2.1. Graphing Integers on a Number Line

Size: px
Start display at page:

Download "2.1. Graphing Integers on a Number Line"

Transcription

1 Ch 2 Integers

2 2.1 Graphing Integers on a Number Line

3 Integers Number Line A line with equal distances marked off to represent numbers

4 Integers Positive Number A number greater than zero Negative Number A number less than zero Zero is neither positive or negative

5 Integers

6 Venn Diagram of Numbers Venn Diagram A diagram that uses circles to show relationships among sets of numbers or objects

7 Venn Diagram of Numbers Natural Numbers 1, 2, 3, 4 Whole Numbers 0, 1, 2, 3 Integers -3, -2, -1, 0, 1, 2, 3

8 Graphing on a Number Line To graph a set of integers, Locate number on number line Place dot ON THE number line Label point above number line Coordinate The number that corresponds to the point

9 Example Name the coordinates of G, H, and J. Graph points K, L, and M on a number line if K has coordinate -4, L has coordinate 2, and M has coordinate -1.

10 Example Name the coordinate of A, B, and C. Graph points X, Y, and Z on a number line if X has coordinate 4, Y has coordinate 0, and Z has coordinate -3.

11 Numbers on the Number Line Numbers increase as they go to the Right So numbers on the right are larger than numbers on the left Or greater than

12 Examples Replace each with < or > to make a true sentence

13 Absolute Value Distance is always positive

14 Example

15 Assignment 1 st Assignment due today P55: nd Assignment due next time P55: 18 26, 30 47, 49, 52, 54 60

16 2.2 The Coordinate Plane

17 Coordinate System Coordinate System Formed by the intersection of two number lines that meet at right angles at their zero points

18 Coordinate System Coordinate Plane The plane that contains the x- and y-axes X-axis The horizontal number line Y-axis The vertical number line Origin The point at which the number lines intersect

19 Ordered Pair Ordered Pair The coordinates of any point on a coordinate plane X-coordinate The first number in an ordered pair Corresponds to a number on the x-axis Y-coordinate The second number in an ordered pair Corresponds to a number on the y-axis Always in parentheses with a comma between the coordinates

20 Ordered Pair (3, 5)

21 Example Write the ordered pair that names each point.

22 Example Graph each ordered pair on the coordinate plane. V(2, 4) W(-4, -1) R(2, -4) S(-1, 4) T(0, -3)

23 Quadrants Each coordinate plane is separated into four regions, called quadrants Named with roman numerals The axes are not in the quadrants

24 Example Name the quadrants in which each point is located. C(-2, -7) D(-4, 9) E(0, -3) F(1, 0) G(3, -1)

25 Example The first zeppelin flown in 1900 flew at a speed of 18 mph. Let x represent the number of hours. Then 18x represents the total distance traveled in x hours. Evaluate the expression to find the distances traveled in 1, 2, and 3 hours. Then graph the ordered pairs (time, distance).

26 Assignments 1 st Assignment due today P61: nd Assignment due next time P62: 23 29, 31 33, Worksheet

27 2.3 Adding Integers

28 Think number line Adding Integers

29 Adding Integers with the Same Sign

30 Example (-8) (-4)

31 Adding Integers Zero Pair Two numbers that cancel each other when added together Ex: Opposite or Additive Inverses Zero pairs Ex:

32 Adding Integers

33 Examples (-8)

34 Example Traci opened a checking account with a deposit of $100. During the next week, she wrote checks for $45 and $65 and made a deposit of $28. Find the balance in her account.

35 Example Simplify: -7y + 6y -8y + 3y 6m + 4m + (-2m)

36 Assignment 1 st Assignment due today P68: 2, nd Assignment due next time P68: even, 57 60, 63 73

37 2.4 Subtracting Integers

38 Think number line

39 Subtracting Integers

40 Examples (-6) (-5)

41 Examples (-10) 5 (-1) -4 6

42 Examples -7 (-2) (-11) 9 3

43 Example Evaluate a b if a = -8 and b = -2. Evaluate m n if m = 5 and n = -3. Evaluate w x + y - z if w = -5, x = -7, y = 10 and z = -5.

44 Example During one school year, 23 new students moved into a school district and 52 students moved out of the school district. Find the change in the number of students resulting from these moves.

45 Assignment 1 st Assignment due today P73: nd Assignment due next time P73: 33 48, P694 (2-2): 1 16 Worksheet(s)

46 2.5 Multiplying Integers

47 Multiplying Integers

48 Example Find each product 4(-3) -2(7) -7(7) 10(-3) 15(-3) 10(4) -8(-6)

49 Find each product 7(-3)(-6) Example 4(-5)(-12)(-5) -2(-3)(4) (-1)(-5)(-2)(-3)

50 Example Evaluate 4ab if a = -3 and b = -5. Evaluate -5n if n = -7. Evaluate 2xy if x = -4 and y = -2.

51 Example Simplify (4m)(-7n). Simplify (2a)(-5b). Simplify 12(-3z).

52 Example The graphs of A(3, 5), B(-2, 4), and C(0, 1) are connected with line segments to form a triangle. Multiply each y-coordinate by -1 and redraw the triangle. Describe how the position of the triangle changed.

