Ones and tens

"Ones and tens" typically refers to a foundational concept in mathematics, particularly in understanding the place value system in base-10 (decimal) notation.

  1. Ones: This represents the single units in a number. For example, in the number 7, the '7' is in the ones place.

  2. Tens: This represents groups of ten. In the number 34, the '3' is in the tens place, indicating 30 (or three groups of ten).

Understanding ones and tens is essential for performing arithmetic operations, as it helps in grasping larger numbers, carrying over digits in addition, and borrowing in subtraction. This concept is foundational in primary education for developing numerical literacy.

Part 1: Intro to place value

Sal uses the number 37 to explain why we use a "ones place" and a "tens place" when writing numbers. 

Here are the key points to learn when studying "Intro to Place Value":

  1. Definition of Place Value: Understand that place value refers to the value of a digit based on its position within a number.

  2. Digits and Positions: Familiarize yourself with the concept that each digit in a number has a specific value determined by its position (units, tens, hundreds, etc.).

  3. Base-10 System: Recognize that the place value system is based on powers of 10, with each position (or place) representing a power of 10.

  4. Reading and Writing Numbers: Practice reading and writing numbers in both standard form (e.g., 345) and expanded form (e.g., 300 + 40 + 5).

  5. Identifying Place Values: Learn how to identify the place value of a specific digit in a number (e.g., in 487, the 8 is in the tens place).

  6. Comparing Numbers: Develop skills in comparing numbers based on their place values (e.g., understanding that 2,500 is greater than 2,049).

  7. Adding and Subtracting with Place Value: Apply place value understanding to perform addition and subtraction, aligning numbers by their place values.

  8. Using Zero: Understand the role of zero in the place value system, especially as a placeholder in larger numbers.

By mastering these fundamentals, you'll build a strong foundation for understanding larger numbers and more complex mathematical concepts.

Part 2: Place value example: 25

Sal shows 25 as 2 tens and 5 ones.

When studying the place value of the number 25, focus on these key points:

  1. Understanding Digits: The number 25 consists of two digits: 2 and 5.

  2. Place Value of Each Digit:

    • Tens place: The digit 2 is in the tens place, meaning it represents 20 (2 x 10).
    • Ones place: The digit 5 is in the ones place, representing 5 (5 x 1).
  3. Total Value: The total value of the number 25 is the sum of the values of its digits: 20 + 5 = 25.

  4. Importance of Position: The position of each digit within the number determines its value.

  5. Visual Representation: Using base-ten blocks or diagrams can help visualize the concept of place value.

By understanding these points, you can grasp the concept of place value effectively.

Part 3: Place value example: 42

Sal shows 42 as 4 tens and 2 ones.

To study the concept of place value using the example of "42," focus on these key points:

  1. Digits and Their Places: The number 42 consists of two digits: '4' and '2'.

  2. Value of Each Digit:

    • The '4' is in the tens place, representing 40 (4 x 10).
    • The '2' is in the units (or ones) place, representing 2 (2 x 1).
  3. Composition of the Number: Combine the values of the digits to understand that 42 equals 40 + 2.

  4. Expanded Form: Write 42 in expanded form as 40 + 2 to illustrate its place values clearly.

  5. Understanding Larger and Smaller Values: Recognize how place value changes the meaning of digits; for example, changing '4' to '40' significantly increases its value.

By mastering these points, one can grasp the foundational concept of place value in numbers.