# Domain and Range 2 TEACHER NOTES

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 Math Objectives Students will be able to identify the domain and range of a relation from its graph. Students will be able to write symbolic expressions to describe the domain and range of a relation. Students will be able to recognize that different relations can have the same domain or the same range. Students will create a graph with a given domain and range. Students will use appropriate tools strategically. (CCSS Mathematical Practice) Vocabulary domain range infinity discrete continuous relation function interval notation About the Lesson This lesson involves finding domain and range by changing the endpoints of a graph. As a result, students will: Manipulate given segments and make conjectures about the relationships between the lengths of the segments and the possibility of forming a triangle. Drag point P along the points in a scatter plot. From the ordered pairs, they will determine the domain and range. Determine the domain and range of several different relations by dragging a point along the graph. Compare domains and ranges that are discrete with those that are continuous over an interval. Sketch graphs given a domain and range. TI-Nspire Navigator System Send out the Domain_and_Range_2.tns file. Monitor student progress using Class Capture. Use Live Presenter to spotlight student answers. Activity Materials Tech Tips: This activity includes screen captures taken from the TI-Nspire CX handheld. It is also appropriate for use with the TI-Nspire family of products including TI- Nspire App. Slight variations to these directions may be required if using other technologies besides the handheld. Watch for additional Tech Tips throughout the activity for the specific technology you are using. Access free tutorials at Nspire software and TI- lators/pd/us/online- Learning/Tutorials Lesson Materials: Student Activity Domain_and_Range_2 _Student.pdf Domain_and_Range_2 _Student.doc TI-Nspire document Domain_and_Range_2.tns Compatible TI Technologies: TI-Nspire CX Handhelds, TI-Nspire Apps for ipad, TI-Nspire Software 2015 Texas Instruments Incorporated 1 education.ti.com

2 Discussion Points and Possible Answers TI-Nspire Navigator Opportunity: Class Capture or Live Presenter See Note 1 at the end of this lesson. Tech Tip: If students experience difficulty dragging a point, check to make sure that they have moved the cursor (arrow) until it becomes a hand ( ) getting ready to grab the point. Also, be sure that the word point appears. Then press / x to grab point P and close the hand ({). When finished moving the point, press d to release the point. Teacher Tip: Students should not begin dragging point P until they have recorded the answer to part a in question 1. If they do, the can click on the reset slider and then drag the point. For pages , there is a reset slider to remove the tracing of the domain and range. Move to page Grab and move point P to each point on the scatter plot and note the changes. a. Name the ordered pair for point P. What is the relationship between this ordered pair and the cross mark on each axis? Answer: Answers may vary for the ordered pair for point P. The cross mark on the x-axis is at the x-coordinate of the ordered pair. If using the TI-Nspire CX handheld or the TI-Nspire ipad app, it is marked in blue. The cross mark on the y- axis is at the y-coordinate of the ordered pair. If using the TI-Nspire CX handheld or the TI-Nspire ipad app, it is marked in red Texas Instruments Incorporated 2 education.ti.com

3 b. Grab and drag point P to each of the circles on the scatter plot. As you move from point to point, record the coordinates in the table. Answer: The completed table is below. x y Teacher Tip: The order in which students place the ordered pairs in the table does not matter. c. State the domain and range of the relation. Answer: Domain: { 4, 0, 2, 3, 5}; Range: { 5, 3, 2, 3, 4} Teacher Tip: It is easier to specify the set if the domain and range are listed from least to greatest, but order is not critical. The values should not be repeated. d. Where on the graph do you see the domain represented? The range represented? Answer: The domain of the graph can be seen as the cross marks on the x-axis or as the highlighted blue section on the x-axis. The range can be seen as the cross marks on the y-axis or as the highlighted red section on the y-axis. Move to page Move point P back and forth along the entire graph. a. What does the highlighted portion along the x-axis represent? Answer: The highlighted portion along the x-axis represents the domain of the graph. If you are using the TI-Nspire CX handheld or the TI-Nspire ipad App, the highlighted portion will be blue Texas Instruments Incorporated 3 education.ti.com

