UNIT 2 LINEAR AND EXPONENTIAL RELATIONSHIPS Station Activities Set 2: Relations Versus Functions/Domain and Range

Size: px
Start display at page:

Download "UNIT 2 LINEAR AND EXPONENTIAL RELATIONSHIPS Station Activities Set 2: Relations Versus Functions/Domain and Range"

Transcription

1 UNIT LINEAR AND EXPONENTIAL RELATIONSHIPS Station Activities Set : Relations Versus Functions/Domain and Range Station You will be given a ruler and graph paper. As a group, use our ruler to determine whether or not each relation below is a function. Beside each graph, write our answer and reasoning.. =. + = continued U-

2 UNIT LINEAR AND EXPONENTIAL RELATIONSHIPS Station Activities Set : Relations Versus Functions/Domain and Range. = + How did ou use our ruler to determine whether each relation was a function?. Use our ruler and graph paper to sketch a function. Use the vertical line test to verif that it is a function. For the relations below, determine whether or not the are functions. Eplain our answer.. {(, ), (, ), (, ), (, )}. {(, ), (, ), (, )} U-

3 UNIT LINEAR AND EXPONENTIAL RELATIONSHIPS Station Activities Set : Comparing Eponential Models Instruction Goal: To provide opportunities for students to develop concepts and skills related to creating and interpreting eponential graphs representing real-world situations Common Core State Standards F IF. F IF. Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a contet. Graph functions epressed smbolicall and show ke features of the graph, b hand in simple cases and using technolog for more complicated cases. d. (+) Graph rational functions, identifing zeros and asmptotes when suitable factorizations are available, and showing end behavior. e. Graph eponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. Student Activities Overview and Answer Ke Station Working with groups, students determine the -intercepts and solutions to eponential functions using their graphs. Then, students are given a pair of points and asked to determine the eponential function that passes through those points. Answers intercept: (, ) < < U-

4 UNIT LINEAR AND EXPONENTIAL RELATIONSHIPS Station Activities Set : Comparing Eponential Models. Instruction (, ) no -intercepts = U-

5 UNIT LINEAR AND EXPONENTIAL RELATIONSHIPS Station Activities Set : Comparing Eponential Models Station Instruction Working with groups, students use calculators to evaluate and graph eponential functions. Answers. f ( ) = f ( ) = no -intercepts U-

6 UNIT LINEAR AND EXPONENTIAL RELATIONSHIPS Station Activities Set : Comparing Eponential Models Instruction. no -intercepts no -intercepts intercept at (, ). The graph must cross the -ais, so the equation must include an addition or subtraction operation in addition to the eponential operation. U-

7 UNIT LINEAR AND EXPONENTIAL RELATIONSHIPS Station Activities Set : Comparing Eponential Models Station Instruction Working with groups, students use eponential functions to calculate compound interest according tn to the formula r A = P + n. Answers. A = +. A = $.. A = +. A = $.. A = + A = $... A = +. A = $.. A = +. = $. A = +. = $. The account with % interest has the better ield since that account will ield approimatel $. and the account with the.% interest rate will ield approimatel $.. Station Students will be given an eponential function and asked to generate a table of values and the graph. Then students will eamine the equation, table of values, and graph for defining characteristics of eponential functions. Answers. Answers will var. See sample answer on the following page. U-

8 UNIT LINEAR AND EXPONENTIAL RELATIONSHIPS Station Activities Set : Comparing Eponential Models Instruction f() / /. -intercepts: none; -intercept:.. Answers will var. Sample answer: variable in eponent. Answers will var. Sample answer: It grows quickl.. Answers will var. Sample answer: It rises to the right and levels off toward the left. Materials List/Setup Station colored pens or pencils Station graphing calculator; colored pens or pencils Station calculator Station none U-

9 UNIT LINEAR AND EXPONENTIAL RELATIONSHIPS Station Activities Set : Comparing Eponential Models Discussion Guide Instruction To support students in reflecting on the activities and to gather some formative information about student learning, use the following prompts to facilitate a class discussion to debrief the station activities. Prompts/Questions. What is an eponential function?. When does a function have an -intercept?. What is compound interest?. Wh can it be difficult to estimate compound interest?. How do ou determine if an equation is eponential?. What is the general shape of the graph of an eponential function? Think, Pair, Share Have students jot down their own responses to questions, then discuss with a partner (who was not in their station group), and then discuss as a whole class. Suggested Appropriate Responses. An eponential function is a function in which the variable is in the eponent.. A function has an -intercept when its graph crosses the -ais.. Compound interest is interest that accumulates according to the total (principal plus interest) alread in the account, not just according to the principal.. The amount on which the percentage is based keeps changing.. An eponential equation has a variable in the eponent.. The general shape is a curve that etends toward infinit on one side and approaches the -ais on the other side. U-

10 UNIT LINEAR AND EXPONENTIAL RELATIONSHIPS Station Activities Set : Comparing Eponential Models Possible Misunderstandings/Mistakes Incorrectl manipulating numbers, variables, or eponents Not understanding the laws of eponents Assuming that all functions have zeros Incorrectl calculating squares, cubes, etc., of integers between and Confusing a negative eponent with a fractional eponent Incorrectl using the eponent function of a calculator Incorrectl appling the formula of compound interest Instruction Not understanding the relationship between an eponential function and its graph Not generating the table of values correctl Plotting points incorrectl Miscalculating the - and -intercepts U-

11 UNIT LINEAR AND EXPONENTIAL RELATIONSHIPS Station Activities Set : Comparing Eponential Models Station Work with our group to answer each question.. Graph =. Where is the -intercept? What are the roots of this function?. Graph =. Does this function have an -intercept? If so, estimate where it is. U- continued

12 UNIT LINEAR AND EXPONENTIAL RELATIONSHIPS Station Activities Set : Comparing Eponential Models. Graph =. Does this function have an -intercept? If so, estimate where it is.. An eponential function passes through the points (, ) and (, ). What is the function? Graph our answer. U-

13 UNIT LINEAR AND EXPONENTIAL RELATIONSHIPS Station Activities Set : Comparing Eponential Models Station Using a calculator, work with our group to graph each function and evaluate the function at the given value.. f ( ) =. f ( ) =. f ( ) =. + f ( ) = continued U-

14 UNIT LINEAR AND EXPONENTIAL RELATIONSHIPS Station Activities Set : Comparing Eponential Models. Graph =. If there is an -intercept, what is it?. Graph =. If there is an -intercept, what is it? continued U-

15 UNIT LINEAR AND EXPONENTIAL RELATIONSHIPS Station Activities Set : Comparing Eponential Models. Graph = ( ). If there is an -intercept, what is it?. Graph = + ( ). If there is an -intercept, what is it?. For an eponential function to have an -intercept, what must be true of the equation? U-

