# 3.1 - Place Value

The student will

a)  read, write, and identify the place and value of each digit in a six-digit whole number, with and without models;

b)  round whole numbers, 9,999 or less, to the nearest ten, hundred, and thousand; and

c)  compare and order whole numbers, each 9,999 or less.

### BIG IDEAS

• So that we can represent any number with just 10 digits.

• So that we can measure and talk about our world.

• So that I can make estimates.

• So that I can build my understanding of greater than, less than, and equal to.

### UNDERSTANDING THE STANDARD

• The structure of the base-ten number system is based upon a simple pattern of tens, where each place is ten times the value of the place to its right. This structure, known as a ten-to-one place value relationship, is helpful in comparing and ordering numbers.
• Models that clearly illustrate the relationships among hundreds, tens, and ones are physically proportional (e.g., the tens piece is ten times larger than the ones piece).
• Place value refers to the value of each digit and depends upon the position of the digit in the number. In the number 7,864, the 8 is in the hundreds place, and the value of the 8 is eight hundred.
• Flexibility in thinking about numbers — or “decomposition” of numbers (e.g., 2,345 is 23 hundreds, 4 tens, and 5 ones, or 2 thousands, 34 tens, and 5 ones, or 22 hundreds, 13 tens, and 15 ones, etc.) — is critical and supports understandings essential to addition/subtraction and multiplication/ division.  This flexibility also builds background understanding for the ideas that students use when regrouping (e.g., When subtracting 18 from 174, a student may choose to regroup and think of 174 as 1 hundred, 6 tens, and 14 ones, while another child might regroup 174 as 1 hundred, 5 tens, and 24 ones.  Then subtract 18 from 24.).
• Whole numbers may be written in a variety of formats:
• Standard: 123,456;
• Written: one hundred twenty-three thousand, four hundred fifty-six; and
• Expanded: 100,000 + 20,000 + 3,000 + 400 + 50 + 6
• Numbers are arranged into groups of three places called periods (ones, thousands, millions, and so on). Places within the periods repeat (hundreds, tens, ones). Commas are used to separate the periods. Knowing the place value and period of a number helps students determine the value of a digit in any number as well as read and write numbers.
• Reading and writing large numbers should be related to numbers that have meanings (e.g., numbers found in the students’ environment). Rounding is an estimation strategy that is often used to assess the reasonableness of a solution or to estimate an amount.
• Students should explore reasons for estimation, using practical experiences, and use rounding to solve practical problems.
• The concept of rounding may be introduced through the use of a number line. When given a number to round, locate it on the number line. Next, determine the closest multiples of ten, hundred, or thousand it is between. Then, identify to which it is closer.

### ESSENTIALS

The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to

• Read six-digit numerals orally. (a)
• Write six-digit numerals in standard form that are stated verbally or written in words. (a)
• Represent numbers up to 9,999 in multiple ways, according to place value (e.g., 256 can be 1 hundred, 14 tens, and 16 ones, but also 25 tens and 6 ones), with and without models. (a)
• Determine the value of each digit in a six-digit whole number (e.g., in 165,724, the 7 represents 7 hundreds and its value is 700).  (a)
• Round a given whole number, 9,999 or less, to the nearest ten, hundred, and thousand. (b)
• Solve problems, using rounding of numbers, 9,999 or less, to the nearest ten, hundred, and thousand. (b)
• Compare two whole numbers, each 9,999 or less, using symbols (>, <, =, or ≠) and/or words (greater than, less than, equal to, and not equal to). (c)
• Order up to three whole numbers, each 9,999 or less, represented with concrete objects, pictorially, or symbolically from least to greatest and greatest to least. (c)

### KEY VOCABULARY

Updated: Aug 22, 2018