4 b. What does the highlighted portion along the y-axis represent? Answer: The highlighted portion along the y-axis represents the range of the graph. If you are using the TI-Nspire CX or the Nspire ipad App, the highlighted portion will be red. c. How do the domain and range in this problem differ from the domain and range in question 1? Answer: The domain and range in this graph are continuous over an interval, whereas the domain and range in question 1 are discrete. d. State the domain as an inequality and in interval notation. Answer: Domain: 4 x 6; x [ 4, 6] Teacher Tip: There may be some confusion between interval notation and an ordered pair. To alleviate this confusion, you may want to use x, which means x is an element of, before the interval notation. e. State the range as an inequality and in interval notation. Answer: Range: 4 y 5; y [ 4, 5] Teacher Tip: There may be some confusion between interval notation and an ordered pair. To alleviate this confusion, you may want to use y, which means y is an element of, before the interval notation. f. If the endpoints of the graph were open circles, how would the domain and range change? State the new domain and range as inequalities and in interval notation. Answer: The domain would be between 4 and 6, not including 4 and 6. The range would be between 4 and 5, not including 4 and 5. Domain: 4 < x < 6 Range: 4 < y < 5 x ( 4, 6) y ( 4, 5) 2015 Texas Instruments Incorporated 4 education.ti.com

5 Teacher Tip: Emphasize what open and closed circles mean on a graph, in words, and in an inequality. The endpoint may or may not be part of the domain and range. In this problem, if the circles were open, the inequality symbols would be strictly less than, not less than or equal to. Move to page Move point P back and forth along the entire graph. a. State the domain and range of the graph. Answer: Domain: 1 x < 5 or x [1, 5) Range: {1, 2, 3, 4} Teacher Tip: As point P is being dragged, make sure that the hand remains close to point P. If the hand moves too far away from point P, the students will not be able to see the entire domain. Point out all of the representations that are being seen. b. How does the domain of this graph compare to the domain of the graph in question 1? Question 2? Answer: The domain of this graph is over an interval (continuous) with two defined endpoints, whereas the domain in question 1 is discrete. The domain in question 2 is like the domain in this graph. It is over an interval with two defined endpoints. However, both endpoints are included in the domain in question 2. c. How does the range of this graph compare to the range of the graph in question 1? Question 2? Answer: The range of this graph is discrete, like the range in question 1. The range in question 2 is over an interval (continuous) with two defined endpoints. Move to page Move point P back and forth along the entire graph. a. State the domain and range as inequalities and in interval notation. Answer: Domain: x > 4 or x ( 4, ) Range: y 0 or y (, 0] 2015 Texas Instruments Incorporated 5 education.ti.com

6 b. What is different about the domain and range of this graph compared to the others? Answer: The domain of this graph is over an interval (continuous) with one defined endpoint. The graph continues infinitely in the positive direction, whereas the domain in question 1 is discrete. The domain in question 2 is like the domain in this graph. It is over an interval. However, the graph in question 2 has two defined endpoints. The range of this graph is over an interval (continuous) with one defined endpoint. The graph continues infinitely in the negative direction, whereas the range in question 1 is discrete. The range in question 2 is like the range in this graph. It is over an interval. However, the graph in question 2 has two defined endpoints. Move to page Move point P back and forth along the entire graph. a. State the domain and range as inequalities and in interval notation. Answer: Domain: < x < or x (, ) Range: y > 0 or y (0, ) b. What is different about the domain and range of this graph compared to the others? Answer: The domain of this graph is the set of all real numbers. The graph continues infinitely in both directions, whereas the domain in question 1 is discrete. The domain in question 2 is like the domain in this graph. It is over an interval. However, the graph in question 2 has two defined endpoints. The range of this graph is the set of all real numbers greater than 0. The graph continues infinitely in the positive direction, whereas the range in question 1 is discrete. The domain in question 2 is like the range in this graph. It is over an interval. However, the graph in question 2 has two defined endpoints Texas Instruments Incorporated 6 education.ti.com

7 Move to page Grab and move the endpoints of the line segment to new locations. a. What do you notice about the domain and range as you drag the endpoints? Answer: As you move the endpoints of the segment, the domain and range change as well to reflect the new domain and range. TI-Nspire Navigator Opportunity: Class Capture or Live Presenter See Note 2 at the end of this lesson. b. Move the open endpoint to ( 1, 4) and the closed endpoint to (2, 3). State the domain and range as inequalities and in interval notation. Answer: Domain: 1 < x 2 or x ( 1, 2] Move to page 6.2. Range: 3 y < 4 or y [ 3, 4) 7. Grab and move the endpoints of the line segment to satisfy each of the following conditions: a. The open endpoint is ( 4, 3) and the closed endpoint is (3, 4). State the domain and range using inequalities and interval notation Answer: Domain: 4 < x 3 or x ( 4, 3] Range: 3 < y 4 or y ( 3, 4] TI-Nspire Navigator Opportunity: Quick Poll See Note 3 at the end of this lesson Texas Instruments Incorporated 7 education.ti.com

