8th grade Mathematics Curriculum Guide


 Austin Campbell
 2 years ago
 Views:
Transcription
1 Unit 6: Systems Time Frame: Quarter 3 and 4 Connections to Previous Learning: This unit focuses on extending the understanding of ratios and proportions that was explored in Grades 6 and 7. Unit rates were explored in Grade 6 as the comparison of two different quantities, (unit rate). In Grade 7 unit rates were expanded to complex fractions and percents through solving multistep problems such as: discounts, interest, taxes, tips, and percent of increase or decrease. Proportional relationships were applied in scale drawings, and students should have developed an informal understanding that the steepness of the graph is the slope or unit rate. From unit 4, students will build off of their learning that proportional relationships are part of a broader group of linear functions, and they are able to identify whether a relationship is linear. Focus within the Grade Level: Students graph a system of two linear equations, recognizing that the ordered pair for the point of intersection is the x value that will generate the given y value for both equations. Students recognize that graphed lines with one point of intersection (different slopes) will have one solution, parallel lines (same slope, different y intercepts) have no solutions, and lines that are the same (same slope, same x intercept) will have infinitely many solutions. Connections to Subsequent Learning: In high school, students use function notation and are able to identify types of nonlinear functions. Graphing will be extended to exponential, rational, and quadratic equations and their graphs. Math 1 further develops the concept of solving systems through standards A.REI.5 and A.REI.6 Unit 1 Clover Park School District 6/10/15 Page 1
2 Common Core Standards in this unit: Understand the connections between proportional relationships, 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 objects has greater speed. Analyze and solve linear equations and pairs of simultaneous linear equations. 8.EE8.Analyze and solve pairs of simultaneous linear equations. a. 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. b. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. c. Solve real world and mathematical problems leading to two linear equation 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. Estimated Days on the Unit Mathematical Practices 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make sure of structure. 8. Look for and express regularity in repeated reasoning Unit 1 Clover Park School District 6/10/15 Page 2
3 Unit 1 Clover Park School District 6/10/15 Page 3
4 Stage 1 Desired Results Transfer Goals Students will be able to independently use their learning to Understand the connections between proportional relationships, lines, and linear equations. Analyze and solve linear equations and pairs of simultaneous linear equations. UNDERSTANDINGS Students will understand that Unit rates can be explained in graphical representation, algebraic equations, and in geometry through similar triangles. The solution to a system of two linear equations in two variables is an ordered pair that satisfies both equations. Some systems of equations have no solutions (parallel lines) and others have infinite solutions (be the same line). Meaning Goals ESSENTIAL QUESTIONS Why is one variable dependent upon the other in relationships? What makes a solution strategy both efficient and effective? How is it determined if multiple solutions to an equation are valid? How does the context of the problem affect the reasonableness of a solution? Why can two equations be added together to get another true equation? What is a solution? Students will know Predictions can be made based on the analysis and interpretation of a set of data. Graphical representations can be used to make interpretations and predictions about real world situations. Linear associations relate to graphs of lines. Nonlinear associations relate to graphs other than lines. Straight lines are widely used to model relationships between two quantitative variables. Different representations (written descriptions, tables, graphs, and equations) of the relationships between varying quantities may have Acquisition Goals Students will be skilled at Unit 1 Clover Park School District 6/10/15 Page 4 Determine whether a relationship is linear. (8.EE.8) Compare graphs, tables, and equations of proportional relationships. (8.EE.5) Graph proportional relationships and interpret the unit rate as the slope. (8.EE.5) Estimate solutions by graphing equations. (8.EE.8) Solve systems by graphing, substitution, or elimination (combination). (8.EE.8) Determine if a system has one solution, no solutions, or many solutions. (8.EE.8) Interpret the solution to a system of equations in context. (8.EE.8)
5 different strengths and weaknesses. Linear functions may be used to represent and generalize real situations. Some data may be misleading based on representation. Unit 1 Clover Park School District 6/10/15 Page 5
6 Stage 1 Established Goals: Common Core State Standards for Mathematics Students will be able to independently use their learning to Analyze and solve linear equations and pairs of simultaneous linear equations. 8.EE.8: Analyze and solve pairs of simultaneous linear equations. a. 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. b. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. c. Solve real world and mathematical problems leading to two linear equations in two variables. Explanations, Examples, and Comments Vocabulary: Systems of equations Simultaneous equations Linear equation Substitution Elimination Solution Pre requisite skills: Slope Slope Intercept Form Graphing Rate of Change Explanations: and have no solution because 3 2 cannot simultaneously be 5 and 6. 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. Systems of linear equations can also have one solution, infinitely many solutions or no solutions. Students will discover these cases as they graph systems of linear equations Stage 3 MATERIALS BY STANDARD(S): Estimated days Holt Algebra: 6 1 Solving Systems by Graphing Holt Course 3: 11 6 Systems of Equations Holt Algebra: 6 2 Solving Systems by Substitution Holt Algebra: Solving Systems by Elimination Holt Algebra: Solving Special Systems Additional Resources Linear Equations Activity Solving Systems by Graphing (TI Activity) Guided Notes 1 Guided Notes 2 Solving Linear Equations by Graphing Partner Activity Race to The Top: Lesson 3 Graphing Cookie Calorie Conundrum (North Carolina Task) Cara s Candles Task DVD Club Race to the Top: Lesson 4 Substitution Race to the Top: Lesson 5 Elimination Race to the Top: Lesson 6 Connections Unit 1 Clover Park School District 6/10/15 Page 6
