Number - Place Value up to 10,000

Place Value Columns: Every four-digit number is made of Thousands ($Th$), Hundreds ($H$), Tens ($T$), and Ones ($O$). Imagine a grid where each digit has its own house; the value of a digit depends on which house it lives in. For example, in $4,521$, the $4$ is in the Thousands house.

Base-10 Visual Representations: We can visualize numbers using blocks. A large 'cube' represents $1,000$, a flat 'square' represents $100$, a 'rod' represents $10$, and a tiny 'unit cube' represents $1$. To show $2,341$, you would draw $2$ large cubes, $3$ flats, $4$ rods, and $1$ unit cube.

Expanded Form: This is writing a number to show the value of each digit as an addition sentence. For the number $8,763$, the expanded form is $8,000 + 700 + 60 + 3$. It helps us see exactly how much each part of the number is worth.

Comparing and Ordering: To find which number is bigger, we compare digits starting from the left (Thousands). If the Thousands are the same, we look at the Hundreds, and so on. We use the 'alligator mouth' symbols: $>$ (greater than), $<$ (less than), and $=$ (equal to).

Rounding to the Nearest 1,000: Visualize a number on a hill. If the Hundreds digit is $0, 1, 2, 3,$ or $4$, the number slides back down to the current thousand. If the Hundreds digit is $5, 6, 7, 8,$ or $9$, it has enough energy to climb over the peak to the next thousand.

Partitioning: Numbers can be split in different ways, not just by place value. For example, $1,500$ can be partitioned into $1,000 + 500$, or it can be seen as $15$ Hundreds or $150$ Tens. This is like sharing $1,500$ marbles into different sized bags.

Number Line Placement: On a number line from $0$ to $10,000$, the halfway point is $5,000$. Visualizing where a number sits (closer to $0$ or closer to $10,000$) helps in understanding the magnitude and scale of large numbers.