9 Wrap Up Upon completion of the discussion, the teacher should ensure that students understand: How to determine the domain and range of a relation from its graph. The connection between graphical and numerical representations. How to read and write symbolic expressions to describe the domain and range of a relation. How to sketch a graph with a given domain and range. TI-Nspire Navigator Note 1 Entire Document, Class Capture or Live Presenter: If students experience difficulty with dragging the point or understanding the results, use Class Capture to show the solution to the students. Highlight the bold areas on the axes that represent the domain and range. Note 2 Question 6a, Class Capture or Live Presenter: Use this opportunity to show different students graphs and point out how the domain and range are affected by changing the endpoints of the segment. Note 3 Question 7a, Quick Poll (Multiple Choice or Open Response): Use Quick Poll as an opportunity to assess students understanding of domain and range for a function. Have students identify the domain and range for this function. As a follow-up question, ask students what kind of line will have a domain of x = Texas Instruments Incorporated 9 education.ti.com

### Transformations: Rotations

Math Objectives Students will identify a rotation as an isometry, also called a congruence transformation. Students will identify which properties (side length, angle measure, perimeter, area, and orientation)

### Power Function Inverses

Math Objectives For power functions of the form f(x)=x n, where n is a positive integer and the domain is all real numbers, students will be able to identify which functions are invertible (odd powers)

### Build an Atom TEACHER NOTES MIDDLE GRADES SCIENCE NSPIRED. Science Objectives

Science Objectives Students will discover that atoms are made up of particles and that the number of particles in an atom affects its properties. Students will learn that these particles protons, neutrons,

### TEACHER NOTES MATH NSPIRED

Math Objectives Students will understand that normal distributions can be used to approximate binomial distributions whenever both np and n(1 p) are sufficiently large. Students will understand that when

### Arithmetic Sequences & Series

About the Lesson Students use formulas to find the differences of the consecutive terms, plot a scatter plot of each sequence, and determine that sequences with common differences (called arithmetic sequences)

### TEACHER NOTES HIGH SCHOOL SCIENCE NSPIRED

Science Objectives Students will describe the variables that affect potential energy and kinetic energy Students will explore the conversion of potential energy to kinetic energy Students will describe

### Introduction to the TI-Nspire CX

Introduction to the TI-Nspire CX Activity Overview: In this activity, you will become familiar with the layout of the TI-Nspire CX. Step 1: Locate the Touchpad. The Touchpad is used to navigate the cursor

### Law of Cosines TEACHER NOTES MATH NSPIRED. Math Objectives. Vocabulary. About the Lesson. TI-Nspire Navigator System

Math Objectives Students will be able to state the Law of Cosines Students will be able to apply the Law of Cosines to find missing sides and angles in a triangle Students will understand why the Law of

### The Cell Cycle TEACHER NOTES MIDDLE GRADES SCIENCE NSPIRED. Science Objectives. Vocabulary. About the Lesson. TI-Nspire Navigator. Activity Materials

Science Objectives Students will identify the changes that occur in cells during each phase of mitosis. Students will correlate these changes to the duration of time cells spend in each phase. While looking

### Graphic Designing with Transformed Functions

Math Objectives Students will be able to identify a restricted domain interval and use function translations and dilations to choose and position a portion of the graph accurately in the plane to match

### Secants, Tangents, and Arcs

Math Objectives Students will understand that if the intersection point P of two lines lies inside a circle, then the measure of the angle formed by the two secants is equal to the average of the measures

### Area Formulas TEACHER NOTES MATH NSPIRED. Math Objectives. Vocabulary. About the Lesson. TI-Nspire Navigator System

Math Objectives Students will be able to describe how the area of a parallelogram relates to the area of a rectangle with the same base and height. Students will be able to describe how the area of a triangle

