# Professor Weissman s Algebra Classroom

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 Introduction To Whole Numbers Unit # Inside this issue: Sets 1 Number Zero 1 Welcome To My Class 2 Inequality Symbols 3 Number Line 3 Read Number 4 Round Numbers 4 Standard & Expanded 4 Rounding Numbers 5 Roman Numerals 5 In The News 6 Professor s Class 7-9 Exercises 10 Fun Page 11 Solutions Page 12 Professor Weissman s Algebra Classroom Martin Weissman, Tamara Farber, Jonathan S. Weissman, & Keith Monse What are Literacy & Numeracy? Literacy: is the ability to read and write. Numeracy: is the ability to use and understand numbers. What is a Set? All of us save things. Perhaps, they re CD s or baseball cards or photos. Whatever they are we usually put them in something, like a box, or an envelope. What do Mathematicians collect? Just about anything you would collect and more. And what do they put them in? They list them, separated by commas and put them between braces. Braces look like curly parentheses. Then they give the set a nickname, usually using a capital letter. For example, a set of symbols used in Mathematics might be called S and look like this: S={ +, -, /,, <, >, ±, } What is the Set of Letters? Letters are the building blocks of words. Words become sentences, paragraphs. Before you know it you have stories, essays, articles. All words are made up of the 26 letters of the alphabet. We ll call the set L={a,b,c,d,e,f,g,h,I,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z} What Are the Counting Numbers? How many different types of numbers do you know? Surely, you ve heard of odd and even numbers. Fractions and decimals are other types. The most basic reason for numbers is to count. What is The Set of Natural Numbers? What is the Set of Digits? Digits are the building blocks of numbers. We will see how numbers become expressions then equations. All numbers are made up of just 10 digits. We ll called them D and list them in set notation using braces, which look like curly parentheses. D={0,1,2,3,4,5,6,7,8,9} And when we count, for example, the number of students in the class we start with the number 1. So what should we call the numbers: 1,2,3,4,5,6 and so on? Why not, the counting numbers.? Mathematicians have another name for the Counting Numbers. They call them the Natural Numbers. We ll call the set of Natural Numbers N The 3 dots at the end are called ellipses and mean and so on. The set is said to be infinite. N={ 1,2,3,4,5,6,7,8,9,10,11, }

2 Page 2 Professor Weissman s Algebra Classroom

3 Page 3 Professor Weissman s Algebra Classroom Why Is The Number Zero Important? At Blastoff, the countdown sounds like 5,4,3,2,1,0 blastoff! Is zero a number? Absolutely yes! Without the number zero it would be difficult to do much of Mathematics. Probably the most important use of zero is as a placeholder. The number 407 would just not be the same without the zero in the middle. What Are The Whole Numbers? Let s add zero to the Natural Numbers. Our collection of numbers is changed. It needs a new name. We call it the set of whole numbers. Let s simply call it W. Here s what it looks like: W={0,1,2,3,4,5,6,7,8,9,10,11, } What are Symbols of Inequality? When 2 numbers are not equal we could use the is not equal symbol between them. 4 6 or 6 4 Better yet we can use two other symbols that compare the numbers. These are the is less than or < symbol and the is more than or > sym- What Is A Number Line? 4 < 6 6 > 4 bol. Note that the < symbol looks like the letter L the first letter of the word Less. Another point worth noting is that whichever symbol you use always point to the smaller number, just like the tall soldier is always pointing to the small soldier. A thermometer is an every day use of a number line. The Number Line is a very useful tool when we want to show the relative positions of numbers. When comparing 2 numbers, just look at the number line. The number that is more to the left is always smaller than the number that is more to the right. Comparing 3 and 7 we see that 3 is more to the left. So, we say, 3 is less than 7 and we write: 3 < 7 At the same time we can say that 7 is more to the right. That means 7 is more than 3 and we write: 7 > 3 The number line is also useful to show what happens when we add or subtract numbers. Moving the left is like subtracting and moving to the right is like adding. We can Graph or locate the number 5 on the number line with a black circle. What number is 2 units to its left? It s 3. That shows the subtraction: 5 2 = 3 Again, locate the number 5 on the number line. What number is 2 units to the right? That would be 7. This illustrates the addition problem: = 7

