Lesson 1.1.5
Comparing & Ordering Numbers
About 13 minutes
Three symbols
We often compare two numbers with three short symbols. “Less than” is written < — the small end points to the smaller number. “Greater than” is written > — the wide opening faces the larger number. When two numbers match, we use an equals sign: =.
Say it in words as well: “24 is less than 31,” “80 is greater than 65,” “17 equals 17.” The symbols are just a compact way to write the same idea.
Number line picture
If two numbers sit on the same number line, the one farther to the right is greater. The gap between them is how far apart they are — like steps you would count going from one to the other.
Try sliding A and B. When they land on the same spot, the numbers are equal and the gap is zero.
Move both sliders. The highlighted segment shows the gap between the two values. On a number line, the greater number always sits to the right.
38 < 72
38 is less than 72. The number farther right is greater.
Gap: 34 units
Bigger numbers: compare by place value
The number line idea still works for large numbers, but we rarely draw a line all the way to thousands. Instead, compare digits from the left. First compare the thousands; if those tie, compare the hundreds; then tens; then ones.
Example: 4,250 and 4,307 both start with 4 thousands — tie. Next column: 2 hundreds vs 3 hundreds. The second number wins, so 4,307 > 4,250. You do not need to look at the tens once the hundreds have decided it.
Ordering more than two
To order a list from smallest to largest, you can pick the smallest number first, then the next smallest, and so on — like standing people in a line by height. Another way is to group those with the same thousands, then sort inside each group.
Always check whether the question asks for smallest-to-largest or largest-to-smallest; reverse the list if needed.
Try it
Answer in your head or on paper, then open “Show answer” to check.
Fill in the symbol: 47 ___ 52
Show answer
47 < 52. Forty-seven is less than fifty-two (fewer steps along the number line from zero).
Fill in the symbol: 190 ___ 91
Show answer
190 > 91. One hundred ninety is greater: it has a digit in the hundreds place while 91 does not.
Fill in the symbol: 605 ___ 605
Show answer
605 = 605. The two numbers are the same, so use the equals sign.
Order from smallest to largest: 420, 42, 402, 240.
Show answer
42, 240, 402, 420. Only 42 is below 100. Among the rest, 240 has the smallest hundreds digit (2), then 402, then 420.
Which is greater, 6,088 or 6,808? Which place value column decides it?
Show answer
6,808 is greater. The thousands tie (6). The hundreds digit decides it: 8 hundreds beats 0 hundreds in the hundreds column.
List from largest to smallest: 1,010, 1,100, 1,001.
Show answer
1,100, 1,010, 1,001. All have 1 thousand; compare hundreds next — 1,100 has 1 hundred while the others have 0. Between 1,010 and 1,001, the tens digit breaks the tie (1 ten vs 0 tens).
End of this module
You can read symbols, use a number line, compare large numbers by place value, and order lists in either direction. That finishes the Numbers & Counting lessons for now — use the Path page any time to revisit a lesson. A short module quiz may arrive later to check what stuck. Next on the Path: module 1.2, Addition & Subtraction.