Place Value Basics: Whole Numbers for Dixon Elementary School’s 5th-Grade Math Classes

Place? Value? Each digit in a number has a PLACE and each digit has a VALUE based on its place. For example, the 2 in each of these numbers is in a different place and has a different value: 2 23 236 2,367 23,679 236,794

So, depending on what place the 2 holds, its value changes: Place? Value? So, depending on what place the 2 holds, its value changes: 2 = 2 (2 ones) 23 = 20 (2 tens) 236 = 200 (2 hundreds) 2,367 = 2,000 (2 thousands) 23,679 = 20,000 (2 ten thousands) 236,794 = 200,000 (2 hundred thousands)

Places & Periods PLACES are organized into PERIODS, and within each period, 3 places repeat: ONES, TENS, and HUNDREDS.

Places & Periods We put commas in numbers where periods end.

Places & Periods The periods also make large numbers easy to read! Just say the numbers in the period, and name the period, until the ones period---just read the numbers there.

Places & Periods 987 million, 654 thousand, 321

Places & Periods: Your Turn! What digits are in the thousands period? In what period would you find the digit, 5? In what place is the digit, 4? How do we read this number? What is the value of the 2?

Places & Periods: Answers The digits 462 are in the thousands period. The digit, 5, is in the millions period. The digit, 4, is in the hundred thousands place. The number reads 591 million, 462 thousand, 873. The value of the 2 is 2,000.

Places & Periods: Your Turn! What PERIOD or PLACE? For this slide, cycle through each box in order beginning with the ONES PERIOD, and then reveal all 3 ONES PLACES (ones, tens, hundreds). Then move to the THOUSANDS PERIOD, and then reveal all 3 THOUSANDS PLACES (ones, tens, hundreds). Finally, click the MILLIONS PERIOD, and then reveal all 3 MILLIONS PLACES (ones, tens, hundreds).

Places & Periods: Out of Order! What PERIOD or PLACE---randomized? ? ? ? ? ? ? ? ? ? ? ? ? For this slide, on the first click, a question mark pops up. Choose a student to tell the place or period, and the next click will reveal the answer.

Numbers in 3 Forms STANDARD form, WORD form, EXPANDED form. When working with place value, we learn to write numbers in 3 different forms: STANDARD form, WORD form, and EXPANDED form.

Standard Form The word, STANDARD, means “normal,” or “regular.” So, when writing in standard form, we simply write numbers in their regular form: 4 28 137 6,903 42,177

Word Form When writing numbers in their WORD forms, we do just that: use the spelled-out word for each number: 4 = four 28 = twenty-eight 137 = one hundred thirty-seven 6,903 = six thousand, nine hundred three 42,177 = forty-two thousand, one hundred seventy-seven

Word Form: Rule #1 There are a couple rules to remember when writing numbers in their word forms: In 2-digit numbers over 20, we hyphenate the words: 28 = twenty-eight 36 = thirty-six 41 = forty-one 94 = ninety-four Those are HYPHENS!

Word Form Rule #1: Your Turn! Write each number in word form: 54 63 122 675 21,136 ANSWERS: fifty-four sixty-three one hundred twenty-two six hundred seventy-five twenty-one thousand, one hundred thirty-six

Forty-two thousand three hundred fifty-nine Word Form Rule #2 Here’s the other rule to remember: 2) When writing numbers with digits in the thousands period or higher, we add commas after the period names (in the same place we put them in the standard form). 42 359= Forty-two thousand three hundred fifty-nine

Word Form Rule #2: Your Turn! Write each number in word form: 8,463 10,241 3) 4,613,566 ANSWERS: eight thousand, four hundred sixty-three ten thousand, two hundred forty-one four million, six hundred thirteen thousand, five hundred sixty-six

Expanded Form To EXPAND something is to stretch it out. In EXPANDED form, we write a number as the SUM (+) of each digit’s place values. We just break (decompose) a number into the value of each digit’s place: 56 = 50 + 6 342 = 300 + 40 + 2 1,789 = 1,000 + 700 + 80 + 9 36,721 = 30,000 + 6,000 + 700 + 20 + 1

Expanded Form: Your Turn! Decompose each number into its expanded form: 47 475 4,753 47,536 475,361 ANSWERS: 40 + 7 400 + 70 + 5 4,000 + 700 + 50 + 3 40,000 + 7,000 + 500 + 30 + 6 400,000 + 70,000 + 5,000 + 300 + 60 + 1

POP QUIZ! Use the following number to answer each question: 84,362. What digits are in the thousands period? In what place is the 4? What digit is in the hundreds place? What is the value of the 8? Write the number in word form. Write the number in expanded form.

POP QUIZ! Use the following number to answer each question: 84,362. ANSWERS: What digits are in the thousands period? 84 In what place is the 4? one thousands place What digit is in the hundreds place? 3 What is the value of the 8? 80,000 Write the number in word form. eighty-four thousand, three hundred sixty-two Write the number in expanded form. 80,000 + 4,000 + 300 + 60 + 2