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

2. 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:
, , ,794

3. 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)

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

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

6. 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.

7. Places & Periods
987 million, 654 thousand, 321

8. 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?

9. 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.

10. 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).

11. 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.

12. 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.

13. Standard Form The word, STANDARD, means “normal,” or “regular.”
So, when writing in standard form, we simply write numbers in their regular form:
, ,177

14. 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

15. 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!

16. 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

17. 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). =
Forty-two thousand three hundred fifty-nine

18. 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

19. 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 =
342 =
1,789 = 1,
36,721 = 30, ,

20. Expanded Form: Your Turn!
Decompose each number into its expanded form: 47
475
4,753
47,536
475,361
ANSWERS:
40 + 7 4,
40, ,
400, , ,000 +

21. 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.

22. 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 , ,