4 Introduction To Whole Numbers Page 4 How Do We Read Numbers? The proper way to read numbers is to emphasize place values. Often, when people are in a rush a number is not read properly. \$ The number 768 read (or written) properly is: Seven hundred sixty-eight. Note the hyphen or dash between the words sixty and eight. What Is Rounding? Rounding replaces an exact number with an approximate number. What Is Rounding Numbers Up? The printer that you bought for \$186 is rounded to \$200 to the nearest \$100. On the number line we see that \$186 is closer to \$200. We say that \$186 was rounded UP to \$200 When a number is rounded and he result is LARGER than the original number, we say that it is rounded UP. Numbers between 21 and 99 would have a hyphen. Except, of course, the numbers that end with a zero, such as, 30, 40, 50 and so on. Some mistakes that are made are writing or saying: MISTAKE:Seven sixty-eight (omitting the word hundred) MISTAKE:Seven hundred and sixty-eight (don t use the and word after the wordhundred, we will see later that the AND word is reserved for the decimal. What Is Rounding Numbers Down? \$ 631 You paid \$631 for the computer. When asked how much did it cost? You respond \$600. You just rounded \$631 to the nearest \$100 Using the number line we can visualize why \$631 is rounded to \$600. We see that it is closer to \$600 than to \$700. Why is it closer to \$600? Because the next digit (the 3 in the tens place) is less than 5. When a number is rounded and the result is SMALLER than the original number, we say that it is rounded DOWN. What are Standard & Expanded Forms? The number 777 uses the 7 digit three times. However each 7 represents a different amount and has a different value. 777 is said to be in Standard Form. It s written the way we usually write numbers. If we want to show the different values for each 7 we can change the number to Expanded Form. 777 written in Expanded Form looks like this: Writing a number in Expanded Form emphasizes the column that each digit is in or its Place Value. 700 = 7 x 100 Hundreds 70 = 7 x 10 Tens 7 = 7 x 1 Ones The Continental Divide in the Americas is an imaginary line that divides the flow of water between the Pacific Ocean and Atlantic Ocean. Rain or snow that drains on the east side of the Continental Divide flows toward the Atlantic Ocean while precipitation on the west side drains and flows toward the Pacific Ocean. At the spot where the picture was taken the elevation was 10,424 or ten thousand four hundred twenty-four feet above sea level.

5 Introduction To Whole Numbers Page 5 How Do We Round Whole Numbers? Here s how to round a whole number: #1 Locate the round digit in the place with the value that you want to round to and draw a cutoff line after that digit. #2 Look at the decision digit which is the digit after the cutoff line. #3 If the decision digit is 5,6,7,8 or 9 add one to the round digit. If the decision digit is 0,1,2,3 or 4 leave the round digit unchanged. #3 Replace all digits after the cutoff line with zeros. Rounding 631 to nearest is in the hundred s place. Cutoff after the 6 digit 6 31 The Decision Digit is Since the decision digit < 5, keep the 6 and change digits after cutoff to zeros > 600 Rounding 186 to nearest is in the hundred s place. Cutoff after the 1 digit 1 86 The Decision Digit is Since the decision digit > 4, add one to the round digit Clock face What number is XLI? Note: Always round from the original value, not from a rounded number. The \$149 lawn mower to the nearest \$10 would be \$150. To Round \$149 to the nearest \$100, don t use the \$150. Instead, look at \$149 and round DOWN to \$100. What Are Roman Numerals? The Romans needed numbers for business and commerce. Around the 1st century AD they invented a system that used letters as symbols for numbers. The set of letters used for Roman Numerals looks like this: R={ I, V, X, L, C, M } I= 1 V=5 X=10 L=50 C=100 M=1000 Using just these 6 symbols we can write any number. But, it s not so easy! The easiest way to show how much was to make marks. So, I means 1, II means 2, III means 3. However, four lines seemed like too many. So the Romans decided to use a V as a symbol for 5. Placing I in front of the V (or placing any smaller number in front of any larger number) means subtraction). So IV means 4. Placing I in after the V (or placing any smaller number after any larger number) means addition). So IV means 4. VI means 6, VII means 7, VIII means 8. X means 10. But wait what about 9? Remember? IX means to subtract I from X, leaving 9. Numbers in the teens, twenties and thirties follow the same form as the first set, only with X's indicating the number of tens. So XXXI is 31, and XXIV is 24. L means 50. How should we write 40? If you guessed XL, you're right 40 = 10 subtracted from 50. Also 60, 70, and 80 are LX, LXX and LXXX. C is the symbol for 100. The subtraction rule means 90 is written as XC and the addition rule means CX=110. Like the X's and L's, the C's are tacked on to the beginning of numbers to indicate how many hundreds there are: CCCLXIX is 369. D stands for 500. As you can probably guess by this time, CD means 400. So CDXLVIII is 448. M is 1,000. Can you understand now, why we stopped using Roman Numerals and switched to our present system whose numerals are called Arabic Numerals?

6 Page 6 In The News The Mercedes car in the ad has 8500 miles and costs \$17,375. The original price was \$34,750. Each of the 3 numbers could have been rounded. The most likely rounded number is the 8500 miles. The 2 zeros at the end of the number make it suspect. Maybe it has 8529 miles or 8479 miles. In fact, it could have been rounded from any number between 8450 miles What 2 numbers can you sandwich the mileage of 31,000 for the Ford Freestar? and Round the Being Sold For Price of the Ford Freestar of \$7995 to the nearest: 1. Ten Thousand 2. Thousand Professor Weissman s Algebra Classroom and 8549 miles. We can sandwich 8500 between 8450 and Round the sales price \$17,375 to the nearest: 1. Ten Thousand 2. Thousand 3. Hundred 4. Ten 3. Hundred 4. Ten Use symbols of inequality to show two relations between the sales prices of the two cars. < > Circle The Numbers That Were Probably Rounded