16 UNIT LINEAR AND EXPONENTIAL RELATIONSHIPS Station Activities Set : Comparing Eponential Models Station The formula for compound interest is r A = P + n, where A is the final total (principal plus interest), P is the initial amount (principal), r is the interest rate, t is the amount of time in ears, and n is the number of times the interest compounds per ear. Work with our group to set up and then solve each equation. Round answers to the nearest penn. tn. An account with an initial balance of $, has interest of.% that compounds quarterl over four ears. What is the balance at the end of the fourth ear?. An account with an initial balance of $, has interest of.% that compounds monthl over two ears. What is the balance at the end of the second ear?. An account with an initial balance of $ has interest of % that compounds ever other month over five ears. What is the balance at the end of the fifth ear?. An account with an initial balance of $, has interest of.% that compounds monthl over three ears. What is the balance at the end of the third ear?. If ou have $, to invest for two ears, which account has the better ield: an account that compounds quarterl at %, or one that compounds monthl at.%? U-

17 UNIT LINEAR AND EXPONENTIAL RELATIONSHIPS Station Activities Set : Comparing Eponential Models Station You will work with an eponential function at this station. Use the eponential function below for the following problems. f() =. Create a table of values for our function. f(). Find the - and -intercepts.. Graph our function below. continued U-

18 UNIT LINEAR AND EXPONENTIAL RELATIONSHIPS Station Activities Set : Comparing Eponential Models. Looking at the equation, what are some defining characteristics of an eponential function?. Looking at the table of values, what are some defining characteristics of an eponential function s table of values?. Looking at the graph, what are some defining characteristics of an eponential function s graph? U-

19 UNIT LINEAR AND EXPONENTIAL RELATIONSHIPS Station Activities Set : Interpreting Eponential Functions Station Instruction Working with groups, students determine properties of the graphs of eponential functions. Answers. a. (, ) b. > if b >, and < if b < c. no d. =. a. all real numbers b. > c. = d. (, ) Station Working with groups, students determine the end behavior of eponential functions. Students use their observations to determine based on the formula whether a formula represents eponential growth or deca. Answers. a. approaches b. grows without bound. a. grows without bound b. approaches. a. decreases without bound b. approaches. Eponential deca; the function approaches as becomes infinitel larger.. Eponential growth; the function approaches infinit or grows without bound as becomes infinitel larger. U-

20 UNIT LINEAR AND EXPONENTIAL RELATIONSHIPS Station Activities Set : Interpreting Eponential Functions Station Instruction Student pairs graph eponential functions, checking their work with a graphing calculator. Answers Materials List/Setup Station graphing calculator Station graphing calculator Station graphing calculator Station graphing calculator; graph paper U-

21 UNIT LINEAR AND EXPONENTIAL RELATIONSHIPS Station Activities Set : Interpreting Eponential Functions Discussion Guide Instruction To support students in reflecting on the activities and to gather some formative information about student learning, use the following prompts to facilitate a class discussion to debrief the station activities. Prompts/Questions. What is an eponent?. What is an eponential function?. What are the differences among the graphs of eponential functions when the base is negative, when the base is a fraction, and when the base is a negative fraction? Think, Pair, Share Have students jot down their own responses to questions, then discuss with a partner (who was not in their station group), and then discuss as a whole class. Suggested Appropriate Responses. An eponent is a number that tells the number of times the base is to be multiplied b itself.. An eponential function is a function in which the variable is in the eponent.. A base that is negative will be reflected over the -ais, and a base that is a fraction will be reflected over the -ais. If the base is a negative fraction, then it will be reflected over both the - and -aes. Possible Misunderstandings/Mistakes Incorrectl manipulating numbers, variables, or eponents Not understanding the laws of eponents Assuming that all functions have zeros Assuming that an eponential function has a vertical asmptote as it tends toward unbounded growth Not understanding the difference between growth and deca Incorrectl calculating squares, cubes, etc., of integers between and Confusing a negative eponent with a fractional eponent U-

22 UNIT LINEAR AND EXPONENTIAL RELATIONSHIPS Station Activities Set : Interpreting Eponential Functions Station Work with our partner to evaluate each epression. Show our work.. f () = f () =. f () = f () = ( ) = ( ) = f f. f ( ) = f () = f f () = =. f () = ( ) = ( ) = ( ) = f f f. f () = f () = ( ) = f. f () = ( ) = ( ) = f f U-

23 UNIT LINEAR AND EXPONENTIAL RELATIONSHIPS Station Activities Set : Interpreting Eponential Functions Station Consider the graph of the given function. Work with our group to answer each question. Show all our work.. = b a. Where is the -intercept? b. What is the range? c. Does the function have an zeros? If so, where are the? d. Does the function have an asmptotes? If so, where?. = a. What is the domain? b. What is the range? c. Does the function have an asmptotes? If so, where? d. Does the function have an zeros? If so, where are the? U-

24 UNIT LINEAR AND EXPONENTIAL RELATIONSHIPS Station Activities Set : Interpreting Eponential Functions Station Work with a group to answer each question. Show all our work.. =. a. What is the end behavior as approaches infinit? b. What is the end behavior as approaches negative infinit?. = a. What is the end behavior as approaches infinit? b. What is the end behavior as approaches negative infinit?. = ( ) a. What is the end behavior as approaches infinit? b. What is the end behavior as approaches negative infinit?. = Does this function represent eponential growth or deca? Eplain.. = Does this function represent eponential growth or deca? Eplain. U-

25 UNIT LINEAR AND EXPONENTIAL RELATIONSHIPS Station Activities Set : Sequences Discussion Guide Instruction To support students in reflecting on the activities and to gather some formative information about student learning, use the following prompts to facilitate a class discussion to debrief the station activities. Prompts/Questions. What is an arithmetic sequence?. What is a series?. Is a sequence finite or infinite?. What is a geometric sequence?. How is a geometric sequence different from an arithmetic sequence?. How could a geometric sequence be related to eponential functions? Think, Pair, Share Have students jot down their own responses to questions, then discuss with a partner (who was not in their station group), and then discuss as a whole class. Suggested Appropriate Responses. An arithmetic sequence is an ordered group of numbers separated b a common difference.. A series is the partial sum of a sequence.. A sequence can be bounded (finite) or infinite.. A geometric sequence is an ordered set of numbers that increase or decrease b a common ratio, r.. An arithmetic sequence is an ordered set of numbers that increase or decrease at a common difference, d. The terms in an arithmetic sequence are defined b addition or subtraction; the terms in a geometric sequence increase or decrease b a common factor.. To find the terms of a geometric sequence, we use an eponential calculation. U-

