# 2.1 - Place Value

The student will

a) read, write, and identify the place and value of each digit in a three-digit numeral, with and without models;

b) identify the number that is 10 more, 10 less, 100 more, and 100 less than a given number up to 999;

c) compare and order whole numbers between 0 and 999; and

d) round two-digit numbers to the nearest ten

### BIG IDEAS

• So that I can understand the value of each number in order to compare them
• So that I can round numbers and get a close number when the exact number is not needed
• So that I can understand that numbers are based on a simple pattern of tens where each place has ten times the value of the place to its right
• So that I can understand that reading, writing and identifying place value is essential to many other concepts in math

### UNDERSTANDING THE STANDARD

• The number system is based on a simple pattern of tens where each place has ten times the value of the place to its right.
• Numbers are written to show how many hundreds, tens, and ones are in the number.
• Opportunities to experience the relationships among hundreds, tens, and ones through hands-on experiences with manipulatives are essential to developing the ten-to-one place value concept of our number system and to understanding the value of each digit in a three-digit number. This structure is helpful when comparing and ordering numbers.
• Manipulatives that can be physically connected and separated into groups of tens and leftover ones (e.g., snap cubes, beans on craft sticks, pennies in cups, bundle of sticks, beads on pipe cleaners, etc.) should be used.
• Ten-to-one trading activities with manipulatives on place value mats provide experiences for developing the understanding of the places in the base-10 system.
• Models that clearly illustrate the relationships among ones, tens, and hundreds, are physically proportional (e.g., the tens piece is ten times larger than the ones piece).
• Flexibility in thinking about numbers is critical (e.g., 84 is equivalent to 8 tens and 4 ones, or 7 tens and 14 ones, or 5 tens and 34 ones, etc.).  This flexibility builds background understanding for the ideas used when regrouping.  When subtracting 18 from 174, a student may choose to regroup and think of 174 as 1 hundred, 6 tens, and 14 ones.
• Hundreds charts can serve as helpful tools as students develop an understanding of 10 more, 10 less, 100 more and 100 less.
• Rounding a number to the nearest ten means determining which two tens the number lies between and then which ten the number is closest to (e.g., 48 is between 40 and 50 and rounded to the nearest ten is 50, because 48 is closer to 50 than it is to 40).
• Rounding is an estimation strategy that is often used to assess the reasonableness of a solution or to give an estimate of an amount.
•  Vertical and horizontal number lines are useful tools for developing the concept of rounding.  Rounding to the nearest ten using a number line is done as follows:
• Locate the number on the number line.
• Identify the two closest tens the number comes between.
• Determine the closest ten.
• If the number in the ones place is 5 (halfway between the two tens), round the number to the higher ten.
• 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

• Demonstrate understanding of the ten-to-one relationships among ones, tens, and hundreds, using manipulatives. (a)
• Write numerals, using a model or pictorial representation (i.e., a picture of base-10 blocks). (a)
• Read three-digit numbers when shown a numeral, a model of the number, or a pictorial representation of the number. (a)
• Identify and write the place (ones, tens, hundreds) of each digit in a three-digit numeral. (a)
• Determine the value of each digit in a three-digit numeral (e.g., in 352, the 5 represents 5 tens and its value is 50). (a)
• Use models to represent numbers in multiple ways, according to place value (e.g., 256 can be 1 hundred, 14 tens, and 16 ones,  25 tens and 6 ones, etc.). (a)
• Use place value understanding to identify the number that is 10 more, 10 less, 100 more, or 100 less than a given number, up to 999. (b)
• Compare two numbers between 0 and 999 represented with concrete objects, pictorially or symbolically, using the symbols (>, <, or =) and the words greater than, less than or equal to. (c)
• Order three whole numbers between 0 and 999 represented with concrete objects, pictorially, or symbolically from least to greatest and greatest to least. (c)
• Round two-digit numbers to the nearest ten. (d)

### KEY VOCABULARY

Updated: Aug 22, 2018