Lesson Plan. Vocabulary


 Kenneth O’Brien’
 1 years ago
 Views:
Transcription
1 S.ID.6c: Use Residuals to Assess Fit of a Function S.ID.6c: Use Residuals to Assess Fit of a Function Summarize, represent, and interpret data on two categorical and quantitative variables 6. Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. c. Informally assess the fit of a function by plotting and analyzing residuals. Overview of Lesson  activate prior knowledge  present vocabulary and/or big ideas associated with the lesson  connect assessment practices with curriculum  model an assessment problem and solution strategy  facilitate guided practice of student activity Optional: Provide or allow students to create additional problem sets  facilitate a summary and share out of student work Optional HW  Write the math assignment. Vocabulary A residual is the vertical distance between where a regression equation predicts a point will appear on a graph and the actual location of the point on the graph (scatterplot). If there is no difference between where a regression equation places a point and the actual position of the point, the residual is zero. A residual can also be understood as the difference in predicted and actual yvalues (dependent variable values) for a given value of x (the independent variable). A residual plot is a scatter plot that shows the residuals as points on a vertical axis (yaxis) above corresponding (paired) values of the independent variable on the horizontal axis (xaxis). Any pattern in a residual plot suggests that the regression equation is not appropriate for the data.residuals on the Graphing Calculator. A residual plot without a pattern and with a near equal distribution of points above and below the x axis suggests that the regression equation is a good fit for the data. Residuals are automatically stored in graphing calculators when regression equations are calculated. To view a residuals scatterplot in the graphing calculator, you must set the Y list variable to RESID, the use Zoom 9 to plot the residuals. REGENTS PROBLEMS
2 1. Which statistic would indicate that a linear function would not be a good fit to model a data set? a. c. b. d.
3 2. Use the data below to write the regression equation ( ) for the raw test score based on the hours tutored. Round all values to the nearest hundredth. Equation: Create a residual plot on the axes below, using the residual scores in the table above. Based on the residual plot, state whether the equation is a good fit for the data. Justify your answer.
4 3. The table below represents the residuals for a line of best fit. Plot these residuals on the set of axes below. Using the plot, assess the fit of the line for these residuals and justify your answer. 4. The residual plots from two different sets of bivariate data are graphed below. Explain, using evidence from graph A and graph B, which graph indicates that the model for the data is a good fit.
5 S.ID.6c: Use Residuals to Assess Fit of a Function Answer Section 1. ANS: C Strategy: Use knowledge of correlation coefficients and residual plots to determine which answer choice is not a good fit to model a data set. STEP 1. A correlation coefficient close to 1 or 1 indicates a good fit, so answer choices a and b can be eliminated. Both suggest a good fit. STEP 2. For a residual plot, there should be no observable pattern and a similar distribution of residuals above and below the xaxis. The residual plot in answer choice d shows a good fit, so answer choice d can be eliminated, leaving answer choice c as the correct answer. DIMS? Does it make sense? Yes. The clear pattern in answer choice c tells us that the linear function is not a good fit to model the data set. PTS: 2 REF: fall1303a1 NAT: S.ID.6c TOP: Correlation Coefficient and Residuals 2. ANS: Based on the residual plot, the equation is a good fit for the data because the residual values are scattered without a pattern and are fairly evenly distributed above and below the xaxis. Strategies: Use linear regression to find a regression equation that fits the first two columns of the table, then create a residuals plot using the first and third columns of the table to see if there is a pattern in the residuals. STEP 1. Input the data from the first two columns of the table into a graphing calculator.