7 and solve them algebraically. A system of linear equations whose graphs meet at one point (intersecting lines) has only one solution, the ordered pair representing the point of intersection. A system of linear equations whose graphs do not meet (parallel lines) has no solutions and the slopes of these lines are the same. A system of linear equations whose graphs are coincident (the same line) has infinitely many solutions, the set of ordered pairs representing all the points on the line. By making connections between algebraic and graphical solutions and the context of the system of linear equations, students are able to make sense of their solutions. Students need opportunities to work with equations and context that include whole number and/or decimals/fractions. Example Problems 1. Find x and y using elimination and then using substitution. o 3x + 4y = 7 o 2x + 8y = Plant A and Plant B are on different watering schedules. This affects their rate of growth. Compare the growth of the two plants to determine when their heights will be the same. Let W = number of weeks Let H = height of the plant after W weeks Plant A Plant B Which Would You Rather Have? I.1 Making Sense of Problem Solving Better Deal Going to The Game (Yummy Math) Diapers (Yummy Math) Sandy s Candy Corporation (North Carolina Task) Faster, Faster! I.7 Making Sense of Problem Solving Solving 2 by 2 Systems by Graphing Stations Solving 2 by 2 Systems by Substitution Stations Solving 2 by 2 Systems by Elimination Stations Foldable for Solving Systems of Equations Comparing Sundaes: Worksheet Classifying Solutions to Systems of Equations: Lesson and PowerPoint Value of Money: Lesson and PowerPoint W H W H 0 4 (0,4) 0 2 (0,2) 1 6 (1,6) 1 6 (1,6) 2 8 (2,8) 2 10 (2,10) 3 10 (3,10) 3 14 (3,14) a. Given each set of coordinates, graph their corresponding lines. Unit 1 Clover Park School District 6/10/15 Page 7
8 b. Write an equation that represents the growth rate of Plant A and Plant B. Solution: Plant A H = 2W + 4 Plant B H = 4W + 2 c. At which week will the plants have the same height? Solution: The plants have the same height after one week. Plant A: H = 2W + 4 Plant B: H = 4W + 2 Plant A: H = 2(1) + 4 Plant B: H = 4(1) + 2 Plant A: H = 6 Plant B: H = 6 d. After one week, the height of Plant A and Plant B are both 6 inches. 3. Unit 1 Clover Park School District 6/10/15 Page 8
9 4. Unit 1 Clover Park School District 6/10/15 Page 9
10 Evaluative Criteria: SBAC Sample Items 8.EE.8 (C.200) 8.EE.8 (D.147) 8.EE.8 (B.149) 8.EE.5 (C.202) Stage 2 Evidence SAMPLE Assessment Evidence PERFORMANCE TASK(S): Comparing Fuel Consumptions: Lesson and PowerPoint Think Tac Toe: Linear Systems CA s: basic calculator allowed (not graphing) 8.EE.8: #1, #2 Washington State Common Core State Mathematics Standards Transition Document: Washington State: Materials to help districts and others understand the organization and content of the standards and the content and evidence base used to support the standards: OTHER ASSESSMENT EVIDENCE: For the vertical progression, see the University of Arizona progression documents. Stage 3 Learning Plan Sample Summary of Key Learning Events and Instruction that serves as a guide to a detailed lesson planning LEARNING ACTIVITIES: NOTES: A suggested guide to layout of unit by days 8.EE.8 Day 1: Linear Review (8.EE.5) Linear Equations Activity Day 2: Systems by Graphing Solving Systems by Graphing (TI Activity) Day 3: Systems by Graphing Unit 1 Clover Park School District 6/10/15 Page 10
11 Holt Algebra: 6 1 Solving Systems by Graphing Guided Notes 1 Stage 3 Learning Plan Sample Day 4: Systems by Graphing Holt Algebra: 6 1 Solving Systems by Graphing Guided Notes 2 Day 5: Systems by Graphing Race to The Top: Lesson 3 Graphing Tiffany s Plants Day 6: Systems by Graphing Race to The Top: Lesson 3 Graphing Equations and Graph Cards Classwork & Homework Day 6: Systems by Graphing Solving Linear Equations by Graphing Partner Activity Comparing Sundaes Day 7: Systems by Substitution Holt Course 3: 11 6 Systems of Equations Cara s Candles Day 8: Systems by Substitution Holt Algebra: 6 2 Solving Systems by Substitution DVD Club Day 9: Systems by Substitution Cookie Calorie Conundrum (North Carolina Task) or Race to the Top: Lesson 4 Substitution Equation Notecards and Math Teachers Café Unit 1 Clover Park School District 6/10/15 Page 11
12 Day 10: Systems by Substitution Solving 2 by 2 Systems by Substitution Stations Stage 3 Learning Plan Sample Day 11: Systems by Elimination Holt Algebra: Solving Systems by Elimination Day 12: Systems by Elimination Solving 2 by 2 Systems by Elimination Stations Day 13: Solving Systems Foldable for Solving Systems of Equations Power Point Find Solutions to Systems Holt Algebra: Solving Special Systems Day 14: Solving Systems Race to the Top: Lesson 6 Connections Day 15: Solving Systems Classifying Solutions to Systems of Equations Day 16: Solving Systems Which Would You Rather Have? I.1 Making Sense of Problem Solving Day 17: Solving Systems Going to The Game (Yummy Math) or Diapers (Yummy Math) or Sandy s Candy Corporation (North Carolina Task) Day 18: Solving Systems Comparing Fuel Consumptions Unit 1 Clover Park School District 6/10/15 Page 12
with functions, expressions and equations which follow in units 3 and 4.
