Multiplying and Dividing Listen & Learn PRESENTED BY MATHMANIAC Mathematics, Grade 8

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "Multiplying and Dividing Listen & Learn PRESENTED BY MATHMANIAC Mathematics, Grade 8"

Transcription

1 Number Sense and Numeration Integers Multiplying and Dividing PRESENTED BY MATHMANIAC Mathematics, Grade 8 Integers Multiplying and Dividing Introduction Welcome to today s topic Parts of Presentation, questions, Q&A Housekeeping Your questions Satisfaction meter Downloading slides 1

2 Integers Multiplying and Dividing What you will learn After viewing this presentation, you will be able to multiply and divide integers using one of two methods: the table method or the like/unlike method. Integers Multiplying and Dividing Agenda Real-life applications Definition and terms Methods to multiply and divide integers Table method Like/unlike method Extensions 2

3 Integers Multiplying and Dividing Agenda Real-life applications Definition and terms Methods to multiply and divide integers Table method Like/unlike method Extensions Integers Multiplying and Dividing Real-life applications You can apply knowledge of integers to real-life situations, such as temperature, sea level, money, and time. 3

4 Integers Multiplying and Dividing Agenda Real-life applications Definition and terms Methods to multiply and divide integers Table method Like/unlike method Extensions Integers Multiplying and Dividing Definition and Terms Integer The set of all positive and negative whole numbers and zero. For example, 75, 112, 0, 3, 24 are considered integers, but 1½ and are NOT considered integers. 4

5 Integers Multiplying and Dividing Definitions and Terms Number Lines The whole numbers you use every day that are greater than zero are positive integers. The number line you may be familiar with begins at zero and moves to the right. Integers Multiplying and Dividing Definitions and Terms Integer Number Line The integer number line includes the negative numbers (numbers that are less than zero). 5

6 Integers Multiplying and Dividing Agenda Real-life applications Definition and terms Methods to multiply and divide integers Table method Like/unlike method Extensions Integers Multiplying and Dividing Agenda Real-life applications Definition and terms Methods to multiply and divide integers Table method Like/unlike method Extensions 6

7 Integers Multiplying and Dividing Solve: 7 x (3) Operation Symbol for 1 st integer Symbol for 2 nd integer x Result Integers Multiplying and Dividing Solve: 7 x (3) Step 1: Look at your first symbol. It is positive. Look at your second symbol. It is positive. Therefore, you are multiplying a positive by a positive. x 7

8 Integers Multiplying and Dividing Solve: 7 x (3) Step 1: Look at your first symbol. It is positive. Look at your second symbol. It is positive. Therefore, you are multiplying a positive by a positive. x Integers Multiplying and Dividing Solve: 7 x (3) Step 1: Look at your first symbol. It is positive. Look at your second symbol. It is positive. Therefore, you are multiplying a positive by a positive. The answer is positive. x 8

9 Integers Multiplying and Dividing Solve: 7 x (3) Step 2: Multiply the numbers as you normally would. 7 x 3 = 21 x Integers Multiplying and Dividing Solve: 7 x (3) Step 1: Look at your first symbol. It is negative. Look at your second symbol. It is positive. Therefore, you are multiplying a negative by a positive. x 9

10 Integers Multiplying and Dividing Solve: 7 x (3) Step 1: Look at your first symbol. It is negative. Look at your second symbol. It is positive. Therefore, you are multiplying a negative by a positive. x Integers Multiplying and Dividing Solve: 7 x (3) Step 1: Look at your first symbol. It is negative. Look at your second symbol. It is positive. Therefore, you are multiplying a negative by a positive. The answer is negative. x 10

11 Integers Multiplying and Dividing Solve: 7 x (3) Step 2: Multiply the numbers as you normally would. 7 x 3 = 21 x Integers Multiplying and Dividing Solve: 7 x (3) Step 3: You know your answer is negative and the product is 21. Put these together to get an answer of 21. x 11

12 Integers Multiplying and Dividing Let s try another question. Solve: 12 x (5) x Integers Multiplying and Dividing Solve: 12 x (5) Step 1: Look at your first symbol. It is negative. Look at your second symbol. It is also negative. Therefore, you are multiplying a negative by a negative. The answer is positive. x 12

13 Integers Multiplying and Dividing Solve: 12 x (5) Step 2: Multiply the numbers as you normally would. 12 x 5 = 60 x Integers Multiplying and Dividing Solve: 12 x (5) Step 3: You know your answer is positive and the product is 60. Put these together to get an answer of 60. x 13

14 Integers Multiplying and Dividing Solve: 9/(3) = 3 Now solve for integer division. Integers Multiplying and Dividing Did you notice a pattern? / / / / 14

15 Integers Multiplying and Dividing Agenda Real-life applications Definition and terms Methods to multiply and divide integers Table method Like/unlike method Extensions Integers Multiplying and Dividing Integers: Like/Unlike Method Solve 28/(7) Step 1: Look at the symbols of the numbers that you are dividing (or multiplying). 15

16 Integers Multiplying and Dividing Integers: Like/Unlike Method Solve 28/(7) Step 1: Look at the symbols of the numbers that you are dividing (or multiplying). Step 2: Are the symbols the same or are they different? Integers Multiplying and Dividing Integers: Like/Unlike Method Solve 28/(7) Step 1: Look at the symbols of the numbers that you are dividing (or multiplying). Step 2: Are the symbols the same or are they different? If the symbols are the same the answer will be POSITIVE (). If the symbols are different the answer will be NEGATIVE (). 16

