3 Chapter Whole Numbers and Their Operations

Slides:



Advertisements
Similar presentations
Division Student Sample. What does it mean to divide? Division can be used to find how many are in each group when an amount is shared equally. This is.
Advertisements

Chapter 2 Polynomial and Rational Functions Copyright © 2014, 2010, 2007 Pearson Education, Inc Dividing Polynomials: Remainder and Factor Theorems.
Division Algorithms By: Jessica Nastasi.
CHAPTER 5 Decimal Notation Slide 2Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 5.1Decimal Notation, Order, and Rounding 5.2Addition and Subtraction.
Whole numbers: How to Dissect and Solve word problems
EXPONENTS ORDER OF OPERATIONS MULTIPLYING / DIVIDING POWER OF A POWER POWER OF A PRODUCT POWER OF A QUOTIENT NEGATIVE EXPONENTS.
Chapter One PROBLEM SOLVING WITH MATH Copyright © 2014 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/Irwin.
Whole Numbers How do we use whole numbers to solve real-life problems?
Division Student Sample. What does it mean to divide? Division can be used to find how many are in each group when an amount is shared equally. This is.
division algorithm Before we study divisibility, we must remember the division algorithm. r dividend = (divisor ⋅ quotient) + remainder.
Chapter 1 Whole Numbers; How to Dissect and Solve Problems McGraw-Hill/Irwin Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved.
1. Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Polynomials CHAPTER 5.1Exponents and Scientific Notation 5.2Introduction.
Chapter 2.2 Scientific Notation. Expresses numbers in two parts: A number between 1 and 10 Ten raised to a power Examples: 2.32 x x
Date: _____________Math 9/9H Place Value Which position is a digit of a number occupying? E.g.: is in the millions place 9 is in the hundred.
© 2010 Pearson Prentice Hall. All rights reserved. CHAPTER 4 Number Representation and Calculation.
Chapter Whole Numbers and Their Operations 3 3 Copyright © 2013, 2010, and 2007, Pearson Education, Inc.
Chapter1, sense and Algebraic thinking. By Joseph.
Decimals.
Exponents and Polynomials
Chapter 3 Whole Numbers Section 3.6 Algorithms for Whole-Number Multiplication and Division.
A Multiplication Algorithm
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Chapter 4 Decimals.
Lesson 5-6 Example Find 312 ÷ 8. Use short division. Step 1Look at the first digit in the dividend. Since the divisor is greater than the first digit,
Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. Chapter 2 Fractions.
1 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 5-1 Polynomials and Polynomial Functions Chapter 5.
Ch 11.5 Dividing Polynomials
5. Divide 4723 by 5. Long Division: Steps in Dividing Whole Numbers Example: 4716  5 STEPS 1. The dividend is The divisor is 5. Write.
Copyright © 2010 Pearson Education, Inc. All rights reserved Sec
Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. Chapter 2 Fractions.
Objectives Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Dividing Whole Numbers; Square Roots; Solving Equations 1. Divide.
Partial Quotient Method In this division algorithm the children record on the right side of the problem. The first thing they do is divide. They ask themselves.
Chapter 1 Polynomial and Rational Functions Copyright © 2014, 2010, 2007 Pearson Education, Inc Dividing Polynomials; Remainder and Factor Theorems.
Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Real Zeros of Polynomial Functions ♦ Divide Polynomials ♦ Understand the.
Addition, Subtraction, Multiplication, Division by a whole number, and Division by a decimal.
Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley.
Unit 1 Review Order of Operations and Whole Numbers.
Warm-Up Divide 1.) 560 ÷ 8 = 2.) 105 ÷ 3 =. Essential question: What are the steps to divide whole numbers? Name date period Long Division Quotient: The.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Chapter 1 Real Numbers and Introduction to Algebra.
Dividing Review SWBAT use division to find quotients; use divisibility rules to predict remainders; estimate quotients; divide whole numbers in thousand.
Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Chapter 1 Whole Numbers.
Objectives Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Dividing Fractions, Mixed Numbers, and Rational Expressions 1.
Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. Chapter 3 Decimals.
Slide Copyright © 2009 Pearson Education, Inc. 5.1 Number Theory.
Chapter 1 Whole Numbers Digit – number from 0-9
The Baker Math Assessment Task 4 th Grade The task challenges a student to demonstrate understanding of the concepts involved in multiplication and division.
CHAPTER 3 Whole Numbers Slide 2Copyright 2011 Pearson Education, Inc. 3.1Least Common Multiples 3.2Addition and Applications 3.3Subtraction, Order, and.
Copyright © Cengage Learning. All rights reserved. Functions 1 Basic Concepts.
STUDY LIST.
Strategies Number – addition, subtraction, multiplication and division
CBA Math Review October 7th.
Number Talks: Building Fluency with Division
3 Chapter Numeration Systems and Whole Number Operations
Long Division With 2 Digit Divisor
Year 6 Autumn Block 2 Four Operations NCLO: To use formal written methods to add and subtract numbers.
3 Chapter Numeration Systems and Whole Number Operations
Division Page 87 – 119.
Exponents, Polynomials, and Polynomial Functions
Computation in Other Bases
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
3 Chapter Whole Numbers and Their Operations
Problems, understanding and solutions
Additional Whole Number Operations
Decimal A number that is written in a system based on multiples of 10. Examples: ,
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
3 Chapter Whole Numbers and Their Operations
3 Chapter Whole Numbers and Their Operations
Division Dividing 3 and 4 Digits by 2 Digits.
7 Chapter Decimals: Rational Numbers and Percent
Unit 1: Number System Fluency
Presentation transcript:

3 Chapter Whole Numbers and Their Operations Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

3-4 Algorithms for Whole-Number Multiplication and Division Multiplication Algorithms Division Algorithms Division by a Two-Digit Divisor Multiplication and Division in Different Bases Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Algorithms for Whole-Number Multiplication and Division They select appropriate methods and apply them accurately to estimate products or calculate them mentally, depending on the context and numbers involved. They develop fluency with efficient procedures, including the standard algorithm, for multiplying whole numbers, understand why the procedures work (on the basis of place value and properties of operations), and use them to solve problems. NCTM grade 4 Focal Points, p. 16 Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Properties of Exponents Definition of an for whole numbers If a, the base and n, the exponent, are whole numbers and n  0, then Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Properties of Exponents Theorem 3-9 For any whole number a and natural numbers m and n: Theorem 3-10 Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Properties of Exponents Theorem 3-11 For any whole number a and natural numbers m and n: Theorem 3-12 If a, m, and n are natural numbers with m > n, then Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Copyright © 2013, 2010, and 2007, Pearson Education, Inc. Example 3-4 Write each of the following with only one exponent. a. b. a. b. Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Multiplication Algorithms Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Multiplication Algorithms Multiplication by 10n To multiply by 10, replace each piece with a base-ten piece that represents the next higher power of 10. Replace each unit with a long, and replace each long with a flat. Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Multiplication Algorithms Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Multiplication Algorithms Multiplication using expanded addition Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Multiplication Algorithms Multiplication with Two-Digit Factors Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Multiplication Algorithms Lattice Multiplication Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Copyright © 2013, 2010, and 2007, Pearson Education, Inc. Division Algorithms Using Repeated Subtraction to Develop the Standard Division Algorithm or Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Copyright © 2013, 2010, and 2007, Pearson Education, Inc. Division Algorithms or Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Copyright © 2013, 2010, and 2007, Pearson Education, Inc. Division Algorithms Using Base-Ten Blocks to Develop the Standard Division Algorithm 1. Represent 726 with base-ten blocks. Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Copyright © 2013, 2010, and 2007, Pearson Education, Inc. 2. Determine how many sets of 6 flats (hundreds) there are. There is one set of 6 flats with 1 flat, 2 longs, and 6 units left over. Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Copyright © 2013, 2010, and 2007, Pearson Education, Inc. 3. Convert the one leftover flat to 10 longs. Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Copyright © 2013, 2010, and 2007, Pearson Education, Inc. 4. Determine how many sets of 6 longs there are in the 12 longs. There are 2 set of 6 longs and 6 units left over. Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Copyright © 2013, 2010, and 2007, Pearson Education, Inc. 5. Now determine how many sets of 6 units there are. There is 1 set of 6 units with no units left over. Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Division Algorithms Short Division Decide where to start. Divide the hundreds. Write the remainder by the tens. Divide the tens. Write the remainder by the ones. Divide the ones. Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Division by a Two-Digit Divisor Four step method: 1. Estimate 2. Multiply 3. Subtract 4. Compare (check) Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Division by a Two-Digit Divisor Divide 1. Estimate the quotient. The quotient is between 10 and 100. 2. Find the number of tens in the quotient. Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Copyright © 2013, 2010, and 2007, Pearson Education, Inc. 3. Find the number of units in the quotient. 4. Check. 32 · 81 + 26 = 2618 Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Multiplication and Division in Different Bases Base-Five Multiplication Table Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Multiplication and Division in Different Bases Multiply 21five · 3five. Fives Ones 2 1  3 → → → Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Multiplication and Division in Different Bases Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Copyright © 2013, 2010, and 2007, Pearson Education, Inc. Example 3-4a Multiply: Copyright © 2013, 2010, and 2007, Pearson Education, Inc.