Place Value of Whole Numbers Lesson 1: Place Value, Value, and Reading Numbers in the Billions Jul 15 9:37 PM Jul 16 10:55 PM Numbers vs. Digits Let's begin with some basic vocabulary. First of all, what is the difference between a number and a digit? Click the box to reveal the answer. A digit is like a letter. A number is like a word. Just like letters make words, digits make numbers. 546 is a number. 4 is a digit in that number. Put the items in the correct column below. Copy the table in your notebook with your notes. Digit Number 7 18 1,879 35 56 678 6 9 2 10 Discuss: How many possible digits exist? How many possible numbers? Place Value vs. Value Let's review what we already know about place value. First of all, what is the difference between place value and value? Click the box to reveal the answer. Place value is the location of a digit or the PLACE that it is in. For example, the place value of the 1 in 561 is the one's place. The 6 is in the ten's place and the 5 is in the hundred's place. Value is how much a digit is worth. For example, in the number 561, the 5 is not worth just 5. It is worth 5 hundreds or 500. The 6 is worth 6 tens or 60, and the 1 is just worth one because it is in the ones place. Hint: When I ask for place value, I am looking for a word like one's, ten's, hundred's, and so on. When I ask for the value, I am looking for a number like 500, 60, 1, and so on. Jul 15 9:43 PM Jul 15 10:02 PM Place Value vs. Value Let's practice with place value vs. value. Given the number 4,567, what is the place value of the following: Place value of the 4? Place Value Chart You can use a place value chart to help you understand whole numbers and the value of each digit. A period is a group of 3 digits within a number separated by a comma. millions period thousands period ones period Place value if the 5? Place value of the 7? Place value of the 6? Given the number 6,892, what is the value of the following digits? Value of the 8? Value of the 6? Value of the 2? Value of the 9? If you look at the headings on the place value chart, you can easily read a number. 4 5 3 4 2 9 8 8 7 Four hundred fifty three million, four hundred twenty nine thousand, eight hundred eighty seven. Jul 15 10:20 PM Jul 15 10:34 PM 1
Let's Review: Reading Numbers up to the Billions Reading numbers in the billions is just a step above reading numbers in the millions. The number shown in the place value chart below shows the number one billion, six hundred million. Since there are zeroes in all of the places below the hundred millions place, there is no more to read in this number. You should already be reading numbers up to the millions. Can you guess what the next largest period is after millions? Click the shape below to find out! billions Click the study jams icon to the right to learn more about reading large numbers. As you watch the video, please take notes on the material. You will be taking a 7 question quiz after the video. Please pull out a separate sheet of paper to write down your answers. Write the proper heading information on the top of your paper. The teacher will go over it afterwards and you will grade your work and turn it in. Jul 15 10:53 PM Jul 15 10:59 PM Homework Your Turn! With a partner, practice reading the following numbers. Write each number into a place value chart and read it to your partner. Work together to perfect the reading of these large numbers. Copy the following into a new page in your math notebook. Use the place value chart in your math notes to help if needed. Read the numbers out loud to someone at home. Given the number 309,454,567 what is the place value of the following: Place value of the 0? 1, 567, 879 Place value if the 5? 3, 567, 000 Place value of the 7? 6, 908, 606, 788 Place value of the 9? 9, 402 Given the number 6,892,390,777 what is the value of the following digits? 7, 456, 765 Value of the 8? Value of the 6? 10, 895 Value of the 2? 23, 235, 333, 234 Value of the 9? Jul 16 10:35 PM Jul 16 10:35 PM Standard, Expanded, and Word Form Lesson 2: You must be able to recognize number in different forms. There are 3 main types which include standard, expanded, and word form. You may also see these called notation rather than form. standard form/notation: a number as it is normally written with digits example: 1,456,765 Writing Numbers in Standard, Expanded, and Word Form expanded form/notation: expanded form involves breaking a number apart into the values of each digit example: for 1,456,765 you would write 1,000,000 + 400,000 + 50,000 + 6,000 + 700 + 60 + 5 word form/notation: with word form, you just have to write the number in words as you hear it example: for 1,456,765 you would write: one million, four hundred fifty-six thousand, seven hundred sixty-five Jul 16 10:56 PM Jul 16 10:59 PM 2
Standard Form/Notation It is important to be able to read and write numbers in standard form/notation. You may need to read and understand your bills, pay bills, get a loan, understand your receipt at the grocery store, and many other situations. 10,546,768 703,111 Let's Practice! Read the following numbers out loud to your partner: Write the following numbers in standard form: 3 million, four hundred fifty-seven thousand, three hundred nineteen nine hundred seventy-seven thousand, nine hundred fifty-five one billion, four hundred eighty million, sixty-five thousand, eighty-seven Expanded Form/Notation: Expanded form/notation is important for showing your understanding of the value of each digit in a number. It involves breaking down a number into its individual digits and recording their value. Click on the study jams crew below to see a video explaining expanded form/notation. As you watch, add to your notes on expanded form. You will be taking a seven question quiz afterwards. Please number a small section in your notes 1-7. Let's Practice! Write the following numbers in expanded notation. Ask yourself, "What place is this number in? What is the number's value?" Then write it down, separating the values with addition signs. Check over your work with a partner. 