# 4.1 - Place Value

The student will

a) read, write, and identify the place and value of each digit in a nine-digit whole number;

b) compare and order whole numbers expressed through millions; and

c) round whole numbers expressed through millions to the nearest thousand, ten thousand, and hundred thousand.

### BIG IDEAS

• So that I can use place value to help me understand the value of a number.

• So that I can use place value to better understand numeric operations.

• So that I can estimate when shopping and spending money.  For example, if  I know I have \$50 to spend, I need to round the price of each item first and then add them together to ensure I have enough money.

### UNDERSTANDING THE STANDARD

• The structure of the base-ten number system is based upon a simple pattern of tens, in which the value of each place is ten times the value of the place to its right.
• Place value refers to the value of each digit and depends upon the position of the digit in the number. For example, in the number 7,864,352, the 8 is in the hundred thousand place, and the value of the 8 is eight hundred thousand or 800,000.
• Whole numbers may be written in a variety of forms:
• Standard: 1,234,567
• Written: one million, two hundred thirty-four thousand, five hundred sixty-seven
• Expanded: (1,000,000 + 200,000 + 30,000 + 4,000 + 500 + 60 + 7)
• Numbers are arranged into groups of three places called periods (ones, thousands, millions).  The value of the places within the periods repeat (hundreds, tens, ones).  Commas are used to separate the periods.  Knowing the value of the place and period of a number helps students determine values of digits in any number as well as read and write numbers.  Students at this level will work with numbers through the millions period (nine-digit numbers).
• Reading and writing large numbers should be meaningful for students.  Experiences can be provided that relate practical situations (e.g., numbers found in the students’ environment including population, number of school lunches sold statewide in a day, etc.).
• Concrete materials such as base-ten blocks or bundles of sticks may be used to represent whole numbers through thousands.  Larger numbers may be represented by digit cards and place value charts or on number lines.
• Number lines are useful tools when developing a conceptual understanding of rounding with whole numbers. When given a number to round, locate it on the number line.  Next, determine the closest multiples of thousand, ten-thousand, or hundred-thousand it is between.  Then, identify to which it is closer.
• Mathematical symbols (>, <) used to compare two unequal numbers are called inequality symbols.

### ESSENTIALS

 The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to Read nine-digit whole numbers, presented in standard form and represent the same number in written form. (a)Write nine-digit whole numbers in standard form when the numbers are presented orally or in written form. (a)Identify and communicate, orally and in written form, the place and value for each digit in a nine-digit whole number. (a)Compare two whole numbers expressed through millions, using the words greater than, less than, equal to, and not equal to or using the symbols >, <,  =, or ≠. (b)Order up to four whole numbers expressed through millions. (b)Round whole numbers expressed through millions to the nearest thousand, ten thousand, and hundred thousand place. (c)Identify the range of numbers that round to a given thousand, ten thousand, and hundred thousand. (c)

### KEY VOCABULARY

Updated: Aug 22, 2018