26 UNIT LINEAR AND EXPONENTIAL RELATIONSHIPS Station Activities Set : Sequences Station Work with our group to answer each question. Show all our work. Use the calculator if ou need help. For problems, let a = t and d = t.. What is a n?. What is a?. What is the sum of the first terms in the sequence? For problems, let a = and d =.. What is a n?. What is a?. What is S? Answer the following questions about sequences.. Look at the sequence,,,,... What is S?. Look at the sequence,,,,,,... Is it arithmetical? Eplain.. Think of the sequence of positive odd integers. What is the th term of that sequence?. What is S of the sequence of positive odd integers? U-

27 UNIT LINEAR AND EXPONENTIAL RELATIONSHIPS Station Activities Set : Sequences Station Working with our group, graph each geometric sequence as an eponential function..,,,,....,,,,... continued U-

28 UNIT LINEAR AND EXPONENTIAL RELATIONSHIPS Station Activities Set : Sequences.,,,,,....,,,,... continued U-

29 UNIT LINEAR AND EXPONENTIAL RELATIONSHIPS Station Activities Set : Sequences.,,,,... U-

30 UNIT REASONING WITH EQUATIONS Station Activities Set : Solving Sstems b Graphing Station At this station, ou will find four inde cards with the following linear sstems of equations written on them: = + = = ; ; = + = + = ; = + + = Work together to match each sstem of linear equations with the appropriate graph below. Write the appropriate sstem of linear equations beside each graph... continued U-

31 UNIT REASONING WITH EQUATIONS Station Activities Set : Solving Sstems b Graphing... What strateg did ou use to match the sstems of linear equations with the appropriate graph? U-

32 UNIT DESCRIPTIVE STATISTICS Station Activities Set : Displaing and Interpreting Data. es. Answers will var but should be in the form = m + b.. Answers will var. Instruction. BMI Hours. No. There are too man other factors involved (such as activit level and diet). There seems to be a correlation, but we can t prove causation.. Yes; (, ) and (,.) Station Working with groups, students analze a data set to find a linear relationship between variables. Students use a calculator to conduct linear regression. Answers. Grade. es. Answers will var. Hours U-

33 UNIT DESCRIPTIVE STATISTICS Station Activities Set : Displaing and Interpreting Data. (, ). =. +.. Yes. The linear relationship is ver close. Instruction. We can t prove causation from this data. As the outlier shows, some people ma not stud because the alread know the material well. However, the data suggests that the more time spent studing, the higher the test grade will be. Materials List/Setup Station Station Station Station graph paper; nine inde cards with the following numbers written on them:,,,,,,,, graph paper; ruler calculator; colored pens or pencils; graph paper calculator; colored pens or pencils U-

34 UNIT DESCRIPTIVE STATISTICS Station Activities Set : Displaing and Interpreting Data Station Work with our group to answer each question about the data set. Use the calculator to calculate medians and create our graphs. A class wants to find out if there is a correlation between the number of hours studied and grades on the midterm eam. The students log their hours and their grades, as follows. Studing (hours) Grade Studing (hours) Grade. Enter the numbers into our calculator to graph the results on a scatter plot. Sketch our plot below. Grade Hours continued U-

35 UNIT DESCRIPTIVE STATISTICS Station Activities Set : Line of Best Fit Instruction Goal: To provide opportunities for students to develop concepts and skills related to creating and analzing scatter plots and lines of best fit to represent a real-world situation Common Core State Standards S ID. S ID. Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. a. Fit a function to the data; use functions fitted to data to solve problems in the contet of the data. Use given functions or choose a function suggested b the contet. Emphasize linear, quadratic, and eponential models. b. Informall assess the fit of a function b plotting and analzing residuals. c. Fit a linear function for a scatter plot that suggests a linear association. Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the contet of the data. Student Activities Overview and Answer Ke Station Students will be given graph paper and a ruler to help them create a scatter plot. Then the will analze the scatter plot to determine the correlation between the data and describe the slope. Answers. Graph: Math Test Score Hours studied The graph is a scatter plot. Test score (%). The test scores increase as the amount of time she studies for each test increases.. Positive correlation; the longer she studied for the test, the higher her test score; positive slope because the line increases from left to right. U-

36 UNIT CONGRUENCE, PROOF, AND CONSTRUCTIONS Station Activities Set : Corresponding Parts, Transformations, and Proof Answers Instruction. (, ), (, ), (, ); (, ), (, ); (, ). Yes, because the size and shape remained the same.. A and B, because corresponding sides and angles are congruent.. Yes, because the size and shape remained the same.. The have the same size and shape. Station Students will be given four inde cards with the following written on them: SSS; SAS; ASA; AAS. Students will work together to match the inde cards to real-world eamples of SSS, SAS, ASA, and AAS. Then the will eplain how SSS, SAS, ASA, and AAS relate to congruent triangles. Answers. ASA. AAS. SSS. SAS. Answers will var.. side-side-side; side-angle-side; angle-side-angle; angle-angle-side. These are was to prove two triangles are congruent. Materials List/Setup Station Station ruler; protractor graph paper; ruler; push pins; rubber bands Station graph paper; ruler; cardboard triangle created from a triangle with vertices (, ), (, ), and (, ) in the coordinate plane Station four inde cards with the following written on them: SSS; SAS; ASA; AAS U-

37 UNIT CONNECTING ALGEBRA AND GEOMETRY THROUGH COORDINATES Station Activities Set : Parallel Lines, Slopes, and Equations Station At this station, ou will find rulers. Use these to help ou determine whether or not the following lines are parallel. Look at the graph below.. Are these lines parallel?. Eplain two was ou can tell lines are parallel.. What is the shortest distance between these two lines?. Draw a line that is parallel to the given line below.. How do ou know our line is parallel? U-

Exponential and Logarithmic Functions

Exponential and Logarithmic Functions Name Date Chapter 3 Eponential and Logarithmic Functions Section 3.1 Eponential Functions and Their Graphs Objective: In this lesson ou learned how to recognize, evaluate, and graph eponential functions.

More information

Chapter Summary. What did you learn? 270 Chapter 3 Exponential and Logarithmic Functions

Chapter Summary. What did you learn? 270 Chapter 3 Exponential and Logarithmic Functions 0_00R.qd /7/05 0: AM Page 70 70 Chapter Eponential and Logarithmic Functions Chapter Summar What did ou learn? Section. Review Eercises Recognize and evaluate eponential functions with base a (p. ). Graph

More information

Investigating Intercepts

Investigating Intercepts Unit: 0 Lesson: 01 1. Can more than one line have the same slope? If more than one line has the same slope, what makes the lines different? a. Graph the following set of equations on the same set of aes.