### Sum or Difference of Cubes

Math Objectives Students will be able to classify expressions as the sum of cubes, difference of cubes, or neither. Students will be able to make connections between the graph of a cubic polynomial, in

### Application of a Circle Angles and Arcs TEACHER NOTES MATH NSPIRED: GEOMETRY

Math Objectives Students will identify and know the difference between central angles and inscribed angles of a circle. Students will identify the relationships between the measures of inscribed angles

### It s Just a Lunar Phase

Science Objectives Students will identify patterns in data associated with the lunar phases. Students will describe how the relative positions of the Earth, the Moon, and the Sun cause lunar phases. Students

### Triangle Trigonometry and Circles

Math Objectives Students will understand that trigonometric functions of an angle do not depend on the size of the triangle within which the angle is contained, but rather on the ratios of the sides of

### Angles & Arcs TEACHER NOTES. About the Lesson. Vocabulary. Teacher Preparation and Notes. Activity Materials

About the Lesson In this activity, students will explore how the measures of angles constructed in a circle are related to the measures of the intercepted arcs. Beginning with central and inscribed angles,

### Building Concepts: Dividing a Fraction by a Whole Number

Lesson Overview This TI-Nspire lesson uses a unit square to explore division of a unit fraction and a fraction in general by a whole number. The concept of dividing a quantity by a whole number, n, can

### Trigonometric Ratios TEACHER NOTES. About the Lesson. Vocabulary. Teacher Preparation and Notes. Activity Materials

About the Lesson In this activity, students discover the trigonometric ratios through measuring the side lengths of similar triangles and calculating their ratios. The formal definitions of the sine, cosine,

### Application of Function Composition

Math Objectives Given functions f and g, the student will be able to determine the domain and range of each as well as the composite functions defined by f ( g( x )) and g( f ( x )). Students will interpret

### Graphic Designing with Transformed Functions

Name Class The teacher will display the completed example to the right as an example to re-create. Work to make the image of the letter M on your handheld. Transformations of parabolas, domain restrictions,

### Type 1 Diabetes - Managing a Critical Ratio

Objectives Students will learn about how ratios and proportions are a key part of managing Type 1 Diabetes Students will learn about the regulation of blood glucose through insulin (hormone) binding with

### Special Segments in Triangles

About the Lesson In this activity, students will construct and explore medians, altitudes, angle bisectors, and perpendicular bisectors of triangles. They then drag the vertices to see where the intersections

### Linear Systems and Calories

Math Objectives Students will model a real-world application with a linear system of equations with three variables. Students will use the technology to solve a system of three equations in three variables

### Transforming Bivariate Data

Math Objectives Students will recognize that bivariate data can be transformed to reduce the curvature in the graph of a relationship between two variables. Students will use scatterplots, residual plots,

### TEACHER NOTES SCIENCE NSPIRED

Science Objectives Students will simulate adjusting the ph of a lake and draw conclusions about the relationship between ph and biodiversity. Students will learn the difference between biotic and abiotic

### TI-Nspire Technology Version 3.2 Release Notes

TI-Nspire Technology Version 3.2 Release Notes Release Notes 1 Introduction Thank you for updating your TI Nspire products to Version 3.2. This version of the Release Notes has updates for all of the following

### https://williamshartunionca.springboardonline.org/ebook/book/27e8f1b87a1c4555a1212b...

of 19 9/2/2014 12:09 PM Answers Teacher Copy Plan Pacing: 1 class period Chunking the Lesson Example A #1 Example B Example C #2 Check Your Understanding Lesson Practice Teach Bell-Ringer Activity Students

### Monopoly and Regression

Math Objectives Students will analyze the linear association between two variables and interpret the association in the context of a given scenario. Students will calculate a least-squares regression line

### Quickstart for Web and Tablet App

Quickstart for Web and Tablet App What is GeoGebra? Dynamic Mathematic Software in one easy-to-use package For learning and teaching at all levels of education Joins interactive 2D and 3D geometry, algebra,

### 7 Relations and Functions

7 Relations and Functions In this section, we introduce the concept of relations and functions. Relations A relation R from a set A to a set B is a set of ordered pairs (a, b), where a is a member of A,

### Body of Evidence Using clues from a decomposing body to solve a mystery

Objectives Students will analyze forensic clues in a story to infer the identity of a decomposing body. Students will interpret histogram plots to deduce the correct missing person. Students will understand