17 Integers Multiplying and Dividing Integers: Like/Unlike Method Solve 28/(7) Step 1: Look at the symbols of the numbers that you are dividing (or multiplying). Step 2: Are the symbols the same or are they different? If the symbols are the same the answer will be POSITIVE (). If the symbols are different the answer will be NEGATIVE (). Step 3: Divide (or multiply) as you normally would and use the sign from step 2. Integers Multiplying and Dividing Integers: Like/Unlike Method Solve 28/(7) Step 1: Look at the symbols of the numbers that you are dividing (or multiplying). 17

18 Integers Multiplying and Dividing Integers: Like/Unlike Method Solve 28/(7) Step 1: Look at the symbols of the numbers that you are dividing (or multiplying). Step 2: Are the symbols the same or are they different? They are different. Integers Multiplying and Dividing Integers: Like/Unlike Method Solve 28/(7) Step 1: Look at the symbols of the numbers that you are dividing (or multiplying). Step 2: Are the symbols the same or are they different? If the symbols are the same the answer will be POSITIVE (). If the symbols are different the answer will be NEGATIVE (). The answer will be NEGATIVE (). 18

19 Integers Multiplying and Dividing Integers: Like/Unlike Method Solve 28/(7) Step 1: Look at the symbols of the numbers that you are dividing (or multiplying). Step 2: Are the symbols the same or are they different? If the symbols are the same the answer will be POSITIVE (). If the symbols are different the answer will be NEGATIVE (). Step 3: Divide (or multiply) as you normally would and use the sign from step 2. 28/(7) = 4 Integers Multiplying and Dividing Methods to Solve Equations Let s apply what you ve learned. You read the weather report for today and it says that it will be 16 degrees Celsius in the morning. The report predicts that the high for the day will be double the morning temperature. What is the predicted high? 19

20 Integers Multiplying and Dividing Methods to Solve Equations You read the weather report for today and it says that it will be 16 degrees Celsius in the morning. The report predicts that the high for the day will be double the morning temperature. What is the predicted high? Step 1: Write out the question. 16 x (2) Integers Multiplying and Dividing Methods to Solve Equations You read the weather report for today and it says that it will be 16 degrees Celsius in the morning. The report predicts that the high for the day will be double the morning temperature. What is the predicted high? Step 2: Look at the symbols. Are they the same or different? 16 x (2) Both symbols are positive, therefore they are the same. 20

21 Integers Multiplying and Dividing Methods to Solve Equations You read the weather report for today and it says that it will be 16 degrees Celsius in the morning. The report predicts that the high for the day will be double the morning temperature. What is the predicted high? Step 3: Multiply the numbers as you normally would and take the symbol from step 2 (). 16 x (2) = 32 Integers Multiplying and Dividing Agenda Real-life applications Definition and terms Methods to multiply and divide integers Table method Like/unlike method Extensions 21

22 Integers Multiplying and Dividing Extensions Integer problems involving: Order of operations Square roots and exponents Addition and subtraction Multiplication and division Solving equations Integers Multiplying and Dividing Questions When multiplying integers, if the symbols are the same, will the answer be positive or negative? a) positive b) negative 22

23 Integers Multiplying and Dividing Questions When multiplying integers, if the symbols are the same, will the answer be positive or negative? a) positive b) negative Integers Multiplying and Dividing Questions When multiplying integers, if the symbols are the same, will the answer be positive or negative? a) positive b) negative The answer is positive whenever both symbols are positive or both are negative. This rule only applies when we are multiplying or dividing two numbers. 23

24 Integers Multiplying and Dividing Questions When dividing integers, if the symbols are different, will the answer be positive or negative? a) positive b) negative Integers Multiplying and Dividing Questions When dividing integers, if the symbols are different, will the answer be positive or negative? a) positive b) negative 24

25 Integers Multiplying and Dividing Questions When dividing integers, if the symbols are different, will the answer be positive or negative? a) positive b) negative Whenever the symbols are different, the answer is negative. This rule only applies when we are multiplying or dividing two numbers. Integers Multiplying and Dividing Questions When solving the expression 5y x (10) will the answer will be positive or negative? a) positive b) negative 25

26 Integers Multiplying and Dividing Questions When solving the expression 5y x (10) will the answer will be positive or negative? a) positive b) negative The answer is positive because both symbols are the same. This rule only applies when we are multiplying or dividing two numbers. Integers Multiplying and Dividing Resources Math League: Integer Help integers/integers.htm Math: Integer Lessons ons/s1u1l12gl.html NLVM: Integer Multiplication 322_g_2_t_1.html?from=grade_g_2.html 26

Welcome to today s topic Parts of Listen & Learn

Welcome to today s topic Parts of Listen & Learn in the form Geometry and Spatial Sense Solving One-Step Equations in the form ax=b PRESENTED BY Mathmaniac Mathematics, Grade 7 Introduction Welcome to today s topic Parts of Presentation, questions, Q&A