More information

Equations of Parallel and Perpendicular Lines

Equations of Parallel and Perpendicular Lines COMMON CORE AB is rise - - 1 - - 0 - - 8 6 Locker LESSON. Equations of Parallel and Perpendicular Lines Name Class Date. Equations of Parallel and Perpendicular Lines Essential Question: How can ou find

More information

Set 6: Understanding the Pythagorean Theorem Instruction

Set 6: Understanding the Pythagorean Theorem Instruction Instruction Goal: To provide opportunities for students to develop concepts and skills related to understanding that the Pythagorean theorem is a statement about areas of squares on the sides of a right

More information

Tennessee Senior Bridge Mathematics

Tennessee Senior Bridge Mathematics A Correlation of to the Mathematics Standards Approved July 30, 2010 Bid Category 13-130-10 A Correlation of, to the Mathematics Standards Mathematics Standards I. Ways of Looking: Revisiting Concepts

More information

Set 1: Ratios and Proportions... 1

Set 1: Ratios and Proportions... 1 Table of Contents Introduction...v Implementation Guide...v Standards Correlations...viii Materials List... x Algebra... 1 Creating Equations Set 1: Solving Inequalities... 14 Set 2: Solving Equations...

More information

UNIT #4 LINEAR FUNCTIONS AND ARITHMETIC SEQUENCES REVIEW QUESTIONS

UNIT #4 LINEAR FUNCTIONS AND ARITHMETIC SEQUENCES REVIEW QUESTIONS Name: Date: UNIT # LINEAR FUNCTIONS AND ARITHMETIC SEQUENCES REVIEW QUESTIONS Part I Questions. Carl walks 30 feet in seven seconds. At this rate, how man minutes will it take for Carl to walk a mile if

More information

Lesson 5.4 Exercises, pages

Lesson 5.4 Exercises, pages Lesson 5.4 Eercises, pages 8 85 A 4. Evaluate each logarithm. a) log 4 6 b) log 00 000 4 log 0 0 5 5 c) log 6 6 d) log log 6 6 4 4 5. Write each eponential epression as a logarithmic epression. a) 6 64

More information

AGS Math Algebra 2 Correlated to Kentucky Academic Expectations for Mathematics Grades 6 High School

AGS Math Algebra 2 Correlated to Kentucky Academic Expectations for Mathematics Grades 6 High School AGS Math Algebra 2 Correlated to Kentucky Academic Expectations for Mathematics Grades 6 High School Copyright 2008 Pearson Education, Inc. or its affiliate(s). All rights reserved AGS Math Algebra 2 Grade

More information

Contents. Introduction to Keystone Algebra I...5. Module 1 Operations and Linear Equations & Inequalities...9

Contents. Introduction to Keystone Algebra I...5. Module 1 Operations and Linear Equations & Inequalities...9 Contents Introduction to Kestone Algebra I... Module Operations and Linear Equations & Inequalities...9 Unit : Operations with Real Numbers and Epressions, Part...9 Lesson Comparing Real Numbers A... Lesson

More information

1 Mathematical Methods Units 1 and 2

1 Mathematical Methods Units 1 and 2 Mathematical Methods Units and Further trigonometric graphs In this section, we will discuss graphs of the form = a sin ( + c) + d and = a cos ( + c) + d. Consider the graph of = sin ( ). The following

More information

Exploring Periodic Data. Objectives To identify cycles and periods of periodic functions To find the amplitude of periodic functions

Exploring Periodic Data. Objectives To identify cycles and periods of periodic functions To find the amplitude of periodic functions CC-3 Eploring Periodic Data Common Core State Standards MACC.9.F-IF.. For a function that models a relationship between two quantities, interpret ke features of graphs... and sketch graphs... Also Prepares

More information

Algebra 1 B Semester Exam Review

Algebra 1 B Semester Exam Review Algebra 1 B 014 MCPS 013 014 Residual: Difference between the observed (actual) value and the predicted (regression) value Slope-Intercept Form of a linear function: f m b Forms of quadratic functions:

More information

3.3 Properties of Logarithms

3.3 Properties of Logarithms Section 3.3 Properties of Logarithms 07 3.3 Properties of Logarithms Change of Base Most calculators have only two types of log keys, one for common logarithms (base 0) and one for natural logarithms (base

More information

Geometry Station Activities for Common Core State Standards

Geometry Station Activities for Common Core State Standards Geometry Station Activities for Common Core State Standards WALCH EDUCATION Table of Contents Standards Correlations...................................................... v Introduction..............................................................vii

More information

Table of Contents. Standards Correlations...v Introduction...vii Materials List... x

Table of Contents. Standards Correlations...v Introduction...vii Materials List... x Table of Contents Standards Correlations...v Introduction...vii Materials List... x...1...1 Set 2: Classifying Triangles and Angle Theorems... 13 Set 3: Corresponding Parts, Transformations, and Proof...

More information

Essential Question: How can you represent a linear function in a way that reveals its slope and y-intercept?

Essential Question: How can you represent a linear function in a way that reveals its slope and y-intercept? COMMON CORE 5 Locker LESSON Slope-Intercept Form Common Core Math Standards The student is epected to: COMMON CORE F-IF.C.7a Graph linear... functions and show intercepts... Also A-CED.A., A-REI.D. Mathematical

More information

Exploring Graphs of Periodic Functions

Exploring Graphs of Periodic Functions 8.2 Eploring Graphs of Periodic Functions GOAL Investigate the characteristics of the graphs of sine and cosine functions. EXPLORE the Math Carissa and Benjamin created a spinner. The glued graph paper

More information

Station Activities. for Mathematics Grade 6

Station Activities. for Mathematics Grade 6 Station Activities for Mathematics Grade 6 WALCH EDUCATION The classroom teacher may reproduce materials in this book for classroom use only. The reproduction of any part for an entire school or school

More information

1.2 Lines in the Plane

1.2 Lines in the Plane 71_1.qd 1/7/6 1:1 AM Page 88 88 Chapter 1 Functions and Their Graphs 1. Lines in the Plane The Slope of a Line In this section, ou will stud lines and their equations. The slope of a nonvertical line represents

More information

GREATER CLARK COUNTY SCHOOLS PACING GUIDE. Algebra I MATHEMATICS G R E A T E R C L A R K C O U N T Y S C H O O L S

GREATER CLARK COUNTY SCHOOLS PACING GUIDE. Algebra I MATHEMATICS G R E A T E R C L A R K C O U N T Y S C H O O L S GREATER CLARK COUNTY SCHOOLS PACING GUIDE Algebra I MATHEMATICS 2014-2015 G R E A T E R C L A R K C O U N T Y S C H O O L S ANNUAL PACING GUIDE Quarter/Learning Check Days (Approx) Q1/LC1 11 Concept/Skill

More information

You may recall from previous work with solving quadratic functions, the discriminant is the value

You may recall from previous work with solving quadratic functions, the discriminant is the value 8.0 Introduction to Conic Sections PreCalculus INTRODUCTION TO CONIC SECTIONS Lesson Targets for Intro: 1. Know and be able to eplain the definition of a conic section.. Identif the general form of a quadratic

More information

HPS Scope Sequence Last Revised June SUBJECT: Math GRADE: 7. Michigan Standard (GLCE) Code & Language. What this Standard means:

HPS Scope Sequence Last Revised June SUBJECT: Math GRADE: 7. Michigan Standard (GLCE) Code & Language. What this Standard means: Number and Numeration MA.7.NS.1 (Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical

More information

Essential Question How can you describe the graph of the equation y = mx + b?

