# Algebra 1 Concepts – 8 th grade math

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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 2012

Algebra 1 Concepts 8th grade mathOutlineTopic Number System 2 weeks8 NS 1 - rational numbers, irrational numbers, real numbers8 NS 2 - identifying and graphing irrational numbers

Topic 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 notation

Topic 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 intercept

Topic 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, triangles

Topic Solve real-world problems involving volume of cylinders, cones, and spheres.2.5 weeks

8 G 9 - volume of prisms, cylinders, cones, spheres

Topic 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 graphing

Topic 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 5

Topic Define, evaluate, and compare functions.4 weeks8.F.1 - linear functions8.F.2. compare functions8.F.3. slope-intercept form

Topic 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 relationships

Topic 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 number

8.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 Questions How 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 :1. Write a rational number as the ratio of two integers. (8.NS.1)2. Identify irrational numbers (8.NS.1)3. Approximate the decimal value of an irrational number (8.NS.2)4. Understand and explain the relationship of rational, irrational, real, integers, and natural numbers (8.NS.1)5. Locate rational, irrational, real, integers and natural numbers on a number line. (8.NS.2)6. Create the decimal expansion of a rational number (8.NS.1)7. Define square root, cube root, perfect square, radical sign, radicand, irrational number, real numbers (8.NS.1)8. Review rules for computation of rational number (8.NS.2)9. Understand and apply the properties of addition, subtraction, division, and multiplication of square roots (8.NS.1)

Interdisciplinary Standards L.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 sides 5.2 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 Technologies Instruction Holt McDougal chapters 1-1 Rational Numbers Lab - Use calculators to find approximate values of irrational numbers Practice from On Core Mathematics chapters 1-5 how to write any rational number as a fraction Instruction Holt McDougal pg 128 Extension identifying and graphing irrational numbers Instruction Big Ideas lesson 6-3 irrational numbers approximating square roots Instruction Big Ideas 6-4 Simplifying square roots Activity Big Ideas pg 244 Approximating square roots with scientific calculator

Enrichment Activities Review 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 Numbers Instruction Holt McDougal extension Identifying and graphing irrational numbers Big Ideas activity pg 252 constructing a golden ratio Big Ideas activity pg 253 The Golden ratio and the human bodyMethods of Assessment/Evaluation: Ticket out the door Interactive Smart Board quest Open Ended Questions Smartboard Lessons (clickers) Study Island Thumbs Up/Thumbs Down Pair/Share Dry Erase Boards Find the Mistake Midterms/Finals Project Observation (Teacher/Small/Whole Group) Independent Work Classwork Homework Calculators Verbal Assessment Group labs Warm up lesson checks Formal and informal tests and quizzes

Resources/Including Online Resources: Online Textbook- my.hrw.com Userid and password to be determined Teacher webpage Study Island Holt McDougal Course 3 Textbook Big 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, 3235 = 33 = 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 Questions How 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 :1. Write numbers with exponents (8.EE.1)2. Convert numbers to and from exponential form (8.EE.1)3. Define power, exponent, and base (8.EE.1)4. Apply exponents in real life problems (8.EE.2)5. Multiply and divide two powers with the same base (8.EE.2)6. Distribute exponential powers correctly (8.EE.2)7. Write numbers in scientific notation and standard notation (8.EE.3)8. Understand and write numbers as powers of 10 (8.EE.3)9. Create and calculate scientific notations on calculator (8.EE.4)10. Do calculations with scientific notation (8.EE.4)11. 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 Technologies Instruction Holt McDougal chapters 3-1 review positive and negative exponents & powers of 10 Instruction Holt McDougal chapters 3-2 properties of exponents Instruction Holt McDougal chapters 3-3 scientific notation Instruction Holt McDougal chapters 3-4 operations with scientific notation Instruction from Big Ideas, chapter 6-1 Finding Square Roots Instruction from Big Ideas chapter 6-3 approximating square roots Instruction Holt McDougal chapters 3-5 Squares and Square roots Instruction Holt McDougal chapters 3-6 Estimating Square roots Instruction Big Ideas, chapter 9-3 quotient of powers property Instruction Big Ideas, chapter 9-4 zero and negative exponents Instruction Big Ideas, chapter 9-5 Reading scientific notation Instruction Big Ideas, chapter 9-6 Writing Scientific Notation Practice On Core 1-2 scientific notation Practice on Core 1-3 operations of scientific notation Practice On Core 1-4 square roots and cube roots Lab Prentice Hall - pg 61 Repeating decimals Lab Holt McDougal chapters 3-4 multiplying scientific notation Problem solving Holt McDougal chapters 3-1 to 3-4 (real life examples)Enrichment Activities Review from Big Ideas, chapter 6-3 Challenge worksheets accompanying the textbook Practice level C worksheets Methods of Assessment/Evaluation: Open notebook quiz Ticket out the door Interactive Smart Board quest Open Ended Questions Smartboard Lessons (clickers) Study Island Thumbs Up/Thumbs Down Pair/Share Dry Erase Boards Find the Mistake Midterms/Finals Project Observation (Teacher/Small/Whole Group) Independent Work Classwork Homework Calculators Verbal Assessment Group labs Warm up lesson checks Formal and informal tests and quizzesResources/Including Online Resources: Online Textbook- my.hrw.com Userid and password to be determined Teacher webpage Study Island Holt McDougal Course 3 Textbook Big Ideas textbook

Topic Understand and apply the Pythagorean Theorem 8.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 Questions How 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 :1. Solve real life problems using the Pythagorean Theorem. (8.G.6)2. Identify a right triangle by using Pythagorean Theorem and the length of the 3 sides.(8.G.6)3. Determine if three side lengths form a right triangle (8.G.7)4. Find the measurement of missing side in right triangle. (8.G.7)5. Define theorem, legs, hypotenuse, Pythagorean Theorem, Pythagorean triple (8.G.6)6. Find the distance between two points on a coordinate plane. (8.G.8)Interdisciplinary Standards 2.5 Sports - finding distance across the baseball diamondActivities including 21st Century Technologies Activity Big Ideas pg 236-237 Discovering the Pythagorean Theorem Instruction Big Ideas 6-2 The Pythagorean Theorem Instruction Big Ideas 6-5 Using the Pythagorean Theorem Activity Big Ideas pg 258-259 Using the Pythagorean Theorem Find 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 s LAB Holt McDougal pg 131 Exploring Right Triangles Instruction Holt McDougal chapters 3-8 Pythagorean Theorem Holt 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 Theorem Instruction Holt McDougal chapters 3-9 Applying the Pythagorean Theorem and its Converse Holt McDougal chapters 3-9 problem solving Lab Prentice Hall Pythagorean Proofs pg CC8Enrichment Activities Holt McDougal pg 143 Real World Connections reasoning abstractly and quantitatively problem solving Big Ideas pg T263 taking the Math Deeper Lab Prentice Hall Using the Pythagorean Theorem with three-dimensional figures pg CC16Methods of Assessment/Evaluation: Open notebook quiz Ticket out the door Interactive Smart Board quest Open Ended Questions Smartboard Lessons (clickers) Study Island Thumbs Up/Thumbs Down Pair/Share Dry Erase Boards Find the Mistake...

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