6 STEP 2. Determine which regression strategy will best fit the data. The problem states that the regression equation should be in the form ( ), which means linear reression. The scatterplot produced by the graphing calculator also suggests linear regression. STEP 3. Execute the lionear regression strategy in the graphing calculator. Round all values to the nearest hundredth: STEP 4. Plot the residual values on the graph provided using data from the first and third columns of the table. The graph shows a near equal number of points above the line and below the line, and the graph shows no pattern. The regression equation appears to be a good fit. NOTE: The graphing calculator will also produce a residuals plot. DIMS: Ask the question, Does It Make Sense (DIMS)? Yes. The regression equation produces the same residuals as shown in the table. PTS: 4 REF: fall1314a1 NAT: S.ID.6c TOP: Correlation Coefficient and Residuals
7 3. ANS: The line is a poor fit because the residuals form a pattern. PTS: 2 REF: a1 NAT: S.ID.6c TOP: Correlation Coefficient and Residuals 4. ANS: Graph A is a good fit because it does not have a clear pattern, whereas Graph B does have a clear pattern.. PTS: 2 REF: AI NAT: S.ID.6b TOP: Correlation Coefficient and Residuals
8 START PART 1. PART 2. PART 3. PART 4. PART 5. PART 6. Standard Writing the Math Assignment Write your name, date, topic of lesson, and class on your paper. Copy the problem from the lesson and underline/highlight key words. State your understanding of what the problem is asking. Answer the problem. Explanation of strategy. Create a new problem that addresses the same mathematical understandings. State the answer to your new problem. Clearly label each of the six parts. Grading Rubric Each homework writing assignment is graded using a fourpoint rubric, as follows: Part 1. Statement of the problem. 1 point is awarded for correctly restating the 2 original problem. Part 2. Statement of what the problem is really asking. point is awarded for correctly identifying 1 2 what the problem is asking you to find or do. Part 3. Solution to the problem. 1 point is awarded for a correct solution to 2 the problem. Part 4. Written analysis of the mathematics Up to 1 point is awarded for an explanation of and solution strategy involved in the problem. the mathematics and solution strategy involved in the problem. Part 5. An alternative version of the problem. Up to 1 point is awarded for creating a new problem that involves similar mathematics and a similar solution strategy. Part 6. Solution to the alternative version of 1 the problem. point is awarded for correctly solving the 2 new problem that you have created. This assignment/activity is designed to incorporate elements of Polya s four step universal algorithm for problem solving with the idea that writing is thinking. Rationale for Assignment Each New York Regents Algebra I (Common Core) examination contains 13 open response problems. An analysis of the first three Algebra I examinations revealed that approximately 51% (20 out of 39) of these open response problems instructed students to: 1) describe; 2) state; 2) explain; 3) justify or otherwise write about their answers. It is theorized that students can benefit from explicit instruction and writing routines that are applicable to solving these problems.
9 EXEMPLAR OF A WRITING THE MATH ASSIGNMENT Student s Name Topic: Date: Class: Part 1. The Problem TOP Electronics is a small business with five employees. The mean (average) weekly salary for the five employees is $360. If the weekly salaries of four of the employees are $340, $340, $345, and $425, what is the salary of the fifth employee? Part 2. What is the problem asking? Find the salary of the fifth employee. Part 3. Answer The salary of the fifth employee is $350 per week. Part 4. Explanation of Strategy The arithmetic mean or average can be represented algebraically as: x1 x2... xn X n I put information from the problem into the formula. The problem says there are 5 employees, so n 5. The problem also gives the mean (average) salary and the salaries of 4 of the employees. These numbers can be substituted into the formula as follows: x x x x5 350 x Check: Part 5. A New Problem Joseph took five math exams this grading period and his average score on all of the exams is 88. He remembers that he received test scores of 78, 87, 94, and 96 on four of the examinations, but he has lost one examination and cannot remember what he scored on it. What was Joseph s score on the missing exam? Part 6. Answer to New Problem Joseph received a score of 85 on the missing examination. EVALUATION Name and Proper Heading Part 4. Explanation of strategy. 1 Point Part 1. Problem copied correctly? 1/2 Point Part 5. New problem. 1 Point Part 2. Understand the problem? 1/2 Point Part 6. Solution to new problem. 1/2 Point Part 3. Correct and complete answer? 1/2 Point TOTAL 4 Points
Vocabulary. S.ID.B.6b: Use Residuals to Assess Fit of a Function
S.ID.B.6b: Use Residuals to Assess Fit of a Function GRAPHS AND STATISTICS S.ID.B.6b: Use Residuals to Assess Fit of a Function B. Summarize, represent, and interpret data on two categorical and quantitative
More informationF.IF.7b: Graph Root, Piecewise, Step, & Absolute Value Functions
F.IF.7b: Graph Root, Piecewise, Step, & Absolute Value Functions F.IF.7b: Graph Root, Piecewise, Step, & Absolute Value Functions Analyze functions using different representations. 7. Graph functions expressed
More informationLesson Plan. Mean Count
S.ID.: Central Tendency and Dispersion S.ID.: Central Tendency and Dispersion Summarize, represent, and interpret data on a single count or measurement variable. Use statistics appropriate to the shape
More informationLesson Plan. N.RN.3: Use properties of rational and irrational numbers.
