SKILLS Students will be skilled at and/or be able
|
|
- Justin Barrett
- 6 years ago
- Views:
Transcription
1 Unit Goals Stage 1 Number of Days: MS 32 1/8/18 2/23/18 HS 32 1/8/18 3/2/18 (1/22/18 to 1/26/18 have been omitted for finals) Unit Description: Students build on their understanding of integer exponents to consider exponential functions with integer domains. They compare and contrast linear and exponential functions, looking for structure in each and distinguishing between additive and multiplicative change. They expand their understanding of arithmetic sequences as linear functions to interpret geometric sequences as exponential functions. Materials: graph paper, calculators, Desmos Standards for Mathematical Practice SMP 1 Make sense of problems and persevere in solving them. SMP 2 Reason abstractly and quantitatively. SMP 3 Construct viable arguments and critique the reasoning of others. SMP 4 Model with mathematics. SMP 5 Use appropriate tools strategically. SMP 6 Attend to precision. SMP 7 Look for and make use of structure. SMP 8 Look for and express regularity in repeated reasoning. Standards for Mathematical Content Clusters Addressed [a] N-RN.A Extend the properties of exponents to rational exponents. [m] A-SSE.A Interpret the structure of expressions. [s] A-SSE.B Write expressions in equivalent forms to solve problems. [m] A-CED.A Create equations that describe numbers or relationships. [m] A-REI.D Represent and solve equations and inequalities graphically. [m] F-IF.A Understand the concept of a [m] F-IF.B function and use function notation. Interpret functions that arise in applications in terms of the context. [s] F-IF.C Analyze functions using different representations. Transfer Goals Students will be able to independently use their learning to Make sense of never-before-seen problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Making Meaning UNDERSTANDINGS Students will understand that A quantity that increases exponentially will eventually exceed a quantity that increases linearly. The process of transforming graphs of exponential functions is the same as it is for other functions. The end behavior of exponential functions is unique in that the domain can be restricted by the context it represents while the range can be restricted by asymptotes. Acquisition KNOWLEDGE Students will know The definition of academic vocabulary words, such as asymptotes, exponential decay, exponential growth, and geometric sequence. Linear functions grow by equal differences over equal intervals, while exponential functions grow by equal factors over equal intervals. Common types of exponential functions are exponential growth and decay. ESSENTIAL QUESTIONS Students will keep considering How do exponential functions compare to linear functions? How do transformations affect the graph of an exponential function? How is the end behavior of an exponential function unique? SKILLS Students will be skilled at and/or be able to Extend the properties of integer exponents to rational exponents. Distinguish between situations that can be modeled with linear functions and with exponential functions. Construct exponential functions given a graph, a description of a relationship, or a table. LONG BEACH UNIFIED SCHOOL DISTRICT 1 Posted 6/19/17
2 [s] F-BF.A Build a function that models a relationship between two quantities. [a] F-BF.B Build new functions from existing functions. [s] F-LE.A Construct and compare linear, quadratic, and exponential models and solve problems. [s] F-LE.B Interpret expressions for functions in terms of the situation they model. Unit Goals Stage 1 Exponential growth has a common ratio that is more than 100%, while exponential decay has a common ratio that is greater than 0% and less than 100%. Graph exponential functions showing intercepts and end behavior and interpret the parameters in terms of a context. Use transformations to build new exponential functions from existing functions. Recognize situations in which a quantity grows or decays by a common ratio. Write geometric sequences both recursively and explicitly. LONG BEACH UNIFIED SCHOOL DISTRICT 2 Posted 6/19/17
3 Assessed Grade Level Standards Standards for Mathematical Practice SMP 1 Make sense of problems and persevere in solving them. SMP 2 Reason abstractly and quantitatively. SMP 3 Construct viable arguments and critique the reasoning of others. SMP 4 Model with mathematics. SMP 5 Use appropriate tools strategically. SMP 6 Attend to precision. SMP 7 Look for and make use of structure. SMP 8 Look for and express regularity in repeated reasoning. Standards for Mathematical Content [a] N-RN.A Extend the properties of exponents to rational exponents. N-RN.1 Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 5 1/3 to be the cube root of 5 because we want (5 1/3 ) 3 = 5 (1/3)3 to hold, so (5 1/3 ) 3 must equal 5. N-RN.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents. [m] A-SSE.A Interpret the structure of expressions [linear, exponential, quadratic.] A.SSE.1 Interpret expressions that represent a quantity in terms of its context. [s] A-SSE.B Write expressions in equivalent forms to solve problems. [Quadratic and exponential.] A-SSE.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expressions. c. Use properties of exponents to transform expressions for exponential functions. For example the expression 1.15 t can be written as (1.15 1/12 ) 12t t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%. [m] A-CED.A Create equations that describe numbers or relationships. [Linear, quadratic, and exponential.] A-CED.1 Create equations and inequalities in one variable including ones with absolute value and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. CA A-CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [m] A-REI.D Represent and solve equations and inequalities graphically. [Linear and exponential; learn as general principle.] A-REI.10 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). A-REI.11 Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. [m] F-IF.A Understand the concept of a function and use function notation. [Learn as general principle; focus on linear and exponential and on arithmetic and geometric sequences.] F-IF.3 Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. [m] F-IF.B Interpret functions that arise in applications in terms of the context. [Linear, quadratic, and exponential.] F-IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where LONG BEACH UNIFIED SCHOOL DISTRICT 3 Posted 6/19/17
