The Number and Operations in Base 10 domain of the CA Common Core Content Standards is about deeply understanding what a base 10 number system means, conceptually. The youngest grades focus on making 10 and realizing that grouping by tens makes counting easier to keep track of. This grows to the understanding of 10 tens to make the next place value (hundreds), and so on. In the upper grades, this becomes the generalization of powers, or the idea that each digit becomes 10 times greater than the digit to the right. This is extended to decimal understanding in grades 4 and 5, in preparation for exponential understanding in middle school and beyond.
The Number and Operations in Base 10 domain of the CA Common Core Content Standards is about deeply understanding what a base 10 number system means, conceptually. The youngest grades focus on making 10 and realizing that grouping by tens makes counting easier to keep track of. This grows to the understanding of 10 tens to make the next place value (hundreds), and so on. In the upper grades, this becomes the generalization of powers, or the idea that each digit becomes 10 times greater than the digit to the right. This is extended to decimal understanding in grades 4 and 5, in preparation for exponential understanding in middle school and beyond.
The better students understand the number system, the easier it is to efficiently reason with quantities and solve problems mentally. In the earliest grades, this means counting by 2s, 5s, and 10s, and the ability to recognize "friendly 10s" such as 40, 50, 60, etc. In grades 1-3, students begin to work with adding and subtracting by 10 at a time (example: knowing 24 + 10 makes 34 without counting). Then they begin partially solving to get to a friendly ten to make the rest of the problem easier (example: 48 + 32 becomes 48 + 2 = 50, plus the remaining 30 makes 80). Combining these skills and using them flexibly makes problem solving more efficient. In grades 4 and 5, this extends to how breaking down multi-digit numbers into their expanded form can help make sense of multi-digit multiplication and division.
The better students understand the number system, the easier it is to efficiently reason with quantities and solve problems mentally. In the earliest grades, this means counting by 2s, 5s, and 10s, and the ability to recognize "friendly 10s" such as 40, 50, 60, etc. In grades 1-3, students begin to work with adding and subtracting by 10 at a time (example: knowing 24 + 10 makes 34 without counting). Then they begin partially solving to get to a friendly ten to make the rest of the problem easier (example: 48 + 32 becomes 48 + 2 = 50, plus the remaining 30 makes 80). Combining these skills and using them flexibly makes problem solving more efficient. In grades 4 and 5, this extends to how breaking down multi-digit numbers into their expanded form can help make sense of multi-digit multiplication and division.