### Examples of Tasks from CCSS Edition Course 3, Unit 5

Examples of Tasks from CCSS Edition Course 3, Unit 5 Getting Started The tasks below are selected with the intent of presenting key ideas and skills. Not every answer is complete, so that teachers can

### Quickstart for Desktop Version

Quickstart for Desktop Version What is GeoGebra? Dynamic Mathematics Software in one easy-to-use package For learning and teaching at all levels of education Joins interactive 2D and 3D geometry, algebra,

### MATH 60 NOTEBOOK CERTIFICATIONS

MATH 60 NOTEBOOK CERTIFICATIONS Chapter #1: Integers and Real Numbers 1.1a 1.1b 1.2 1.3 1.4 1.8 Chapter #2: Algebraic Expressions, Linear Equations, and Applications 2.1a 2.1b 2.1c 2.2 2.3a 2.3b 2.4 2.5

### Rotational Motion and Torque

Science Objectives Students will describe how different forces can be balanced. Students will relate the balance of a lever to torque on a wrench. Students will develop an understanding of torques as they

### CORRELATED TO THE SOUTH CAROLINA COLLEGE AND CAREER-READY FOUNDATIONS IN ALGEBRA

We Can Early Learning Curriculum PreK Grades 8 12 INSIDE ALGEBRA, GRADES 8 12 CORRELATED TO THE SOUTH CAROLINA COLLEGE AND CAREER-READY FOUNDATIONS IN ALGEBRA April 2016 www.voyagersopris.com Mathematical

### Calibration and Linear Regression Analysis: A Self-Guided Tutorial

Calibration and Linear Regression Analysis: A Self-Guided Tutorial Part 1 Instrumental Analysis with Excel: The Basics CHM314 Instrumental Analysis Department of Chemistry, University of Toronto Dr. D.

### TImath.com Algebra 1. Absolutely!

Absolutely! ID: 8791 Time required 45 minutes Activity Overview In this activity, students first solve linear absolute value equations in a single variable using the definition of absolute value to write

### TI-83/84 Plus Graphing Calculator Worksheet #2

TI-83/8 Plus Graphing Calculator Worksheet #2 The graphing calculator is set in the following, MODE, and Y, settings. Resetting your calculator brings it back to these original settings. MODE Y Note that

### Prentice Hall Mathematics: Algebra 2 2007 Correlated to: Utah Core Curriculum for Math, Intermediate Algebra (Secondary)

Core Standards of the Course Standard 1 Students will acquire number sense and perform operations with real and complex numbers. Objective 1.1 Compute fluently and make reasonable estimates. 1. Simplify

### Perpendicular and Angle Bisectors

Perpendicular and Angle Bisectors Mathematics Objectives Students will investigate and define perpendicular bisector and angle bisector. Students will discover and describe the property that any point

### Addition by Division TEACHER NOTES SCIENCE NSPIRED

Science Objectives Students will identify the changes that occur in cells during each phase of the cell cycle. Students will correlate these changes to the duration of time cells spend in each phase. While

### Calculator Notes for the TI-Nspire and TI-Nspire CAS

CHAPTER 4 Calculator Notes for the Note 4A: Function Notation The handheld uses function notation automatically. You can define a function in the Calculator, Graphs & Geometry, and Data & Statistics applications.

Introduction to Quadratic Functions The St. Louis Gateway Arch was constructed from 1963 to 1965. It cost 13 million dollars to build..1 Up and Down or Down and Up Exploring Quadratic Functions...617.2

### First Steps with. Technology for teaching and learning mathematics. Seven Introductory Tutorials for the Handheld

First Steps with Technology for teaching and learning mathematics Seven Introductory Tutorials for the Handheld 2012 Texas Instruments Education Technology Page 1 About this document This document includes

### The River of Life TEACHER NOTES SCIENCE NSPIRED. Science Objectives. Math Objectives. Materials Needed. Vocabulary.

Science Objectives Students will calculate the volume of blood in their own bodies. Students will analyze and quantify some of the components of their blood. Math Objectives Students will use tabular data

### Functions. MATH 160, Precalculus. J. Robert Buchanan. Fall 2011. Department of Mathematics. J. Robert Buchanan Functions

Functions MATH 160, Precalculus J. Robert Buchanan Department of Mathematics Fall 2011 Objectives In this lesson we will learn to: determine whether relations between variables are functions, use function