4 Assessed Grade Level Standards the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. F-IF.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. [s] F-IF.C Analyze functions using different representations. [Linear, exponential, quadratic, absolute value, step, piecewise-defined.] F-IF.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. e. Graph exponential and logarithmic functions, showing intercepts and end behavior. F-IF.8 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. b. Use properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y=(1.02) t, y=(0.97) t, y=(1.01) 12t, y=(1.2) t/10, and classify them as representing exponential growth or decay. F-IF.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. [s] F-BF.A Build a function that models a relationship between two quantities. [Linear, quadratic, and exponential.] F-BF.1 Write a function that describes a relationship between two quantities. a. Determine an explicit expression, a recursive process, or steps for calculation from a context. F-BF.2 Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. [a] F-BF.B Build new functions from existing functions. [Linear, quadratic, exponential, and absolute value.] F-BF.3 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. [s] F-LE.A Construct and compare linear, quadratic, and exponential models and solve problems. F-LE.1 F-LE.2 F-LE.3 Distinguish between situations that can be modeled with linear functions and with exponential functions. a. Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals. b. Recognize situations in which one quantity changes at a constant rate per unit interval relative to another. c. Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. [s] F-LE.B Interpret expressions for functions in terms of the situation they model. F-LE.5 Interpret the parameters in a linear or exponential function in terms of a context. Key: [m] = major clusters; [s] = supporting clusters, [a] = additional clusters Indicates a modeling standard linking mathematics to everyday life, work, and decision-making CA Indicates a California-only standard LONG BEACH UNIFIED SCHOOL DISTRICT 4 Posted 6/19/17
5 Assessment Evidence Unit Assessment Evidence of Learning Stage 2 Claim 1: Students can explain and apply mathematical concepts and carry out mathematical procedures with precision and fluency. Concepts and skills that may be assessed in Claim1: N-RN.A The student rewrites expressions in radical form into an equivalent expression with rational exponents. The student rewrites expressions with rational exponents into an equivalent expression in radical form. The student uses the properties of exponents to write equivalent expressions involving radicals and rational exponents. The student solves equations that require an understanding of the definitions of radicals and rational exponents. A-SSE.A The student uses the structure of an expression to identify ways of rewriting it. A-SSE.B The student uses the properties of exponents to transform exponential expressions. A-CED.A The student graphs equations on coordinate axes with labels and scales to represent the solution to a contextual problem. The student creates equations in two variables to represent a relationship between quantities. A-REI.D The student understands that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). The student finds solutions (either exact or approximate as appropriate) to the equation f ( x) = g( x). F-IF.A The student recognizes any necessary restrictions that need to be placed on the domain in order to represent a function. The student understands that the graph of f is the graph of f (x). The student recognizes that sequences are functions whose domain is a subset of the integers. F-IF.B The student interprets key features of a graph or a table representing an exponential function modeling a relationship between two quantities. The student sketches graphs showing key features given a verbal description of an exponential relationship between two quantities. The student relates the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. F-IF.C The student graphs functions expressed symbolically and shows key features of the graph. The student writes an exponential function defined by an expression in an equivalent form using the properties of exponents to reveal and explain different properties of the functions and to classify them as representing growth or decay. The student compares properties of two functions each represented in a different way (e.g., as equations, tables, graphs, or written descriptions). F-BF.A The student writes explicit or recursive functions to describe relationships between two quantities in a context. The student translates between explicit formulas and recursively defined functions. The student writes geometric sequences both recursively and with an explicit formula. LONG BEACH UNIFIED SCHOOL DISTRICT 5 Posted 6/19/17
6 Evidence of Learning Stage 2 Assessment Evidence F-BF.B The student identifies the effects of transformations on the graphs of exponential functions by replacing f(x) with f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative) and finds the value of k given the graphs. F-LE.A The student distinguishes between situations that can be modeled with linear functions and exponential functions. The student compares linear and exponential models. The student constructs linear and exponential models given a graph, a description of a relationship, or input-output pairs (including reading these from a table). The student understands that a quantity increasing exponentially eventually exceeds a quantity increasing linearly or quadratically. F-LE.B The student interprets the parameters in an exponential function in terms of a context. Claim 2: Students can solve a range of wellposed problems in pure and applied mathematics, making productive use of knowledge and problem-solving strategies. Standard clusters that may be assessed in Claim 2: A-SSE.A A-SSE.B A.CED.A A-REI.D F-IF.A F-IF.B F-IF.C F-BF.A Claim 3: The student can clearly and precisely construct viable arguments to support their own reasoning and critique the reasoning of others. Standard clusters that may be assessed in Claim 3: N-RN.A A-REI.D F-IF.B F-IF.C Claim 4: The student can analyze complex, real-world scenarios and can construct and use mathematical models to interpret and solve problems. Standard clusters that may be assessed in Claim 4: A-SSE.B A-CED.A F-IF.C F-BF.A F-LE.A F-LE.B Other Evidence Formative Assessment Opportunities Informal teacher observations Checking for understanding using active participation strategies Exit slips/summaries Tasks Modeling Lessons (SMP 4) Formative Assessment Lessons (FAL) Quizzes / Chapter Tests SBAC Interim Assessment Blocks Access Using Formative Assessment for Differentiation for suggestions. Located on the LBUSD website M Mathematics Curriculum Documents LONG BEACH UNIFIED SCHOOL DISTRICT 6 Posted 6/19/17
