Number Sense: The student understands place value and how numbers relate, and fluently performs basic mental calculations and written operations.
Understanding the value of each digit within a number is important to understanding the value of the whole number and how it compares to other numbers. Every grade level begins the year discussing place value and how we can represent numbers in multiple ways:
Place Value Chart: As pictured above, a chart that clearly shows how a number is composed of multiple places. We can use standard numbers, or base ten blocks, or other manipulatives with a place value chart.
Standard Form: 14,389
This form shows the regular numeric representation of a number
Expanded Form: 10,000 + 4,000 + 300 + 80 + 9
This form shows the values contained within a number
Word Form: fourteen thousand, three hundred eighty-nine
This form shows how we write and say numbers correctly
Note: We do not use the word "and" in whole number word form (e.g., One hundred and forty-two). In American English, "and" is used only to indicate a decimal point (e.g. One hundred forty-two and five tenths).
We can use place value charts to help us see how arithmetic operations affect numbers (especially with regrouping from one place to an adjacent place):
When discussing numbers, ask about the value of the digits within the number
When completing vertically-oriented algorithms, ensure the place of each number is lined up properly. Grid paper can help provide visual cues for lining up numbers.
Use a place value chart if a student is struggling to understand why regrouping is needed when performing arithmetic operations. You can quickly draw one, or print out one of these pre-made charts: A4, A3. Buttons, dried beans, poker chips, toothpicks, and paperclips can represent numbers on a physical place value chart.