### Supply and Demand Curves and Market Price Equilibrium

Teacher Notes Activity at a Glance Subject: Social Studies Subject Area: Economics Category: Production, Distribution, and Consumption Supply and Demand Curves and Market Price Equilibrium Activity 1 Exploring

### Prentice Hall Mathematics Algebra 1 2004 Correlated to: Alabama Course of Study: Mathematics (Grades 9-12)

Alabama Course of Study: Mathematics (Grades 9-12) NUMBER AND OPERATIONS 1. Simplify numerical expressions using properties of real numbers and order of operations, including those involving square roots,

### GeoGebra. 10 lessons. Gerrit Stols

GeoGebra in 10 lessons Gerrit Stols Acknowledgements GeoGebra is dynamic mathematics open source (free) software for learning and teaching mathematics in schools. It was developed by Markus Hohenwarter

### Prentice 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

### Mathematics Curriculum Guide Precalculus 2015-16. Page 1 of 12

Mathematics Curriculum Guide Precalculus 2015-16 Page 1 of 12 Paramount Unified School District High School Math Curriculum Guides 2015 16 In 2015 16, PUSD will continue to implement the Standards by providing

### Balancing Chemical Equations Practice

Science Objectives Students will describe what reactants and products in a chemical equation mean. Students will explain the difference between coefficients and subscripts in chemical equations. Students

### TImath.com Algebra 2. Combinations

Algebra 2 Combinations ID:8433 Time required 35 minutes Activity Overview This activity introduces students to combinations. They derive the formula for the number of combinations of n objects taken r

Problem 1 The Parabola Examine the data in L 1 and L to the right. Let L 1 be the x- value and L be the y-values for a graph. 1. How are the x and y-values related? What pattern do you see? To enter the

### Educator s Guide to Excel Graphing

Educator s Guide to Excel Graphing Overview: Students will use Excel to enter data into a spreadsheet and make a graph. Grades and Subject Areas: Grade 3-6 Subject Math Objectives: Students will: make

### Higher Education Math Placement

Higher Education Math Placement Placement Assessment Problem Types 1. Whole Numbers, Fractions, and Decimals 1.1 Operations with Whole Numbers Addition with carry Subtraction with borrowing Multiplication

### Unit 3: Algebra. Date Topic Page (s) Algebra Terminology 2. Variables and Algebra Tiles 3 5. Like Terms 6 8. Adding/Subtracting Polynomials 9 12

Unit 3: Algebra Date Topic Page (s) Algebra Terminology Variables and Algebra Tiles 3 5 Like Terms 6 8 Adding/Subtracting Polynomials 9 1 Expanding Polynomials 13 15 Introduction to Equations 16 17 One

### F.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

### LESSON 7: IMPORTING AND VECTORIZING A BITMAP IMAGE

LESSON 7: IMPORTING AND VECTORIZING A BITMAP IMAGE In this lesson we ll learn how to import a bitmap logo, transform it into a vector and perform some editing on the vector to clean it up. The concepts

### Basic Understandings

Activity: TEKS: Exploring Transformations Basic understandings. (5) Tools for geometric thinking. Techniques for working with spatial figures and their properties are essential to understanding underlying

### TI-Nspire Technology Version 3.0 Release Notes

TI-Nspire Technology Version 3.0 Release Notes Release Notes 1 Introduction Thank you for updating your TI Nspire products to Version 3.0. This version of the Release Notes has updates for all of the following

### Grade level: secondary Subject: mathematics Time required: 45 to 90 minutes

TI-Nspire Activity: Paint Can Dimensions By: Patsy Fagan and Angela Halsted Activity Overview Problem 1 explores the relationship between height and volume of a right cylinder, the height and surface area,

### MATH 65 NOTEBOOK CERTIFICATIONS

MATH 65 NOTEBOOK CERTIFICATIONS Review Material from Math 60 2.5 4.3 4.4a Chapter #8: Systems of Linear Equations 8.1 8.2 8.3 Chapter #5: Exponents and Polynomials 5.1 5.2a 5.2b 5.3 5.4 5.5 5.6a 5.7a 1