7 Days Learning Target Expectations 1 day I will explore exponential functions by participating in the Opening Task. Learning Plan Stage 3 Suggested Sequence of Key Learning Events and Instruction OPENING TASK Football Drills This Opening Task is a Solo-Team-Teach activity. First, pass out the activity, Football Drills, and have students work independently. Next, have students work with their team. After working together, facilitate a class discussion about their method(s) for choosing the football drill utilizing Talk Moves. This task is a gateway into the entire unit on exponential functions. Big Ideas Math Algebra 1 (Explorations and Lessons) Supplemental Resources Conceptual Understanding: Football Drills 4-5 I will use the properties of rational exponents by Using patterns to create conjectures for the rules of zero and integer exponents. (SMP 7) Using expanded form to look for patterns to create conjectures for multiplying powers with the same base, dividing powers with the same base, and raising a power to a power. (SMP 7) Evaluate expressions with rational exponents. Rewriting expressions involving rational exponents (fractional exponents) and radicals using properties of exponents. Explaining how the meaning of fractional exponents extends from the properties of integer exponents. (SMP 3) Answering questions such as o Justify each exponent property using expanded form. o Why is the value of the base irrelevant (except for zero) when it is raised to the zero power? o How do you write and evaluate an n th root of a number? o How are radicals related to exponents? o How do you rewrite expressions involving radicals and rational exponents using the properties of exponents? o Synergy Item Bank: Item ID 63724, Section 6.1 Section 6.2 Conceptual Understanding: Evaluating a Special Exponential Expression Task Evaluating Exponential Expressions Task Rational Exponents Task Procedural Skills and Fluency: Positive Exponents Product Game Negative Exponents Product Game Exponents Math-O Fractional Exponents Solo-Team-Teach Application: How High Can You Count on Your Fingers? Video LONG BEACH UNIFIED SCHOOL DISTRICT 7 Posted 6/19/17
8 7-8 Learning Plan Stage 3 Suggested Sequence of Key Learning Events and Instruction Days Learning Target Expectations Big Ideas Math Algebra 1 (Explorations and Lessons) I will explore Section 6.3 exponential functions by Distinguishing between linear and exponential functions. Explaining that a quantity increasing exponentially will eventually exceed a quantity increasing linearly. (SMP 3) Identifying exponential functions in different representations, such as graphically, algebraically, numerically in tables, or by verbal descriptions. Graphing simple exponential functions by hand and using technology for more complicated cases. (SMP 5) Identifying key features of exponential functions, such as intercepts and end behavior, and interpreting the parameters in terms of a context, including asymptotes. Interpreting the domain and range of an exponential function and relating them to the relationship it describes. Graphing exponential functions in the form x h f ( x) = ab + k, where b > 0. Identifying the effect of transformations on the x graph of the exponential function f ( x) = b by replacing f(x) with f(x) + k, k f(x), and f(x + k) for specific values of k (both positive and negative). (SMP 7) Answering questions such as o What are some characteristics of an exponential function? o How are the graphs of linear and exponential functions similar? How are they different? o How do you graph an exponential function? o How does changing the values of a, h, and k affect the graph of an exponential function? o Synergy Item Bank: Item ID 58365, 59090, 58736, Supplemental Resources Conceptual Understanding: Desmos: Avi and Benita s Repair Shop Pay It Forward Sample Lesson with Video Clip Power of Two Activity The Penny Experiment Activity and Graph Exponential Functions Which One Doesn t Belong? Exponential Parameters Task Procedural Skills and Fluency: Desmos: Polygraph Exponentials Desmos: What Comes Next? Desmos: Marbleslides Exponentials Exponential Curves Matching Activity Application: Desmos: Penny Circle Linear and Exponential Functions Task Population and Food Supply Task Exponential vs. Linear Growth Task Linear or Exponential? Task Modeling: Domino Skyscraper (SMP 4) LONG BEACH UNIFIED SCHOOL DISTRICT 8 Posted 6/19/17
9 Learning Plan Stage 3 Suggested Sequence of Key Learning Events and Instruction Days Learning Target Expectations Big Ideas Math Algebra 1 (Explorations and Lessons) I will write, graph, Section 6.4 and interpret exponential growth and decay functions by 4-5 Distinguishing between exponential growth and decay from inspecting an equation, a table, or graph. Describing situations that represent exponential growth or exponential decay, such as compound interest and half-life. Identifying key features of exponential growth and decay functions, such as intercepts and end behavior, and interpreting the parameters in terms of a context, including asymptotes. (SMP 2) Interpreting the domain and range of exponential growth and decay functions from equations, graphs, and tables. Graphing simple exponential growth and decay functions by hand and using technology for more complicated graphs. (SMP 5) Answering questions such as o How do you write, graph, and interpret exponential growth and decay functions? o How is the formula for exponential decay similar to the formula for exponential growth? o How is compound interest different from simple interest? o Synergy Item Bank: Item ID 54980, Supplemental Resources Conceptual Understanding: Compound Interest Simulator Procedural Skills and Fluency: Desmos: Card Sort Exponentials Graphing Exponential Growth and Decay PowerPoint Application: Desmos: iphone 6s Opening Weekend Sales (SMP 4) Interesting Interest Rates Task Predicting Your Financial Future Task Saving for College Activity Modeling: Fry s Bank (SMP 4) Modeling: How Much Did Peterson Loose by Not Cashing his Check? (SMP 4) 2-3 I will solve exponential equations Algebraically. Graphically (i.e. system of a linear and exponential function). Answering questions such as o How can you solve exponential equations with the same base? With unlike bases? o How can you solve exponential equations by graphing? o Synergy Item Bank: Item ID Section 6.5 Procedural Skills and Fluency: Solving Exponential Equations Card Sort LONG BEACH UNIFIED SCHOOL DISTRICT 9 Posted 6/19/17