203,567 2,345,122 32,888,904 90,495,844 5,456,732,003 Jul 16 10:59 PM Jul 16 10:59 PM Word Form/Notation Word form is fairly simple. All you need to do is read a number and write exactly what you say. There are a few other simple grammatical rules to remember when writing numbers in word form 1. Put commas in the word form of a number in the same place they are in the standard form (where you naturally pause). When you come to a comma, you would be writing one of the following words: billion, million, or thousand, depending on which comma you are on. 2. When writing number parts like sixty-five and eighty-one, include a hyphen (dash) between the number words 3. DO NOT say or write the word "and" when reading/writing a number! **The most important thing is to get the word written down. You can edit your work to correct any mistakes involving the rules above afterwards. Let's Practice! Read the following numbers and write them in word form. Refer to your notes for help. 23,456 13,800,450 4,444,324,209 124,879 1,560,444 Lesson 3: Fifth Grade (and higher) Expanded Form Jul 21 3:39 PM Jul 21 3:54 PM What is 5th Grade Expanded Form You already know how to write numbers in expanded form. Now, we will take that a step further. With 5th grade expanded form, you will break down each digit's value even further. To write a number in 5th grade expanded form, multiply each digit by its place value, and then write an addition expression. Here's how: You used to write the number 1,456,765 in expanded form as 1,000,000 + 400,000 + 50,000 + 6,000 + 700 +60 + 5 ---------------------------------------------------------------------------------------------------- Now you will write the number using multiplication. Basically, you are saying how many of each place value you have. For example, the number above would be written like this: (1 x 1,000,000) + (4 0,000) + (5,000) + (6 x 1,000) + (7 0) + (6 ) + (5 x 1) There is 1 million, 4 hundred thousands, 5 ten thousands, 6 thousands, 7 hundreds, 6 tens, and 5 ones. Let's Look at a Few More Examples 2,367,089 two million, three hundred sixty-seven thousand, eighty-nine (2 x 1,000,000) + (3 0,000) + (7 x 1,000) + (8 ) + (9 x 1) ** Notice that since there was a 0 in the hundreds place, that was left out of my expanded form. If there is nothing in a place, then that place has no value in that particular number. -------------------------------------------------------------------------------------------------- 315,400,454 three hundred fifteen million, four hundred thousand, four hundred fifty-four (3 0,000,000) + (1,000,000) + (5 x 1,000,000) + (4 0,000) + (4 0) + (5 ) + (4 x 1) -------------------------------------------------------------------------------------------------- 1,333,222,099 one billion, three hundred thirty-three million, two hundred twenty-two thousand, ninety-nine (1 x 1,000,000,000) + (3 0,000,000) + (3,000,000) + (3 x 1,000,000) + (2 0,000) + (2,000) + (2 x 1,000) + (9 ) + (9 x 1) Jul 21 3:54 PM Jul 21 4:16 PM 3
Let's Try It! Write the numbers below in 5th grade expanded form. Refer to your notes if needed and check with a partner to compare answers when you finish. 43,444 234,409 111,111,890 388,903,897 Lesson 4: Comparing and Ordering Whole Numbers 3,456,009,877 Jul 21 4:36 PM Comparing Whole Numbers Comparing Whole Numbers When you compare numbers, you are telling which is greater, less, or if the numbers are equal (the same). Use the symbol > for greater than, < for less than, and = for equal to. You can also use the "cross-out" strategy. For this strategy, you cross out a digit in each number until one is greater than the other. You must begin on the left side of each number (the digit with the largest value). Here's how: 545,524 540,820 The hundred thousands digit (5) and the ten thousands digit (4) match, so they can be crossed out. We then come to the thousands digit. The first number has a 5 in the thousands place and the second number has a 0 in the thousands place, therefore the first number is larger. We would place the greater than sign in the blank. Remember that the greater than and less than signs are like mouths, the mouth eats the larger number. Ordering Whole Numbers Let's Practice Together Write the following problems in your math notebook. Follow along as the teacher demonstrates how to solve the problems. Click the StudyJams Crew below to see a demonstration of ordering numbers. Jul 22 10:57 AM 4
On Your Own! Ordering Whole Numbers Practice makes perfect! Copy the following problems onto a new page in your notebook. These will be taken up after you finish. Be sure to copy your header information. You can also use the cross-out strategy to put whole numbers in order from least to greatest or from greatest to least. It is very important to underline the words "least to greatest" or "greatest to least" in the problem so that you know which order to put the numbers in. Let's put these numbers in order from least to greatest. Here's how: 4,789,316 5,789,001 4,789,230 Looking at the first digit of each number which are all in the millions place, I can see that the 5 is the largest, so that number will go at the end of my answer list. I will eliminate it now. Now I am left with the other 2 numbers. I will start crossing out at the largest digits. 