53 Assignment 1 st Assignment due today P77: nd Assignment due next time P78: 14 46, 49, Need graph paper for both!

54 2.6 Dividing Integers

55 Dividing Integers

56 Summary of Multiplying/Dividing X = X = = =

57 Examples (-10) (-4) 16 (-2)

58 Examples Evaluate (6x) y if x = -4 and y = 8. Evaluate -12 x if x = -3.

59 Example In the last 5 years at a high school, the number of students with no tardies during the entire school year dropped from 315 to 95. What was the average change in the number of students without a tardy for each of those 5 years?

60 Assignment 1 st Assignment due today P84: nd Assignment due next time P84: 13 42, 47 57

All points on the coordinate plane are described with reference to the origin. What is the origin, and what are its coordinates?

All points on the coordinate plane are described with reference to the origin. What is the origin, and what are its coordinates? Classwork Example 1: Extending the Axes Beyond Zero The point below represents zero on the number line. Draw a number line to the right starting at zero. Then, follow directions as provided by the teacher.

More information

Number Sense and Operations

Number Sense and Operations Number Sense and Operations representing as they: 6.N.1 6.N.2 6.N.3 6.N.4 6.N.5 6.N.6 6.N.7 6.N.8 6.N.9 6.N.10 6.N.11 6.N.12 6.N.13. 6.N.14 6.N.15 Demonstrate an understanding of positive integer exponents

More information

6th Grade Vocabulary Words

6th Grade Vocabulary Words 1. sum the answer when you add Ex: 3 + 9 = 12 12 is the sum 2. difference the answer when you subtract Ex: 17-9 = 8 difference 8 is the 3. the answer when you multiply Ex: 7 x 8 = 56 56 is the 4. quotient

More information

100 Math Facts 6 th Grade

100 Math Facts 6 th Grade 100 Math Facts 6 th Grade Name 1. SUM: What is the answer to an addition problem called? (N. 2.1) 2. DIFFERENCE: What is the answer to a subtraction problem called? (N. 2.1) 3. PRODUCT: What is the answer

More information

TYPES OF NUMBERS. Example 2. Example 1. Problems. Answers

TYPES OF NUMBERS. Example 2. Example 1. Problems. Answers TYPES OF NUMBERS When two or more integers are multiplied together, each number is a factor of the product. Nonnegative integers that have exactly two factors, namely, one and itself, are called prime

More information

Graph Ordered Pairs on a Coordinate Plane

Graph Ordered Pairs on a Coordinate Plane Graph Ordered Pairs on a Coordinate Plane Student Probe Plot the ordered pair (2, 5) on a coordinate grid. Plot the point the ordered pair (-2, 5) on a coordinate grid. Note: If the student correctly plots

More information

This assignment will help you to prepare for Algebra 1 by reviewing some of the things you learned in Middle School. If you cannot remember how to complete a specific problem, there is an example at the

More information

Using the Quadrant. Protractor. Eye Piece. You can measure angles of incline from 0º ( horizontal ) to 90º (vertical ). Ignore measurements >90º.

Using the Quadrant. Protractor. Eye Piece. You can measure angles of incline from 0º ( horizontal ) to 90º (vertical ). Ignore measurements >90º. Using the Quadrant Eye Piece Protractor Handle You can measure angles of incline from 0º ( horizontal ) to 90º (vertical ). Ignore measurements 90º. Plumb Bob ø

More information

Domain Essential Question Common Core Standards Resources

Domain Essential Question Common Core Standards Resources Middle School Math 2016-2017 Domain Essential Question Common Core Standards First Ratios and Proportional Relationships How can you use mathematics to describe change and model real world solutions? How

More information

Integers (pages 294 298)

Integers (pages 294 298) A Integers (pages 294 298) An integer is any number from this set of the whole numbers and their opposites: { 3, 2,, 0,, 2, 3, }. Integers that are greater than zero are positive integers. You can write

More information

Interactive Math Glossary Terms and Definitions

Interactive Math Glossary Terms and Definitions Terms and Definitions Absolute Value the magnitude of a number, or the distance from 0 on a real number line Additive Property of Area the process of finding an the area of a shape by totaling the areas

More information

What are the place values to the left of the decimal point and their associated powers of ten?

What are the place values to the left of the decimal point and their associated powers of ten? The verbal answers to all of the following questions should be memorized before completion of algebra. Answers that are not memorized will hinder your ability to succeed in geometry and algebra. (Everything

More information

Campbellsport School District Understanding by Design (UbD) Template

Campbellsport School District Understanding by Design (UbD) Template Campbellsport School District Understanding by Design (UbD) Template Class Curriculum/Content Area: Math Course Length: 1 year Course Title: 6 th Grade Math Date last reviewed: April 24, 2015 Prerequisites:

More information

Vocabulary Words and Definitions for Algebra

Vocabulary Words and Definitions for Algebra Name: Period: Vocabulary Words and s for Algebra Absolute Value Additive Inverse Algebraic Expression Ascending Order Associative Property Axis of Symmetry Base Binomial Coefficient Combine Like Terms

More information

Basic Math Refresher A tutorial and assessment of basic math skills for students in PUBP704.