More information

Listen and Learn PRESENTED BY MATHEMAGICIAN Mathematics, Grade 7

Listen and Learn PRESENTED BY MATHEMAGICIAN Mathematics, Grade 7 Number Sense and Numeration Integers Adding and Subtracting Listen and Learn PRESENTED BY MATHEMAGICIAN Mathematics, Grade 7 Introduction Welcome to today s topic Parts of Presentation, questions, Q&A

More information

eday Lessons Mathematics Grade 8 Student Name:

eday Lessons Mathematics Grade 8 Student Name: eday Lessons Mathematics Grade 8 Student Name: Common Core State Standards- Expressions and Equations Work with radicals and integer exponents. 3. Use numbers expressed in the form of a single digit times

More information

Grade 7/8 Math Circles October 7/8, Exponents and Roots - SOLUTIONS

Grade 7/8 Math Circles October 7/8, Exponents and Roots - SOLUTIONS Faculty of Mathematics Waterloo, Ontario N2L 3G1 Centre for Education in Mathematics and Computing Grade 7/8 Math Circles October 7/8, 2014 Exponents and Roots - SOLUTIONS This file has all the missing

More information

Rules of Signs for Decimals

Rules of Signs for Decimals CHAPTER 6 C Rules of Signs for Decimals c GOAL Apply the rules of signs for calculating with decimals. You will need number lines a calculator with a sign change key Learn about the Math Positive and negative

More information

Zero: If P is a polynomial and if c is a number such that P (c) = 0 then c is a zero of P.

Zero: If P is a polynomial and if c is a number such that P (c) = 0 then c is a zero of P. MATH 11011 FINDING REAL ZEROS KSU OF A POLYNOMIAL Definitions: Polynomial: is a function of the form P (x) = a n x n + a n 1 x n 1 + + a x + a 1 x + a 0. The numbers a n, a n 1,..., a 1, a 0 are called

More information

Solution: There are TWO square roots of 196, a positive number and a negative number. So, since and 14 2

Solution: There are TWO square roots of 196, a positive number and a negative number. So, since and 14 2 5.7 Introduction to Square Roots The Square of a Number The number x is called the square of the number x. EX) 9 9 9 81, the number 81 is the square of the number 9. 4 4 4 16, the number 16 is the square

More information

For any two different places on the number line, the integer on the right is greater than the integer on the left.

For any two different places on the number line, the integer on the right is greater than the integer on the left. Positive and Negative Integers Positive integers are all the whole numbers greater than zero: 1, 2, 3, 4, 5,.... Negative integers are all the opposites of these whole numbers: -1, -2, -3, -4, -5,. We

More information

Sometimes it is easier to leave a number written as an exponent. For example, it is much easier to write

Sometimes it is easier to leave a number written as an exponent. For example, it is much easier to write 4.0 Exponent Property Review First let s start with a review of what exponents are. Recall that 3 means taking four 3 s and multiplying them together. So we know that 3 3 3 3 381. You might also recall

More information

PRESENTED BY TROTTER. Welcome to today s topic Parts of Listen & Learn. Presentation, questions, Q&A

PRESENTED BY TROTTER. Welcome to today s topic Parts of Listen & Learn. Presentation, questions, Q&A Number Sense and Numeration PRESENTED BY TROTTER Mathematics, Grade 7 Introduction Welcome to today s topic Parts of Presentation, questions, Q&A Housekeeping NOT the Chat Room Your questions Satisfaction

More information

a b Grade 6 Math Circles Fall 2010 Exponents and Binary Numbers Powers What is the product of three 2s? =

a b Grade 6 Math Circles Fall 2010 Exponents and Binary Numbers Powers What is the product of three 2s? = 1 University of Waterloo Faculty of Mathematics Centre for Education in Mathematics and Computing Powers What is the product of three 2s? 2 2 2 = What is the product of five 2s? 2 2 2 2 2 = Grade 6 Math

More information

3.1. RATIONAL EXPRESSIONS

3.1. RATIONAL EXPRESSIONS 3.1. RATIONAL EXPRESSIONS RATIONAL NUMBERS In previous courses you have learned how to operate (do addition, subtraction, multiplication, and division) on rational numbers (fractions). Rational numbers

More information

Calculating the Surface Area of a Cylinder

Calculating the Surface Area of a Cylinder Calculating the Measurement Calculating The Surface Area of a Cylinder PRESENTED BY CANADA GOOSE Mathematics, Grade 8 Introduction Welcome to today s topic Parts of Presentation, questions, Q&A Housekeeping

More information

Chapter 15 Radical Expressions and Equations Notes

Chapter 15 Radical Expressions and Equations Notes Chapter 15 Radical Expressions and Equations Notes 15.1 Introduction to Radical Expressions The symbol is called the square root and is defined as follows: a = c only if c = a Sample Problem: Simplify

More information

Grade 9 Mathematics Unit #1 Number Sense Sub-Unit #1 Rational Numbers. with Integers Divide Integers

Grade 9 Mathematics Unit #1 Number Sense Sub-Unit #1 Rational Numbers. with Integers Divide Integers Page1 Grade 9 Mathematics Unit #1 Number Sense Sub-Unit #1 Rational Numbers Lesson Topic I Can 1 Ordering & Adding Create a number line to order integers Integers Identify integers Add integers 2 Subtracting

More information

Welcome to today s topic Parts of Listen & Learn

Welcome to today s topic Parts of Listen & Learn Number Sense and Algebra Solving Equations: Multiple-step PRESENTED BY ALGESTAR Mathematics, Grade 9 Introduction Welcome to today s topic Parts of Presentation, questions, Q&A Housekeeping NOT the Chat

More information

MULTIPLYING AND DIVIDING INTEGERS Guided Notes

MULTIPLYING AND DIVIDING INTEGERS Guided Notes Notes Name: Date: Period: MULTIPLYING AND DIVIDING INTEGERS Guided Notes Target Objective 1: Multiply, and divide integers Target Objective 2: Describe situations involving arithmetic operations with integers

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

2 is the BASE 5 is the EXPONENT. Power Repeated Standard Multiplication. To evaluate a power means to find the answer in standard form.