Grade 8 Overview View unit yearlong overview here The unit design was created in line with the areas of focus for grade 8 Mathematics as identified by the Common Core State Standards and the PARCC Model
More informationTennessee Department of Education
Tennessee Department of Education Task: Pool Patio Problem Algebra I A hotel is remodeling their grounds and plans to improve the area around a 20 foot by 40 foot rectangular pool. The owner wants to use
More informationPowerTeaching i3: Algebra I Mathematics
PowerTeaching i3: Algebra I Mathematics Alignment to the Common Core State Standards for Mathematics Standards for Mathematical Practice and Standards for Mathematical Content for Algebra I Key Ideas and
More informationGeorgia Standards of Excellence Curriculum Map. Mathematics. GSE 8 th Grade
Georgia Standards of Excellence Curriculum Map Mathematics GSE 8 th Grade These materials are for nonprofit educational purposes only. Any other use may constitute copyright infringement. GSE Eighth Grade
More informationOverview of Math Standards
Algebra 2 Welcome to math curriculum design maps for Manhattan Ogden USD 383, striving to produce learners who are: Effective Communicators who clearly express ideas and effectively communicate with diverse
More informationCreating, Solving, and Graphing Systems of Linear Equations and Linear Inequalities
Algebra 1, Quarter 2, Unit 2.1 Creating, Solving, and Graphing Systems of Linear Equations and Linear Inequalities Overview Number of instructional days: 15 (1 day = 45 60 minutes) Content to be learned
More informationGRADE 8 MATH: TALK AND TEXT PLANS
GRADE 8 MATH: TALK AND TEXT PLANS UNIT OVERVIEW This packet contains a curriculumembedded Common Core standards aligned task and instructional supports. The task is embedded in a three week unit on systems
More informationMathematics Curriculum Guide Precalculus 201516. Page 1 of 12
Mathematics Curriculum Guide Precalculus 201516 Page 1 of 12 Paramount Unified School District High School Math Curriculum Guides 2015 16 In 2015 16, PUSD will continue to implement the Standards by providing
More informationMath at a Glance for April
Audience: School Leaders, Regional Teams Math at a Glance for April The Math at a Glance tool has been developed to support school leaders and region teams as they look for evidence of alignment to Common
More informationTask: Will and Latisha s Tile Problem Algebra I
Tennessee Department of Education Task: Will and Latisha s Tile Problem Algebra I In math class, Will and Latisha were challenged to create their own pattern with tiles. Latisha built the first three arrangements
More informationStudents will understand 1. use numerical bases and the laws of exponents
Grade 8 Expressions and Equations Essential Questions: 1. How do you use patterns to understand mathematics and model situations? 2. What is algebra? 3. How are the horizontal and vertical axes related?
More informationMathematics. Curriculum Content for Elementary School Mathematics. Fulton County Schools Curriculum Guide for Elementary Schools
Mathematics Philosophy Mathematics permeates all sectors of life and occupies a wellestablished position in curriculum and instruction. Schools must assume responsibility for empowering students with
More informationMathematics GradeLevel Instructional Materials Evaluation Tool
Mathematics GradeLevel Instructional Materials Evaluation Tool Quality Review GRADE 8 Textbooks and their digital counterparts are vital classroom tools but also a major expense, and it is worth taking
More informationGeometry Mathematics Curriculum Guide Unit 6 Trig & Spec. Right Triangles 2016 2017
Unit 6: Trigonometry and Special Right Time Frame: 14 Days Primary Focus This topic extends the idea of triangle similarity to indirect measurements. Students develop properties of special right triangles,
More informationPennsylvania System of School Assessment
Pennsylvania System of School Assessment The Assessment Anchors, as defined by the Eligible Content, are organized into cohesive blueprints, each structured with a common labeling system that can be read
More information612 ELA and Mathematics Guidelines address student rights to high quality literacy, including written expression, and mathematics instruction.