Basic Math Refresher A tutorial and assessment of basic math skills for students in PUBP704. Basic Math Refresher A tutorial and assessment of basic math skills for students in PUBP704. The purpose of this Basic Math Refresher is to review basic math concepts so that students enrolled in PUBP704:

More information

ALGEBRA I A PLUS COURSE OUTLINE

ALGEBRA I A PLUS COURSE OUTLINE ALGEBRA I A PLUS COURSE OUTLINE OVERVIEW: 1. Operations with Real Numbers 2. Equation Solving 3. Word Problems 4. Inequalities 5. Graphs of Functions 6. Linear Functions 7. Scatterplots and Lines of Best

More information

MATH 60 NOTEBOOK CERTIFICATIONS

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

More information

Algebra Cheat Sheets

Algebra Cheat Sheets Sheets Algebra Cheat Sheets provide you with a tool for teaching your students note-taking, problem-solving, and organizational skills in the context of algebra lessons. These sheets teach the concepts

More information

Sect Properties of Real Numbers and Simplifying Expressions

Sect Properties of Real Numbers and Simplifying Expressions Sect 1.6 - Properties of Real Numbers and Simplifying Expressions Concept #1 Commutative Properties of Real Numbers Ex. 1a.34 + 2.5 Ex. 1b 2.5 + (.34) Ex. 1c 6.3(4.2) Ex. 1d 4.2( 6.3) a).34 + 2.5 = 6.84

More information

Math Foundations IIB Grade Levels 9-12

Math Foundations IIB Grade Levels 9-12 Math Foundations IIB Grade Levels 9-12 Math Foundations IIB introduces students to the following concepts: integers coordinate graphing ratio and proportion multi-step equations and inequalities points,

More information

EXPONENTS. To the applicant: KEY WORDS AND CONVERTING WORDS TO EQUATIONS

EXPONENTS. To the applicant: KEY WORDS AND CONVERTING WORDS TO EQUATIONS To the applicant: The following information will help you review math that is included in the Paraprofessional written examination for the Conejo Valley Unified School District. The Education Code requires

More information

Fractions Associate a fraction with division to calculate decimal fraction equivalents (e.g ) for a simple fraction (e.g. 3/8).

Fractions Associate a fraction with division to calculate decimal fraction equivalents (e.g ) for a simple fraction (e.g. 3/8). : Autumn 1 Numeracy Curriculum Objectives Number, Place Value and Rounding Read, write, order and compare numbers up to 10,000,000 and determine the value of each digit. Round any whole number to a required

More information

Helpsheet. Giblin Eunson Library LINEAR EQUATIONS. library.unimelb.edu.au/libraries/bee. Use this sheet to help you:

Helpsheet. Giblin Eunson Library LINEAR EQUATIONS. library.unimelb.edu.au/libraries/bee. Use this sheet to help you: Helpsheet Giblin Eunson Library LINEAR EQUATIONS Use this sheet to help you: Solve linear equations containing one unknown Recognize a linear function, and identify its slope and intercept parameters Recognize

More information

EQUATIONS and INEQUALITIES

EQUATIONS and INEQUALITIES EQUATIONS and INEQUALITIES Linear Equations and Slope 1. Slope a. Calculate the slope of a line given two points b. Calculate the slope of a line parallel to a given line. c. Calculate the slope of a line

More information

Topic: Integers. Addition Subtraction Multiplication Division Same signs: Add & keep sign = = - 10.

Topic: Integers. Addition Subtraction Multiplication Division Same signs: Add & keep sign = = - 10. Topic: Integers Examples: Addition Subtraction Multiplication Division Same signs: Add & keep sign + 6 + + 5 = + - 8 + - 2 = - 0 Different signs: Subtract & take sign of larger value + 9 + - 5 = + 4-6

More information

Observation 1. Observation 2. What is the sign of the answer to the problem L3 Q L11?

Observation 1. Observation 2. What is the sign of the answer to the problem L3 Q L11? Name Date Number Sense: Integers Student Worksheet Overview The Overview introduces the topics covered in Observations and Activities. Scroll through the Overview using " (! to review, if necessary). Read

More information

FURTHER VECTORS (MEI)

FURTHER VECTORS (MEI) Mathematics Revision Guides Further Vectors (MEI) (column notation) Page of MK HOME TUITION Mathematics Revision Guides Level: AS / A Level - MEI OCR MEI: C FURTHER VECTORS (MEI) Version : Date: -9-7 Mathematics

More information

Mathematics 1. Lecture 5. Pattarawit Polpinit

Mathematics 1. Lecture 5. Pattarawit Polpinit Mathematics 1 Lecture 5 Pattarawit Polpinit Lecture Objective At the end of the lesson, the student is expected to be able to: familiarize with the use of Cartesian Coordinate System. determine the distance

More information

Florida Department of Education/Office of Assessment January 2012. Grade 7 FCAT 2.0 Mathematics Achievement Level Descriptions

Florida Department of Education/Office of Assessment January 2012. Grade 7 FCAT 2.0 Mathematics Achievement Level Descriptions Florida Department of Education/Office of Assessment January 2012 Grade 7 FCAT 2.0 Mathematics Grade 7 FCAT 2.0 Mathematics Reporting Category Geometry and Measurement Students performing at the mastery

More information

The Product Property of Square Roots states: For any real numbers a and b, where a 0 and b 0, ab = a b.