7 Introduction To Whole Numbers Page 7 Professor Weissman Meet His Class For The First Time

8 Page 8 Professor Weissman s Algebra Classroom

9 Introduction To Whole Numbers Page 9

10 Page 10 Professor Weissman s Algebra Classroom Exercise Set 1 1. Graph the number 7 on the number line. 2. On the number line which number is... a. 5 less than 7? b. 3 units to the right of 7? c. 1 more than 7? d. 3 units to the left of 7? 3. What is the correct symbol, > or <, that goes between the two numbers? a. 23 and 32 b. 8 and 0 c. 0 and 5 d. 504 and Write these numbers in words. a. 78 b. 8 c. 561 d. 8,345 e. 7,002 f. 16,800 g. 908 h. 444 i. 165,165 j. 7,654,321 k. 5,004,003 l. 8, Write the numbers in Standard Form. a. seventeen b. seventy c. sixty-six d. five hundred eighty-one e. five hundred one f. one thousand four g. one thousand forty h. seventeen thousand three hundred thirty-four i. seventy thousand thirtyfour j. three hundred nineteen thousand three hundred nineteen k. two hundred three thousand l. two thousand two hundred 6. Write these numbers in Expanded form. a. 678 b. 307 c. 7,153 d. 8,060 e. 34,217 f. 342,017 g. 1,234, Round to the given place value. a. 387 (100) b. 129 (100) c. 125 (10) d. 387 (10) e. 4,876 (1000) f. 596 (100) g. 596 (10) h. 888 (1000) i. 49 (100) j. 34,567 (10,000) k. 34,667 (1000) l. 99,999 (100) 8. Sets a. What are braces? b. Name this set: {0,1,2,3,4,5,6,7,8, } c. Write the set of Natural Numbers using set notation d. How many digits are there? e. Using braces write the set of digits. f. What are ellipses? 9. Roman Numerals a. Write the set of the first six symbols used for Roman Numerals. b. What are IX and XI using Roman Numeral? Explain. c. What are the values of these symbols: C, I, M, L, and V in Roman Numerals? d. How do you write 40 and 60 using Roman Numerals? e. How do you write 90 and 110 using Roman Numerals?

11 Introduction To Whole Numbers Page 11 Crossword #1 1 ACROSS there are 10 of these 4 numbers; 1,2,3 4 and so on the number 80 7 place value of 7 in the number the number 40 9 smallest whole number 10 change 387 to DOWN 1 form of Jokes Set # < symbol (3 words) 5 form of number 978 A student visiting a museum was admiring a Tyrannosaurus fossil, and asked the guide how old it was."that skeleton's sixty million and eighteen days old," the employee replied. "How can you know it that well?" "Well, when I started working here, I asked a scientist the exact question, and he said it was sixty million years old and that was eighteen days ago." There are 3 types of people. Those that can count and those that can not count. A college student from Trinity Listed all the numbers to infinity But it gave him the fidgets To write down all those digits, So he dropped Math and took up divinity. Brain Teasers Set #1 #1 Find the next letter in the sequence O,T,T,F,F,S,S,? #2. Why are 1966 pennies worth almost twenty dollars? #3 Using the digits 4, 8, 3, 9 write the largest counting number that is smaller than 5,000 and the smallest counting number that is greater than 5,000 #4 Sally's Mom had three daughters. 1. April 2. May 3. What was the third one's name? #5 Complete this Magic Square using the missing digits: 2,4,5 and 8. All rows, columns and diagonals should add to 15.

12 Introduction To Whole Numbers Page 12 Crossword #1 Solution Brain Teaser #1 Answers E X D I G I T S P S N A T U R A L S N E I G H T Y D S A E S T E N S D F O R T Y D H A A Z E R O R O U N D D #1 The letters represent the first letter of each of the counting numbers One, Two, Three, Four, Five, Six, Seven,... So of course the next letter of the sequence would be "E" for the number 8. #5 # pennies equals \$19 and 96 cents which is about \$20 #3 The largest number smaller than 5,000 is 4,983 and the smallest number larger than 5,000 is 8,349 #4 Sally s mother had three daughters. 1. April 2. May 3. Sally Answers to Exercise Set 1 1. e) 5000 f) 600 g) 600 h)1000 i) 0 j) k) a) 2 b) 10 c) 8 d) 4 3. a) < b) > c) < d) < 4. a) seventy-eight b) eight c) five hundred sixty-one d) eight thousand three hundred forty-five e) seven thousand two f) sixteen thousand eight hundred g) nine hundred eight h) four hundred forty-four i) one hundred sixty-five thousand one hundred sixty-five j) seven million six hundred fifty-four thousand three hundred twenty-one k) five million four thousand three l a) Curly braces { and } used to enclose a set b) The set of whole numbers c) N = { 1, 2, 3, 4, 5, 6, 7, } d) There are 10 digits e) D = { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 } f) three dots used to mean and so on 9. a) { I, V, X, L, C, M } b) I=1, X=10. I before X means subtract 10-1=9 I after X means add 10+1=11 c) 100, 1, 1000, 50, 5 d) XL=40, LX=60 e) XC=90, CX=110 l) eight thousand eight hundred 5. a) 17 b) 70 c) 66 d) 581 e) 501 f) 1,004 g) 1,040 h) 17,344 i) 319,319 j) 203,000 k) 2, a) b) c) d) e) f) g) a) 400 b) 100 c) 130 d)390