10 Days Learning Target Expectations 2-3 I will check my understanding of exponential functions by participating in the FAL. Learning Plan Stage 3 Suggested Sequence of Key Learning Events and Instruction FORMATIVE ASSESSMENT LESSON (choose 1) Representing Linear and Exponential Growth (SMP 1, 2, 4,5, 7, 8) Modeling Population Growth: Having Kittens (SMP 1, 2, 3, 4, 5, 6, 7, 8) Big Ideas Math Algebra 1 (Explorations and Lessons) Supplemental Resources 4-5 I will discover geometric sequences by Writing an explicit rule for a geometric sequence. Writing a recursive rule for a geometric sequence. Comparing the graph of a geometric sequence to the graph of an exponential function. Translating between explicit formulas and recursively-defined functions. Answering questions such as o How is a geometric sequence different from an arithmetic sequence? o Compare and contrast recursive and explicit rules. o How are geometric sequences related to exponential functions? o How can you tell whether a common ratio will be greater than one or less than one? o Synergy Item Bank: Item ID 51336, 55686, Section 6.6 Section 6.7 Procedural Skills and Fluency: Recursive and Exponential Rules Activity Application: Arithmetic vs. Geometric Sequences Task Seeing Music Task day I will prepare for the unit assessment on exponential functions by Incorporating the Standards for Mathematical Practice (SMPs) along with the content standards to review the unit. Ch. 6 Review (p ) Unit Assessment Students will take the Synergy Online Unit Assessment. Application: Basketball Bounces Task Desmos: 2015 NBA Draft Salary Prediction (SMP 4) Exponential Functions Application Problems National Debt and Wars Task Modeling: XBOX Xponential (SMP 4) Unit Assessment Resources (Word or PDF) can be used throughout the unit. LONG BEACH UNIFIED SCHOOL DISTRICT 10 Posted 6/19/17
Statewide Framework Document for:
Statewide Framework Document for: 270301 Standards may be added to this document prior to submission, but may not be removed from the framework to meet state credit equivalency requirements. Performance
More informationUnit 3 Ratios and Rates Math 6
Number of Days: 20 11/27/17 12/22/17 Unit Goals Stage 1 Unit Description: Students study the concepts and language of ratios and unit rates. They use proportional reasoning to solve problems. In particular,
More informationAGS THE GREAT REVIEW GAME FOR PRE-ALGEBRA (CD) CORRELATED TO CALIFORNIA CONTENT STANDARDS
AGS THE GREAT REVIEW GAME FOR PRE-ALGEBRA (CD) CORRELATED TO CALIFORNIA CONTENT STANDARDS 1 CALIFORNIA CONTENT STANDARDS: Chapter 1 ALGEBRA AND WHOLE NUMBERS Algebra and Functions 1.4 Students use algebraic
More informationAlgebra 1, Quarter 3, Unit 3.1. Line of Best Fit. Overview
Algebra 1, Quarter 3, Unit 3.1 Line of Best Fit Overview Number of instructional days 6 (1 day assessment) (1 day = 45 minutes) Content to be learned Analyze scatter plots and construct the line of best
More informationGrade 6: Correlated to AGS Basic Math Skills
Grade 6: Correlated to AGS Basic Math Skills Grade 6: Standard 1 Number Sense Students compare and order positive and negative integers, decimals, fractions, and mixed numbers. They find multiples and
More informationHonors Mathematics. Introduction and Definition of Honors Mathematics
Honors Mathematics Introduction and Definition of Honors Mathematics Honors Mathematics courses are intended to be more challenging than standard courses and provide multiple opportunities for students
More informationExtending Place Value with Whole Numbers to 1,000,000
Grade 4 Mathematics, Quarter 1, Unit 1.1 Extending Place Value with Whole Numbers to 1,000,000 Overview Number of Instructional Days: 10 (1 day = 45 minutes) Content to Be Learned Recognize that a digit
More information1.11 I Know What Do You Know?
50 SECONDARY MATH 1 // MODULE 1 1.11 I Know What Do You Know? A Practice Understanding Task CC BY Jim Larrison https://flic.kr/p/9mp2c9 In each of the problems below I share some of the information that
More informationMathematics subject curriculum
Mathematics subject curriculum Dette er ei omsetjing av den fastsette læreplanteksten. Læreplanen er fastsett på Nynorsk Established as a Regulation by the Ministry of Education and Research on 24 June
More informationMath 96: Intermediate Algebra in Context
: Intermediate Algebra in Context Syllabus Spring Quarter 2016 Daily, 9:20 10:30am Instructor: Lauri Lindberg Office Hours@ tutoring: Tutoring Center (CAS-504) 8 9am & 1 2pm daily STEM (Math) Center (RAI-338)
More informationMathematics. Mathematics
Mathematics Program Description Successful completion of this major will assure competence in mathematics through differential and integral calculus, providing an adequate background for employment in
More informationMath 098 Intermediate Algebra Spring 2018
Math 098 Intermediate Algebra Spring 2018 Dept. of Mathematics Instructor's Name: Office Location: Office Hours: Office Phone: E-mail: MyMathLab Course ID: Course Description This course expands on the
More informationMathematics Assessment Plan
Mathematics Assessment Plan Mission Statement for Academic Unit: Georgia Perimeter College transforms the lives of our students to thrive in a global society. As a diverse, multi campus two year college,
More informationLearning Disability Functional Capacity Evaluation. Dear Doctor,
Dear Doctor, I have been asked to formulate a vocational opinion regarding NAME s employability in light of his/her learning disability. To assist me with this evaluation I would appreciate if you can
More informationMontana Content Standards for Mathematics Grade 3. Montana Content Standards for Mathematical Practices and Mathematics Content Adopted November 2011
Montana Content Standards for Mathematics Grade 3 Montana Content Standards for Mathematical Practices and Mathematics Content Adopted November 2011 Contents Standards for Mathematical Practice: Grade