4,789,316 4,789,230 I crossed out all of the matching digits and I am left with a 3 in the hundreds place of the first number and a 2 in the hundreds place of the second number. Since 3 is larger than 2, the first number is larger that the second, so it will go second in my answer. Answer: 4,789,230 4,789,316 Name: Date: Comparing and Ordering Numbers Grade: Put <, >, or = in the circle to compare. 1. Order the numbers from greatest to least. 7. 2. 8. 3. 9. 4. 10. 5. 6. 5,789,001 Jul 22 11:01 AM Jul 22 10:54 AM Number Lines Number lines can help you to show a number in relation to other numbers. In order to place a number onto a number line, you need to know which numbers are greater and less than that number. Let's begin by placing the number 36 on a number line. Lesson 5: Rounding Whole Numbers The number 36 is between 30 and 40. We can place it between 30 and 40 on a number line. First we need to label the lines for 30, 40, and the halfway point which is 35. Next we will find where 36 would fall and place a point on the line there. 30 35 40 36 Let's try it with the number 237. We will place it on 2 different number lines. 237 235 230 237 200 240 300 250 What is the difference between these 2 number lines? Which one is more precise (as close as it gets to the real number)? Jul 22 11:51 AM Rounding Whole Numbers You can use a number line and other strategies to round numbers. The type of number line you draw depends on how the problem wants you to round the number. In the example below, the problem wants you to round to the nearest hundred. Notice how they drew their number line. Jul 22 2:05 PM Rounding Whole Numbers Click on the Study Jams Crew to the right to review and practice rounding numbers. Add to your notes as you watch and follow along as we take the quiz. Here is another strategy for rounding. You can look closely at the digits to see what a number is closest to. Let's take the number 18,465. We will round this number to the nearest thousand. First, underline the place you are rounding. 18,465 Next, circle the digit to the right of the underlined digit. This is the digit that tells you how to round. 18,465 If the number you circled is 4 or less, then you let that circled digit rest or stay the same. If the circled number is 5 or more, you will raise that circled number by one more. The rest of the digits to the right of the circled number turn into zeros whether you rounded up or down. 18,400 4 or less, let it rest. 5 or more, raise the score! Jul 22 11:51 AM Jul 22 11:51 AM 5
Let's Try it Together Work with a partner on the problems below. Both partners need to write the problems and the answers. Round each number to the place of the underlined digit. Click on an object below to play a rounding game. 1. 16 2. 561 3. 13,456 4. 427,841 5. 166,652 6. 7,582,663 Answer the following word problems. 7. To round 7,458 to the nearest hundred, which digit do you look at? What is 7,458 rounded to the nearest hundred? 8. A runner is running on the track with markers every 10 meters. If the runner runs 368 meters, is she closer to the 360-meter marker or the 370-meter marker? Lesson 6: Place Value Relationships Review: What is the place value of a digit? Give an example. What is the value of a digit? Give an example. Place value relationships refers to the way the different place values are related to one another. In 4th grade, you learned that the value of a digit increases (gets larger) by 10 times each time you move to the left in place value. millions hundred ten thousands hundreds tens ones thousands thousands the tens place is 10 times larger than the ones place the hundreds place is 10 times larger than tens place the thousands place is 10 times larger than hundreds place the ten thousands place is 10 times larger than thousands place the hundred thousands place is 10 times larger than ten thousands place the millions place is 10 times larger than the hundred thousands place Jul 22 6:40 PM If you multiply what you have in the ones place by 10, you will get a tens rod (long). Ten ones make a ten. If you multiply what you have in the tens place by 10, you will get a flat (hundred). Ten tens make a hundred. If you multiply what you have in the hundreds place by 10, you will get a large cube (thousand). Ten hundreds make a thousand. Let's say you make 2 moves to the left. If the value increases by 10 times with EACH shift to the left, how much does place value increase with 2 shifts to the left? For example, how much greater is the hundreds place than the ones place? HINT: How much must you multiply 1 by to get 100? Click for a hint! Jul 22 6:55 PM 6
Now you know that for each shift to the left in place value, the value increases 10 times. What do you think might happen with each shift to the right in place value? For example, instead of hopping from the ones place to the tens place, we hop from the tens place to the ones place. Dividing by 10 is the same as finding one-tenth of a number. It takes 10 ones to make 10, so one is one-tenth of ten. With each movement to the right in place value, you are taking one-tenth of the value. Jul 22 7:03 PM Let's Review the hundreds place is 1/10 of the thousands place the tens place is 1/10 of the hundreds place the ones place is 1/10 of the tens place Jul 22 7:03 PM Practice 1. What is the relationship between the 3 in 3,546 and the 3 in 2,345? ** Ask: What place is the 3 in the first number in? What place is the 3 in the second number in? How many places do you jump from one place to the other? To the right or to the left? 2. What is the relationship between the 4 in 23,486 and the 4 in 23,564? 3. What is the relationship between the 8 in 800,779 and the 8 in 12,897? Jul 22 7:03 PM Jul 22 7:27 PM Aug 10 11:38 AM 7