskers Plots (mean, median, mode)Big Ideas Activity pg 280 Drawing a Box and Whisker PlotInstruction Big Ideas 7-3 Scatter Plots and Lines of Best FitBig Ideas Activity pg 288-289 Representing Data by a Linear EquationPractice On Core 6-1 Scatter plots and AssociationsPractice On Core 6-2 scatter plots and predictionsPractice On Core 6-3 Two way tablesInstruction Holt McDougal Extension Patterns in Two Way Tables Instruction Big Ideas 7-3b Two Way TablesInstruction and Activity Prentice Hall Pearson pg CC18 Exploring Bivariate DataEnrichment ActivitiesHolt McDougal pg 399 Focusing on Problem Solving – make sense of problems and preserve to solving them.Big Ideas pg T279 Taking Math DeeperBig Ideas pg T285 Taking Math Deeper – box-and-whisker benefits and limitationsBig Ideas pg T295 Taking Math Deeper – Proportions of a ManMethods of Assessment/Evaluation:Open notebook quizTicket out the doorInteractive Smart Board questOpen Ended QuestionsSmartboard Lessons (clickers)Study IslandThumbs Up/Thumbs DownPair/ShareDry Erase BoardsFind the MistakeMidterms/FinalsProjectObservation (Teacher/Small/Whole Group)Independent WorkClassworkHomeworkCalculatorsVerbal AssessmentGroup labsWarm up lesson checksFormal and informal tests and quizzesResources/Including Online Resources:Online Textbook- my. Userid and password to be determinedTeacher webpage Holt McDougal Course 3 TextbookBig Ideas textbook by Holt McDougalPrentice Hall Pearson Course 3 Mathematics textbook Topic Define, evaluate, and compare functions.8.F.1 Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.18.F.2 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change.8.F.3. Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line3 weeks for UnitEssential QuestionsHow can you find the domain and range of a function? How can you decide whether the domain of a function is discrete or continuous?How can you use a linear function to describe a linear pattern? ?????How can you recognize when a pattern in real life is linear or nonlinear? ?????Upon Completion of the unit students will be able to :Develop an understanding of domain and range by exploring similar problems. (8.F.1)Identify domain and range from a graph or table of values (8.F.2)Write an equation in function form. (8.F.3)Develop an understanding of discrete and continuous domains. (8.F.1)Graph functions and determine if the domain is discrete or continuous. (8.F.1)Develop an understanding of linear patterns in tables and graphs to write linear equations. (8.F.3)Describe four ways to represent a function. (8.F.3)Compare and identify tables and graphs of linear and nonlinear functions. (8.F.2)Compare and identify proportional relationships and functions (8.F.3)Interdisciplinary StandardsBiology – spiders rates of decentPsychics – rates of change History – population studiesAstronomy Activities – including 21st Century TechnologiesInstruction Holt McDougal chapters 2-4 FunctionsInstruction Holt McDougal chapters 2-5 Equations Tables and graphsInstruction Big Ideas 4-1 Domain and Range of a FunctionActivity Big Ideas pg 148-149 The Domain and Range of a functionPractice On Core 2-1 Functions tables and graphsPractice On Core 2-5 writing equations to describe a functionInstruction Big Ideas 4-2 Discrete and Continuous DomainsActivity Big Ideas pg 154-155 Discrete or Continuous DomainsInstruction Big Ideas 4-3 Linear Function PatternsActivity Big Ideas pg 162-163 Finding Linear PatternsInstruction Big Ideas 4-4 Comparing Linear and Nonlinear FunctionsActivity Big Ideas pg 168-169 Finding Patterns for Similar FiguresInstruction Big Ideas 4-4b Comparing RatesInstruction Holt McDougal chapters 9-3 Linear FunctionsInstruction Holt McDougal chapters 9-4 Comparing Multiple RepresentationsEnrichment ActivitiesHolt McDougal pg 409 Real World Connections – reasoning abstractly and quantitatively problem solvingMethods of Assessment/Evaluation:Open notebook quizTicket out the doorInteractive Smart Board questOpen Ended QuestionsSmartboard Lessons (clickers)Study IslandThumbs Up/Thumbs DownPair/ShareDry Erase BoardsFind the MistakeMidterms/FinalsProjectObservation (Teacher/Small/Whole Group)Independent WorkClassworkHomeworkCalculatorsVerbal AssessmentGroup labsWarm up lesson checksFormal and informal tests and quizzesResources/Including Online Resources:Online Textbook- my. Userid and password to be determinedTeacher webpage Holt McDougal Course 3 TextbookBig Ideas textbook by Holt McDougalTopic Use functions to model relationships between quantities.8.F.4. Construct a function to model a linear relationship between two quantities. Determine the rate of change? and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.8.F.5. Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.3 weeks for UnitEssential QuestionsHow can you write an equation of line when you are given the slope and the y-intercept of the line?How can you write an equation of a line when you are given two points on the line?How can you use a linear equation in two variables to model and solve a real-life problem?How can you use a linear function to describe a linear pattern? How can you recognize when a pattern in real life is linear or nonlinear? How can you identify and write a linear function?Upon Completion of the unit students will be able to :Write, solve and graph two step linear equations. (8.F.4)Write an equation in slope-intercept form when given the slope and the y intercept. (8.F.4)Write an equation when given two points on the line. (8.F.4)Calculate the slope from two points (not graphed). (8.F.4)Solve real life problems using linear equations. (8.F.4)Write a linear equation for a graphed function. (8.F.5)Write linear functions by recognizing patters in graphical and tabular information. (8.F.6)Interdisciplinary StandardsPhysics – rate of fallingChemistry – tracking chemical changesActivities – including 21st Century TechnologiesInstruction Big Ideas 3-2 Writing equations using a slope and point (repeat from (8.EE.6)Activity Big Ideas pg 112 Writing equations of lines.Instruction Big Ideas 3-3 Writing equations using two pointsActivity Big Ideas pg 118-119 Writing equations of linesInstruction Big Ideas 3-4 Solving Real Life Problems (repeat from (8.EE.6)Activity Big Ideas pg 126-127 Writing a Story / drawing graphsInstruction Big Ideas 4-3 Linear Function Patterns (repeat from (8.F.3)Practice On Core 2-6 comparing functionsPractice On Core 2-7 analyzing graphs Activity Big Ideas pg 162-163 Find Linear PattersInstruction Big Ideas 4-4 Comparing Linear and Nonlinear Functions (repeat from (8.F.3)Instruction Holt McDougal chapters 8-5 Direct Variation (8.f.5)Instruction Holt McDougal chapters 9-3 Linear FunctionsEnrichment ActivitiesInstruction Holt McDougal chapters 2-5 Equations, tables and graphs (review from 8.F.1)Big Ideas pg T117 Taking Math Deeper tracking biology informationBig Ideas pg T123 Taking Math Deeper real life problemsBig Ideas pg T131 Taking Math Deeper business problemsMethods of Assessment/Evaluation:Open notebook quizTicket out the doorInteractive Smart Board questOpen Ended QuestionsSmartboard Lessons (clickers)Study IslandThumbs Up/Thumbs DownPair/ShareDry Erase BoardsFind the MistakeMidterms/FinalsProjectObservation (Teacher/Small/Whole Group)Independent WorkClassworkHomeworkCalculatorsVerbal AssessmentGroup labsWarm up lesson checksFormal and informal tests and quizzesResources/Including Online Resources:Online Textbook- my. Userid and password to be determinedTeacher webpage Holt McDougal Course 3 TextbookBig Ideas textbook by Holt McDougal ................
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