A student looks at the numerals 47 and 74 and says they must be 'about the same' because they use the same digits. What is wrong with this thinking?
ANothing — 47 and 74 are close in value because they share the same digits
BThe digits are the same so the numbers are the same; they just look different
CThe position of each digit changes its value: in 47 the 4 means 4 tens (40), but in 74 the 4 means only 4 ones (4)
D47 and 74 are different only because of how they are written, not because of their actual values
Position is everything in our number system. In 47, the 4 is in the tens place, meaning 4 × 10 = 40. In 74, the 4 is in the ones place, meaning just 4. So 47 = 40 + 7 and 74 = 70 + 4 — completely different values separated by 27. The misconception that the same digits make a 'similar' number ignores that place value, not the digit alone, determines what a numeral represents.
Question 2 Multiple Choice
What does the numeral 53 represent?
AEight, because 5 + 3 = 8
BFifty-three — five tens and three ones
CThirty-five — reading the digits from right to left
DFifteen — because the digits 5 and 3 both appear once
53 means five tens (50) and three ones (3) — the spoken name 'fifty-three' encodes this directly. Adding the digits together (5 + 3 = 8, option A) ignores place value entirely and treats the digits as simple numbers rather than position-dependent values. Reading right to left (option C) would give 35, which is a different number. The numeral's value comes from WHERE each digit sits, not from the digits themselves in isolation.
Question 3 True / False
In the numeral 47, the digit 4 represents 40 (four tens), not just the number 4.
TTrue
FFalse
Answer: True
The 4 in 47 is in the tens place, so its value is 4 × 10 = 40. This is the core insight of place value: the same digit can represent completely different quantities depending on its position. A 4 in the ones place is worth 4; in the tens place it is worth 40; in the hundreds place it would be worth 400. Recognizing this positional meaning is what separates numeral recognition from genuine number sense.
Question 4 True / False
The numeral 31 and the numeral 13 represent the same quantity because they use the same digits.
TTrue
FFalse
Answer: False
31 = 3 tens + 1 one = 31. 13 = 1 ten + 3 ones = 13. They are completely different quantities — 31 is nearly twice as large as 13. Using the same digits does not produce the same number; position determines value. This is the same principle that makes 47 ≠ 74. The teen numbers (13–19) make this especially tricky because the spoken name ('thirteen') puts the smaller part first, even though the numeral 13 places the ten on the left.
Question 5 Short Answer
Why does the position of a digit in a numeral matter when recognizing two-digit numbers?
Think about your answer, then reveal below.
Model answer: In a two-digit numeral, the left digit tells you how many tens and the right digit tells you how many ones. The position determines the digit's value — the same digit 4 means 40 in the tens place but only 4 in the ones place. Without understanding position, you cannot correctly identify what quantity a numeral represents.
Our number system is a place-value system: each position is worth ten times more than the position to its right. So 47 is not '4 and 7' but rather '4 tens and 7 ones.' This is why number recognition goes beyond knowing digit shapes — it requires connecting the written numeral to the place-value structure it encodes, which is the foundation for all arithmetic that follows.