2 is the BASE 5 is the EXPONENT. Power Repeated Standard Multiplication. To evaluate a power means to find the answer in standard form. Grade 9 Mathematics Unit : Powers and Exponent Rules Sec.1 What is a Power 5 is the BASE 5 is the EXPONENT The entire 5 is called a POWER. 5 = written as repeated multiplication. 5 = 3 written in standard

More information

The wavelength of infrared light is meters. The digits 3 and 7 are important but all the zeros are just place holders.

The wavelength of infrared light is meters. The digits 3 and 7 are important but all the zeros are just place holders. Section 6 2A: A common use of positive and negative exponents is writing numbers in scientific notation. In astronomy, the distance between 2 objects can be very large and the numbers often contain many

More information

Subtracting Negative Integers

Subtracting Negative Integers Subtracting Negative Integers Notes: Comparison of CST questions to the skill of subtracting negative integers. 5 th Grade/65 NS2.1 Add, subtract, multiply and divide with decimals; add with negative integers;

More information

2.5 Zeros of a Polynomial Functions

2.5 Zeros of a Polynomial Functions .5 Zeros of a Polynomial Functions Section.5 Notes Page 1 The first rule we will talk about is Descartes Rule of Signs, which can be used to determine the possible times a graph crosses the x-axis and

More information

COGNITIVE TUTOR ALGEBRA

COGNITIVE TUTOR ALGEBRA COGNITIVE TUTOR ALGEBRA Numbers and Operations Standard: Understands and applies concepts of numbers and operations Power 1: Understands numbers, ways of representing numbers, relationships among numbers,

More information

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 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

More information

First Degree Equations First degree equations contain variable terms to the first power and constants.

First Degree Equations First degree equations contain variable terms to the first power and constants. Section 4 7: Solving 2nd Degree Equations First Degree Equations First degree equations contain variable terms to the first power and constants. 2x 6 = 14 2x + 3 = 4x 15 First Degree Equations are solved

More information

Math 8 PRACTICE TEST - Integers

Math 8 PRACTICE TEST - Integers Name: Date: Math 8 PRACTICE TEST Integers Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Which expression has the same product as 2(3)? a. 2( 3) c. 2(

More information

CONNECT: Powers and logs POWERS, INDICES, EXPONENTS, LOGARITHMS THEY ARE ALL THE SAME!

CONNECT: Powers and logs POWERS, INDICES, EXPONENTS, LOGARITHMS THEY ARE ALL THE SAME! CONNECT: Powers and logs POWERS, INDICES, EXPONENTS, LOGARITHMS THEY ARE ALL THE SAME! You may have come across the terms powers, indices, exponents and logarithms. But what do they mean? The terms power(s),

More information

Project 4: Simplifying Expressions with Radicals

Project 4: Simplifying Expressions with Radicals Project 4: Simplifying Expressions with Radicals Defintion A radical, which we symbolize with the sign, is just the opposite of an exponent. In this class, the only radical we will focus on is square roots,

More information

Algebra 1A and 1B Summer Packet

Algebra 1A and 1B Summer Packet Algebra 1A and 1B Summer Packet Name: Calculators are not allowed on the summer math packet. This packet is due the first week of school and will be counted as a grade. You will also be tested over the

More information

About Singapore Math. Fewer Topics; More Depth. Start with the Concrete. vii

About Singapore Math. Fewer Topics; More Depth. Start with the Concrete. vii About Singapore MATH About Singapore Math This math course is based on the textbook series Math in Focus, which was developed using the principles of the highly successful Singapore math program. Singapore

More information

Introduce Decimals with an Art Project Criteria Charts, Rubrics, Standards By Susan Ferdman

Introduce Decimals with an Art Project Criteria Charts, Rubrics, Standards By Susan Ferdman Introduce Decimals with an Art Project Criteria Charts, Rubrics, Standards By Susan Ferdman hundredths tenths ones tens Decimal Art An Introduction to Decimals Directions: Part 1: Coloring Have children

More information

Mth 95 Module 2 Spring 2014

Mth 95 Module 2 Spring 2014 Mth 95 Module Spring 014 Section 5.3 Polynomials and Polynomial Functions Vocabulary of Polynomials A term is a number, a variable, or a product of numbers and variables raised to powers. Terms in an expression

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

Property: Rule: Example:

Property: Rule: Example: Math 1 Unit 2, Lesson 4: Properties of Exponents Property: Rule: Example: Zero as an Exponent: a 0 = 1, this says that anything raised to the zero power is 1. Negative Exponent: Multiplying Powers with

More information

Calculating the Area of a Trapezoid. Listen and Learn PRESENTED BY CANADA GOOSE Mathematics, Grade 8