### Linear 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

### THE TOP TEN TIPS FOR USING QUALTRICS AT BYU

THE TOP TEN TIPS FOR USING QUALTRICS AT BYU TIP #1: CREATING A SURVEY FROM A COPY AND COLLABORATING ON SURVEYS TIP #2: CREATING AND USING PANELS TIP #3: LIBRARIES AND HOW TO USE THEM TIP #4: BASIC SKIP

### Transformational Geometry in the Coordinate Plane Rotations and Reflections

Concepts Patterns Coordinate geometry Rotation and reflection transformations of the plane Materials Student activity sheet Transformational Geometry in the Coordinate Plane Rotations and Reflections Construction

### Grade 8 Classroom Assessments Based on State Standards (CABS)

Grade 8 Classroom Assessments Based on State Standards (CABS) A. Mathematical Processes and E. Statistics and Probability (From the WKCE-CRT Mathematics Assessment Framework, Beginning of Grade 10) A.

### CHAPTER 1 Linear Equations

CHAPTER 1 Linear Equations 1.1. Lines The rectangular coordinate system is also called the Cartesian plane. It is formed by two real number lines, the horizontal axis or x-axis, and the vertical axis or

### 7. Solving Linear Inequalities and Compound Inequalities

7. Solving Linear Inequalities and Compound Inequalities Steps for solving linear inequalities are very similar to the steps for solving linear equations. The big differences are multiplying and dividing

### This activity will show you how to draw graphs of algebraic functions in Excel.

This activity will show you how to draw graphs of algebraic functions in Excel. Open a new Excel workbook. This is Excel in Office 2007. You may not have used this version before but it is very much the

### Slope Investigation. Grade 8, Algebra 1, or Math 1 in a unit with rate of change and slope

NATIONAL MATH + SCIENCE INITIATIVE Mathematics Slope Investigation LEVEL Grade 8, Algebra 1, or Math 1 in a unit with rate of change and slope MODULE/CONNECTION TO AP* Rate of Change *Advanced Placement

### Math 0980 Chapter Objectives. Chapter 1: Introduction to Algebra: The Integers.

Math 0980 Chapter Objectives Chapter 1: Introduction to Algebra: The Integers. 1. Identify the place value of a digit. 2. Write a number in words or digits. 3. Write positive and negative numbers used

### SDC. Schroff Development Corporation WWW.SDCACAD.COM PUBLICATIONS. MultiMedia CD by Jack Zecher

MultiMedia CD by Jack Zecher An audioi/visual presentation of the tutorial exercises SDC PUBLICATIONS Schroff Development Corporation WWW.SDCACAD.COM AutoCAD 2002 Tutorial 2-1 Lesson 2 Geometric Construction

### Algebra and Geometry Review (61 topics, no due date)

Course Name: Math 112 Credit Exam LA Tech University Course Code: ALEKS Course: Trigonometry Instructor: Course Dates: Course Content: 159 topics Algebra and Geometry Review (61 topics, no due date) Properties

### General Information Online Assessment Tutorial before Options for Completing the Online Assessment Tutorial

General Information Online Assessment Tutorial Schools must ensure every student participating in an online assessment has completed the Online Assessment Tutorial for the associated assessment at least

### Calculator Notes for the TI-Nspire and TI-Nspire CAS

CHAPTER 13 Calculator Notes for the Note 13A: Unit Circle Complete the following steps to graph the unit circle using parametric equations. a. Make sure your handheld is in Degree mode. If you need help

### o Text-to-Speech and Text-to-Speech Tracking Enhanced Accessibility Mode) o Toolbar Buttons

Ohio s State Tests English Language Arts and Mathematics Sample Items Science and Social Studies Practice Tests and Released Items Guidance Document Updated Dec. 28, 2015 This document covers the following

### GeoGebra Statistics and Probability

GeoGebra Statistics and Probability Project Maths Development Team 2013 www.projectmaths.ie Page 1 of 24 Index Activity Topic Page 1 Introduction GeoGebra Statistics 3 2 To calculate the Sum, Mean, Count,

### First Level: 2D Fundamentals. by Randy H. Shih Oregon Institute of Technology

AutoCAD 2008 Tutorial First Level: 2D Fundamentals by Randy H. Shih Oregon Institute of Technology MultiMedia CD by Jack Zecher Indiana University Purdue University Indianapolis SDC PUBLICATIONS Schroff