The Tennessee Department of Education supports a comprehensive and cohesive English Language Arts (ELA) and mathematics program of study for all 612 students. Programs should be consistent with the Common
More informationPerformance Level Descriptors Grade 6 Mathematics
Performance Level Descriptors Grade 6 Mathematics Multiplying and Dividing with Fractions 6.NS.12 Grade 6 Math : SubClaim A The student solves problems involving the Major Content for grade/course with
More informationPrentice Hall Connected Mathematics 2, 7th Grade Units 2009
Prentice Hall Connected Mathematics 2, 7th Grade Units 2009 Grade 7 C O R R E L A T E D T O from March 2009 Grade 7 Problem Solving Build new mathematical knowledge through problem solving. Solve problems
More informationDENTAL IMPRESSIONS TARGET COMMON CORE STATE STANDARD(S) IN MATHEMATICS: NQ.1:
This task was developed by high school and postsecondary mathematics and health sciences educators, and validated by content experts in the Common Core State Standards in mathematics and the National Career
More informationPA Academic Standards. 2.4. Mathematical Reasoning and Connections 2.5. Mathematical Problem Solving and Communication
Curriculum Category Shift Standard Areas Grades K8 and High School PA Academic Standards 2.4. Mathematical Reasoning and Connections 2.5. Mathematical Problem Solving and Communication PA Common Core
More informationNorwalk La Mirada Unified School District. Algebra Scope and Sequence of Instruction
1 Algebra Scope and Sequence of Instruction Instructional Suggestions: Instructional strategies at this level should include connections back to prior learning activities from K7. Students must demonstrate
More informationContent Emphases for Grade 7 Major Cluster 70% of time
Critical Area: Geometry Content Emphases for Grade 7 Major Cluster 70% of time Supporting Cluster 20% of Time Additional Cluster 10% of Time 7.RP.A.1,2,3 7.SP.A.1,2 7.G.A.1,2,3 7.NS.A.1,2,3 7.SP.C.5,6,7,8
More informationPreAlgebra 2008. Academic Content Standards Grade Eight Ohio. Number, Number Sense and Operations Standard. Number and Number Systems
Academic Content Standards Grade Eight Ohio PreAlgebra 2008 STANDARDS Number, Number Sense and Operations Standard Number and Number Systems 1. Use scientific notation to express large numbers and small
More informationInfinite Algebra 1 supports the teaching of the Common Core State Standards listed below.
Infinite Algebra 1 Kuta Software LLC Common Core Alignment Software version 2.05 Last revised July 2015 Infinite Algebra 1 supports the teaching of the Common Core State Standards listed below. High School
More informationCORE Assessment Module Module Overview
CORE Assessment Module Module Overview Content Area Mathematics Title Speedy Texting Grade Level Grade 7 Problem Type Performance Task Learning Goal Students will solve reallife and mathematical problems
More informationTo represent mathematical relationships using graphs. 41 Activity: Relating Quantities See Department Chair for File 1 day A.REI.10, F.IF.
CCSS for Mathematical Practice: 1. Make sense of problems and persevere in solving them 2. Reason abstractly and quantitatively 3. Construct viable arguments and critique the reasoning of others 4. Model
More informationPearson Algebra 1 Common Core 2015
A Correlation of Pearson Algebra 1 Common Core 2015 To the Common Core State Standards for Mathematics Traditional Pathways, Algebra 1 High School Copyright 2015 Pearson Education, Inc. or its affiliate(s).