The Product Property of Square Roots states: For any real numbers a and b, where a 0 and b 0, ab = a b. Chapter 9. Simplify Radical Expressions Any term under a radical sign is called a radical or a square root expression. The number or expression under the the radical sign is called the radicand. The radicand

More information

Add and subtract 1-digit and 2-digit numbers to 20, including zero. Measure and begin to record length, mass, volume and time

Add and subtract 1-digit and 2-digit numbers to 20, including zero. Measure and begin to record length, mass, volume and time Year 1 Maths - Key Objectives Count to and across 100 from any number Count, read and write numbers to 100 in numerals Read and write mathematical symbols: +, - and = Identify "one more" and "one less"

More information

Example SECTION 13-1. X-AXIS - the horizontal number line. Y-AXIS - the vertical number line ORIGIN - the point where the x-axis and y-axis cross

Example SECTION 13-1. X-AXIS - the horizontal number line. Y-AXIS - the vertical number line ORIGIN - the point where the x-axis and y-axis cross CHAPTER 13 SECTION 13-1 Geometry and Algebra The Distance Formula COORDINATE PLANE consists of two perpendicular number lines, dividing the plane into four regions called quadrants X-AXIS - the horizontal

More information

Lecture 8 : Coordinate Geometry. The coordinate plane The points on a line can be referenced if we choose an origin and a unit of 20

Lecture 8 : Coordinate Geometry. The coordinate plane The points on a line can be referenced if we choose an origin and a unit of 20 Lecture 8 : Coordinate Geometry The coordinate plane The points on a line can be referenced if we choose an origin and a unit of 0 distance on the axis and give each point an identity on the corresponding

More information

1. By how much does 1 3 of 5 2 exceed 1 2 of 1 3? 2. What fraction of the area of a circle of radius 5 lies between radius 3 and radius 4? 3.

1. By how much does 1 3 of 5 2 exceed 1 2 of 1 3? 2. What fraction of the area of a circle of radius 5 lies between radius 3 and radius 4? 3. 1 By how much does 1 3 of 5 exceed 1 of 1 3? What fraction of the area of a circle of radius 5 lies between radius 3 and radius 4? 3 A ticket fee was $10, but then it was reduced The number of customers

More information

Bell Ringer. Solve each equation. Show you work. Check the solution. 8 = -7 + m = m 15 = m = 7 + m 8 = = 8

Bell Ringer. Solve each equation. Show you work. Check the solution. 8 = -7 + m = m 15 = m = 7 + m 8 = = 8 Bell Ringer Solve each equation. Show you work. the solution. 1. 8 = 7 + m 8 = -7 + m 8 + 7 = -7 + 7 + m 15 = m 8 = -7 + m 8 = -7 + 15 8 = 8 Answers to Homework Worksheet 2-1 Today s Objectives Solving

More information

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

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

More information

Algebra 1 Chapter 3 Vocabulary. equivalent - Equations with the same solutions as the original equation are called.

Algebra 1 Chapter 3 Vocabulary. equivalent - Equations with the same solutions as the original equation are called. Chapter 3 Vocabulary equivalent - Equations with the same solutions as the original equation are called. formula - An algebraic equation that relates two or more real-life quantities. unit rate - A rate

More information

Section 9.1 Vectors in Two Dimensions

Section 9.1 Vectors in Two Dimensions Section 9.1 Vectors in Two Dimensions Geometric Description of Vectors A vector in the plane is a line segment with an assigned direction. We sketch a vector as shown in the first Figure below with an

More information

Opposites are all around us. If you move forward two spaces in a board game

Opposites are all around us. If you move forward two spaces in a board game Two-Color Counters Adding Integers, Part II Learning Goals In this lesson, you will: Key Term additive inverses Model the addition of integers using two-color counters. Develop a rule for adding integers.

