Study Guide
Math Unit—Numbers and Place Value
Learning Targets
At the end of this unit—
1) I can read, write, and model six-digit numerals and identify the place
value positions, value of each digit, and the relationship of each place
value position to the next.
2) I can round whole numbers, 9,999 or less, to the nearest ten,
hundred, and thousand and represent my thinking using pictures,
numbers, and words.
3) I can compare two whole numbers between 0 and 9,999, using
symbols (<, >, or =) and words (greater than, less than, equal to).
Vocabulary
Place Value
place value—the value of a digit based on its position in a number
5
,
Ones
3
Tens
Thousands
2
Hundreds
Ten Thousands
value—how much a
number is worth
Hundred Thousands
The comma is critical!
4
8
6
The value of the “8” is 80.
The value of the “5” is 5,000.
digit—0, 1, 2, 3, 4, 5, 6, 7, 8, 9
standard form—writing a number using digits; example: 374,512
expanded form—writing a number using each number’s value
example: 300,000 + 70,000 + 4,000 + 500 + 10 + 2 or
(3 x 100,000) + (7 x 10,000) + (4 x 1,000) + (5 x 100) + (1 x 10) + (2 x 1)
word form—writing a number using words
period—a group of three digits in a number separated by a comma
example: 374,512
374 is called the thousands period and 512 is called the units period
whole number—the numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, etc.
(counting numbers, no fractions)
numeral—a digit, used alone or with others, to express a number
Rounding Numbers
round—write a number to the nearest ten, hundred, or thousand
examples:
38 to the nearest ten = 40
238 to the nearest hundred = 200
1,238 to the nearest thousand = 1,000
7,286
7,286 to the nearest ten = 7,290
7,286 to the nearest hundred = 7,300
7,286 to the nearest thousand = 7,000
estimate—to give an approximate number or answer; to tell about how
many
Rounding Rule
6 9 rounded to the nearest ten
69
The circled digit is a 9, so the underlined digit is
rounded up to the next ten—7 0
1. Underline the place value you want to round.
2. Circle
the digit to the right.
Is the circled digit a
Is the circled digit a
1, 2, 3, or 4?
5, 6, 7, 8, or 9?
The underlined digit
stays the same.
The underlined digit is
rounded up.
4 and below…
LET IT GO
5 and above…
GIVE IT A SHOVE
Comparing Numbers
compare—decide if numbers are equal to (=), less than (<), or greater
than (>) each other
examples:
504 < 732
3,673 > 3,214
6,748 = 6,748
Examples of what each student will be able to do:
Place Value
Given a number, the student will write the number in standard form,
expanded form, and word form.
standard form—457,612
expanded form—
400,000 + 50,000 + 7,000 + 600 + 10 + 2 or
(4 x 100,000) + (5 x 10,000) + (7 x 1,000) + (6 x 100) + (1 x 10) + (2 x 1)
400,000
50,000
7,000
600
10
+
2
457,612
word form—four hundred fifty-seven thousand,
six hundred twelve
(The student should also be able to read
the number orally.)
Rounding Numbers
7,612 rounded to the nearest ten = 7,610
7,612 rounded to the nearest hundred = 7,600
7,612 rounded to the nearest thousand = 8,000
Comparing Numbers
Begin comparing the numbers in the thousands place. If they are the
same, move on.
7,824
7,842
Next, look at the hundreds place. If they are the same, move on.
7,824
7,842
Then, look at the tens place.
7,824
7,842
The 2 is less than the 4, so 7,824 is less than 7,842.
7,824 < 7,842