### One million, eight hundred forty-five thousand, twenty-seven dollars. 1, 8 4 5, 0 2 7

Section 1.1 Place Value Whole numbers appear in everyday situations. We encounter whole numbers in ATM machines when we withdraw money, conduct an inventory, carry out a census count, and when counting

### Accuplacer Arithmetic Study Guide

Accuplacer Arithmetic Study Guide Section One: Terms Numerator: The number on top of a fraction which tells how many parts you have. Denominator: The number on the bottom of a fraction which tells how

### NBT4-1 Place Value Ones, Tens, Hundreds, Page 24

NBT4-1 Place Value Ones, Tens, Hundreds, Page 24 and Thousands STANDARDS 4.NBT.A.2 Goals Students will identify the place value of digits in 2-, 3-, and 4-digit numbers. Vocabulary hundreds ones place

### Unit 6 Number and Operations in Base Ten: Decimals

Unit 6 Number and Operations in Base Ten: Decimals Introduction Students will extend the place value system to decimals. They will apply their understanding of models for decimals and decimal notation,

### Decimals Worksheets. The decimal point separates the whole numbers from the fractional part of a number.

Decimal Place Values The decimal point separates the whole numbers from the fractional part of a number. 8.09 In a whole number the decimal point is all the way to the right, even if it is not shown in

### Roman Numeral Table. Basic Calculations Review

Basic Calculations Review I. Okay. It has been a long time since we have had to even THINK about Roman numerals vs. Arabic numerals, right? So just to refresh, a Roman numeral looks like this XVI but an

### Multiplication of Whole Numbers & Factors

Lesson Number 3 Multiplication of Whole Numbers & Factors Professor Weissman s Algebra Classroom Martin Weissman, Jonathan S. Weissman. & Tamara Farber What Are The Different Ways To Show Multiplication?

### Unit 2 Number and Operations in Base Ten: Place Value, Addition, and Subtraction

Unit 2 Number and Operations in Base Ten: Place Value, Addition, and Subtraction Introduction In this unit, students will review the place value system for reading and writing numbers in base ten. Students

### Accuplacer Elementary Algebra Study Guide for Screen Readers

Accuplacer Elementary Algebra Study Guide for Screen Readers The following sample questions are similar to the format and content of questions on the Accuplacer Elementary Algebra test. Reviewing these

### Place Value. Key Skills. Complete the daily exercises to focus on improving this skill.

Day 1 1 Write Four Million, Four Hundred and Twelve Thousand, Eight Hundred and Seventy One in digits 2 Write 6330148 in words 3 Write 12630 in words 4 Write 71643 in words 5 Write 28009 in words 6 Write

### Contents. Remember boxes and speech bubbles Important key points and tips. Special Features of Start Up Mathematics 3-5

Contents 1. Numbers Beyond 999 1 2. Roman Numerals 23 3. Addition 26 Assessment Sheet 1 37 4. Subtraction 38 5. Multiplication 50 6. Division 69 Assessment Sheet 2 84 Let s Review 1 85 7. Fractions 87

### Unit 2 Number and Operations in Base Ten: Place Value, Addition, and Subtraction

Unit 2 Number and Operations in Base Ten: Place Value, Addition, and Subtraction Introduction In this unit, students will review place value to 1,000,000 and understand the relative sizes of numbers in

### Whole Numbers. hundred ten one

Whole Numbers WHOLE NUMBERS: WRITING, ROUNDING The digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. The natural numbers (counting numbers) are 1, 2, 3, 4, 5, and so on. The whole numbers are 0, 1, 2, 3, 4,

### Rounding to Hundreds Multiple-Digit Addition with Regrouping

LESSON Rounding to Hundreds Multiple-Digit Addition with Regrouping As always, add the units first. A student may become so proficient at adding multiple digit numbers that he can add from the left, but

### Level I Math Black Line Masters Toolkit

Level I Math Black Line Masters Toolkit NSSAL (Draft) C. David Pilmer 2012 (Last Updated: February, 2013) This resource is the intellectual property of the Adult Education Division of the Nova Scotia Department

### Exercise 4. Converting Numbers To Words And Words To Numbers. (This will help you to write cheques, stories and legal papers)

Exercise 4 Converting Numbers To Words And Words To Numbers. (This will help you to write cheques, stories and legal papers) At the end of this exercise you will: Be able to convert numbers to the written

### Section 4.1 Inequalities & Applications. Inequalities. Equations. 3x + 7 = 13 y = 7 3x + 2y = 6. 3x + 7 < 13 y > 7 3x + 2y 6. Symbols: < > 4.