More informationINFORMATIONAL GUIDE FOR THE MATHEMATICS PORTFOLIO APPEALS PROCESS
INFORMATIONAL GUIDE FOR THE MATHEMATICS PORTFOLIO APPEALS PROCESS The most important part of the PARCC Portfolio Appeal process is the evidence gathered to show the student s ability to demonstrate the
More informationLesson Plan Mine Shaft Grade 8 Slope
CCSSM: Grade 8 DOMAIN: Expressions and Equations Cluster: Understand the connections between proportional relationships, lines, and linear equations. Standard: 8.EE.5: Graph proportional relationships,
More informationSeventh Grade: Mathematics Unit #2: Ratio, Proportion, and Percent
Seventh Grade: Mathematics Unit #2: Overarching Question: How do you use proportional reasoning to make sense of mathematical and realworld problems? Previous Unit: Similar Figures This Unit: Next Unit:
More informationEQUATIONS and INEQUALITIES
EQUATIONS and INEQUALITIES Linear Equations and Slope 1. Slope a. Calculate the slope of a line given two points b. Calculate the slope of a line parallel to a given line. c. Calculate the slope of a line
More informationRUTHERFORD HIGH SCHOOL Rutherford, New Jersey COURSE OUTLINE STATISTICS AND PROBABILITY
RUTHERFORD HIGH SCHOOL Rutherford, New Jersey COURSE OUTLINE STATISTICS AND PROBABILITY I. INTRODUCTION According to the Common Core Standards (2010), Decisions or predictions are often based on data numbers
More informationPrentice Hall: Middle School Math, Course 1 2002 Correlated to: New York Mathematics Learning Standards (Intermediate)
New York Mathematics Learning Standards (Intermediate) Mathematical Reasoning Key Idea: Students use MATHEMATICAL REASONING to analyze mathematical situations, make conjectures, gather evidence, and construct
More informationAlgebra I. In this technological age, mathematics is more important than ever. When students
In this technological age, mathematics is more important than ever. When students leave school, they are more and more likely to use mathematics in their work and everyday lives operating computer equipment,
More informationBig Ideas in Mathematics
Big Ideas in Mathematics which are important to all mathematics learning. (Adapted from the NCTM Curriculum Focal Points, 2006) The Mathematics Big Ideas are organized using the PA Mathematics Standards
More informationMathematics Interim Assessment Blocks Blueprint V
67 Blueprint V.5.7.6 The Smarter Balanced Interim Assessment Blocks (IABs) are one of two distinct types of interim assessments being made available by the Consortium; the other type is the Interim Comprehensive
More informationFor example, estimate the population of the United States as 3 times 10⁸ and the
CCSS: Mathematics The Number System CCSS: Grade 8 8.NS.A. Know that there are numbers that are not rational, and approximate them by rational numbers. 8.NS.A.1. Understand informally that every number
More informationCommon Core Unit Summary Grades 6 to 8
Common Core Unit Summary Grades 6 to 8 Grade 8: Unit 1: Congruence and Similarity 8G18G5 rotations reflections and translations,( RRT=congruence) understand congruence of 2 d figures after RRT Dilations
More informationAlgebra 12. A. Identify and translate variables and expressions.
St. Mary's College High School Algebra 12 The Language of Algebra What is a variable? A. Identify and translate variables and expressions. The following apply to all the skills How is a variable used
More informationPlanned Course of Study. Algebra I Part 1 NORTHWESTERN LEHIGH SCHOOL DISTRICT 6493 ROUTE 309 NEW TRIPOLI, PA 18066
Planned Course of Study Algebra I Part 1 NORTHWESTERN LEHIGH SCHOOL DISTRICT 6493 ROUTE 309 NEW TRIPOLI, PA 18066 NORTHWESTERN LEHIGH SCHOOL BOARD 2013 Darryl S. Schafer, President LeRoy Sorenson, Vice
More informationCORRELATED TO THE SOUTH CAROLINA COLLEGE AND CAREERREADY FOUNDATIONS IN ALGEBRA
We Can Early Learning Curriculum PreK Grades 8 12 INSIDE ALGEBRA, GRADES 8 12 CORRELATED TO THE SOUTH CAROLINA COLLEGE AND CAREERREADY FOUNDATIONS IN ALGEBRA April 2016 www.voyagersopris.com Mathematical
More informationparent ROADMAP MATHEMATICS SUPPORTING YOUR CHILD IN HIGH SCHOOL
parent ROADMAP MATHEMATICS SUPPORTING YOUR CHILD IN HIGH SCHOOL HS America s schools are working to provide higher quality instruction than ever before. The way we taught students in the past simply does
More informationIndiana State Core Curriculum Standards updated 2009 Algebra I
Indiana State Core Curriculum Standards updated 2009 Algebra I Strand Description Boardworks High School Algebra presentations Operations With Real Numbers Linear Equations and A1.1 Students simplify and
More informationGlencoe. correlated to SOUTH CAROLINA MATH CURRICULUM STANDARDS GRADE 6 33, 58 84, 87 16, 49
Glencoe correlated to SOUTH CAROLINA MATH CURRICULUM STANDARDS GRADE 6 STANDARDS 68 Number and Operations (NO) Standard I. Understand numbers, ways of representing numbers, relationships among numbers,
More informationExtra Credit Assignment Lesson plan. The following assignment is optional and can be completed to receive up to 5 points on a previously taken exam.
Extra Credit Assignment Lesson plan The following assignment is optional and can be completed to receive up to 5 points on a previously taken exam. The extra credit assignment is to create a typed up lesson
More informationMath 0980 Chapter Objectives. Chapter 1: Introduction to Algebra: The Integers.
