A teacher gives a student the cards 5, 12, 3, 9 and asks her to put them in order from least to greatest. Which order is correct?
A3, 5, 9, 12
B12, 9, 5, 3
C5, 3, 12, 9
D3, 9, 5, 12
Ordering from least to greatest means arranging numbers as they appear from left to right on the number line. 3 is leftmost (smallest), then 5, then 9, then 12 (greatest). Option B is greatest to least. Options C and D are scrambled with no consistent ordering.
Question 2 Multiple Choice
A student says '9 is bigger than 10 because 9 comes earlier when you count.' What is wrong with this reasoning?
ANothing is wrong — numbers that appear earlier in counting are always larger
BComing earlier in counting means a number is less than what comes after it, so 9 is less than 10
CThe student is right for single-digit numbers but wrong for two-digit numbers
DThe comparison only works if both numbers are on the same number line
On the number line, earlier means smaller — numbers to the left (coming sooner in the count) are less than numbers to the right. 9 comes before 10 in counting, which means 9 is less than 10, not greater. This misconception often arises because students confuse 'earlier in the sequence' with 'more.'
Question 3 True / False
On a number line, a number that appears to the left of another number is greater than that number.
TTrue
FFalse
Answer: False
Left means smaller on a standard number line. Numbers increase as you move to the right. A number to the left is always less than numbers to its right. So if 5 is to the left of 8, then 5 < 8.
Question 4 True / False
The number 15 is greater than the number 8 because 15 is farther to the right on the number line.
TTrue
FFalse
Answer: True
The number line rule is consistent: farther right always means greater. 15 is well to the right of 8 on a 0–20 number line, confirming 15 > 8. This rule applies to all numbers, not just round ones.
Question 5 Short Answer
Why is the number line a useful tool for ordering numbers?
Think about your answer, then reveal below.
Model answer: The number line places every number in a fixed position that reflects its size. Numbers to the right are always greater; numbers to the left are always smaller. To order a set of numbers, you find where each one lives on the line and read them in the requested direction — left to right for least to greatest, right to left for greatest to least.
The number line makes relative size visual and immediate. Rather than comparing pairs of numbers abstractly, you can locate each number in space and read the ordering directly. This also builds intuition that 'greater' has a consistent, spatial meaning — a foundation for all later work with magnitude.