More informationCharacteristics of Functions
Characteristics of Functions Unit: 01 Lesson: 01 Suggested Duration: 10 days Lesson Synopsis Students will collect and organize data using various representations. They will identify the characteristics
More informationMath-U-See Correlation with the Common Core State Standards for Mathematical Content for Third Grade
Math-U-See Correlation with the Common Core State Standards for Mathematical Content for Third Grade The third grade standards primarily address multiplication and division, which are covered in Math-U-See
More informationCal s Dinner Card Deals
Cal s Dinner Card Deals Overview: In this lesson students compare three linear functions in the context of Dinner Card Deals. Students are required to interpret a graph for each Dinner Card Deal to help
More informationFoothill College Summer 2016
Foothill College Summer 2016 Intermediate Algebra Math 105.04W CRN# 10135 5.0 units Instructor: Yvette Butterworth Text: None; Beoga.net material used Hours: Online Except Final Thurs, 8/4 3:30pm Phone:
More informationSAT MATH PREP:
SAT MATH PREP: 2015-2016 NOTE: The College Board has redesigned the SAT Test. This new test will start in March of 2016. Also, the PSAT test given in October of 2015 will have the new format. Therefore
More informationMath 150 Syllabus Course title and number MATH 150 Term Fall 2017 Class time and location INSTRUCTOR INFORMATION Name Erin K. Fry Phone number Department of Mathematics: 845-3261 e-mail address erinfry@tamu.edu
More informationCAAP. Content Analysis Report. Sample College. Institution Code: 9011 Institution Type: 4-Year Subgroup: none Test Date: Spring 2011
CAAP Content Analysis Report Institution Code: 911 Institution Type: 4-Year Normative Group: 4-year Colleges Introduction This report provides information intended to help postsecondary institutions better
More informationPage 1 of 11. Curriculum Map: Grade 4 Math Course: Math 4 Sub-topic: General. Grade(s): None specified
Curriculum Map: Grade 4 Math Course: Math 4 Sub-topic: General Grade(s): None specified Unit: Creating a Community of Mathematical Thinkers Timeline: Week 1 The purpose of the Establishing a Community
More informationBENCHMARK MA.8.A.6.1. Reporting Category
Grade MA..A.. Reporting Category BENCHMARK MA..A.. Number and Operations Standard Supporting Idea Number and Operations Benchmark MA..A.. Use exponents and scientific notation to write large and small
More informationGUIDE TO THE CUNY ASSESSMENT TESTS
GUIDE TO THE CUNY ASSESSMENT TESTS IN MATHEMATICS Rev. 117.016110 Contents Welcome... 1 Contact Information...1 Programs Administered by the Office of Testing and Evaluation... 1 CUNY Skills Assessment:...1
More informationDublin City Schools Mathematics Graded Course of Study GRADE 4
I. Content Standard: Number, Number Sense and Operations Standard Students demonstrate number sense, including an understanding of number systems and reasonable estimates using paper and pencil, technology-supported
More informationProbability and Statistics Curriculum Pacing Guide
Unit 1 Terms PS.SPMJ.3 PS.SPMJ.5 Plan and conduct a survey to answer a statistical question. Recognize how the plan addresses sampling technique, randomization, measurement of experimental error and methods
More informationTechnical Manual Supplement
VERSION 1.0 Technical Manual Supplement The ACT Contents Preface....................................................................... iii Introduction....................................................................
More informationAP Calculus AB. Nevada Academic Standards that are assessable at the local level only.
Calculus AB Priority Keys Aligned with Nevada Standards MA I MI L S MA represents a Major content area. Any concept labeled MA is something of central importance to the entire class/curriculum; it is a
More informationSyllabus ENGR 190 Introductory Calculus (QR)
Syllabus ENGR 190 Introductory Calculus (QR) Catalog Data: ENGR 190 Introductory Calculus (4 credit hours). Note: This course may not be used for credit toward the J.B. Speed School of Engineering B. S.
More informationInstructor: Matthew Wickes Kilgore Office: ES 310
MATH 1314 College Algebra Syllabus Instructor: Matthew Wickes Kilgore Office: ES 310 Longview Office: LN 205C Email: mwickes@kilgore.edu Phone: 903 988-7455 Prerequistes: Placement test score on TSI or
More informationMissouri Mathematics Grade-Level Expectations
A Correlation of to the Grades K - 6 G/M-223 Introduction This document demonstrates the high degree of success students will achieve when using Scott Foresman Addison Wesley Mathematics in meeting the
More informationMath 121 Fundamentals of Mathematics I
I. Course Description: Math 121 Fundamentals of Mathematics I Math 121 is a general course in the fundamentals of mathematics. It includes a study of concepts of numbers and fundamental operations with
More informationGrading Policy/Evaluation: The grades will be counted in the following way: Quizzes 30% Tests 40% Final Exam: 30%
COURSE SYLLABUS FALL 2010 MATH 0408 INTERMEDIATE ALGEBRA Course # 0408.06 Course Schedule/Location: TT 09:35 11:40, A-228 Instructor: Dr. Calin Agut, Office: J-202, Department of Mathematics, Brazosport
More informationFirst Grade Standards
These are the standards for what is taught throughout the year in First Grade. It is the expectation that these skills will be reinforced after they have been taught. Mathematical Practice Standards Taught
More informationLLD MATH. Student Eligibility: Grades 6-8. Credit Value: Date Approved: 8/24/15
PUBLIC SCHOOLS OF EDISON TOWNSHIP DIVISION OF CURRICULUM AND INSTRUCTION LLD MATH Length of Course: Elective/Required: School: Full Year Required Middle Schools Student Eligibility: Grades 6-8 Credit Value:
More informationAlgebra 2- Semester 2 Review
Name Block Date Algebra 2- Semester 2 Review Non-Calculator 5.4 1. Consider the function f x 1 x 2. a) Describe the transformation of the graph of y 1 x. b) Identify the asymptotes. c) What is the domain
More informationCommon Core Standards Alignment Chart Grade 5
Common Core Standards Alignment Chart Grade 5 Units 5.OA.1 5.OA.2 5.OA.3 5.NBT.1 5.NBT.2 5.NBT.3 5.NBT.4 5.NBT.5 5.NBT.6 5.NBT.7 5.NF.1 5.NF.2 5.NF.3 5.NF.4 5.NF.5 5.NF.6 5.NF.7 5.MD.1 5.MD.2 5.MD.3 5.MD.4
More informationFocus of the Unit: Much of this unit focuses on extending previous skills of multiplication and division to multi-digit whole numbers.