Math 0980 Chapter Objectives Chapter 1: Introduction to Algebra: The Integers. 1. Identify the place value of a digit. 2. Write a number in words or digits. 3. Write positive and negative numbers used
More informationSouth Carolina College and CareerReady (SCCCR) Algebra 1
South Carolina College and CareerReady (SCCCR) Algebra 1 South Carolina College and CareerReady Mathematical Process Standards The South Carolina College and CareerReady (SCCCR) Mathematical Process
More informationNCTM Curriculum Focal Points for Grade 5. Everyday Mathematics, Grade 5
NCTM Curriculum Focal Points and, Grade 5 NCTM Curriculum Focal Points for Grade 5 Number and Operations and Algebra: Developing an understanding of and fluency with division of whole numbers Students
More informationAlgebra I Credit Recovery
Algebra I Credit Recovery COURSE DESCRIPTION: The purpose of this course is to allow the student to gain mastery in working with and evaluating mathematical expressions, equations, graphs, and other topics,
More informationThis unit will lay the groundwork for later units where the students will extend this knowledge to quadratic and exponential functions.
Algebra I Overview View unit yearlong overview here Many of the concepts presented in Algebra I are progressions of concepts that were introduced in grades 6 through 8. The content presented in this course
More informationGraph Ordered Pairs on a Coordinate Plane
Graph Ordered Pairs on a Coordinate Plane Student Probe Plot the ordered pair (2, 5) on a coordinate grid. Plot the point the ordered pair (2, 5) on a coordinate grid. Note: If the student correctly plots
More informationRECOMMENDED MATHEMATICS COURSE(S): Algebra 1 or Geometry; Integrated Math I or II; Animal Science; Agribusiness Management; Food Science
This task was developed by high school and postsecondary mathematics and agriculture sciences educators, and validated by content experts in the Common Core State Standards in mathematics and the National
More informationAlgebra Unpacked Content For the new Common Core standards that will be effective in all North Carolina schools in the 201213 school year.
This document is designed to help North Carolina educators teach the Common Core (Standard Course of Study). NCDPI staff are continually updating and improving these tools to better serve teachers. Algebra
More informationAcquisition Lesson Planning Form Key Standards addressed in this Lesson: MM2A2c Time allotted for this Lesson: 5 Hours
Acquisition Lesson Planning Form Key Standards addressed in this Lesson: MM2A2c Time allotted for this Lesson: 5 Hours Essential Question: LESSON 2 Absolute Value Equations and Inequalities How do you
More informationWentzville School District Algebra 1: Unit 8 Stage 1 Desired Results
Wentzville School District Algebra 1: Unit 8 Stage 1 Desired Results Unit Title: Quadratic Expressions & Equations Course: Algebra I Unit 8  Quadratic Expressions & Equations Brief Summary of Unit: At
More informationNumber and Numeracy SE/TE: 43, 49, 140145, 367369, 457, 459, 479
Ohio Proficiency Test for Mathematics, New Graduation Test, (Grade 10) Mathematics Competencies Competency in mathematics includes understanding of mathematical concepts, facility with mathematical skills,
More informationTennessee Department of Education. Task: Sally s Car Loan
Tennessee Department of Education Task: Sally s Car Loan Sally bought a new car. Her total cost including all fees and taxes was $15,. She made a down payment of $43. She financed the remaining amount
More informationSolving Equations Involving Parallel and Perpendicular Lines Examples
Solving Equations Involving Parallel and Perpendicular Lines Examples. The graphs of y = x, y = x, and y = x + are lines that have the same slope. They are parallel lines. Definition of Parallel Lines
More informationAlgebra 1 2008. Academic Content Standards Grade Eight and Grade Nine Ohio. Grade Eight. Number, Number Sense and Operations Standard
Academic Content Standards Grade Eight and Grade Nine Ohio Algebra 1 2008 Grade Eight STANDARDS Number, Number Sense and Operations Standard Number and Number Systems 1. Use scientific notation to express
More information2027 Mathematics Grade 8
Instructional Material Bureau Summer 2012 Adoption Review Institute Form F: Publisher Alignment Form & Review Scoring Rubric Publisher information and instructions: Corporation or Publisher: Pearson Education,
More informationWhat if systems are not in y = mx + b form? Strategies for Solving Systems and Special Cases Lesson Objective:
What if systems are not in y = mx + b form? Strategies for Solving Systems and Special Cases Lesson Objective: Length of Activity: Students will continue work with solving systems of equations using the
More informationMATH 65 NOTEBOOK CERTIFICATIONS
MATH 65 NOTEBOOK CERTIFICATIONS Review Material from Math 60 2.5 4.3 4.4a Chapter #8: Systems of Linear Equations 8.1 8.2 8.3 Chapter #5: Exponents and Polynomials 5.1 5.2a 5.2b 5.3 5.4 5.5 5.6a 5.7a 1
More informationModuMath Algebra Lessons
ModuMath Algebra Lessons Program Title 1 Getting Acquainted With Algebra 2 Order of Operations 3 Adding & Subtracting Algebraic Expressions 4 Multiplying Polynomials 5 Laws of Algebra 6 Solving Equations
More informationMATH 60 NOTEBOOK CERTIFICATIONS
MATH 60 NOTEBOOK CERTIFICATIONS Chapter #1: Integers and Real Numbers 1.1a 1.1b 1.2 1.3 1.4 1.8 Chapter #2: Algebraic Expressions, Linear Equations, and Applications 2.1a 2.1b 2.1c 2.2 2.3a 2.3b 2.4 2.5
More informationPrentice Hall Mathematics: Algebra 1 2007 Correlated to: Michigan Merit Curriculum for Algebra 1
STRAND 1: QUANTITATIVE LITERACY AND LOGIC STANDARD L1: REASONING ABOUT NUMBERS, SYSTEMS, AND QUANTITATIVE SITUATIONS Based on their knowledge of the properties of arithmetic, students understand and reason
More informationAcquisition Lesson Plan for the Concept, Topic or SkillNot for the Day
Acquisition Lesson Plan Concept: Linear Systems Author Name(s): HighSchool Delaware Math Cadre Committee Grade: Ninth Grade Time Frame: Two 45 minute periods Prerequisite(s): Write algebraic expressions
More informationPolynomial Operations and Factoring
Algebra 1, Quarter 4, Unit 4.1 Polynomial Operations and Factoring Overview Number of instructional days: 15 (1 day = 45 60 minutes) Content to be learned Identify terms, coefficients, and degree of polynomials.
