A student claims 43 and 34 are the same number because they use the same digits — a 3 and a 4. What is wrong with this reasoning?
AThe digits are not the same because 43 shows the 4 first and 34 shows the 3 first
BThe numbers are different because position matters: in 43 the 4 means 40, but in 34 the 4 means only 4
CThe numbers are the same; 4+3 = 3+4 = 7, so they represent the same total
DThe student is correct — numbers with the same digits always have the same value
The student is ignoring place value. In 43, the digit 4 is in the tens place — it means 40. In 34, the digit 4 is in the ones place — it means 4. These are completely different values: 43 = 40 + 3, while 34 = 30 + 4. Option C is a common mistake that confuses digit sums with number values. Place value means a digit's meaning depends entirely on its position.
Question 2 Multiple Choice
In the number 72, how much more is the tens digit worth than the ones digit?
A5 more, because 7 − 2 = 5
B7 times as much, because the tens place multiplies by 7
C68 more, because the tens digit means 70 and the ones digit means 2, and 70 − 2 = 68
DThey cannot be compared because they are in different places
In 72, the digit 7 is in the tens place, representing 70. The digit 2 is in the ones place, representing 2. The difference is 70 − 2 = 68. Option A (7 − 2 = 5) treats the digits as raw numbers rather than place-value quantities — the most common error. The point of place value is precisely that the same digit means different amounts depending on where it sits.
Question 3 True / False
In the number 55, both digits represent the same value because they are both the digit 5.
TTrue
FFalse
Answer: False
Although both digits look the same, their positions give them different values. The left 5 is in the tens place and represents 50. The right 5 is in the ones place and represents 5. So 55 = 50 + 5 — the two fives are worth very different amounts. This example perfectly illustrates why place value, not the digit itself, determines value.
Question 4 True / False
The digit 3 in the number 30 represents three groups of ten, not three individual ones.
TTrue
FFalse
Answer: True
In 30, the digit 3 occupies the tens place, meaning it represents 3 × 10 = 30. There are zero ones. This contrasts with the digit 3 in a number like 13, where the 3 is in the ones place and means 3. Place value is the system that gives digits their meaning — the digit alone tells you nothing without knowing its position.
Question 5 Short Answer
Why do 34 and 43 represent different quantities even though they use the same two digits? Use place value to explain.
Think about your answer, then reveal below.
Model answer: Place value means a digit's value depends on its position. In 34, the 3 is in the tens place (= 30) and the 4 is in the ones place (= 4), giving 30 + 4 = 34. In 43, the 4 is in the tens place (= 40) and the 3 is in the ones place (= 3), giving 40 + 3 = 43. The same digits in different positions represent completely different totals — 43 is 9 more than 34.
This is the core insight of place value: a digit is not a fixed quantity. It is a symbol whose meaning is determined by where it appears. Students who understand this can explain why digit order matters; students who don't will make errors with addition, comparison, and eventually multiplication and division that all depend on position-based reasoning.