A student compares 73 and 69 by looking at the ones digits first: 3 < 9, so she concludes 69 > 73. What went wrong?
AShe should have compared the tens first; 7 tens > 6 tens, so 73 > 69
BShe should have added all digits: 7+3=10, 6+9=15, so 69 is larger
CShe was correct; 3 is less than 9, so 73 is smaller
DThe comparison doesn't work for numbers with different ones digits
Tens are compared first because the tens digit determines roughly how large a number is. 73 has 7 tens and 69 has only 6 tens — since 7 tens (70) is greater than 6 tens (60), we know 73 > 69 without even looking at the ones. The ones digit only matters when the tens digits are equal.
Question 2 Multiple Choice
Two numbers both have 5 tens. One has 8 ones; the other has 2 ones. Which is greater?
AThe number with 2 ones, because 2 is the first ones digit you see and you compare left to right
BThe number with 8 ones, because when tens are equal, the ones digit decides
CThey are equal because they both have 5 tens
DYou cannot compare them without knowing the complete two-digit numbers
When the tens digits are equal, we move to the ones place to break the tie. 58 and 52 both have 5 tens — so we compare the ones: 8 ones > 2 ones, therefore 58 > 52. Option C is the classic trap: equal tens does not mean equal numbers.
Question 3 True / False
When comparing 48 and 51, you should look at both the tens digit and the ones digit to determine which number is greater.
TTrue
FFalse
Answer: False
Only the tens digits are needed here. 51 has 5 tens and 48 has only 4 tens — since 5 tens > 4 tens, 51 > 48 without any need to examine the ones digits. You only need the ones when the tens are equal.
Question 4 True / False
In the number 67, the digit 6 represents a greater value than the digit 7.
TTrue
FFalse
Answer: True
The digit 6 is in the tens place, meaning it represents 60. The digit 7 is in the ones place, meaning it represents 7. Even though 7 > 6 as raw digits, their place values reverse the comparison: 60 >> 7. This is exactly why we always compare tens first.
Question 5 Short Answer
Explain why the tens digit is compared first when comparing two-digit numbers, rather than looking at both digits at once.
Think about your answer, then reveal below.
Model answer: The tens digit represents groups of ten, so it captures the bulk of each number's value. One group of ten (10) is always larger than any number of ones (at most 9), so whoever has more tens has the larger number — regardless of the ones. The ones digit is a tiebreaker that only matters when both numbers have the same number of tens.
Understanding this requires seeing digits as place-value quantities, not just symbols. 7 in the tens place means 70; 9 in the ones place means 9. 70 > 9, which is why the tens comparison dominates. Students who compare 'digit by digit' without this understanding often make errors on pairs like 73 vs. 69 or 81 vs. 97.