Calculating the Area of a Trapezoid. Listen and Learn PRESENTED BY CANADA GOOSE Mathematics, Grade 8 Calculating the Measurement Calculating the Area of a Trapezoid Listen and Learn PRESENTED BY CANADA GOOSE Mathematics, Grade 8 Introduction Welcome to today s topic Parts of tutorial Presentation, questions,

More information

Grade 6 Math Circles. Exponents

Grade 6 Math Circles. Exponents Faculty of Mathematics Waterloo, Ontario N2L 3G1 Centre for Education in Mathematics and Computing Grade 6 Math Circles November 4/5, 2014 Exponents Quick Warm-up Evaluate the following: 1. 4 + 4 + 4 +

More information

1.3 Order of Operations

1.3 Order of Operations 1.3 Order of Operations As it turns out, there are more than just 4 basic operations. There are five. The fifth basic operation is that of repeated multiplication. We call these exponents. There is a bit

More information

Integration Unit 5 Quadratic Toolbox 1: Working with Square Roots. Using your examples above, answer the following:

Integration Unit 5 Quadratic Toolbox 1: Working with Square Roots. Using your examples above, answer the following: Integration Unit 5 Quadratic Toolbox 1: Working with Square Roots Name Period Objective 1: Understanding Square roots Defining a SQUARE ROOT: Square roots are like a division problem but both factors must

More information

Solving Equations with Integers

Solving Equations with Integers Solving Equations with Integers Properties for solving equations: Addition property - the same number can be added to each side of an equation without changing the equation Subtraction property - the same

More information

1.6 The Order of Operations

1.6 The Order of Operations 1.6 The Order of Operations Contents: Operations Grouping Symbols The Order of Operations Exponents and Negative Numbers Negative Square Roots Square Root of a Negative Number Order of Operations and Negative

More information

Summer Mathematics Packet Say Hello to Algebra 2. For Students Entering Algebra 2

Summer Mathematics Packet Say Hello to Algebra 2. For Students Entering Algebra 2 Summer Math Packet Student Name: Say Hello to Algebra 2 For Students Entering Algebra 2 This summer math booklet was developed to provide students in middle school an opportunity to review grade level

More information

Variable. 1.1 Order of Operations. August 17, evaluating expressions ink.notebook. Standards. letter or symbol used to represent a number

Variable. 1.1 Order of Operations. August 17, evaluating expressions ink.notebook. Standards. letter or symbol used to represent a number 1.1 evaluating expressions ink.notebook page 8 Unit 1 Basic Equations and Inequalities 1.1 Order of Operations page 9 Square Cube Variable Variable Expression Exponent page 10 page 11 1 Lesson Objectives

More information

Curriculum Guide for the Academic School Year

Curriculum Guide for the Academic School Year MATH 7 Curriculum Guide for the Academic School Year 7 TH GRADE MATH CORTEZ TRAK 2014-2015 Link to: Math 7 Curriculum Framework Cortez Model covers boxed items Days Date SOL Description Cortez 14 8/18

More information

Linear Equations and Inequalities

Linear Equations and Inequalities Linear Equations and Inequalities Section 1.1 Prof. Wodarz Math 109 - Fall 2008 Contents 1 Linear Equations 2 1.1 Standard Form of a Linear Equation................ 2 1.2 Solving Linear Equations......................

More information

parent ROADMAP MATHEMATICS SUPPORTING YOUR CHILD IN GRADE FIVE

parent ROADMAP MATHEMATICS SUPPORTING YOUR CHILD IN GRADE FIVE TM parent ROADMAP MATHEMATICS SUPPORTING YOUR CHILD IN GRADE FIVE 5 America s schools are working to provide higher quality instruction than ever before. The way we taught students in the past simply does

More information

Solving Rational Equations

Solving Rational Equations Lesson M Lesson : Student Outcomes Students solve rational equations, monitoring for the creation of extraneous solutions. Lesson Notes In the preceding lessons, students learned to add, subtract, multiply,

More information

Common Core Standards for Fantasy Sports Worksheets. Page 1

Common Core Standards for Fantasy Sports Worksheets. Page 1 Scoring Systems Concept(s) Integers adding and subtracting integers; multiplying integers Fractions adding and subtracting fractions; multiplying fractions with whole numbers Decimals adding and subtracting

More information

Conceptual Understanding of Operations of Integers

Conceptual Understanding of Operations of Integers Grade 7 Mathematics, Quarter 2, Unit 2.1 Conceptual Understanding of Operations of Integers Overview Number of instructional days: 10 (1 day = 45 60 minutes) Content to be learned Demonstrate conceptual

More information

Practice Math Placement Exam

Practice Math Placement Exam Practice Math Placement Exam The following are problems like those on the Mansfield University Math Placement Exam. You must pass this test or take MA 0090 before taking any mathematics courses. 1. What

More information

No Solution Equations Let s look at the following equation: 2 +3=2 +7

No Solution Equations Let s look at the following equation: 2 +3=2 +7 5.4 Solving Equations with Infinite or No Solutions So far we have looked at equations where there is exactly one solution. It is possible to have more than solution in other types of equations that are

More information

Eureka Math Tips for Parents

Eureka Math Tips for Parents Eureka Math Tips for Parents Place Value and Decimal Fractions In this first module of, we will extend 4 th grade place value work to multi-digit numbers with decimals to the thousandths place. Students

More information

Isolate the absolute value expression. Add 5 to both sides and then divide by 2.