Section 4.1 Inequalities & Applications Equations 3x + 7 = 13 y = 7 3x + 2y = 6 Inequalities 3x + 7 < 13 y > 7 3x + 2y 6 Symbols: < > 4.1 1 Overview of Linear Inequalities 4.1 Study Inequalities with One

### Place Value and Rounding

4.1 Place Value and Rounding 4.1 OBJECTIVES 1. Identify place value in a decimal fraction 2. Write a decimal in words 3. Write a decimal as a fraction or mixed number 4. Compare the size of several decimals

### We have five new employees. I counted 22 adults and 14 children at the wedding reception. Of the 150 people there, only 5 were late.

Numbers Numbers are classified as cardinal numbers, ordinal numbers, or Roman numerals. Cardinal numbers are also known as Arabic numbers, and they are the numbers we use for counting (e.g. one, two, three

### Whole Number and Decimal Place Values

Whole Number and Decimal Place Values We will begin our review of place values with a look at whole numbers. When writing large numbers it is common practice to separate them into groups of three using

### Introduction to Whole Numbers

Section 1.1 PRE-ACTIVITY PREPARATION Introduction to Whole Numbers Annette has just landed a terrific job as a middle school teacher. Instead of renting an apartment, she decides to buy a small condominium.

### Number: Fractions (including Decimals and Percentages) Reasoning

Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 COUNTING IN FRACTIONAL STEPS Pupils should count in fractions up to 10, starting from any number and using the1/2 and 2/4 equivalence on the number line (Non Statutory

### Pre-Algebra Lecture 6

Pre-Algebra Lecture 6 Today we will discuss Decimals and Percentages. Outline: 1. Decimals 2. Ordering Decimals 3. Rounding Decimals 4. Adding and subtracting Decimals 5. Multiplying and Dividing Decimals

### 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

### PQRST 11 PUZZLE COMPETITION

PQRST PUZZLE COMPETITION PUZZLE 0 (0+0 points penalty for wrong answers) + points Wild Operations You re writing mathematical operations, using letters instead of digits to represent numbers. You take

### Order of Operations. 2 1 r + 1 s. average speed = where r is the average speed from A to B and s is the average speed from B to A.

Order of Operations Section 1: Introduction You know from previous courses that if two quantities are added, it does not make a difference which quantity is added to which. For example, 5 + 6 = 6 + 5.

### Math. Writing Numbers as Words Through 1 Million. 1) 5,451 five thousand, four hundred fifty-one. 2) 32,617 thirty-two thousand, six hundred seventeen

1) 5,451 five thousand, four hundred fifty-one 2) 32,617 thirty-two thousand, six hundred seventeen 3) 995,333 nine hundred ninety-five thousand, three hundred thirty-three 4) 811,967 eight hundred eleven

### DECIMAL COMPETENCY PACKET

DECIMAL COMPETENCY PACKET Developed by: Nancy Tufo Revised: Sharyn Sweeney 2004 Student Support Center North Shore Community College 2 In this booklet arithmetic operations involving decimal numbers are

### HESI ENTRANCE EXAMINATION STUDY GUIDE

HESI ENTRANCE EXAMINATION STUDY GUIDE TABLE OF CONTENTES HESI Study Packet Introduction HESI Test Overview (Math, Reading, Comprehension, Vocabulary, Grammar) Math (face sheets precedes each section pages

### 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

### Math. Writing Numbers through 1 Million. Answers. 1) five thousand, four hundred sixty-six. 2) seven thousand, six hundred eighty-two

1) five thousand, four hundred sixty-six 2) seven thousand, six hundred eighty-two 3) three thousand, seven hundred forty-five 4) one hundred twenty-three thousand, six hundred seventy-six 5) eighty-three

DECIMALS PRACTICE BOOKLET TABLE OF CONTENTS SKILL 1: Representing Decimals and Place Value...3 SKILL 2: Graph Decimals on a Number Line...5 SKILL 3: Comparing Decimals...7 SKILL 4: Ordering Decimals...9

### Unit 1 Number Sense. In this unit, students will study repeating decimals, percents, fractions, decimals, and proportions.

Unit 1 Number Sense In this unit, students will study repeating decimals, percents, fractions, decimals, and proportions. BLM Three Types of Percent Problems (p L-34) is a summary BLM for the material

### 27) fifty thousand and two millionths 28) ninety thousand and six millionths

-2-23) ten thousand, nine and nine hundred thousand, nine 24) eighty thousand and four 25) ten thousand, one hundred and three hundred thousand, seven hundred eight 26) nine hundred five thousand and three

### Place Value of Whole Numbers

Chapter 1 Review of Basic Arithmetic 3 1.1 Place Value of Numbers and Rounding Numbers Place value is the value of a digit as determined by its position in a number, such as ones, tens, hundreds, etc.