More information

An inscribed polygon is a polygon whose vertices are points of a circle. in means in and scribed means written

An inscribed polygon is a polygon whose vertices are points of a circle. in means in and scribed means written Geometry Week 6 Sec 3.5 to 4.1 Definitions: section 3.5 A A B D B D C Connect the points in consecutive order with segments. C The square is inscribed in the circle. An inscribed polygon is a polygon whose

More information

of surface, 569-571, 576-577, 578-581 of triangle, 548 Associative Property of addition, 12, 331 of multiplication, 18, 433

of surface, 569-571, 576-577, 578-581 of triangle, 548 Associative Property of addition, 12, 331 of multiplication, 18, 433 Absolute Value and arithmetic, 730-733 defined, 730 Acute angle, 477 Acute triangle, 497 Addend, 12 Addition associative property of, (see Commutative Property) carrying in, 11, 92 commutative property

More information

Use order of operations to simplify. Show all steps in the space provided below each problem. INTEGER OPERATIONS

Use order of operations to simplify. Show all steps in the space provided below each problem. INTEGER OPERATIONS ORDER OF OPERATIONS In the following order: 1) Work inside the grouping smbols such as parenthesis and brackets. ) Evaluate the powers. 3) Do the multiplication and/or division in order from left to right.

More information

2. THE x-y PLANE 7 C7

2. THE x-y PLANE 7 C7 2. THE x-y PLANE 2.1. The Real Line When we plot quantities on a graph we can plot not only integer values like 1, 2 and 3 but also fractions, like 3½ or 4¾. In fact we can, in principle, plot any real

More information

Section 9.4 Trigonometric Functions of any Angle

Section 9.4 Trigonometric Functions of any Angle Section 9. Trigonometric Functions of any Angle So far we have only really looked at trigonometric functions of acute (less than 90º) angles. We would like to be able to find the trigonometric functions

More information

STRAND: ALGEBRA Unit 3 Solving Equations

STRAND: ALGEBRA Unit 3 Solving Equations CMM Subject Support Strand: ALGEBRA Unit Solving Equations: Tet STRAND: ALGEBRA Unit Solving Equations TEXT Contents Section. Algebraic Fractions. Algebraic Fractions and Quadratic Equations. Algebraic

More information

Section 1.8 Coordinate Geometry

Section 1.8 Coordinate Geometry Section 1.8 Coordinate Geometry The Coordinate Plane Just as points on a line can be identified with real numbers to form the coordinate line, points in a plane can be identified with ordered pairs of

More information

Higher Education Math Placement

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

More information

New York State Mathematics Content Strands, Grade 6, Correlated to Glencoe MathScape, Course 1 and Quick Review Math Handbook Book 1

New York State Mathematics Content Strands, Grade 6, Correlated to Glencoe MathScape, Course 1 and Quick Review Math Handbook Book 1 New York State Mathematics Content Strands, Grade 6, Correlated to Glencoe MathScape, Course 1 and The lessons that address each Performance Indicator are listed, and those in which the Performance Indicator

More information

Grade 6 Mathematics Assessment. Eligible Texas Essential Knowledge and Skills

Grade 6 Mathematics Assessment. Eligible Texas Essential Knowledge and Skills Grade 6 Mathematics Assessment Eligible Texas Essential Knowledge and Skills STAAR Grade 6 Mathematics Assessment Mathematical Process Standards These student expectations will not be listed under a separate

More information

ascending order decimal denominator descending order Numbers listed from largest to smallest equivalent fraction greater than or equal to SOL 7.

ascending order decimal denominator descending order Numbers listed from largest to smallest equivalent fraction greater than or equal to SOL 7. SOL 7.1 ascending order Numbers listed in order from smallest to largest decimal The numbers in the base 10 number system, having one or more places to the right of a decimal point denominator The bottom

More information

GRAPHING (2 weeks) Main Underlying Questions: 1. How do you graph points?

GRAPHING (2 weeks) Main Underlying Questions: 1. How do you graph points? GRAPHING (2 weeks) The Rectangular Coordinate System 1. Plot ordered pairs of numbers on the rectangular coordinate system 2. Graph paired data to create a scatter diagram 1. How do you graph points? 2.

More information

Vocabulary Cards and Word Walls Revised: June 29, 2011

Vocabulary Cards and Word Walls Revised: June 29, 2011 Vocabulary Cards and Word Walls Revised: June 29, 2011 Important Notes for Teachers: The vocabulary cards in this file match the Common Core, the math curriculum adopted by the Utah State Board of Education,

More information

Grade 7 Math The Number System Grade 7 Math Grade 7 Math Start Date: August 30, 2012 End Date : September 28, 2012

Grade 7 Math The Number System Grade 7 Math Grade 7 Math Start Date: August 30, 2012 End Date : September 28, 2012 Unit Overview Students will be able to: describe real life situations for quantities that combine to make zero understand the distance between two on a number line show how opposites have a sum of zero

More information

RIT scores between 191 and 200

RIT scores between 191 and 200 Measures of Academic Progress for Mathematics RIT scores between 191 and 200 Number Sense and Operations Whole Numbers Solve simple addition word problems Find and extend patterns Demonstrate the associative,

More information

Name: Date: Adding Zero. Addition. Worksheet A

Name: Date: Adding Zero. Addition. Worksheet A A DIVISION OF + + + + + Adding Zero + + + + + + + + + + + + + + + Addition Worksheet A + + + + + Adding Zero + + + + + + + + + + + + + + + Addition Worksheet B + + + + + Adding Zero + + + + + + + + + +

More information

Annotated work sample portfolios are provided to support implementation of the Foundation Year 10 Australian Curriculum.