N.RN.3: Use properties of rational irrational numbers. N.RN.3: Use Properties of Rational Irrational Numbers Use properties of rational irrational numbers. 3. Explain why the sum or product of two rational
More informationA correlation exists between two variables when one of them is related to the other in some way.
Lecture #10 Chapter 10 Correlation and Regression The main focus of this chapter is to form inferences based on sample data that come in pairs. Given such paired sample data, we want to determine whether
More informationElementary Statistics. Scatter Plot, Regression Line, Linear Correlation Coefficient, and Coefficient of Determination
Scatter Plot, Regression Line, Linear Correlation Coefficient, and Coefficient of Determination What is a Scatter Plot? A Scatter Plot is a plot of ordered pairs (x, y) where the horizontal axis is used
More informationAlgebra I: Lesson 54 (5074) SAS Curriculum Pathways
TwoVariable Quantitative Data: Lesson Summary with Examples Bivariate data involves two quantitative variables and deals with relationships between those variables. By plotting bivariate data as ordered
More informationRelationship of two variables
Relationship of two variables A correlation exists between two variables when the values of one are somehow associated with the values of the other in some way. Scatter Plot (or Scatter Diagram) A plot
More informationBasic Math Refresher A tutorial and assessment of basic math skills for students in PUBP704.
Basic Math Refresher A tutorial and assessment of basic math skills for students in PUBP704. The purpose of this Basic Math Refresher is to review basic math concepts so that students enrolled in PUBP704:
More informationSection 3.2. Graphing linear equations
Section 3.2 Graphing linear equations Learning objectives Graph a linear equation by finding and plotting ordered pair solutions Graph a linear equation and use the equation to make predictions Vocabulary:
More informationStudy Resources For Algebra I. Unit 1C Analyzing Data Sets for Two Quantitative Variables
Study Resources For Algebra I Unit 1C Analyzing Data Sets for Two Quantitative Variables This unit explores linear functions as they apply to data analysis of scatter plots. Information compiled and written
More informationRegents Exam Questions A2.S.8: Correlation Coefficient
A2.S.8: Correlation Coefficient: Interpret within the linear regression model the value of the correlation coefficient as a measure of the strength of the relationship 1 Which statement regarding correlation
More informationTEACHER: Spaghetti Residuals & Correlation
Summary In this task, students will analyze the data from Breaking Spaghetti. Develop understanding of residuals. Use technology to draw residual plot. Use residual plots to determine whether a linear
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 information9.8 Rockin the Residuals
SECONDARY MATH 1 // MODULE 9 43 9.8 Rockin the Residuals A Solidify Understanding Task The correlation coefficient is not the only tool that statisticians use to analyze whether or not a line is a good
More informationSCATTER PLOTS AND TREND LINES
1 SCATTER PLOTS AND TREND LINES INSTRUCTIONAL ACTIVITY Lesson 1 LEARNING GOAL Students will create a scatter plot with appropriately labeled and scaled axes and estimate new data values. The critical outcome
More informationDomain: Statistics and Probability (SP) Cluster: Investigate patterns of association in bivariate data.
