Number - Comparing and Ordering Numbers

Place Value Columns: To compare numbers, we look at the value of each digit based on its position. Imagine a grid with columns for Thousands ($Th$), Hundreds ($H$), Tens ($T$), and Ones ($O$). When comparing two numbers like $4,532$ and $4,519$, we line them up in these columns to see which digits are different.

The Alligator Rule (Comparison Symbols): We use special symbols to show which number is bigger. The 'Greater Than' symbol ($>$) and the 'Less Than' symbol ($<$) look like an open alligator's mouth. The 'mouth' always opens toward the larger number. The 'Equal To' symbol ($=$) is used when both numbers have the exact same value.

Left-to-Right Comparison: Always start comparing from the largest place value (the digit furthest to the left). For example, in the numbers $3,450$ and $2,999$, we look at the Thousands place first. Since $3,000 > 2,000$, we know $3,450$ is greater without even looking at the other digits.

Counting Digits: A quick way to compare is to count how many digits a number has. A number with more digits is always greater than a number with fewer digits. For example, $1,000$ (4 digits) is always larger than $999$ (3 digits). Visualise this as a tall stack of blocks versus a shorter stack.

Ascending Order: This means arranging numbers from the smallest value to the largest value. Think of this like climbing up a staircase, where the first step is the lowest number (e.g., $10 \rightarrow 20 \rightarrow 30$).

Descending Order: This means arranging numbers from the largest value to the smallest value. Think of this like walking down a slide or a staircase, starting from the top with the biggest number (e.g., $500 \rightarrow 400 \rightarrow 300$).

The Number Line: Numbers can be placed on a horizontal line with arrows at both ends. On a number line, values increase as you move to the right and decrease as you move to the left. If number $A$ is to the right of number $B$, then $A > B$.

Tie-Breaking: If the digits in the highest place value are the same, move one column to the right and compare those digits. Continue this process until you find digits that are different. For example, to compare $6,782$ and $6,791$, both have $6$ thousands and $7$ hundreds, so we compare the tens: $8$ tens is less than $9$ tens.