Annotated work sample portfolios are provided to support implementation of the Foundation Year 10 Australian Curriculum. Work sample portfolio summary WORK SAMPLE PORTFOLIO Annotated work sample portfolios are provided to support implementation of the Foundation Year 10 Australian Curriculum. Each portfolio is an example

More information

Teaching & Learning Plans. Using Pythagoras Theorem to establish the Distance Formula (Draft) Junior Certificate Syllabus

Teaching & Learning Plans. Using Pythagoras Theorem to establish the Distance Formula (Draft) Junior Certificate Syllabus Teaching & Learning Plans Using Pythagoras Theorem to establish the Distance Formula (Draft) Junior Certificate Syllabus The Teaching & Learning Plans are structured as follows: Aims outline what the lesson,

More information

MAT 0950 Course Objectives

MAT 0950 Course Objectives MAT 0950 Course Objectives 5/15/20134/27/2009 A student should be able to R1. Do long division. R2. Divide by multiples of 10. R3. Use multiplication to check quotients. 1. Identify whole numbers. 2. Identify

More information

Measurement with Ratios

Measurement with Ratios Grade 6 Mathematics, Quarter 2, Unit 2.1 Measurement with Ratios Overview Number of instructional days: 15 (1 day = 45 minutes) Content to be learned Use ratio reasoning to solve real-world and mathematical

More information

Trigonometric Functions: The Unit Circle

Trigonometric Functions: The Unit Circle Trigonometric Functions: The Unit Circle This chapter deals with the subject of trigonometry, which likely had its origins in the study of distances and angles by the ancient Greeks. The word trigonometry

More information

Name Period Date MATHLINKS GRADE 8 STUDENT PACKET 1 INTEGERS REVIEW

Name Period Date MATHLINKS GRADE 8 STUDENT PACKET 1 INTEGERS REVIEW Name Period Date 8-1 STUDENT PACKET MATHLINKS GRADE 8 STUDENT PACKET 1 INTEGERS REVIEW 1.1 Integer Operations: Patterns Explore the meaning of integer addition, subtraction, multiplication, and division.

More information

MATH 65 NOTEBOOK CERTIFICATIONS

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

More information

Algebra 1: Topic 1 Notes

Algebra 1: Topic 1 Notes Algebra 1: Topic 1 Notes Review: Order of Operations Please Parentheses Excuse Exponents My Multiplication Dear Division Aunt Addition Sally Subtraction Table of Contents 1. Order of Operations & Evaluating

More information

Mathematics Common Core Cluster Mathematics Common Core Standard Resources. EE.6.1 Write and evaluate numerical expressions involving wholenumber

Mathematics Common Core Cluster Mathematics Common Core Standard Resources. EE.6.1 Write and evaluate numerical expressions involving wholenumber Unit 2 2 2 Unit : Operations and Properties Mathematics Common Core Domain Mathematics Common Core Cluster Mathematics Common Core Standard Resources NS..2 Fluently divide multi-digit numbers using the

More information

Year 8 - Maths Autumn Term

Year 8 - Maths Autumn Term Year 8 - Maths Autumn Term Whole Numbers and Decimals Order, add and subtract negative numbers. Recognise and use multiples and factors. Use divisibility tests. Recognise prime numbers. Find square numbers

More information

Exam 2 Review. 3. How to tell if an equation is linear? An equation is linear if it can be written, through simplification, in the form.

Exam 2 Review. 3. How to tell if an equation is linear? An equation is linear if it can be written, through simplification, in the form. Exam 2 Review Chapter 1 Section1 Do You Know: 1. What does it mean to solve an equation? To solve an equation is to find the solution set, that is, to find the set of all elements in the domain of the

More information

Mathematics. Mathematical Practices

Mathematics. Mathematical Practices Mathematical Practices 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with

More information

Geometry Unit 1. Basics of Geometry

Geometry Unit 1. Basics of Geometry Geometry Unit 1 Basics of Geometry Using inductive reasoning - Looking for patterns and making conjectures is part of a process called inductive reasoning Conjecture- an unproven statement that is based

More information

Whole Numbers and Integers (44 topics, no due date)

Whole Numbers and Integers (44 topics, no due date) Course Name: PreAlgebra into Algebra Summer Hwk Course Code: GHMKU-KPMR9 ALEKS Course: Pre-Algebra Instructor: Ms. Rhame Course Dates: Begin: 05/30/2015 End: 12/31/2015 Course Content: 302 topics Whole

More information

Chapter 12. The Straight Line

Chapter 12. The Straight Line 302 Chapter 12 (Plane Analytic Geometry) 12.1 Introduction: Analytic- geometry was introduced by Rene Descartes (1596 1650) in his La Geometric published in 1637. Accordingly, after the name of its founder,

More information

MODERN APPLICATIONS OF PYTHAGORAS S THEOREM

MODERN APPLICATIONS OF PYTHAGORAS S THEOREM UNIT SIX MODERN APPLICATIONS OF PYTHAGORAS S THEOREM Coordinate Systems 124 Distance Formula 127 Midpoint Formula 131 SUMMARY 134 Exercises 135 UNIT SIX: 124 COORDINATE GEOMETRY Geometry, as presented

More information

MA.7.G.4.2 Predict the results of transformations and draw transformed figures with and without the coordinate plane.