### Lesson 1 Order of Operations

Lesson 1 Order of Operations "Operations" means things like add, subtract, multiply, divide Student A solved the following problem: 17-7 x 2 = 20. Is he correct? Why or why not? Lesson 1 Order of Operations

### Grade. Place Value II. By Monica Yuskaitis

rd 3 Grade Place Value II By Monica Yuskaitis California Standard Addressed Number Sense Third Grade 1.1 Count, read, and write whole numbers to 10,000. California Standard Addressed Number Sense Third

### Simply Math. Everyday Math Skills NWT Literacy Council

Simply Math Everyday Math Skills 2009 NWT Literacy Council Acknowledgement The NWT Literacy Council gratefully acknowledges the financial assistance for this project from the Department of Education, Culture

### Math. Rewriting Number Sentences. Answers. 1) 'J' times Twelve equals Four hundred Forty-Four. 2) 'K' times Fifteen equals One hundred Five

1) 'J' times Twelve equals Four hundred Forty-Four 1. 2) 'K' times Fifteen equals One hundred Five 2. 3) One thousand, Two hundred Eighty divided by 'X' equals Two 3. 4) Two plus 'Z' equals Eight 4. 5)

### Properties of Numbers

Properties of Numbers 1. 2. 3. 4. What is the next number? fifteen, twenty, twenty-five Is the next number in this sequence odd or even? Thirty, twenty-seven, twenty-four,... Write the number which comes

### Squares and Square Roots

SQUARES AND SQUARE ROOTS 89 Squares and Square Roots CHAPTER 6 6.1 Introduction You know that the area of a square = side side (where side means the length of a side ). Study the following table. Side

### Excel Math Placement Tests A grade-level evaluation tool

Excel Math Placement Tests A grade-level evaluation tool Attached are six tests that can be used to evaluate a student s preparedness for Excel Math. The tests are labeled A - F, which correspond to first

### 3.1.1 Decimals and Fractions

3.. Decimals and Fractions Learning Objective(s) Read and write numbers in decimal notation. 2 Write decimals as fractions. 3 Write fractions as decimals. Introduction In addition to fraction notation,

### 1.1 Place Value of Whole Numbers

1.1 Place Value of Whole Numbers Whole Numbers: Whole numbers can be listed as 0,1,2,3,4,5,6,7,8,9,10,11,... The "..." means that the pattern of numbers continues without end. Whole Number Operations Workbook

### Quick Reference ebook

This file is distributed FREE OF CHARGE by the publisher Quick Reference Handbooks and the author. Quick Reference ebook Click on Contents or Index in the left panel to locate a topic. The math facts listed

### Teacher Tam. Microsoft Word

Teacher Tam Microsoft Word Name Date Math Practice: Reading and Writing Numbers Directions: Write each number in written form. Example: 231 Two hundred thirty-one a. 19 b. 291 c. 9,215 d. 11,000 e. 114,378

### and so on (81,129,638,414,606,681,695,789,005,144,064) brad thiele 2011

and so on (81,129,638,414,606,681,695,789,005,144,064) brad thiele 2011 in zen they say: if something is boring after two minutes, try it for four. if still boring try it for eight, sixteen, thirty-two

### 118 One hundred Eighteen

1 2 3 4 5 6 7 8 9 10 ten 11 Eleven 12 Twelve 13 Thirteen 14 Fourteen 15 Fifteen 16 Sixteen 17 Seventeen 18 Eighteen 19 Nineteen 20 Twenty 21 Twenty 22 Twenty 23 Twenty 24 Twenty 25 Twenty 26 Twenty 27

### 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

### EduSahara Learning Center Assignment

06/05/2014 11:23 PM http://www.edusahara.com 1 of 5 EduSahara Learning Center Assignment Grade : Class VI, CBSE Chapter : Knowing Our Numbers Name : Words and Figures Licensed To : Teachers and Students

### Exponents. Exponents tell us how many times to multiply a base number by itself.

Exponents Exponents tell us how many times to multiply a base number by itself. Exponential form: 5 4 exponent base number Expanded form: 5 5 5 5 25 5 5 125 5 625 To use a calculator: put in the base number,

### Math in Focus Vocabulary. First Grade

Math in Focus Vocabulary First Grade Chapter Word Definition 1 zero 0 1 one 1 1 two 2 1 three 3 1 four 4 1 five 5 1 six 6 1 seven 7 1 eight 8 1 nine 9 1 ten 10 1 same equal to 1 more 4 eggs is more than

1 5th Grade Division 2015 11 25 www.njctl.org 2 Division Unit Topics Click on the topic to go to that section Divisibility Rules Patterns in Multiplication and Division Division of Whole Numbers Division

### 4 9 7, 5 4 8, 6 0 1, 3 7 2.

1.1 Digits and Place Value 1. Understand Digits and Place Value Digits are mathematical symbols that are arranged in a specific order to represent numeric values. There are ten different digits in our

### DECIMALS are special fractions whose denominators are powers of 10.

DECIMALS DECIMALS are special fractions whose denominators are powers of 10. Since decimals are special fractions, then all the rules we have already learned for fractions should work for decimals. The

### Introduction to Decimals

Introduction to Decimals Reading and Writing Decimals: Note: There is a relationship between fractions and numbers written in decimal notation. Three-tenths 10 0. 1 zero 1 decimal place Three- 0. 0 100

### Numbers Galore using. Print. font

Numbers Galore! Numbers Galore using Print font 0 zero Draw Tally 0 0 zero 1 one Draw Tally 1 1 1 1 1 one one 2 two Draw Tally 2 2 2 2 two two 3 three Draw Tally 3 3 3 3 three 4 four Draw Tally 4 4 4 4

### Absolute Value of Reasoning

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

### Mathematics Navigator. Misconceptions and Errors

Mathematics Navigator Misconceptions and Errors Introduction In this Guide Misconceptions and errors are addressed as follows: Place Value... 1 Addition and Subtraction... 4 Multiplication and Division...