Domain: Statistics and Probability (SP) Standard: 8.SP.1. Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns
More informationGraphing Linear Equations in Two Variables
Math 123 Section 3.2  Graphing Linear Equations Using Intercepts  Page 1 Graphing Linear Equations in Two Variables I. Graphing Lines A. The graph of a line is just the set of solution points of the
More information10.1 NotesGraphing Quadratics
Name: Period: 10.1 NotesGraphing Quadratics Section 1: Identifying the vertex (minimum/maximum), the axis of symmetry, and the roots (zeros): State the maximum or minimum point (vertex), the axis of symmetry,
More informationChapter 2: Looking at Data Relationships (Part 1)
Chapter 2: Looking at Data Relationships (Part 1) Dr. Nahid Sultana Chapter 2: Looking at Data Relationships 2.1: Scatterplots 2.2: Correlation 2.3: LeastSquares Regression 2.5: Data Analysis for TwoWay
More informationWhat does the number m in y = mx + b measure? To find out, suppose (x 1, y 1 ) and (x 2, y 2 ) are two points on the graph of y = mx + b.
PRIMARY CONTENT MODULE Algebra  Linear Equations & Inequalities T37/H37 What does the number m in y = mx + b measure? To find out, suppose (x 1, y 1 ) and (x 2, y 2 ) are two points on the graph of
More informationSession 7 Bivariate Data and Analysis
Session 7 Bivariate Data and Analysis Key Terms for This Session Previously Introduced mean standard deviation New in This Session association bivariate analysis contingency table covariation least squares
More informationSCATTER PLOTS AND TREND LINES
Name SCATTER PLOTS AND TREND LINES VERSION 2 Lessons 1 3 1. You have collected the following data while researching the Winter Olympics. You are trying to determine if there is a relationship between the
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 1. ELG HS.S.2: Summarize, represent, and interpret data on two categorical and quantitative variables
Vertical Progression: 7 th Grade 8 th Grade Algebra 2 Draw informal comparative inferences about two populations. o 7.SP.4 Use measures of center and measures of variability for numerical data from random
More informationLinear Regressions Getting started with Making a Scatter Plot on your Calculator Group Acitivity 1 STEM Project Week #3
Linear Regressions Getting started with Making a Scatter Plot on your Calculator Group Acitivity 1 STEM Project Week #3 Regression analysis is a method used to create a mathematical model to show the relationship
More informationID X Y
Dale Berger SPSS StepbyStep Regression Introduction: MRC01 This stepbystep example shows how to enter data into SPSS and conduct a simple regression analysis to develop an equation to predict from.
More informationAlgebra II End of Course Exam Answer Key Segment I. Scientific Calculator Only
Algebra II End of Course Exam Answer Key Segment I Scientific Calculator Only Question 1 Reporting Category: Algebraic Concepts & Procedures Common Core Standard: AAPR.3: Identify zeros of polynomials
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 informationManhattan Center for Science and Math High School Mathematics Department Curriculum
Content/Discipline Algebra 1 Semester 2: Marking Period 1  Unit 8 Polynomials and Factoring Topic and Essential Question How do perform operations on polynomial functions How to factor different types
More informationLinear Equations. Find the domain and the range of the following set. {(4,5), (7,8), (1,3), (3,3), (2,3)}
Linear Equations Domain and Range Domain refers to the set of possible values of the xcomponent of a point in the form (x,y). Range refers to the set of possible values of the ycomponent of a point in
More informationChapter 2. Looking at Data: Relationships. Introduction to the Practice of STATISTICS SEVENTH. Moore / McCabe / Craig. Lecture Presentation Slides
Chapter 2 Looking at Data: Relationships Introduction to the Practice of STATISTICS SEVENTH EDITION Moore / McCabe / Craig Lecture Presentation Slides Chapter 2 Looking at Data: Relationships 2.1 Scatterplots
More informationRigorous Curriculum Design Authentic Performance Tasks
Rigorous Curriculum Design Authentic Performance Tasks 1 of 14 Subject Grade/Course Unit of Study Duration of Unit Math 8 th Grade/ Math Unit 6 Scatter plots and statistics 34 Weeks Engaging Scenario
More informationChapter 3: Describing Relationships
Chapter 3: Describing Relationships The Practice of Statistics, 4 th edition For AP* STARNES, YATES, MOORE Chapter 3 2 Describing Relationships 3.1 Scatterplots and Correlation 3.2 Learning Targets After