### Pre-Calculus Math 12 First Assignment

Name: Pre-Calculus Math 12 First Assignment This assignment consists of two parts, a review of function notation and an introduction to translating graphs of functions. It is the first work for the Pre-Calculus

### Prentice Hall Mathematics, Algebra 1 2009

Prentice Hall Mathematics, Algebra 1 2009 Grades 9-12 C O R R E L A T E D T O Grades 9-12 Prentice Hall Mathematics, Algebra 1 Program Organization Prentice Hall Mathematics supports student comprehension

### What's the Spin? - Discover Properties of Geometric Rotations

What's the Spin? - Discover Properties of Geometric Rotations Geometry Major Topics: Rotations and their relation to reflections NCTM Principles and Standards: Content Standards Geometry Apply transformations

### MATH 095, College Prep Mathematics: Unit Coverage Pre-algebra topics (arithmetic skills) offered through BSE (Basic Skills Education)

MATH 095, College Prep Mathematics: Unit Coverage Pre-algebra topics (arithmetic skills) offered through BSE (Basic Skills Education) Accurately add, subtract, multiply, and divide whole numbers, integers,

### Relations and Functions

Section 5. Relations and Functions 5.1. Cartesian Product 5.1.1. Definition: Ordered Pair Let A and B be sets and let a A and b B. An ordered pair ( a, b) is a pair of elements with the property that:

### Absolute Value of Reasoning

About Illustrations: Illustrations of the Standards for Mathematical Practice (SMP) consist of several pieces, including a mathematics task, student dialogue, mathematical overview, teacher reflection

### Math Review. for the Quantitative Reasoning Measure of the GRE revised General Test

Math Review for the Quantitative Reasoning Measure of the GRE revised General Test www.ets.org Overview This Math Review will familiarize you with the mathematical skills and concepts that are important

### Name of Lesson: Properties of Equality A Review. Mathematical Topic: The Four Properties of Equality. Course: Algebra I

Name of Lesson: Properties of Equality A Review Mathematical Topic: The Four Properties of Equality Course: Algebra I Time Allocation: One (1) 56 minute period Pre-requisite Knowledge: The students will

### A Correlation of. to the. South Carolina Data Analysis and Probability Standards

A Correlation of to the South Carolina Data Analysis and Probability Standards INTRODUCTION This document demonstrates how Stats in Your World 2012 meets the indicators of the South Carolina Academic Standards

### Quadratic and Square Root Functions. Square Roots & Quadratics: What s the Connection?

Activity: TEKS: Overview: Materials: Grouping: Time: Square Roots & Quadratics: What s the Connection? (2A.9) Quadratic and square root functions. The student formulates equations and inequalities based

### General Information Online Assessment Tutorial before Options for Completing the Online Assessment Tutorial

General Information Online Assessment Tutorial Schools must ensure every student participating in an online assessment has completed the Online Assessment Tutorial for the associated assessment at least

### Inequalities - Compound Inequalities

3.2 Inequalities - Compound Inequalities Objective: Solve, graph and give interval notation to the solution of compound inequalities. Several inequalities can be combined together to form what are called

### Lesson 22: Solution Sets to Simultaneous Equations

Student Outcomes Students identify solutions to simultaneous equations or inequalities; they solve systems of linear equations and inequalities either algebraically or graphically. Classwork Opening Exercise

### Cool Smart Board Tricks and Tools

Cool Smart Board Tricks and Tools Dual Page Display and Pinning You can easily toggle between dual and single page display with the dual page button on the toolbar. When in Dual Page mode you can pin one

### Entering data and doing repetitive calculations with Excel

Entering data and doing repetitive calculations with Excel Start by entering preliminary data in columns. Label each column. If you need to do repetitive calculations on your data before you make a graph,

### Georgia Standards of Excellence Curriculum Frameworks. Mathematics. GSE Geometry. Unit 1: Transformations in the Coordinate Plane

Georgia Standards of Excellence Curriculum Frameworks GSE Geometry Mathematics Unit 1: Transformations in the Coordinate Plane Unit 1 Transformations in the Coordinate Plane Table of Contents OVERVIEW...

### PoW-TER Problem Packet A Phone-y Deal? (Author: Peggy McCloskey)

PoW-TER Problem Packet A Phone-y Deal? (Author: Peggy McCloskey) 1. The Problem: A Phone-y Deal? [Problem #3280] With cell phones being so common these days, the phone companies are all competing to earn