Approximate Time Frame: 3-4 weeks Connections to Previous Learning: In fourth grade, students fluently multiply (4-digit by 1-digit, 2-digit by 2-digit) and divide (4-digit by 1-digit) using strategies
More informationSOUTHERN MAINE COMMUNITY COLLEGE South Portland, Maine 04106
SOUTHERN MAINE COMMUNITY COLLEGE South Portland, Maine 04106 Title: Precalculus Catalog Number: MATH 190 Credit Hours: 3 Total Contact Hours: 45 Instructor: Gwendolyn Blake Email: gblake@smccme.edu Website:
More informationWritten by Wendy Osterman
Pre-Algebra Written by Wendy Osterman Editor: Alaska Hults Illustrator: Corbin Hillam Designer/Production: Moonhee Pak/Cari Helstrom Cover Designer: Barbara Peterson Art Director: Tom Cochrane Project
More informationClassroom Connections Examining the Intersection of the Standards for Mathematical Content and the Standards for Mathematical Practice
Classroom Connections Examining the Intersection of the Standards for Mathematical Content and the Standards for Mathematical Practice Title: Considering Coordinate Geometry Common Core State Standards
More informationIntroducing the New Iowa Assessments Mathematics Levels 12 14
Introducing the New Iowa Assessments Mathematics Levels 12 14 ITP Assessment Tools Math Interim Assessments: Grades 3 8 Administered online Constructed Response Supplements Reading, Language Arts, Mathematics
More informationThis scope and sequence assumes 160 days for instruction, divided among 15 units.
In previous grades, students learned strategies for multiplication and division, developed understanding of structure of the place value system, and applied understanding of fractions to addition and subtraction
More informationMATH 108 Intermediate Algebra (online) 4 Credits Fall 2008
MATH 108 Intermediate Algebra (online) 4 Credits Fall 2008 Instructor: Nolan Rice Math Lab: T 2:00 2:50 Office: SHL 206-F Office Hours: M/F 2:00 2:50 Phone/Voice Mail: 732.6819 W 4:30 5:20 E-mail: nrice@csi.edu
More informationSouth Carolina College- and Career-Ready Standards for Mathematics. Standards Unpacking Documents Grade 5
South Carolina College- and Career-Ready Standards for Mathematics Standards Unpacking Documents Grade 5 South Carolina College- and Career-Ready Standards for Mathematics Standards Unpacking Documents
More informationArizona s College and Career Ready Standards Mathematics
Arizona s College and Career Ready Mathematics Mathematical Practices Explanations and Examples First Grade ARIZONA DEPARTMENT OF EDUCATION HIGH ACADEMIC STANDARDS FOR STUDENTS State Board Approved June
More informationPage 1 of 8 REQUIRED MATERIALS:
INSTRUCTOR: OFFICE: PHONE / EMAIL: CONSULTATION: INSTRUCTOR WEB SITE: MATH DEPARTMENT WEB SITES: http:/ Online MATH 1010 INTERMEDIATE ALGEBRA Spring Semester 2013 Zeph Smith SCC N326 - G 957-3229 / zeph.smith@slcc.edu
More informationPhysics 270: Experimental Physics
2017 edition Lab Manual Physics 270 3 Physics 270: Experimental Physics Lecture: Lab: Instructor: Office: Email: Tuesdays, 2 3:50 PM Thursdays, 2 4:50 PM Dr. Uttam Manna 313C Moulton Hall umanna@ilstu.edu
More informationUNIT ONE Tools of Algebra
UNIT ONE Tools of Algebra Subject: Algebra 1 Grade: 9 th 10 th Standards and Benchmarks: 1 a, b,e; 3 a, b; 4 a, b; Overview My Lessons are following the first unit from Prentice Hall Algebra 1 1. Students
More informationAre You Ready? Simplify Fractions
SKILL 10 Simplify Fractions Teaching Skill 10 Objective Write a fraction in simplest form. Review the definition of simplest form with students. Ask: Is 3 written in simplest form? Why 7 or why not? (Yes,
More informationRadius STEM Readiness TM
Curriculum Guide Radius STEM Readiness TM While today s teens are surrounded by technology, we face a stark and imminent shortage of graduates pursuing careers in Science, Technology, Engineering, and
More informationStandard 1: Number and Computation
Standard 1: Number and Computation Standard 1: Number and Computation The student uses numerical and computational concepts and procedures in a variety of situations. Benchmark 1: Number Sense The student
More informationCommon Core State Standards
Common Core State Standards Common Core State Standards 7.NS.3 Solve real-world and mathematical problems involving the four operations with rational numbers. Mathematical Practices 1, 3, and 4 are aspects
More informationMath Techniques of Calculus I Penn State University Summer Session 2017
Math 110 - Techniques of Calculus I Penn State University Summer Session 2017 Instructor: Sergio Zamora Barrera Office: 018 McAllister Bldg E-mail: sxz38@psu.edu Office phone: 814-865-4291 Office Hours:
More informationMAT 122 Intermediate Algebra Syllabus Summer 2016
Instructor: Gary Adams Office: None (I am adjunct faculty) Phone: None Email: gary.adams@scottsdalecc.edu Office Hours: None CLASS TIME and LOCATION: Title Section Days Time Location Campus MAT122 12562
More informationCourse Syllabus for Math
Course Syllabus for Math 1090-003 Instructor: Stefano Filipazzi Class Time: Mondays, Wednesdays and Fridays, 9.40 a.m. - 10.30 a.m. Class Place: LCB 225 Office hours: Wednesdays, 2.00 p.m. - 3.00 p.m.,
More informationAfm Math Review Download or Read Online ebook afm math review in PDF Format From The Best User Guide Database
Afm Math Free PDF ebook Download: Afm Math Download or Read Online ebook afm math review in PDF Format From The Best User Guide Database C++ for Game Programming with DirectX9.0c and Raknet. Lesson 1.