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 informationLecture 8 : Coordinate Geometry. The coordinate plane The points on a line can be referenced if we choose an origin and a unit of 20
Lecture 8 : Coordinate Geometry The coordinate plane The points on a line can be referenced if we choose an origin and a unit of 0 distance on the axis and give each point an identity on the corresponding
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 informationAP * Statistics Review. Linear Regression
AP * Statistics Review Linear Regression Teacher Packet Advanced Placement and AP are registered trademark of the College Entrance Examination Board. The College Board was not involved in the production
More informationLinear Equations. 5 Day Lesson Plan Unit: Linear Equations Grade Level: Grade 9 Time Span: 50 minute class periods By: Richard Weber
Linear Equations 5 Day Lesson Plan Unit: Linear Equations Grade Level: Grade 9 Time Span: 50 minute class periods By: Richard Weber Tools: Geometer s Sketchpad Software Overhead projector with TI 83
More informationStatistics Review Solutions
Statistics Review Solutions 1. Katrina must take five exams in a math class. If her scores on the first four exams are 71, 69, 85, and 83, what score does she need on the fifth exam for her overall mean
More informationScatterplots. Section 3.1 Scatterplots & Correlation. Scatterplots. Explanatory & Response Variables. Scatterplots and Correlation
Section 3.1 Scatterplots & Correlation Scatterplots A scatterplot shows the relationship between two quantitative variables measured on the same individuals. The values of one variable appear on the horizontal
More informationStraightening Data in a Scatterplot Selecting a Good ReExpression Model
Straightening Data in a Scatterplot Selecting a Good ReExpression What Is All This Stuff? Here s what is included: Page 3: Graphs of the three main patterns of data points that the student is likely to
More information2.3 Writing Equations of Lines
. Writing Equations of Lines In this section ou will learn to use pointslope form to write an equation of a line use slopeintercept form to write an equation of a line graph linear equations using the
More informationAlgebra I Sample Questions. 1 Which ordered pair is not in the solution set of (1) (5,3) (2) (4,3) (3) (3,4) (4) (4,4)
1 Which ordered pair is not in the solution set of (1) (5,3) (2) (4,3) (3) (3,4) (4) (4,4) y 1 > x + 5 and y 3x 2? 2 5 2 If the quadratic formula is used to find the roots of the equation x 2 6x 19 = 0,
More informationCHAPTER 3: GRAPHS OF QUADRATIC RELATIONS
CHAPTER 3: GRAPHS OF QUADRATIC RELATIONS Specific Expectations Addressed in the Chapter Collect data that can be represented as a quadratic relation, from experiments using appropriate equipment and technology
More information3.1 Scatterplots and Correlation
3.1 Scatterplots and Correlation Most statistical studies examine data on more than one variable. Exploring Bivariate data follows many of the same principles for individual data. 1. Plot the data, then
More informationIsolate the absolute value expression. Add 5 to both sides and then divide by 2.
11 of 21 8/14/2014 2:35 PM of a variable expression. You can use the definition of absolute value to solve absolute value equations algebraically. Since then the equation ax + b = c is equivalent to (ax
More informationModeling Situations with Linear Equations
Modeling Situations with Linear Equations MATHEMATICAL GOALS This lesson unit is intended to help you assess how well students use algebra in context, and in particular, how well students: Explore relationships
More informationPlot the following two points on a graph and draw the line that passes through those two points. Find the rise, run and slope of that line.
Objective # 6 Finding the slope of a line Material: page 117 to 121 Homework: worksheet NOTE: When we say line... we mean straight line! Slope of a line: It is a number that represents the slant of a line
More informationSuggested Time Frame Time Frame: 4 th Six Weeks Suggested Duration: 13 days. Vertical Alignment Expectations
Title Scatterplots and Data Analysis Big Ideas/Enduring Understandings The student will understand how patterns are used when comparing two quantities. Suggested Time Frame Time Frame: 4 th Six Weeks Suggested
More informationStatistics and Probability Investigate patterns of association in bivariate data.