Essential Question How can you describe the graph of the equation y = mx + b? .5 Graphing Linear Equations in Slope-Intercept Form COMMON CORE Learning Standards HSA-CED.A. HSF-IF.B. HSF-IF.C.7a HSF-LE.B.5 Essential Question How can ou describe the graph of the equation = m + b?

More information

Algebra 2. Slope of waste pipes

Algebra 2. Slope of waste pipes Algebra 2 Slope of waste pipes Subject Area: Math Grade Levels: 9-12 Date: Aug 25 th -26 th Lesson Overview: Students will first complete a worksheet reviewing slope, rate of change,, and plotting points.

More information

WITH MATH INTERMEDIATE/MIDDLE (IM) GRADE 6

WITH MATH INTERMEDIATE/MIDDLE (IM) GRADE 6 May 06 VIRGINIA MATHEMATICS STANDARDS OF LEARNING CORRELATED TO MOVING WITH MATH INTERMEDIATE/MIDDLE (IM) GRADE 6 NUMBER AND NUMBER SENSE 6.1 The student will identify representations of a given percent

More information

4.5 Equations of Parallel and Perpendicular Lines

4.5 Equations of Parallel and Perpendicular Lines Name Class Date.5 Equations of Parallel and Perpendicular Lines Essential Question: How can ou find the equation of a line that is parallel or perpendicular to a given line? Resource Locker Eplore Eploring

More information

3.2 Exercises. rise y (ft) run x (ft) Section 3.2 Slope Suppose you are riding a bicycle up a hill as shown below.

3.2 Exercises. rise y (ft) run x (ft) Section 3.2 Slope Suppose you are riding a bicycle up a hill as shown below. Section 3.2 Slope 261 3.2 Eercises 1. Suppose ou are riding a biccle up a hill as shown below. Figure 1. Riding a biccle up a hill. a) If the hill is straight as shown, consider the slant, or steepness,

More information

Learn new definitions of familiar shapes such as parabolas, hyperbolas, and circles.

Learn new definitions of familiar shapes such as parabolas, hyperbolas, and circles. CHAPTER 11 To begin this chapter, you will revisit the parabola by investigating the principle that makes a satellite dish work. You will discover a new way to define a parabola and will use that new definition

More information

Grades 6 8 Innoventure Components That Meet Common Core Mathematics Standards

Grades 6 8 Innoventure Components That Meet Common Core Mathematics Standards Grades 6 8 Innoventure Components That Meet Common Core Mathematics Standards Strand Ratios and Relationships The Number System Expressions and Equations Anchor Standard Understand ratio concepts and use

More information

TImath.com Calculus. ln(a + h) ln(a) 1. = and verify the Logarithmic Rule for

TImath.com Calculus. ln(a + h) ln(a) 1. = and verify the Logarithmic Rule for The Derivative of Logs ID: 9093 Time required 45 minutes Activity Overview Students will use the graph of the natural logarithm function to estimate the graph of the derivative of this function. They will

More information

Math + 4 (Red) SEMESTER 1. { Pg. 1 } Unit 1: Whole Number Sense. Unit 2: Whole Number Operations. Unit 3: Applications of Operations

Math + 4 (Red) SEMESTER 1.  { Pg. 1 } Unit 1: Whole Number Sense. Unit 2: Whole Number Operations. Unit 3: Applications of Operations Math + 4 (Red) This research-based course focuses on computational fluency, conceptual understanding, and problem-solving. The engaging course features new graphics, learning tools, and games; adaptive

More information

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Review.1 -. Name Solve the problem. 1) The rabbit population in a forest area grows at the rate of 9% monthl. If there are 90 rabbits in September, find how man rabbits (rounded to the nearest whole number)

More information

The study of conic sections provides

The study of conic sections provides Planning the Unit Unit The stud of conic sections provides students with the opportunit to make man connections between algebra and geometr. Students are engaged in creating conic sections based on their

More information

A slope of a line is the ratio between the change in a vertical distance (rise) to the change in a horizontal

A slope of a line is the ratio between the change in a vertical distance (rise) to the change in a horizontal The Slope of a Line (2.2) Find the slope of a line given two points on the line (Objective #1) A slope of a line is the ratio between the change in a vertical distance (rise) to the change in a horizontal

More information

Building Concepts: Visualizing Quadratic Expressions

Building Concepts: Visualizing Quadratic Expressions Building Concepts: Visualizing Quadratic Epressions Lesson Overview In this TI-Nspire lesson, students manipulate geometric figures to eplore equivalent epressions that can be epressed in the form b c

More information

NSCAS - Math Table of Specifications

NSCAS - Math Table of Specifications NSCAS - Math Table of Specifications MA 3. MA 3.. NUMBER: Students will communicate number sense concepts using multiple representations to reason, solve problems, and make connections within mathematics

More information

Slope. Domain 2 Lesson 11. Getting the Idea

Slope. Domain 2 Lesson 11. Getting the Idea Domain Lesson Slope Common Core Standard: 8.EE. Getting the Idea The graph of a linear equation is a straight line. The steepness of the line is called its slope. The slope shows the rate at which two

More information

Chapter 3 Exponential and Logarithmic Functions

Chapter 3 Exponential and Logarithmic Functions Chapter 3 Exponential and Logarithmic Functions Section 1 Section 2 Section 3 Section 4 Section 5 Exponential Functions and Their Graphs Logarithmic Functions and Their Graphs Properties of Logarithms

More information

NAME DATE PERIOD 6(7 5) 3v t 5s t. rv 3 s

NAME DATE PERIOD 6(7 5) 3v t 5s t. rv 3 s - NAME DATE PERID Skills Practice Epressions and Formulas Find the value of each epression.. 8 2 3 2. 9 6 2 3. (3 8) 2 (4) 3 4. 5 3(2 2 2) 6(7 5) 5. [ 9 0(3)] 6. 3 4 7. (68 7)3 2 4 3 8. [3(5) 28 2 2 ]5

More information

Unit D Parallel and Perpendicular Lines

Unit D Parallel and Perpendicular Lines Baltimore Count Public Schools Unit D Essential Question Parallel and Perpendicular Lines How can vocabular and proofs associated with parallel lines improve logical and critical thinking skills? Sections

More information

Answers Investigation 1

Answers Investigation 1 Applications. Students ma use various sketches. Here are some eamples including the rectangle with the maimum area. In general, squares will have the maimum area for a given perimeter. Long and thin rectangles

More information

Chapter 14 Trig Graphs and Reciprocal Functions Algebra II Common Core

Chapter 14 Trig Graphs and Reciprocal Functions Algebra II Common Core Chapter 14 Trig Graphs and Reciprocal Functions Algebra II Common Core LESSON 1: BASIC GRAPHS OF SINE AND COSINE LESSON : VERTICAL SHIFTING OF SINUSOIDAL GRAPHS LESSON 3 : THE FREQUENCY AND PERIOD OF A

More information

JMG. Review Module 1 Lessons 1-20 for Mid-Module. Prepare for Endof-Unit Assessment. Assessment. Module 1. End-of-Unit Assessment.