### Version 01 7540004662. Part 1 Multiplication

Version 01 7540004662 Part 1 Multiplication Part 1 Multiplication Multiplication and Division i This content is Copyright 2005 Open School BC, all rights reserved. Open School BC content and may neither

### Representing Decimals (pages 102 105)

A Representing Decimals (pages 102 105) Decimals are numbers that are expressed using a decimal point. The decimal point separates the whole number part of the decimal from the part that is less than one.

### 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

### Introduction 6 National curriculum objectives 7

Contents Introduction 6 National curriculum objectives 7 Number Add/subtract Lesson Plan 1 Place value Code book 8 Lesson Plan 2 Counting Stepping stones 12 Lesson Plan 3 Negative numbers Fairground ride

### Section P.9 Notes Page 1 P.9 Linear Inequalities and Absolute Value Inequalities

Section P.9 Notes Page P.9 Linear Inequalities and Absolute Value Inequalities Sometimes the answer to certain math problems is not just a single answer. Sometimes a range of answers might be the answer.

### MENTAL TEST 1 MENTAL TEST 2

MENTAL TEST 1 1. Add eight and six. 2. Multiply seven by nine. 3. Add six, four, eight and five. 4. Take twenty six from forty three. 5. Add thirty five and twenty four. 6. What change would you get from

### Name of Lecturer: Mr. J.Agius LESSON 1. Place Values: Whole numbers. Hundreds Tens Units 1 1 0 1 0 0 1, 0 0 0 1 0, 0 0 0 1 0 0, 0 0 0 1, 0 0 0, 0 0 0

LESSON 1 1.1 Place value, whole/decimal numbers Place Values: Whole numbers Million 100 Thousands 10 Thousands Thousands Hundreds Tens Units 1 1 0 1 0 0 1, 0 0 0 1 0, 0 0 0 1 0 0, 0 0 0 1, 0 0 0, 0 0 0

### Chapter 1 Whole Numbers

Chapter 1 Whole Numbers 1.1 Place Value and Rounding We begin our study of number systems with the whole numbers, which are the counting numbers starting with 0,1,2,3,. Our number system is referred to

### 5 3.00 0.60 5 3.00-30 00 1 3 = 3 5 = Step 1: Divide the numerator by the denominator to get a decimal.

Mixed Numbers Decimals Changing A MIXED NUMBER TO A DECIMAL: Step 1: Divide the numerator by the denominator to get a decimal. whole number numerator denominator 1 3 3 5 numerator denominator decimal 5

### Mental Mathematics Test Questions Here are previously asked SATS Mental Maths questions for you to practice (enjoy ) 5-Second Questions

Mental Mathematics Test Questions Here are previously asked SATS Mental Maths questions for you to practice (enjoy ) 5-Second Questions A. Money How many fifty-pence pieces in four pounds? How many twenty-pence

### 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

### Assessment For The California Mathematics Standards Grade 3

Introduction: Summary of Goals GRADE THREE By the end of grade three, students deepen their understanding of place value and their understanding of and skill with addition, subtraction, multiplication,

### Second Grade Math Standards and I Can Statements

Second Grade Math Standards and I Can Statements Standard CC.2.OA.1 Use addition and subtraction within 100 to solve one and two-step word problems involving situations of adding to, taking from, putting

### OA3-10 Patterns in Addition Tables

OA3-10 Patterns in Addition Tables Pages 60 63 Standards: 3.OA.D.9 Goals: Students will identify and describe various patterns in addition tables. Prior Knowledge Required: Can add two numbers within 20

### Decimals are absolutely amazing We have only 10 symbols, yet can represent any number, large or small We use zero (0) as a place holder to allow us

Decimals 1 Decimals are absolutely amazing We have only 10 symbols, yet can represent any number, large or small We use zero (0) as a place holder to allow us to do this 2 Some Older Number Systems 3 Can

### Placement Test Review Materials for

Placement Test Review Materials for 1 To The Student This workbook will provide a review of some of the skills tested on the COMPASS placement test. Skills covered in this workbook will be used on the

### How do you compare numbers? On a number line, larger numbers are to the right and smaller numbers are to the left.

The verbal answers to all of the following questions should be memorized before completion of pre-algebra. Answers that are not memorized will hinder your ability to succeed in algebra 1. Number Basics

### IWCF United Kingdom Branch

IWCF United Kingdom Branch Drilling Calculations Distance Learning Programme Part 1 Introduction to Calculations IWCF UK Branch Distance Learning Programme - DRILLING CALCULATIONS Contents Introduction

### Place Value of Whole Numbers Through One Million

Place Value of Whole Numbers Through One Million Brief Overview: This learning unit develops and reviews place value concepts through millions. It involves the utilization of manipulatives. The lessons

### STRAND A: NUMBER. UNIT A6 Number Systems: Text. Contents. Section. A6.1 Roman Numerals. A6.2 Number Classification* A6.