Performance Assessment Task Scatter Diagram Grade 9 task aligns in part to CCSSM grade 8 This task challenges a student to select and use appropriate statistical methods to analyze data. A student must
More informationLesson 18 Student Outcomes Lesson Notes
Lesson 18 Analyzing Residuals Student Outcomes Students use a graphing calculator to construct the residual plot for a given data set. Students use a residual plot as an indication of whether or not the
More information4 th Grade Math Lesson Plan Coordinate Planes
Context: Objective: 4 th Grade Math Lesson Plan Coordinate Planes This lesson designed for a 4 th grade class at Kraft Elementary School. This class contains 16 students. No students have IEPs and none
More informationScope and Sequence. AM CC Algebra 1 Library
The Accelerated Math scope and sequence is based on extensive mathematics and standards research and consultation from mathematics educators, mathematicians, and university researchers. You're sure to
More informationSimple Regression Theory I 2010 Samuel L. Baker
SIMPLE REGRESSION THEORY I 1 Simple Regression Theory I 2010 Samuel L. Baker Regression analysis lets you use data to explain and predict. A simple regression line drawn through data points In Assignment
More information51. Lesson Objective. Lesson Presentation Lesson Review
51 Using Transformations to Graph Quadratic Functions Lesson Objective Transform quadratic functions. Describe the effects of changes in the coefficients of y = a(x h) 2 + k. Lesson Presentation Lesson
More informationHomework 11. Part 1. Name: Score: / null
Name: Score: / Homework 11 Part 1 null 1 For which of the following correlations would the data points be clustered most closely around a straight line? A. r = 0.50 B. r = 0.80 C. r = 0.10 D. There is
More informationGRAPHING LINEAR EQUATIONS IN TWO VARIABLES
GRAPHING LINEAR EQUATIONS IN TWO VARIABLES The graphs of linear equations in two variables are straight lines. Linear equations may be written in several forms: SlopeIntercept Form: y = mx+ b In an equation
More informationThe Cartesian Plane The Cartesian Plane. Performance Criteria 3. PreTest 5. Coordinates 7. Graphs of linear functions 9. The gradient of a line 13
6 The Cartesian Plane The Cartesian Plane Performance Criteria 3 PreTest 5 Coordinates 7 Graphs of linear functions 9 The gradient of a line 13 Linear equations 19 Empirical Data 24 Lines of best fit
More informationLines, Lines, Lines!!! SlopeIntercept Form ~ Lesson Plan
Lines, Lines, Lines!!! SlopeIntercept Form ~ Lesson Plan I. Topic: SlopeIntercept Form II. III. Goals and Objectives: A. The student will write an equation of a line given information about its graph.
More informationTEACHER NOTES MATH NSPIRED
Math Objectives Students will use a moveable line to find a line of fit for a data set. Students will interpret the slope and yintercept of the equation of their line of fit. Students will make predictions
More informationExpressions and Equations Understand the connections between proportional relationships, lines, and linear equations.
Performance Assessment Task Squares and Circles Grade 8 The task challenges a student to demonstrate understanding of the concepts of linear equations. A student must understand relations and functions,
More informationRationale. Instructional Task
AE Strand(s): Algebra and Probability/Statistics. Sample Courses: Middle School Course 1, Middle School Course 2, Middle School OneYear Advanced Course, Integrated 3, Algebra I, and Algebra II. Topic/Expectation
More informationProcedure In each case, draw and extend the given series to the fifth generation, then complete the following tasks:
Math IV Nonlinear Algebra 1.2 Growth & Decay Investigation 1.2 B: Nonlinear Growth Introduction The previous investigation introduced you to a pattern of nonlinear growth, as found in the areas of a series
More informationUnit 5: Scatter Plots
Unit 5: Scatter Plots scatter plot regression correlation line of best fit/trend line correlation coefficient residual residual plot observed value predicted value I. Vocabulary List Definitions will be
More informationPPS TI83 Activities Algebra 12 Teacher Notes
PPS TI83 Activities Algebra 12 Teacher Notes It is an expectation in Portland Public Schools that all teachers are using the TI83 graphing calculator in meaningful ways in Algebra 12. This does not
More informationTYPES OF NUMBERS. Example 2. Example 1. Problems. Answers
TYPES OF NUMBERS When two or more integers are multiplied together, each number is a factor of the product. Nonnegative integers that have exactly two factors, namely, one and itself, are called prime
More informationEquations of Lines Derivations
Equations of Lines Derivations If you know how slope is defined mathematically, then deriving equations of lines is relatively simple. We will start off with the equation for slope, normally designated
More informationGraphing Linear Equations
Graphing Linear Equations I. Graphing Linear Equations a. The graphs of first degree (linear) equations will always be straight lines. b. Graphs of lines can have Positive Slope Negative Slope Zero slope
More informationExponential Growth and Modeling
Exponential Growth and Modeling Is it Really a Small World After All? I. ASSESSSMENT TASK OVERVIEW & PURPOSE: Students will apply their knowledge of functions and regressions to compare the U.S. population
More informationCan Gas Prices be Predicted?