MA.7.G.4.2 Predict the results of transformations and draw transformed figures with and without the coordinate plane. MA.7.G.4.2 Predict the results of transformations and draw transformed figures with and without the coordinate plane. Symmetry When you can fold a figure in half, with both sides congruent, the fold line

More information

Chapter 6 Notes. Section 6.1 Solving One-Step Linear Inequalities

Chapter 6 Notes. Section 6.1 Solving One-Step Linear Inequalities Chapter 6 Notes Name Section 6.1 Solving One-Step Linear Inequalities Graph of a linear Inequality- the set of all points on a number line that represent all solutions of the inequality > or < or circle

More information

Algebra Tiles Activity 1: Adding Integers

Algebra Tiles Activity 1: Adding Integers Algebra Tiles Activity 1: Adding Integers NY Standards: 7/8.PS.6,7; 7/8.CN.1; 7/8.R.1; 7.N.13 We are going to use positive (yellow) and negative (red) tiles to discover the rules for adding and subtracting

More information

Algebra 2: Themes for the Big Final Exam

Algebra 2: Themes for the Big Final Exam Algebra : Themes for the Big Final Exam Final will cover the whole year, focusing on the big main ideas. Graphing: Overall: x and y intercepts, fct vs relation, fct vs inverse, x, y and origin symmetries,

More information

DO NOW Geometry Regents Lomac Date. due. Coordinate Plane: Equation of a Circle

DO NOW Geometry Regents Lomac Date. due. Coordinate Plane: Equation of a Circle DO NOW Geometry Regents Lomac 2014-2015 Date. due. Coordinate Plane: Equation of a Circle 8.5 (DN) TEAR OFF The Circle PAGE AND THEN DO THE DO NOW ON BACK OF PACKET (1) What do right triangles have to

More information

Mathematical Procedures

Mathematical Procedures CHAPTER 6 Mathematical Procedures 168 CHAPTER 6 Mathematical Procedures The multidisciplinary approach to medicine has incorporated a wide variety of mathematical procedures from the fields of physics,

More information

Class 9 Coordinate Geometry

Class 9 Coordinate Geometry ID : in-9-coordinate-geometry [1] Class 9 Coordinate Geometry For more such worksheets visit www.edugain.com Answer t he quest ions (1) Find the coordinates of the point shown in the picture. (2) Find

More information

Chapter 1 Linear Equations and Graphs

Chapter 1 Linear Equations and Graphs Chapter 1 Linear Equations and Graphs Section 1.1 - Linear Equations and Inequalities Objectives: The student will be able to solve linear equations. The student will be able to solve linear inequalities.

More information

Elements of a graph. Click on the links below to jump directly to the relevant section

Elements of a graph. Click on the links below to jump directly to the relevant section Click on the links below to jump directly to the relevant section Elements of a graph Linear equations and their graphs What is slope? Slope and y-intercept in the equation of a line Comparing lines on

More information

Transformational Geometry in the Coordinate Plane Rotations and Reflections

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

More information

Sample Problems. Lecture Notes Similar Triangles page 1

Sample Problems. Lecture Notes Similar Triangles page 1 Lecture Notes Similar Triangles page 1 Sample Problems 1. The triangles shown below are similar. Find the exact values of a and b shown on the picture below. 2. Consider the picture shown below. a) Use

More information

Mathematics Placement

Mathematics Placement Mathematics Placement The ACT COMPASS math test is a self-adaptive test, which potentially tests students within four different levels of math including pre-algebra, algebra, college algebra, and trigonometry.

More information

ModuMath Algebra Lessons

ModuMath Algebra Lessons ModuMath Algebra Lessons Program Title 1 Getting Acquainted With Algebra 2 Order of Operations 3 Adding & Subtracting Algebraic Expressions 4 Multiplying Polynomials 5 Laws of Algebra 6 Solving Equations

More information

Oral and Mental calculation

Oral and Mental calculation Oral and Mental calculation Read and write any integer and know what each digit represents. Read and write decimal notation for tenths and hundredths and know what each digit represents. Order and compare

More information

29 Wyner PreCalculus Fall 2016

29 Wyner PreCalculus Fall 2016 9 Wyner PreCalculus Fall 016 CHAPTER THREE: TRIGONOMETRIC EQUATIONS Review November 8 Test November 17 Trigonometric equations can be solved graphically or algebraically. Solving algebraically involves