STRAND A: NUMBER A6 Number Systems Text Contents Section A6.1 Roman Numerals A6. Number Classification* A6.3 Binary Numbers* A6.4 Adding and Subtracting Binary Numbers* A6 Number Systems A6.1 Roman Numerals

### NS3-1: Place Value Ones, Tens, and Hundreds page 33

NS3-1: Place Value Ones, Tens, and Hundreds page 33 1. Write the place value of the underlined digit. a) 17 ones b) 98 REMEMBER: 3 7 5 c) 24 d) 63 e) 381 f) 972 g) 457 h) 79 i) 261 j) 8 2. Give the place

### 5.1 Introduction to Decimals, Place Value, and Rounding

5.1 Introduction to Decimals, Place Value, and Rounding 5.1 OBJECTIVES 1. Identify place value in a decimal fraction 2. Write a decimal in words 3. Write a decimal as a fraction or mixed number 4. Compare

### NS4-99 Decimal Tenths

WORKBOOK 4:2 PAGE 263 NS4-99 Decimal Tenths GOALS Students will learn the notation for decimal tenths. Students will add decimal tenths with sum up to 1.0. Students will recognize and be able to write

### Mini-Posters. LES 1 Shopping at the Co-op

Mini-Posters LES 1 Shopping at the Co-op Application Situation 1 p. 1 Application Situation 2 p. 48 Application Situation 3 p. 53 Application Situation 4 p. 54 Table of Contents APPLICATION SITUATION 1

### Chapter 5. Decimals. Use the calculator.

Chapter 5. Decimals 5.1 An Introduction to the Decimals 5.2 Adding and Subtracting Decimals 5.3 Multiplying Decimals 5.4 Dividing Decimals 5.5 Fractions and Decimals 5.6 Square Roots 5.7 Solving Equations

### Reading and Writing Small Numbers

Reading Writing Small Numbers Objective To read write small numbers in stard exped notations wwweverydaymathonlinecom epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family Letters Assessment

### Sunny Hills Math Club Decimal Numbers Lesson 4

Are you tired of finding common denominators to add fractions? Are you tired of converting mixed fractions into improper fractions, just to multiply and convert them back? Are you tired of reducing fractions

### BREATHITT COUNTY SCHOOLS KINDERGARTEN MATH CURRICULUM

Weeks 1-2 Instructional Emphasis: Counting and Cardinality Topic 1: One to Five K.CC.3: Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count

### Wigan LEA Numeracy Centre. Year 6 Mental Arithmetic Tests. Block 1

Wigan LEA Numeracy Centre Year 6 Mental Arithmetic Tests Block 1 6 Produced by Wigan Numeracy Centre July 2001 Year Six Mental Arithmetic Test 1 (5 seconds response time) 1. Write the number three hundred

### Fractions to decimals

Worksheet.4 Fractions and Decimals Section Fractions to decimals The most common method of converting fractions to decimals is to use a calculator. A fraction represents a division so is another way of

### Investigate Investigate

Name Place Value and Patterns Essential Question How can you describe the relationship between two place-value positions? Lesson 1.1 COMMON CORE STANDARD CC.5.NBT.1 Understand the place value system. Investigate

### Assessment For The California Mathematics Standards Grade 2

Introduction: Summary of Goals GRADE TWO By the end of grade two, students understand place value and number relationships in addition and subtraction and they use simple concepts of multiplication. They

### POINTS FOR QUICK REVISION

CHAPTER 1 Knowing Our Numbers POINTS FOR QUICK REVISION l Natural Numbers: To count and calculate we use numbers 1, 2, 3, 4,... which are called counting numbers or natural numbers. l There is no greatest

### Permission is given for the making of copies for use in the home or classroom of the purchaser only.

Copyright 2005 Second Edition 2008 Teresa Evans. All rights reserved. Permission is given for the making of copies for use in the home or classroom of the purchaser only. Part 1 Math Card Games to Play

### Rounding Whole Numbers

Section 1.2 PRE-ACTIVITY PREPARATION Rounding Whole Numbers Dollar stores have sprung up around the country as spin-offs of the dollar days promotions of major retailers. Their prices vary only slightly

### USING PLACE VALUE TO WRITE NUMBERS

The Improving Mathematics Education in Schools (TIMES) Project USING PLACE VALUE TO WRITE NUMBERS NUMBER AND ALGEBRA Module 5 A guide for teachers - Years 4 7 June 2011 4YEARS 7 Using Place Value to Write

### NWT Apprenticeship Support Materials

NWT Apprenticeship Support Materials Math Reading Comprehension Science * Module 1 Foundations * Module 2 Patterns and Relations * Module 3 Variables and Equations * Module 4 Measuring Time, Shapes and