More informationMathematics process categories
Mathematics process categories All of the UK curricula define multiple categories of mathematical proficiency that require students to be able to use and apply mathematics, beyond simple recall of facts
More informationOFFICE SUPPORT SPECIALIST Technical Diploma
OFFICE SUPPORT SPECIALIST Technical Diploma Program Code: 31-106-8 our graduates INDEMAND 2017/2018 mstc.edu administrative professional career pathway OFFICE SUPPORT SPECIALIST CUSTOMER RELATIONSHIP PROFESSIONAL
More informationSANTIAGO CANYON COLLEGE Reading & English Placement Testing Information
SANTIAGO CANYON COLLEGE Reaing & English Placement Testing Information DO YOUR BEST on the Reaing & English Placement Test The Reaing & English placement test is esigne to assess stuents skills in reaing
More informationHelping Your Children Learn in the Middle School Years MATH
Helping Your Children Learn in the Middle School Years MATH Grade 7 A GUIDE TO THE MATH COMMON CORE STATE STANDARDS FOR PARENTS AND STUDENTS This brochure is a product of the Tennessee State Personnel
More informationAP Statistics Summer Assignment 17-18
AP Statistics Summer Assignment 17-18 Welcome to AP Statistics. This course will be unlike any other math class you have ever taken before! Before taking this course you will need to be competent in basic
More informationPre-AP Geometry Course Syllabus Page 1
Pre-AP Geometry Course Syllabus 2015-2016 Welcome to my Pre-AP Geometry class. I hope you find this course to be a positive experience and I am certain that you will learn a great deal during the next
More informationExemplar 6 th Grade Math Unit: Prime Factorization, Greatest Common Factor, and Least Common Multiple
Exemplar 6 th Grade Math Unit: Prime Factorization, Greatest Common Factor, and Least Common Multiple Unit Plan Components Big Goal Standards Big Ideas Unpacked Standards Scaffolded Learning Resources
More informationTabletClass Math Geometry Course Guidebook
TabletClass Math Geometry Course Guidebook Includes Final Exam/Key, Course Grade Calculation Worksheet and Course Certificate Student Name Parent Name School Name Date Started Course Date Completed Course
More informationSURVIVING ON MARS WITH GEOGEBRA
SURVIVING ON MARS WITH GEOGEBRA Lindsey States and Jenna Odom Miami University, OH Abstract: In this paper, the authors describe an interdisciplinary lesson focused on determining how long an astronaut
More informationCourse Name: Elementary Calculus Course Number: Math 2103 Semester: Fall Phone:
Course Name: Elementary Calculus Course Number: Math 2103 Semester: Fall 2011 Instructor s Name: Ricky Streight Hours Credit: 3 Phone: 405-945-6794 email: ricky.streight@okstate.edu 1. COURSE: Math 2103
More informationUsing Proportions to Solve Percentage Problems I
RP7-1 Using Proportions to Solve Percentage Problems I Pages 46 48 Standards: 7.RP.A. Goals: Students will write equivalent statements for proportions by keeping track of the part and the whole, and by
More informationINTERMEDIATE ALGEBRA PRODUCT GUIDE
Welcome Thank you for choosing Intermediate Algebra. This adaptive digital curriculum provides students with instruction and practice in advanced algebraic concepts, including rational, radical, and logarithmic
More informationRendezvous with Comet Halley Next Generation of Science Standards
Next Generation of Science Standards 5th Grade 6 th Grade 7 th Grade 8 th Grade 5-PS1-3 Make observations and measurements to identify materials based on their properties. MS-PS1-4 Develop a model that
More informationBittinger, M. L., Ellenbogen, D. J., & Johnson, B. L. (2012). Prealgebra (6th ed.). Boston, MA: Addison-Wesley.
Course Syllabus Course Description Explores the basic fundamentals of college-level mathematics. (Note: This course is for institutional credit only and will not be used in meeting degree requirements.
More informationGeorgia Department of Education Georgia Standards of Excellence Framework GSE Sophisticated Shapes Unit 1
CONSTRUCTING TASK: What the Heck is Rekenrek? The Rekenrek can be used throughout the year and incorporated in a variety of tasks to enforce concrete representation of numbers and strategies. Adapted from
More informationLivermore Valley Joint Unified School District. B or better in Algebra I, or consent of instructor
Livermore Valley Joint Unified School District DRAFT Course Title: AP Macroeconomics Grade Level(s) 11-12 Length of Course: Credit: Prerequisite: One semester or equivalent term 5 units B or better in
More informationProblem of the Month: Movin n Groovin
: 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: Make sense of
More informationGetting Started with TI-Nspire High School Science
Getting Started with TI-Nspire High School Science 2012 Texas Instruments Incorporated Materials for Institute Participant * *This material is for the personal use of T3 instructors in delivering a T3
More informationDigital Fabrication and Aunt Sarah: Enabling Quadratic Explorations via Technology. Michael L. Connell University of Houston - Downtown
Digital Fabrication and Aunt Sarah: Enabling Quadratic Explorations via Technology Michael L. Connell University of Houston - Downtown Sergei Abramovich State University of New York at Potsdam Introduction
More informationCUNY ASSESSMENT TESTS Webinar for International Students
CUNY ASSESSMENT TESTS Webinar for International Students 1 Today s Agenda ITEM 1 Description Overview of the CUNY ASSESSMENT TEST (CAT) What is the CUNY Assessment Test Why students need to take the CAT
More informationGrade 2: Using a Number Line to Order and Compare Numbers Place Value Horizontal Content Strand
Grade 2: Using a Number Line to Order and Compare Numbers Place Value Horizontal Content Strand Texas Essential Knowledge and Skills (TEKS): (2.1) Number, operation, and quantitative reasoning. The student
More informationCharacterizing Mathematical Digital Literacy: A Preliminary Investigation. Todd Abel Appalachian State University
Characterizing Mathematical Digital Literacy: A Preliminary Investigation Todd Abel Appalachian State University Jeremy Brazas, Darryl Chamberlain Jr., Aubrey Kemp Georgia State University This preliminary
More informationSouth Carolina English Language Arts
South Carolina English Language Arts A S O F J U N E 2 0, 2 0 1 0, T H I S S TAT E H A D A D O P T E D T H E CO M M O N CO R E S TAT E S TA N DA R D S. DOCUMENTS REVIEWED South Carolina Academic Content
More informationGrade 5 + DIGITAL. EL Strategies. DOK 1-4 RTI Tiers 1-3. Flexible Supplemental K-8 ELA & Math Online & Print
Standards PLUS Flexible Supplemental K-8 ELA & Math Online & Print Grade 5 SAMPLER Mathematics EL Strategies DOK 1-4 RTI Tiers 1-3 15-20 Minute Lessons Assessments Consistent with CA Testing Technology
More informationMath Grade 3 Assessment Anchors and Eligible Content
Math Grade 3 Assessment Anchors and Eligible Content www.pde.state.pa.us 2007 M3.A Numbers and Operations M3.A.1 Demonstrate an understanding of numbers, ways of representing numbers, relationships among
More informationSchool of Innovative Technologies and Engineering
School of Innovative Technologies and Engineering Department of Applied Mathematical Sciences Proficiency Course in MATLAB COURSE DOCUMENT VERSION 1.0 PCMv1.0 July 2012 University of Technology, Mauritius
More informationPlease read this entire syllabus, keep it as reference and is subject to change by the instructor.