More informationIntroduction to the Mathematics Correlation
Introduction to the Mathematics Correlation Correlation between National Common Core Standards for Mathematics and the North American Association for Environmental Education Guidelines for Excellence in
More informationNCTM Content Standard/National Science Education Standard:
Title: Do These Systems Meet Your Expectations Brief Overview: This concept development unit is designed to develop the topic of systems of equations. Students will be able to graph systems of equations
More informationMyMathLab ecourse for Developmental Mathematics
MyMathLab ecourse for Developmental Mathematics, North Shore Community College, University of New Orleans, Orange Coast College, Normandale Community College Table of Contents Module 1: Whole Numbers and
More informationProblem of the Month: Perfect Pair
Problem of the Month: The Problems of the Month (POM) are used in a variety of ways to promote problem solving and to foster the first standard of mathematical practice from the Common Core State Standards:
More informationCurriculum Alignment Project
Curriculum Alignment Project Math Unit Date: Unit Details Title: Solving Linear Equations Level: Developmental Algebra Team Members: Michael Guy Mathematics, Queensborough Community College, CUNY Jonathan
More informationCollege Readiness Math MOOC
College Readiness Math MOOC Instructor Information: Dr. Jennifer Kosiak, jkosiak@uwlax.edu General email: mathmooc@uwlax.edu Mathematics Department, University of Wisconsin La Crosse Description: The
More informationGreater Nanticoke Area School District Math Standards: Grade 6
Greater Nanticoke Area School District Math Standards: Grade 6 Standard 2.1 Numbers, Number Systems and Number Relationships CS2.1.8A. Represent and use numbers in equivalent forms 43. Recognize place
More informationInvestigating Area Under a Curve
Mathematics Investigating Area Under a Curve About this Lesson This lesson is an introduction to areas bounded by functions and the xaxis on a given interval. Since the functions in the beginning of the
More informationAlgebra 1 Course Objectives
Course Objectives The Duke TIP course corresponds to a high school course and is designed for gifted students in grades seven through nine who want to build their algebra skills before taking algebra in
More informationMathematics. Mathematical Practices
Mathematical Practices 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with
More informationLesson 22: Solution Sets to Simultaneous Equations
Student Outcomes Students identify solutions to simultaneous equations or inequalities; they solve systems of linear equations and inequalities either algebraically or graphically. Classwork Opening Exercise
More informationAlgebra II Unit Number 4
Title Polynomial Functions, Expressions, and Equations Big Ideas/Enduring Understandings Applying the processes of solving equations and simplifying expressions to problems with variables of varying degrees.
More informationSuch As Statements, Kindergarten Grade 8
Such As Statements, Kindergarten Grade 8 This document contains the such as statements that were included in the review committees final recommendations for revisions to the mathematics Texas Essential
More informationUtah Core Curriculum for Mathematics
Core Curriculum for Mathematics correlated to correlated to 2005 Chapter 1 (pp. 2 57) Variables, Expressions, and Integers Lesson 1.1 (pp. 5 9) Expressions and Variables 2.2.1 Evaluate algebraic expressions
More informationMATH 0110 Developmental Math Skills Review, 1 Credit, 3 hours lab
MATH 0110 Developmental Math Skills Review, 1 Credit, 3 hours lab MATH 0110 is established to accommodate students desiring noncourse based remediation in developmental mathematics. This structure will
More informationCarroll County Public Schools Elementary Mathematics Instructional Guide (5 th Grade) AugustSeptember (12 days) Unit #1 : Geometry
Carroll County Public Schools Elementary Mathematics Instructional Guide (5 th Grade) Common Core and Research from the CCSS Progression Documents Geometry Students learn to analyze and relate categories
More informationDefinition 8.1 Two inequalities are equivalent if they have the same solution set. Add or Subtract the same value on both sides of the inequality.