Isolate the absolute value expression. Add 5 to both sides and then divide by 2. 11 of 21 8/14/2014 2:35 PM of a variable expression. You can use the definition of absolute value to solve absolute value equations algebraically. Since then the equation ax + b = c is equivalent to (ax

More information

Section 1.5 Exponents, Square Roots, and the Order of Operations

Section 1.5 Exponents, Square Roots, and the Order of Operations Section 1.5 Exponents, Square Roots, and the Order of Operations Objectives In this section, you will learn to: To successfully complete this section, you need to understand: Identify perfect squares.

More information

Roots of Real Numbers

Roots of Real Numbers Roots of Real Numbers Math 97 Supplement LEARNING OBJECTIVES. Calculate the exact and approximate value of the square root of a real number.. Calculate the exact and approximate value of the cube root

More information

UNIT TWO POLYNOMIALS MATH 421A 22 HOURS. Revised May 2, 00

UNIT TWO POLYNOMIALS MATH 421A 22 HOURS. Revised May 2, 00 UNIT TWO POLYNOMIALS MATH 421A 22 HOURS Revised May 2, 00 38 UNIT 2: POLYNOMIALS Previous Knowledge: With the implementation of APEF Mathematics at the intermediate level, students should be able to: -

More information

5.1 Radical Notation and Rational Exponents

5.1 Radical Notation and Rational Exponents Section 5.1 Radical Notation and Rational Exponents 1 5.1 Radical Notation and Rational Exponents We now review how exponents can be used to describe not only powers (such as 5 2 and 2 3 ), but also roots

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

Example 1: If the sum of seven and a number is multiplied by four, the result is 76. Find the number.

Example 1: If the sum of seven and a number is multiplied by four, the result is 76. Find the number. EXERCISE SET 2.3 DUE DATE: STUDENT INSTRUCTOR: 2.3 MORE APPLICATIONS OF LINEAR EQUATIONS Here are a couple of reminders you may need for this section: perimeter is the distance around the outside of the

More information

Polynomials can be added or subtracted simply by adding or subtracting the corresponding terms, e.g., if

Polynomials can be added or subtracted simply by adding or subtracting the corresponding terms, e.g., if 1. Polynomials 1.1. Definitions A polynomial in x is an expression obtained by taking powers of x, multiplying them by constants, and adding them. It can be written in the form c 0 x n + c 1 x n 1 + c

More information

2. Simplify. College Algebra Student Self-Assessment of Mathematics (SSAM) Answer Key. Use the distributive property to remove the parentheses

2. Simplify. College Algebra Student Self-Assessment of Mathematics (SSAM) Answer Key. Use the distributive property to remove the parentheses College Algebra Student Self-Assessment of Mathematics (SSAM) Answer Key 1. Multiply 2 3 5 1 Use the distributive property to remove the parentheses 2 3 5 1 2 25 21 3 35 31 2 10 2 3 15 3 2 13 2 15 3 2

More information

Instructions for SA Completion

Instructions for SA Completion Instructions for SA Completion 1- Take notes on these Pythagorean Theorem Course Materials then do and check the associated practice questions for an explanation on how to do the Pythagorean Theorem Substantive

More information

Repton Manor Primary School. Maths Targets

Repton Manor Primary School. Maths Targets Repton Manor Primary School Maths Targets Which target is for my child? Every child at Repton Manor Primary School will have a Maths Target, which they will keep in their Maths Book. The teachers work

More information

CONNECT: Algebra. 3x = 20 5 REARRANGING FORMULAE

CONNECT: Algebra. 3x = 20 5 REARRANGING FORMULAE CONNECT: Algebra REARRANGING FORMULAE Before you read this resource, you need to be familiar with how to solve equations. If you are not sure of the techniques involved in that topic, please refer to CONNECT:

More information

Variable Dilemma G + G + G = D J + E = J G 2 = D B + G = D F - B = C I / H = A (H > A) A x C = A

Variable Dilemma G + G + G = D J + E = J G 2 = D B + G = D F - B = C I / H = A (H > A) A x C = A Each letter in the equations below stand for a different number (0-9). Look at each equation carefully. Think about the knowledge you have of how numbers work. Find the values of each letter (A - J). You

More information

Solving One Step Equations Guided Notes

Solving One Step Equations Guided Notes CW/HW Pre-Algebra Name: Date: Period: Solving One Step Equations Guided Notes I. Equations A. Vocabulary An _equation is a mathematical sentence with an equal sign. The following are all considered to

More information

All you have to do is THINK!

All you have to do is THINK! Mathematician s Notes BE A MATHEMATICIAN! All you have to do is THINK! Imagination is more important than knowledge. Albert Einstein We only think when confronted with a problem. John Dewey It s not that

More information

parent ROADMAP MATHEMATICS SUPPORTING YOUR CHILD IN GRADE TWO

parent ROADMAP MATHEMATICS SUPPORTING YOUR CHILD IN GRADE TWO TM parent ROADMAP MATHEMATICS SUPPORTING YOUR CHILD IN GRADE TWO 2 America s schools are working to provide higher quality instruction than ever before. The way we taught students in the past simply does

More information

Anticipatory Set: Students should know how to add, subtract, multiply and divide positive and negative integers.

