· The structure of the Base-10 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 eight is in the hundred thousands place, and the value of the 8 is eight hundred thousand or 800,000. · Whole numbers may be written in a variety of formats: · Standard: 1,234,567 · Written: one million, two hundred thirty-four thousand, five hundred sixty-seven · Expanded: (1 ´ 1,000,000) + (2 ´ 100,000) + (3 ´ 10,000) + (4 ´ 1,000) + (5 ´ 100) + (6 ´ 10) + (7 ´ 1) · Numbers are arranged into groups of three places called *periods* (ones, thousands, millions, …). 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 find values of digits in any number as well as read and write 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-10 blocks and bundles of sticks may be used to represent whole numbers through thousands. Larger numbers may be represented by digit cards and place value charts. · Mathematical symbols (>, <) used to compare two unequal numbers are called *inequality symbols*. · A procedure for comparing two numbers by examining place value may include the following: ** ** – Compare the digits in the numbers to determine which number is greater (or which is less). – Use a number line to identify the appropriate placement of the numbers based on the place value of the digits. – Use the appropriate symbol > or < or words *greater than* or *less than* to compare the numbers in the order in which they are presented. – If both numbers have the same value, use the symbol = or words *equal to*. – A strategy for rounding numbers to the nearest thousand, ten thousand, and hundred thousand is as follows: Use a number line to determine the rounded number (e.g., when rounding4,367,925 to the nearest thousand, identify the ‘thousands’ the number would fall between on the number line, then determine the thousand that the number is closest to): Look one place to the right of the digit to which you wish to round. If the digit is less than 5, leave the digit in the rounding place as it is, and change the digits to the right of the rounding place to zero. If the digit is 5 or greater, add 1 to the digit in the rounding place and change the digits to the right of the rounding place to zero. | All students should · Understand the base ten place value system. · Use the patterns in the place value system to read and write numbers. · Understand that reading place value correctly is essential when comparing numbers. · Understand that rounding gives a close number to use when exact numbers are not needed for the situation at hand. · Develop strategies for rounding. **Essential Questions:**
· How do patterns in our place value number system help us read, write, order and compare whole numbers? · How can a whole number be represented using models? · What does it mean to round numbers, and when is it appropriate? · What are strategies for rounding whole numbers? | · Identify and communicate, both orally and in written form, the placed value for each digit in whole numbers expressed through the one millions place. · Identify and communicate, both orally and in written form, the placed value for each digit in whole numbers expressed through the one millions place. · Read whole numbers through the one millions place that are presented in standard format, and select the matching number in written format. · Write whole numbers through the one millions place in standard format when the numbers are presented orally or in written format. · Identify and use the symbols for *greater than*, *less than*, and *equal to*. · Compare two whole numbers expressed through the one millions, using symbols >, <, or =. · Round whole numbers expressed through the one millions place to the nearest thousand, ten thousand, and hundred-thousand place. |