Can Gas Prices be Predicted? Chris Vaughan, Reynolds High School A Statistical Analysis of Annual Gas Prices from 19762005 Level/Course: This lesson can be used and modified for teaching High School Math,
More informationGraphing Quadratic Functions
Graphing Quadratic Functions In our consideration of polynomial functions, we first studied linear functions. Now we will consider polynomial functions of order or degree (i.e., the highest power of x
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 informationUnderstanding Geometric Sequences
6 Locker LESSON 1.1 Understanding Geometric Sequences Texas Math Standards The student is expected to: A1.1.D Write a formula for the nth term of arithmetic and geometric sequences, given the value of
More informationAlgebra 1 Chapter 3 Vocabulary. equivalent  Equations with the same solutions as the original equation are called.
Chapter 3 Vocabulary equivalent  Equations with the same solutions as the original equation are called. formula  An algebraic equation that relates two or more reallife quantities. unit rate  A rate
More informationTeaching & Learning Plans. The Correlation Coefficient. Leaving Certificate Syllabus
Teaching & Learning Plans The Correlation Coefficient Leaving Certificate Syllabus The Teaching & Learning Plans are structured as follows: Aims outline what the lesson, or series of lessons, hopes to
More informationCH 9. Quadratic Equations and Functions
9.1: Graph 9.2: Graph 9.3: Solve Quadratic Equations by Graphing 9.4: Use Square Roots to Solve Quadratic Equations 9.5: Solve Quadratic Equations by Completing the Square 9.6: Solve Quadratic Equations
More informationExaminer Tips for AS and A Level Physics (9702)
Examiner Tips for AS and A Level Physics (9702) How to Use These Tips These tips highlight some common mistakes made by students. They are collected under various subheadings to help you when you revise
More informationGRAPHING (2 weeks) Main Underlying Questions: 1. How do you graph points?
GRAPHING (2 weeks) The Rectangular Coordinate System 1. Plot ordered pairs of numbers on the rectangular coordinate system 2. Graph paired data to create a scatter diagram 1. How do you graph points? 2.
More informationCHAPTER 3 Describing Relationships
CHAPTER 3 Describing Relationships 3.1 Scatterplots and Correlation The Practice of Statistics, 5th Edition Starnes, Tabor, Yates, Moore Bedford Freeman Worth Publishers Scatterplots and Correlation Learning
More informationWhat students need to know for... ALGEBRA II
What students need to know for... ALGEBRA II 20152016 NAME Students expecting to take Algebra II at Cambridge Rindge & Latin School should demonstrate the ability to... General: o Keep an organized notebook
More informationHigh School Algebra 1 Common Core Standards & Learning Targets
High School Algebra 1 Common Core Standards & Learning Targets Unit 1: Relationships between Quantities and Reasoning with Equations CCS Standards: Quantities NQ.1. Use units as a way to understand problems
More informationTHE COST OF COLLEGE EDUCATION PROJECT PACKET
THE COST OF COLLEGE EDUCATION PROJECT PACKET Introduction We live in a society where a college education is considered the norm and not the exception. While everyone is expected to attend a college or
More informationTitle: Take a B.R.E.A.T.H. with Us! (Balloon Regression Experiment Analyzing Time vs. Height) Activity
Title: Take a B.R.E.A.T.H. with Us! (Balloon Regression Experiment Analyzing Time vs. Height) Activity Brief Overview: The lesson introduces the concepts of line of bestfit (linear regression) and residuals.