Anticipatory Set: Students should know how to add, subtract, multiply and divide positive and negative integers. Lesson Plan Subject: Pre Algebra The Distributive Property Grade Level: 9th Grade Length: 20 minute session Common Core Standards: CCSS.Math.Content.6.EE.A.3 Apply the properties of operations to generate

More information

Integers are positive and negative whole numbers, that is they are; {... 3, 2, 1,0,1,2,3...}. The dots mean they continue in that pattern.

Integers are positive and negative whole numbers, that is they are; {... 3, 2, 1,0,1,2,3...}. The dots mean they continue in that pattern. INTEGERS Integers are positive and negative whole numbers, that is they are; {... 3, 2, 1,0,1,2,3...}. The dots mean they continue in that pattern. Like all number sets, integers were invented to describe

More information

Rules for Exponents and the Reasons for Them

Rules for Exponents and the Reasons for Them Print this page Chapter 6 Rules for Exponents and the Reasons for Them 6.1 INTEGER POWERS AND THE EXPONENT RULES Repeated addition can be expressed as a product. For example, Similarly, repeated multiplication

More information

West Windsor-Plainsboro Regional School District Algebra I Part 2 Grades 9-12

West Windsor-Plainsboro Regional School District Algebra I Part 2 Grades 9-12 West Windsor-Plainsboro Regional School District Algebra I Part 2 Grades 9-12 Unit 1: Polynomials and Factoring Course & Grade Level: Algebra I Part 2, 9 12 This unit involves knowledge and skills relative

More information

Math Help and Additional Practice Websites

Math Help and Additional Practice Websites Name: Math Help and Additional Practice Websites http://www.coolmath.com www.aplusmath.com/ http://www.mathplayground.com/games.html http://www.ixl.com/math/grade-7 http://www.softschools.com/grades/6th_and_7th.jsp

More information

Algebra. Indiana Standards 1 ST 6 WEEKS

Algebra. Indiana Standards 1 ST 6 WEEKS Chapter 1 Lessons Indiana Standards - 1-1 Variables and Expressions - 1-2 Order of Operations and Evaluating Expressions - 1-3 Real Numbers and the Number Line - 1-4 Properties of Real Numbers - 1-5 Adding

More information

27 = 3 Example: 1 = 1

27 = 3 Example: 1 = 1 Radicals: Definition: A number r is a square root of another number a if r = a. is a square root of 9 since = 9 is also a square root of 9, since ) = 9 Notice that each positive number a has two square

More information

equals equals equals equals

equals equals equals equals Addition of Integers Rules Same Sign ---------------- Add --------------- Keep the Sign Different Signs -------- Subtract ------- Take the sign of the integer with the larger absolute value plus plus plus

More information

Mathematics Chapter 8 and 10 Test Summary 10M2

Mathematics Chapter 8 and 10 Test Summary 10M2 Quadratic expressions and equations Expressions such as x 2 + 3x, a 2 7 and 4t 2 9t + 5 are called quadratic expressions because the highest power of the variable is 2. The word comes from the Latin quadratus

More information

Inequalities (Year 9)

Inequalities (Year 9) Inequalities (Year 9) Contents What is an inequality? Displaying inequalities on a number line Solving inequalities 4 Showing Inequalities on a graph 4 What is an inequality? An inequality is a mathematical

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 Journal HMH Mega Math. itools Number

Math Journal HMH Mega Math. itools Number Lesson 1.1 Algebra Number Patterns CC.3.OA.9 Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. Identify and

More information

(- 7) + 4 = (-9) = - 3 (- 3) + 7 = ( -3) = 2

(- 7) + 4 = (-9) = - 3 (- 3) + 7 = ( -3) = 2 WORKING WITH INTEGERS: 1. Adding Rules: Positive + Positive = Positive: 5 + 4 = 9 Negative + Negative = Negative: (- 7) + (- 2) = - 9 The sum of a negative and a positive number: First subtract: The answer

More information

Grade 4 Mathematics Patterns, Relations, and Functions: Lesson 3

Grade 4 Mathematics Patterns, Relations, and Functions: Lesson 3 Grade 4 Mathematics Patterns, Relations, and Functions: Lesson 3 Read aloud to the students the material that is printed in boldface type inside the boxes. Information in regular type inside the boxes

More information

Florida Math 0028. Correlation of the ALEKS course Florida Math 0028 to the Florida Mathematics Competencies - Upper

Florida Math 0028. Correlation of the ALEKS course Florida Math 0028 to the Florida Mathematics Competencies - Upper Florida Math 0028 Correlation of the ALEKS course Florida Math 0028 to the Florida Mathematics Competencies - Upper Exponents & Polynomials MDECU1: Applies the order of operations to evaluate algebraic

More information

Paramedic Program Pre-Admission Mathematics Test Study Guide

Paramedic Program Pre-Admission Mathematics Test Study Guide Paramedic Program Pre-Admission Mathematics Test Study Guide 05/13 1 Table of Contents Page 1 Page 2 Page 3 Page 4 Page 5 Page 6 Page 7 Page 8 Page 9 Page 10 Page 11 Page 12 Page 13 Page 14 Page 15 Page