More information

P.E.R.T. Math Study Guide

P.E.R.T. Math Study Guide A guide to help you prepare for the Math subtest of Florida s Postsecondary Education Readiness Test or P.E.R.T. P.E.R.T. Math Study Guide www.perttest.com PERT - A Math Study Guide 1. Linear Equations

More information

Applications of Integration Day 1

Applications of Integration Day 1 Applications of Integration Day 1 Area Under Curves and Between Curves Example 1 Find the area under the curve y = x2 from x = 1 to x = 5. (What does it mean to take a slice?) Example 2 Find the area under

More information

Section 2.1 Rectangular Coordinate Systems

Section 2.1 Rectangular Coordinate Systems P a g e 1 Section 2.1 Rectangular Coordinate Systems 1. Pythagorean Theorem In a right triangle, the lengths of the sides are related by the equation where a and b are the lengths of the legs and c is

More information

Common Core Unit Summary Grades 6 to 8

Common Core Unit Summary Grades 6 to 8 Common Core Unit Summary Grades 6 to 8 Grade 8: Unit 1: Congruence and Similarity- 8G1-8G5 rotations reflections and translations,( RRT=congruence) understand congruence of 2 d figures after RRT Dilations

More information

Course: Math 7. engage in problem solving, communicating, reasoning, connecting, and representing

Course: Math 7. engage in problem solving, communicating, reasoning, connecting, and representing Course: Math 7 Decimals and Integers 1-1 Estimation Strategies. Estimate by rounding, front-end estimation, and compatible numbers. Prentice Hall Textbook - Course 2 7.M.0 ~ Measurement Strand ~ Students

More information

Ordered Pairs. Graphing Lines and Linear Inequalities, Solving System of Linear Equations. Cartesian Coordinates System.

Ordered Pairs. Graphing Lines and Linear Inequalities, Solving System of Linear Equations. Cartesian Coordinates System. Ordered Pairs Graphing Lines and Linear Inequalities, Solving System of Linear Equations Peter Lo All equations in two variables, such as y = mx + c, is satisfied only if we find a value of x and a value

More information

Chapter 5 Polar Coordinates; Vectors 5.1 Polar coordinates 1. Pole and polar axis

Chapter 5 Polar Coordinates; Vectors 5.1 Polar coordinates 1. Pole and polar axis Chapter 5 Polar Coordinates; Vectors 5.1 Polar coordinates 1. Pole and polar axis 2. Polar coordinates A point P in a polar coordinate system is represented by an ordered pair of numbers (r, θ). If r >

More information

Algorithm set of steps used to solve a mathematical computation. Area The number of square units that covers a shape or figure

Algorithm set of steps used to solve a mathematical computation. Area The number of square units that covers a shape or figure Fifth Grade CCSS Math Vocabulary Word List *Terms with an asterisk are meant for teacher knowledge only students need to learn the concept but not necessarily the term. Addend Any number being added Algorithm

More information

The slope m of the line passes through the points (x 1,y 1 ) and (x 2,y 2 ) e) (1, 3) and (4, 6) = 1 2. f) (3, 6) and (1, 6) m= 6 6

The slope m of the line passes through the points (x 1,y 1 ) and (x 2,y 2 ) e) (1, 3) and (4, 6) = 1 2. f) (3, 6) and (1, 6) m= 6 6 Lines and Linear Equations Slopes Consider walking on a line from left to right. The slope of a line is a measure of its steepness. A positive slope rises and a negative slope falls. A slope of zero means

More information

Lines and Linear Equations. Slopes

Lines and Linear Equations. Slopes Lines and Linear Equations Slopes Consider walking on a line from left to right. The slope of a line is a measure of its steepness. A positive slope rises and a negative slope falls. A slope of zero means

More information

4 th Grade Math Lesson Plan Coordinate Planes

4 th Grade Math Lesson Plan Coordinate Planes Context: Objective: 4 th Grade Math Lesson Plan Coordinate Planes This lesson designed for a 4 th grade class at Kraft Elementary School. This class contains 16 students. No students have IEPs and none

More information

Transformations Packet Geometry

Transformations Packet Geometry Transformations Packet Geometry 1 Name: Geometry Chapter 14: Transformations Date Due Section Topics Assignment 14.1 14.2 14.3 Preimage Image Isometry Mapping Reflections Note: Notation is different in

More information

The x-intercepts of the graph are the x-values for the points where the graph intersects the x-axis. A parabola may have one, two, or no x-intercepts.

The x-intercepts of the graph are the x-values for the points where the graph intersects the x-axis. A parabola may have one, two, or no x-intercepts. Chapter 10-1 Identify Quadratics and their graphs A parabola is the graph of a quadratic function. A quadratic function is a function that can be written in the form, f(x) = ax 2 + bx + c, a 0 or y = ax

More information

In this section, we ll review plotting points, slope of a line and different forms of an equation of a line.

In this section, we ll review plotting points, slope of a line and different forms of an equation of a line. Math 1313 Section 1.2: Straight Lines In this section, we ll review plotting points, slope of a line and different forms of an equation of a line. Graphing Points and Regions Here s the coordinate plane:

More information