Put these numbers in order from least to greatest: 37, 31, 45, 39. Which list is correct?
A31, 37, 39, 45
B31, 39, 37, 45 — order by ones digit (1, 9, 7, 5)
C45, 39, 37, 31 — that is greatest to least
D37, 31, 39, 45 — put the smaller 30s first in any order
All four numbers have tens digits of 3, 3, 3, and 4. The 40s number (45) is largest, so it goes last. Among the three 30s, compare ones digits: 1 < 7 < 9, giving 31, 37, 39. Option B is the classic error — sorting by ones digit rather than tens digit first.
Question 2 Multiple Choice
You are ordering 54, 47, and 58. Which number belongs in the middle position?
A47 — it has the smallest tens digit
B54 — it is between 47 and 58
C58 — it has the largest ones digit
D51 — it is halfway between 47 and 58
47 has a tens digit of 4; 54 and 58 both have tens digits of 5. So 47 is least. Between 54 and 58, compare ones: 4 < 8, so 54 < 58. The order is 47, 54, 58 — and 54 is in the middle. Option D names a number not even in the set, which is a common error when students try to calculate a middle rather than ordering what they were given.
Question 3 True / False
When two numbers share the same tens digit, you compare their ones digits to determine which is smaller.
TTrue
FFalse
Answer: True
Correct. The tens digit is the primary sort key. Only when tens digits are equal do you move to the ones digit as a tiebreaker. For example, 47 and 43 both have tens digit 4, so you compare 7 and 3: since 3 < 7, the number 43 is smaller.
Question 4 True / False
When ordering the numbers 63, 28, and 71 from least to greatest, the best first step is to compare their ones digits.
TTrue
FFalse
Answer: False
The tens digit is always compared first. Here the tens digits are 6, 2, and 7 — all different — so the order is determined immediately: 28 (2 tens), 63 (6 tens), 71 (7 tens). You only need to examine ones digits when two or more numbers share the same tens digit.
Question 5 Short Answer
A student arranges 42, 18, 47, and 23 as: 18, 23, 42, 47. Explain the rule the student used to get this correct order.
Think about your answer, then reveal below.
Model answer: The student sorted by tens digit first: 18 (1 ten) comes before 23 (2 tens), which comes before 42 and 47 (4 tens each). For the two numbers that share a tens digit (42 and 47), the student then compared ones digits: 2 < 7, so 42 comes before 47.
This two-step rule — tens first, ones as a tiebreaker — is the core of ordering two-digit numbers. It mirrors place value: tens represent larger groups, so they dominate the comparison. Ones only matter when tens are equal, just as you sort houses by block before sorting by house number within a block.