More information

4. Changing the Subject of a Formula

4. Changing the Subject of a Formula 4. Changing the Subject of a Formula This booklet belongs to aquinas college maths dept. 2010 1 Aims and Objectives Changing the subject of a formula is the same process as solving equations, in that we

More information

Lesson 4: Convert Fractions, Review Order of Operations

Lesson 4: Convert Fractions, Review Order of Operations Lesson 4: Convert Fractions, Review Order of Operations LESSON 4: Convert Fractions, Do Order of Operations Weekly Focus: fractions, decimals, percent, order of operations Weekly Skill: convert, compute

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

Using Patterns of Integer Exponents

Using Patterns of Integer Exponents 8.EE.1 Know and apply the properties of integer exponents to generate equivalent numerical expressions. How can you develop and use the properties of integer exponents? The table below shows powers of

More information

Chapter 4 -- Decimals

Chapter 4 -- Decimals Chapter 4 -- Decimals $34.99 decimal notation ex. The cost of an object. ex. The balance of your bank account ex The amount owed ex. The tax on a purchase. Just like Whole Numbers Place Value - 1.23456789

More information

Standards-Based Progress Mathematics. Progress in Mathematics

Standards-Based Progress Mathematics. Progress in Mathematics SADLIER Standards-Based Progress Mathematics Aligned to SADLIER Progress in Mathematics Grade 5 Contents Chapter 1 Place Value, Addition, and Subtraction......... 2 Chapter 2 Multiplication....................................

More information

Direct Translation is the process of translating English words and phrases into numbers, mathematical symbols, expressions, and equations.

Direct Translation is the process of translating English words and phrases into numbers, mathematical symbols, expressions, and equations. Section 1 Mathematics has a language all its own. In order to be able to solve many types of word problems, we need to be able to translate the English Language into Math Language. is the process of translating

More information

Solving Logarithmic Equations

Solving Logarithmic Equations Solving Logarithmic Equations Deciding How to Solve Logarithmic Equation When asked to solve a logarithmic equation such as log (x + 7) = or log (7x + ) = log (x + 9), the first thing we need to decide

More information

Training Manual. Pre-Employment Math. Version 1.1

Training Manual. Pre-Employment Math. Version 1.1 Training Manual Pre-Employment Math Version 1.1 Created April 2012 1 Table of Contents Item # Training Topic Page # 1. Operations with Whole Numbers... 3 2. Operations with Decimal Numbers... 4 3. Operations

More information

1 Computation Students will practice multiplication, division, addition, and subtraction. Order of operation will also be reviewed.

1 Computation Students will practice multiplication, division, addition, and subtraction. Order of operation will also be reviewed. Fairfax Collegiate 703 481-3080 www.fairfaxcollegiate.com FCS FAIRFAX COLLEGIATE Intro to Pre-Algebra 6-8 Syllabus SUMMER PROGRAM Course Goals 1 Solidify Previous Knowledge Students will solidify previous

More information

Florida Math 0018. Correlation of the ALEKS course Florida Math 0018 to the Florida Mathematics Competencies - Lower

Florida Math 0018. Correlation of the ALEKS course Florida Math 0018 to the Florida Mathematics Competencies - Lower Florida Math 0018 Correlation of the ALEKS course Florida Math 0018 to the Florida Mathematics Competencies - Lower Whole Numbers MDECL1: Perform operations on whole numbers (with applications, including

More information

Unit 7 The Number System: Multiplying and Dividing Integers

Unit 7 The Number System: Multiplying and Dividing Integers Unit 7 The Number System: Multiplying and Dividing Integers Introduction In this unit, students will multiply and divide integers, and multiply positive and negative fractions by integers. Students will

More information

2.3. Finding polynomial functions. An Introduction:

2.3. Finding polynomial functions. An Introduction: 2.3. Finding polynomial functions. An Introduction: As is usually the case when learning a new concept in mathematics, the new concept is the reverse of the previous one. Remember how you first learned

More information

Math 1111 Journal Entries Unit I (Sections , )

Math 1111 Journal Entries Unit I (Sections , ) Math 1111 Journal Entries Unit I (Sections 1.1-1.2, 1.4-1.6) Name Respond to each item, giving sufficient detail. You may handwrite your responses with neat penmanship. Your portfolio should be a collection

More information

TI-86 Graphing Calculator Keystroke Guide

TI-86 Graphing Calculator Keystroke Guide TI-86 Graphing Calculator Keystroke Guide In your textbook you will notice that on some pages a key-shaped icon appears next to a brief description of a feature on your graphing calculator. In this guide

More information

STRAND B: Number Theory. UNIT B2 Number Classification and Bases: Text * * * * * Contents. Section. B2.1 Number Classification. B2.

STRAND B: Number Theory. UNIT B2 Number Classification and Bases: Text * * * * * Contents. Section. B2.1 Number Classification. B2. STRAND B: Number Theory B2 Number Classification and Bases Text Contents * * * * * Section B2. Number Classification B2.2 Binary Numbers B2.3 Adding and Subtracting Binary Numbers B2.4 Multiplying Binary

More information

Factoring Numbers. Factoring numbers means that we break numbers down into the other whole numbers that multiply

Factoring Numbers. Factoring numbers means that we break numbers down into the other whole numbers that multiply Factoring Numbers Author/Creation: Pamela Dorr, September 2010. Summary: Describes two methods to help students determine the factors of a number. Learning Objectives: To define prime number and composite

More information