Place value
Place value
Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases.

Learning Outcomes:

  1. Recognize the value of digits in three-digit numbers:

    • Students will understand that in a three-digit number, the first digit represents hundreds, the second represents tens, and the third represents ones.
  2. Decompose three-digit numbers:

    • Students will break down three-digit numbers into hundreds, tens, and ones. For example, they will recognize that 237 is made up of 200 (2 hundreds), 30 (3 tens), and 7 (7 ones).
  3. Identify place values:

    • Students will correctly identify the place value of digits in any three-digit number. For example, in the number 456, they will locate that 4 represents 400, 5 represents 50, and 6 represents 6.
  4. Compare numbers using place value:

    • Students will compare two three-digit numbers based on the values of the hundreds, tens, and one digits. For example, they will understand that 472 is greater than 465 because 7 tens is greater than 6 tens.
  5. Use place value to understand the size of numbers:

    • Students will develop an understanding that larger digits in the hundreds place represent larger amounts than those in the tens or ones places (e.g., knowing that 300 is much larger than 30 or 3).
  6. Apply place value in practical contexts:

    • Students will apply their understanding of hundreds, tens, and ones to real-world situations, such as counting large quantities of objects or understanding large numbers in everyday contexts.

These outcomes ensure that students build a solid foundation in place value, preparing them for more complex number operations.

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Place value helps us understand why a digit means something different depending on where it is in a number. Without place value, numbers would just be a jumble of digits! However, with place value, each digit has a specific role.

Definition:

Place value is the value a digit holds based on its position in a number. The farther left a digit is, the bigger its value becomes. Let’s break it down using a three-digit number like 706.

  • The 7 is in the hundreds place, representing 7 hundreds, or 700.
  • The 0 is in the tens place, which means there are no tens. So, its value is 0.
  • The 6 is in the ones place, representing 6 ones.

Together, 706 is made up of 7 hundreds, 0 tens, and 6 ones. You can see how each digit’s position gives it a different value, even though they're just single digits.

Special Case Examples:

  • 100: The 1 is in the hundreds place, so it means 1 hundred, with no tens or ones.
  • 300 – Here, the 3 in the hundreds place means 3 hundreds, and again, no tens or ones.

Whether you’re working with a simple number like 706 or larger numbers in the thousands or millions, understanding place value is the foundation for understanding math!

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