8 Inequalities Concepts: Equivalent Inequalities Linear and Nonlinear Inequalities Absolute Value Inequalities (Sections 4.6 and 1.1) 8.1 Equivalent Inequalities Definition 8.1 Two inequalities are equivalent
More informationCCGPS Curriculum Map. Mathematics. 7 th Grade
CCGPS Curriculum Map Mathematics 7 th Grade These materials are for nonprofit educational purposes only. Any other use may constitute copyright infringement. Unit 1 Operations with Rational Numbers a b
More informationUnit 4: Analyze and Graph Linear Equations, Functions, and Relations
Unit 4 Table of Contents Unit 4: Analyze and Graph Linear Equations, Functions and Relations Video Overview Learning Objectives 4.2 Media Run Times 4.3 Instructor Notes 4.4 The Mathematics of Analyzing
More informationNEW YORK STATE TEACHER CERTIFICATION EXAMINATIONS
NEW YORK STATE TEACHER CERTIFICATION EXAMINATIONS TEST DESIGN AND FRAMEWORK September 2014 Authorized for Distribution by the New York State Education Department This test design and framework document
More informationThis is a function because no vertical line can be drawn so that it intersects the graph more than once.
Determine whether each relation is a function. Explain. A function is a relation in which each element of the domain is paired with exactly one element of the range. So, this relation is a function. A
More informationEssential Question How can you solve a system of linear equations? $15 per night. Cost, C (in dollars) $75 per Number of. Revenue, R (in dollars)
5.1 Solving Sstems of Linear Equations b Graphing Essential Question How can ou solve a sstem of linear equations? Writing a Sstem of Linear Equations Work with a partner. Your famil opens a bedandbreakfast.
More informationAlgebra 1. Curriculum Map
Algebra 1 Curriculum Map Table of Contents Unit 1: Expressions and Unit 2: Linear Unit 3: Representing Linear Unit 4: Linear Inequalities Unit 5: Systems of Linear Unit 6: Polynomials Unit 7: Factoring
More informationLAGUARDIA COMMUNITY COLLEGE CITY UNIVERSITY OF NEW YORK DEPARTMENT OF MATHEMATICS, ENGINEERING, AND COMPUTER SCIENCE
LAGUARDIA COMMUNITY COLLEGE CITY UNIVERSITY OF NEW YORK DEPARTMENT OF MATHEMATICS, ENGINEERING, AND COMPUTER SCIENCE MAT 119 STATISTICS AND ELEMENTARY ALGEBRA 5 Lecture Hours, 2 Lab Hours, 3 Credits Pre
More informationAlgebra I Vocabulary Cards
Algebra I Vocabulary Cards Table of Contents Expressions and Operations Natural Numbers Whole Numbers Integers Rational Numbers Irrational Numbers Real Numbers Absolute Value Order of Operations Expression
More informationLesson 4: Solving and Graphing Linear Equations
Lesson 4: Solving and Graphing Linear Equations Selected Content Standards Benchmarks Addressed: A2M Modeling and developing methods for solving equations and inequalities (e.g., using charts, graphs,
More informationUnit 1: Integers and Fractions
Unit 1: Integers and Fractions No Calculators!!! Order Pages (All in CC7 Vol. 1) 31 Integers & Absolute Value 191194, 203206, 195198, 207210 32 Add Integers 33 Subtract Integers 215222 34 Multiply
More informationNumeracy and mathematics Experiences and outcomes
Numeracy and mathematics Experiences and outcomes My learning in mathematics enables me to: develop a secure understanding of the concepts, principles and processes of mathematics and apply these in different
More informationPerformance Based Learning and Assessment Task
Performance Based Learning and Assessment Task Staircases and Ramps I. ASSESSSMENT TASK OVERVIEW & PURPOSE: The students will use slope to describe the characteristics of ramps versus the stairs between
More informationOverview. Essential Questions. Precalculus, Quarter 4, Unit 4.5 Build Arithmetic and Geometric Sequences and Series
Sequences and Series Overview Number of instruction days: 4 6 (1 day = 53 minutes) Content to Be Learned Write arithmetic and geometric sequences both recursively and with an explicit formula, use them
More informationSummer Assignment for incoming Fairhope Middle School 7 th grade Advanced Math Students
Summer Assignment for incoming Fairhope Middle School 7 th grade Advanced Math Students Studies show that most students lose about two months of math abilities over the summer when they do not engage in
More informationAlgebra 1 Course Information
Course Information Course Description: Students will study patterns, relations, and functions, and focus on the use of mathematical models to understand and analyze quantitative relationships. Through
More informationGRADE 7 SKILL VOCABULARY MATHEMATICAL PRACTICES Add linear expressions with rational coefficients. 7.EE.1
Common Core Math Curriculum Grade 7 ESSENTIAL QUESTIONS DOMAINS AND CLUSTERS Expressions & Equations What are the 7.EE properties of Use properties of operations? operations to generate equivalent expressions.
More information