JMG. Review Module 1 Lessons 1-20 for Mid-Module. Prepare for Endof-Unit Assessment. Assessment. Module 1. End-of-Unit Assessment. Lesson Plans Lesson Plan WEEK 161 December 5- December 9 Subject to change 2016-2017 Mrs. Whitman 1 st 2 nd Period 3 rd Period 4 th Period 5 th Period 6 th Period H S Mathematics Period Prep Geometry Math

More information

Appendix M TERMINOLOGY. Slope of a Line. Slope. Undefined Slope. Slope-Intercept Form

Appendix M TERMINOLOGY. Slope of a Line. Slope. Undefined Slope. Slope-Intercept Form Appendices : Slope of a Line TERMINOLOGY For each of the following terms, provide ) a definition in our own words, 2) the formal definition (as provided b our text or instructor), and ) an example of the

More information

Chapter 3 Parallel and Perpendicular Lines Geometry. 4. For, how many perpendicular lines pass through point V? What line is this?

Chapter 3 Parallel and Perpendicular Lines Geometry. 4. For, how many perpendicular lines pass through point V? What line is this? Chapter 3 Parallel and Perpendicular Lines Geometry Name For 1-5, use the figure below. The two pentagons are parallel and all of the rectangular sides are perpendicular to both of them. 1. Find two pairs

More information

5.4 Multiple-Angle Identities

5.4 Multiple-Angle Identities 4 CHAPTER 5 Analytic Trigonometry 5.4 Multiple-Angle Identities What you ll learn about Double-Angle Identities Power-Reducing Identities Half-Angle Identities Solving Trigonometric Equations... and why

More information

Graphing Linear Nonproportional Relationships Using Slope and y-intercept

Graphing Linear Nonproportional Relationships Using Slope and y-intercept L E S S O N. Florida Standards The student is epected to: Functions.F.. Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the

More information

Lesson 5: Identifying Proportional and Non-Proportional Relationships in Graphs

Lesson 5: Identifying Proportional and Non-Proportional Relationships in Graphs NYS COMMON CORE MATHEMATICS CURRICULUM Lesson Lesson : Identifing Proportional and Non-Proportional Relationships in Graphs Student Outcomes Students decide whether two quantities are proportional to each

More information

INTRODUCTION TO LOGARITHMS

INTRODUCTION TO LOGARITHMS INTRODUCTION TO LOGARITHMS Dear Reader Logarithms are a tool originally designed to simplify complicated arithmetic calculations. They were etensively used before the advent of calculators. Logarithms

More information

constant EXAMPLE #4:

constant EXAMPLE #4: Linear Equations in One Variable (1.1) Adding in an equation (Objective #1) An equation is a statement involving an equal sign or an expression that is equal to another expression. Add a constant value

More information

Section 2.3 Task List

Section 2.3 Task List Summer 2017 Math 108 Section 2.3 67 Section 2.3 Task List Work through each of the following tasks, carefully filling in the following pages in your notebook. Section 2.3 Function Notation and Applications

More information

Name Date. and y = 5.

Name Date. and y = 5. Name Date Chapter Fair Game Review Evaluate the epression when = and =.... 0 +. 8( ) Evaluate the epression when a = 9 and b =.. ab. a ( b + ) 7. b b 7 8. 7b + ( ab ) 9. You go to the movies with five

More information

Appendix: Sketching Planes and Conics in the XYZ Coordinate System

Appendix: Sketching Planes and Conics in the XYZ Coordinate System Appendi: D Sketches Contemporar Calculus Appendi: Sketching Planes and Conics in the XYZ Coordinate Sstem Some mathematicians draw horrible sketches of dimensional objects and the still lead productive,

More information

Lesson 5: Identifying Proportional and Non-Proportional Relationships in Graphs

Lesson 5: Identifying Proportional and Non-Proportional Relationships in Graphs NYS COMMON CORE MATHEMATICS CURRICULUM Lesson Lesson : Identifing Proportional and Non-Proportional Relationships in Graphs Student Outcomes Students decide whether two quantities are proportional to each

More information

Algebra I Notes Unit Seven: Writing Linear Equations

Algebra I Notes Unit Seven: Writing Linear Equations Sllabus Objective.6 The student will be able to write the equation of a linear function given two points, a point and the slope, table of values, or a graphical representation. Slope-Intercept Form of

More information

2.1 Slope and Parallel Lines

2.1 Slope and Parallel Lines Name Class ate.1 Slope and Parallel Lines Essential Question: How can ou use slope to solve problems involving parallel lines? Eplore Proving the Slope Criteria for Parallel Lines Resource Locker The following

More information

Second Practice Test 1 Level 5-7

Second Practice Test 1 Level 5-7 Mathematics Second Practice Test 1 Level 5-7 Calculator not allowed Please read this page, but do not open your booklet until your teacher tells you to start. Write your name and the name of your school

More information

The Slope of a Line. units corresponds to a horizontal change of. m y x y 2 y 1. x 1 x 2. Slope is not defined for vertical lines.

The Slope of a Line. units corresponds to a horizontal change of. m y x y 2 y 1. x 1 x 2. Slope is not defined for vertical lines. 0_0P0.qd //0 : PM Page 0 0 CHAPTER P Preparation for Calculus Section P. (, ) = (, ) = change in change in Figure P. Linear Models and Rates of Change Find the slope of a line passing through two points.

More information

Selected Answers for Core Connections Algebra

Selected Answers for Core Connections Algebra Selected Answers for Core Connections Algebra Lesson 1.1.1 1-4. a: = 2! 6 and then =! 5 b: Yes, reverse the order of the machines ( =! 5 and then = 2! 6 ) and use an input of = 6. 1-5. a: 54 b:!7 3 5 c:

More information

In Exercises 1-12, graph one cycle of the given function. State the period, amplitude, phase shift and vertical shift of the function.

In Exercises 1-12, graph one cycle of the given function. State the period, amplitude, phase shift and vertical shift of the function. 0.5 Graphs of the Trigonometric Functions 809 0.5. Eercises In Eercises -, graph one ccle of the given function. State the period, amplitude, phase shift and vertical shift of the function.. = sin. = sin.