More informationPatterns, Relationships, and Algebraic Thinking
Patterns, Relationships, and Algebraic Thinking Activity: TEKS: Sequences, Sequences Everywhere! (8.5) Patterns, relationships, and algebraic thinking. The student uses graphs, tables, and algebraic representations
More informationRelationships Between Two Variables: Scatterplots and Correlation
Relationships Between Two Variables: Scatterplots and Correlation Example: Consider the population of cars manufactured in the U.S. What is the relationship (1) between engine size and horsepower? (2)
More informationch12 practice test SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
ch12 practice test 1) The null hypothesis that x and y are is H0: = 0. 1) 2) When a twosided significance test about a population slope has a Pvalue below 0.05, the 95% confidence interval for A) does
More informationBrunswick High School has reinstated a summer math curriculum for students Algebra 1, Geometry, and Algebra 2 for the 20142015 school year.
Brunswick High School has reinstated a summer math curriculum for students Algebra 1, Geometry, and Algebra 2 for the 20142015 school year. Goal The goal of the summer math program is to help students
More informationName Period Date MATHLINKS: GRADE 7 STUDENT PACKET 1 FRACTIONS AND DECIMALS
Name Period Date 7 STUDENT PACKET MATHLINKS: GRADE 7 STUDENT PACKET FRACTIONS AND DECIMALS. Terminating Decimals Convert between fractions and terminating decimals. Compute with simple fractions.. Repeating
More informationHow strong is a linear relationship?
Lesson 19 Interpreting Correlation Student Outcomes Students use technology to determine the value of the correlation coefficient for a given data set. Students interpret the value of the correlation coefficient
More informationALGEBRA I (Common Core) Thursday, January 28, 2016 1:15 to 4:15 p.m., only
ALGEBRA I (COMMON CORE) The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION ALGEBRA I (Common Core) Thursday, January 28, 2016 1:15 to 4:15 p.m., only Student Name: School Name: The
More informationExercise 1.12 (Pg. 2223)
Individuals: The objects that are described by a set of data. They may be people, animals, things, etc. (Also referred to as Cases or Records) Variables: The characteristics recorded about each individual.
More informationgraphs, Equations, and inequalities
graphs, Equations, and inequalities You might think that New York or Los Angeles or Chicago has the busiest airport in the U.S., but actually it s HartsfieldJackson Airport in Atlanta, Georgia. In 010,
More informationMathematics Success Grade 8
T308 Mathematics Success Grade 8 [OBJECTIVE] The student will analyze the constant rate of proportionality between similar triangles, construct triangles between two points on a line, and compare the ratio
More informationGeorgia Standards of Excellence Curriculum Map. Mathematics. GSE Algebra I
Georgia Standards of Excellence Curriculum Map Mathematics GSE Algebra I These materials are for nonprofit educational purposes only. Any other use may constitute copyright infringement. Georgia Department
More informationThe PointSlope Form
7. The PointSlope Form 7. OBJECTIVES 1. Given a point and a slope, find the graph of a line. Given a point and the slope, find the equation of a line. Given two points, find the equation of a line y Slope
More informationExam 2 Review. 3. How to tell if an equation is linear? An equation is linear if it can be written, through simplification, in the form.
Exam 2 Review Chapter 1 Section1 Do You Know: 1. What does it mean to solve an equation? To solve an equation is to find the solution set, that is, to find the set of all elements in the domain of the
More informationCorrelation key concepts:
CORRELATION Correlation key concepts: Types of correlation Methods of studying correlation a) Scatter diagram b) Karl pearson s coefficient of correlation c) Spearman s Rank correlation coefficient d)
More informationLisa Rosenberg Mathematics and Statistics Department
Long Assignment for General Statistics Mathematics 110 Lisa Rosenberg Mathematics and Statistics Department Introduction for Faculty Colleagues This assignment is intended for General Statistics (MTH 110)
More information