Math 125: Intermediate Algebra Syllabus Section # 3288 Fall 2013 TTh 4:10-6:40 PM MATH 1412 INSTRUCTOR: Nisakorn Srichoom (Prefer to be call Ms. Nisa or Prof. Nisa) OFFICE HOURS: Tuesday at 6:40-7:40 PM
More informationAnswers To Hawkes Learning Systems Intermediate Algebra
Answers To Hawkes Learning Free PDF ebook Download: Answers To Download or Read Online ebook answers to hawkes learning systems intermediate algebra in PDF Format From The Best User Guide Database Double
More informationHOLMER GREEN SENIOR SCHOOL CURRICULUM INFORMATION
HOLMER GREEN SENIOR SCHOOL CURRICULUM INFORMATION Subject: Mathematics Year Group: 7 Exam Board: (For years 10, 11, 12 and 13 only) Assessment requirements: Students will take 3 large assessments during
More informationFlorida Mathematics Standards for Geometry Honors (CPalms # )
A Correlation of Florida Geometry Honors 2011 to the for Geometry Honors (CPalms #1206320) Geometry Honors (#1206320) Course Standards MAFS.912.G-CO.1.1: Know precise definitions of angle, circle, perpendicular
More informationWelcome to ACT Brain Boot Camp
Welcome to ACT Brain Boot Camp 9:30 am - 9:45 am Basics (in every room) 9:45 am - 10:15 am Breakout Session #1 ACT Math: Adame ACT Science: Moreno ACT Reading: Campbell ACT English: Lee 10:20 am - 10:50
More informationNumeracy Medium term plan: Summer Term Level 2C/2B Year 2 Level 2A/3C
Numeracy Medium term plan: Summer Term Level 2C/2B Year 2 Level 2A/3C Using and applying mathematics objectives (Problem solving, Communicating and Reasoning) Select the maths to use in some classroom
More informationPre-Algebra A. Syllabus. Course Overview. Course Goals. General Skills. Credit Value
Syllabus Pre-Algebra A Course Overview Pre-Algebra is a course designed to prepare you for future work in algebra. In Pre-Algebra, you will strengthen your knowledge of numbers as you look to transition
More informationDIDACTIC MODEL BRIDGING A CONCEPT WITH PHENOMENA
DIDACTIC MODEL BRIDGING A CONCEPT WITH PHENOMENA Beba Shternberg, Center for Educational Technology, Israel Michal Yerushalmy University of Haifa, Israel The article focuses on a specific method of constructing
More informationStrategies for Solving Fraction Tasks and Their Link to Algebraic Thinking
Strategies for Solving Fraction Tasks and Their Link to Algebraic Thinking Catherine Pearn The University of Melbourne Max Stephens The University of Melbourne
More informationCHAPTER 4: REIMBURSEMENT STRATEGIES 24
CHAPTER 4: REIMBURSEMENT STRATEGIES 24 INTRODUCTION Once state level policymakers have decided to implement and pay for CSR, one issue they face is simply how to calculate the reimbursements to districts
More informationCurriculum Guide 7 th Grade
Curriculum Guide 7 th Grade Kesling Middle School LaPorte Community School Corporation Mr. G. William Wilmsen, Principal Telephone (219) 362-7507 Mr. Mark Fridenmaker, Assistant Principal Fax (219) 324-5712
More informationExploring Derivative Functions using HP Prime
Exploring Derivative Functions using HP Prime Betty Voon Wan Niu betty@uniten.edu.my College of Engineering Universiti Tenaga Nasional Malaysia Wong Ling Shing Faculty of Health and Life Sciences, INTI
More informationICTCM 28th International Conference on Technology in Collegiate Mathematics
DEVELOPING DIGITAL LITERACY IN THE CALCULUS SEQUENCE Dr. Jeremy Brazas Georgia State University Department of Mathematics and Statistics 30 Pryor Street Atlanta, GA 30303 jbrazas@gsu.edu Dr. Todd Abel
More informationPearson Grade 8 Practice And Homework
Pearson Grade 8 And Free PDF ebook Download: Pearson Grade 8 And Download or Read Online ebook pearson grade 8 practice and homework in PDF Format From The Best User Guide Database 3rd Grade EOG Prep.
More informationHistory of CTB in Adult Education Assessment
TASC Overview Copyright 2014 by CTB/McGraw-Hill LLC. All rights reserved. The Test Assessing Secondary Completion is a trademark of McGraw-Hill School Education Holdings LLC. McGraw-Hill Education is not
More information