More information

Mathematics Expectations Page 1 Grade 04

Mathematics Expectations Page 1 Grade 04 Mathematics Expectations Page 1 Problem Solving Mathematical Process Expectations 4m1 develop, select, and apply problem-solving strategies as they pose and solve problems and conduct investigations, to

More information

Mathematics Success Grade 8

Mathematics Success Grade 8 Mathematics Success Grade 8 T429 [OBJECTIVE] The student will solve systems of equations by graphing. [PREREQUISITE SKILLS] solving equations [MATERIALS] Student pages S207 S220 Rulers [ESSENTIAL QUESTIONS]

More information

NAME DATE PERIOD increased by three times a number 6. the difference of 17 and 5 times a number

NAME DATE PERIOD increased by three times a number 6. the difference of 17 and 5 times a number DATE PERID 1-1 Variables and Epressions Write an algebraic epression for each verbal epression. 1. the sum of a number and 10. 15 less than k 3. the product of 18 and q 4. 6 more than twice m 5. 8 increased

More information

M7NS-Ia-2 2 Grade 7 LG-Math (pp.5-9) Pictures, PowerPoint presentation 3 Uses Venn Diagrams to represent sets, subsets, and set operations.

M7NS-Ia-2 2 Grade 7 LG-Math (pp.5-9) Pictures, PowerPoint presentation 3 Uses Venn Diagrams to represent sets, subsets, and set operations. FIRST QUARTER NUMBER SENSE 1 Describes well-defined sets, subsets, and the null set and cardinality of sets. M7NS-Ia-1 4 Grade 7 LG-Math (pp.1-4) Pictures, PowerPoint presentation 2 Illustrates the union

More information

Honors Algebra 2 Assignment Sheet - Chapter 1

Honors Algebra 2 Assignment Sheet - Chapter 1 Assignment Sheet - Chapter 1 #01: Read the text and the examples in your book for the following sections: 1.1, 1., and 1.4. Be sure you read and understand the handshake problem. Also make sure you copy

More information

Additional Practice. Name Date Class

Additional Practice. Name Date Class Pearson Education, Inc., publishing as Pearson Prentice Hall. All rights reserved. Name Date Class Additional Practice Investigation For Eercises 1 4, write an equation and sketch a graph for the line

More information

Unit: Logarithms (Logs)

Unit: Logarithms (Logs) Unit: Logarithms (Logs) NAME Per http://www.mathsisfun.com/algera/logarithms.html /8 pep rally Introduction of Logs HW: Selection from Part 1 /1 ELA A.11A Introduction & Properties of Logs (changing forms)

More information

Analytic Geometry/ Trigonometry

Analytic Geometry/ Trigonometry Analytic Geometry/ Trigonometry Course Numbers 1206330, 1211300 Lake County School Curriculum Map Released 2010-2011 Page 1 of 33 PREFACE Teams of Lake County teachers created the curriculum maps in order

More information

Using Tables of Equivalent Ratios

Using Tables of Equivalent Ratios LESSON Using Tables of Equivalent Ratios A table can be used to show the relationship between two quantities. You can use equivalent ratios to find a missing value in a table. EXAMPLE A The table shows

More information

Chapter 8: SINUSODIAL FUNCTIONS

Chapter 8: SINUSODIAL FUNCTIONS Chapter 8 Math 0 Chapter 8: SINUSODIAL FUNCTIONS Section 8.: Understanding Angles p. 8 How can we measure things? Eamples: Length - meters (m) or ards (d.) Temperature - degrees Celsius ( o C) or Fahrenheit

More information

The Math Projects Journal

The Math Projects Journal PROJECT OBJECTIVE The House Painter lesson series offers students firm acquisition of the skills involved in adding, subtracting and multipling polnomials. The House Painter lessons accomplish this b offering

More information

GAP CLOSING. Powers and Roots. Intermediate / Senior Facilitator Guide

GAP CLOSING. Powers and Roots. Intermediate / Senior Facilitator Guide GAP CLOSING Powers and Roots Intermediate / Senior Facilitator Guide Powers and Roots Diagnostic...5 Administer the diagnostic...5 Using diagnostic results to personalize interventions...5 Solutions...5

More information

Section 4.7 Fitting Exponential Models to Data

Section 4.7 Fitting Exponential Models to Data Section.7 Fitting Eponential Models to Data 289 Section.7 Fitting Eponential Models to Data In the previous section, we saw number lines using logarithmic scales. It is also common to see two dimensional

More information

MCAS/DCCAS Mathematics Correlation Chart Grade 4

MCAS/DCCAS Mathematics Correlation Chart Grade 4 MCAS/DCCAS Mathematics Correlation Chart Grade 4 MCAS Finish Line Mathematics Grade 4 MCAS Standard DCCAS Standard DCCAS Standard Description Unit 1: Number Sense Lesson 1: Whole Number Place Value Lesson

More information

2.6. Slope-Intercept Form Working Under Pressure. My My Notes ACTIVITY

2.6. Slope-Intercept Form Working Under Pressure. My My Notes ACTIVITY Slope-Intercept Form SUGGESTED LEARNING STRATEGIES: Shared Reading, Marking the Tet, Questioning the Tet, Visualization, Create Representations, Think/Pair/Share, Note Taking M M Notes ACTIVITY. When a

More information

Core Connections, Course 3 Checkpoint Materials

Core Connections, Course 3 Checkpoint Materials Core Connections, Course 3 Checkpoint Materials Notes to Students (and their Teachers) Students master different skills at different speeds. No two students learn eactl the same wa at the same time. At

More information

Connected Mathematics 2, 6th Grade Units (c) 2006 Correlated to: Utah Core Curriculum for Math (Grade 6)

Connected Mathematics 2, 6th Grade Units (c) 2006 Correlated to: Utah Core Curriculum for Math (Grade 6) Core Standards of the Course Standard I Students will acquire number sense and perform operations with rational numbers. Objective 1 Represent whole numbers and decimals in a variety of ways. A. Change

More information

Are You Ready? Find Perimeter

Are You Ready? Find Perimeter SKILL 3 Find Perimeter Teaching Skill 3 Objective Find the perimeter of figures. Instruct students to read the definition at the top of the page. Stress that the shape of the figure does not matter the

More information

Decide how many topics you wish to revise at a time (let s say 10)

Decide how many topics you wish to revise at a time (let s say 10) 1 Minute Maths for the Higher Exam (grades B, C and D topics*) Too fast for a first-time use but... brilliant for topics you have already understood and want to quickly revise. for the Foundation Exam

More information

Selected Answers for Core Connections Algebra

Selected Answers for Core Connections Algebra Selected Answers for Core Connections Algebra Lesson 8.1.1 8-6. (2x 3)(x + 2y 4) = 2x 2 + 4xy 11x 6y +12 8-7. a: 12x 2 +17x 5 b: 4x 2 28x + 49 8-8. a: t(n) = 500 +1500(n 1) b: t(n) = 30!5 n 1 8-9. a: b:

More information

Instructor Notes for Chapter 4

Instructor Notes for Chapter 4 Section 4.1 One to One Functions (Day 1) Instructor Notes for Chapter 4 Understand that an inverse relation undoes the original Understand why the line y = xis a line of symmetry for the graphs of relations

More information

Paper 1. Calculator not allowed. Mathematics test. First name. Last name. School. Remember KEY STAGE 3 TIER 5 7. satspapers.org

Paper 1. Calculator not allowed. Mathematics test. First name. Last name. School. Remember KEY STAGE 3 TIER 5 7. satspapers.org Ma KEY STAGE 3 Mathematics test TIER 5 7 Paper 1 Calculator not allowed First name Last name School 2009 Remember The test is 1 hour long. You must not use a calculator for any question in this test. You

More information

Graphs of Polynomial Functions. Quadratic Functions

Graphs of Polynomial Functions. Quadratic Functions Graphs of Polnomials 1 Graphs of Polnomial Functions Recall that the degree of a polnomial is the highest power of the independent variable appearing in it. A polnomial can have no more roots than its

More information

HANDS-ON TRANSFORMATIONS: RIGID MOTIONS AND CONGRUENCE (Poll Code 39934)

HANDS-ON TRANSFORMATIONS: RIGID MOTIONS AND CONGRUENCE (Poll Code 39934) HANDS-ON TRANSFORMATIONS: RIGID MOTIONS AND CONGRUENCE (Poll Code 39934) Presented by Shelley Kriegler President, Center for Mathematics and Teaching shelley@mathandteaching.org Fall 2014 8.F.1 8.G.1a

More information

Math is Cool Masters

Math is Cool Masters Sponsored by: Algebra II January 6, 008 Individual Contest Tear this sheet off and fill out top of answer sheet on following page prior to the start of the test. GENERAL INSTRUCTIONS applying to all tests:

More information

Paper 1. Calculator not allowed. Mathematics test. First name. Last name. School. Remember KEY STAGE 3 TIER 6 8

Paper 1. Calculator not allowed. Mathematics test. First name. Last name. School. Remember KEY STAGE 3 TIER 6 8 Ma KEY STAGE 3 Mathematics test TIER 6 8 Paper 1 Calculator not allowed First name Last name School 2007 Remember The test is 1 hour long. You must not use a calculator for any question in this test. You

More information

TenMarks Curriculum Alignment Guide: EngageNY/Eureka Math, Grade 7

TenMarks Curriculum Alignment Guide: EngageNY/Eureka Math, Grade 7 EngageNY Module 1: Ratios and Proportional Relationships Topic A: Proportional Relationships Lesson 1 Lesson 2 Lesson 3 Understand equivalent ratios, rate, and unit rate related to a Understand proportional

More information

Mathematics Geometry Grade 6AB

Mathematics Geometry Grade 6AB Mathematics Geometry Grade 6AB It s the Right Thing Subject: Mathematics: Geometry: Ratio and Proportion Level: Grade 7 Abstract: Students will learn the six types of triangles and the characteristics

More information

Enter the Maths Zone: Algebra Net NotesPLUS

Enter the Maths Zone: Algebra Net NotesPLUS Programme Worksheet : Palindromic Pursuits Take a number. Reverse it. Add the two numbers. Reverse the answer. Add the two numbers. Reverse the answer. Add the two numbers. Reverse the answer. Add the

More information

Radical Expressions and Graph (7.1) EXAMPLE #1: EXAMPLE #2: EXAMPLE #3: Find roots of numbers (Objective #1) Figure #1:

Radical Expressions and Graph (7.1) EXAMPLE #1: EXAMPLE #2: EXAMPLE #3: Find roots of numbers (Objective #1) Figure #1: Radical Expressions and Graph (7.1) Find roots of numbers EXAMPLE #1: Figure #1: Find principal (positive) roots EXAMPLE #2: Find n th roots of n th powers (Objective #3) EXAMPLE #3: Figure #2: 7.1 Radical

More information

Investigate Slope. 1. By observation, A B arrange the lines shown in order of steepness, from least steep to steepest. Explain your. reasoning.

Investigate Slope. 1. By observation, A B arrange the lines shown in order of steepness, from least steep to steepest. Explain your. reasoning. 6.5 Slope Focus on determining the slope of a line using slope to draw lines understanding slope as a rate of change solving problems involving slope The national, provincial, and territorial parks of

More information

3.4 The Slope of a Line

3.4 The Slope of a Line CHAPTER Graphs and Functions. The Slope of a Line S Find the Slope of a Line Given Two Points on the Line. Find the Slope of a Line Given the Equation of a Line. Interpret the Slope Intercept Form in an

More information

Performance Task. Asteroid Aim. Chapter 8. Instructional Overview

Performance Task. Asteroid Aim. Chapter 8. Instructional Overview Instructional Overview Performance Task Launch Question Summary Teacher Notes Supplies Mathematical Discourse Writing/Discussion Prompts Apps take a long time to design and program. One app in development

More information

Trigonometry, Exam 2 Review, Spring (b) y 4 cos x

Trigonometry, Exam 2 Review, Spring (b) y 4 cos x Trigonometr, Eam Review, Spring 8 Section.A: Basic Sine and Cosine Graphs. Sketch the graph indicated. Remember to label the aes (with numbers) and to carefull sketch the five points. (a) sin (b) cos Section.B:

More information

7.3. Slope-Point Form. Investigate Equations in Slope-Point Form. 370 MHR Chapter 7

7.3. Slope-Point Form. Investigate Equations in Slope-Point Form. 370 MHR Chapter 7 7. Slope-Point Form Focus on writing the equation of a line from its slope and a point on the line converting equations among the various forms writing the equation of a line from two points on the line

More information

5-1. Rate of Change and Slope. Vocabulary. Review. Vocabulary Builder. Use Your Vocabulary

5-1. Rate of Change and Slope. Vocabulary. Review. Vocabulary Builder. Use Your Vocabulary - Rate of Change and Slope Vocabular Review. Circle the rate that matches this situation: Ron reads books ever weeks. weeks books. Write alwas, sometimes, or never. A rate is a ratio. books weeks books

More information

Math 122: Final Exam Review Sheet

Math 122: Final Exam Review Sheet Exam Information Math 1: Final Exam Review Sheet The final exam will be given on Wednesday, December 1th from 8-1 am. The exam is cumulative and will cover sections 5., 5., 5.4, 5.5, 5., 5.9,.1,.,.4,.,

More information

7 th grade Math Standards Priority Standard (Bold) Supporting Standard (Regular)

7 th grade Math Standards Priority Standard (Bold) Supporting Standard (Regular) 7 th grade Math Standards Priority Standard (Bold) Supporting Standard (Regular) Unit #1 7.NS.1 Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers;

More information