Maria and José each have an identical pizza. Maria's is cut into 8 equal slices; José's is cut into 6 equal slices. Who gets more pizza if each takes 1 slice?
AMaria, because 8 is a bigger number than 6
BJosé, because his pizza was cut into fewer pieces, making each slice larger
CThey get the same amount, because they each take exactly 1 slice
DMaria, because fractions with larger denominators represent larger amounts
More cuts from the same whole means smaller pieces. José's pizza was divided into only 6 pieces, so each slice is larger than if the same pizza had been cut into 8. María's 8 slices are thinner. So 1/6 > 1/8. Options A and D are the core misconception: a larger denominator signals more cuts, which produces smaller pieces — the opposite of what the number's size might suggest.
Question 2 Multiple Choice
Which correctly orders these unit fractions from smallest to largest?
A1/2, 1/4, 1/6, 1/8
B1/8, 1/6, 1/4, 1/2
C1/6, 1/8, 1/4, 1/2
D1/8, 1/4, 1/6, 1/2
Unit fractions order opposite to their denominators. 1/8 is smallest (8 tiny pieces), then 1/6, then 1/4, then 1/2 (only 2 large pieces). The bigger the denominator, the smaller the fraction. This ordering runs counter to how whole numbers order (8 > 6 > 4 > 2), which is exactly what makes it counterintuitive and worth practicing explicitly.
Question 3 True / False
A strip of paper folded in half three times has 8 equal sections, and each section (1/8) is smaller than each section after only two folds (1/4).
TTrue
FFalse
Answer: True
Each fold doubles the number of sections and halves the size of each piece. After 1 fold: 2 sections of 1/2. After 2 folds: 4 sections of 1/4. After 3 folds: 8 sections of 1/8. More folds = more sections = smaller each section. This is a physical demonstration of why a larger denominator corresponds to a smaller unit fraction.
Question 4 True / False
1/6 is larger than 1/4 because 6 is a larger number than 4.
TTrue
FFalse
Answer: False
This is the core misconception. The denominator tells you how many equal parts the whole is divided into — a bigger denominator means more cuts, which means smaller pieces. 1/4 means the whole is split into 4 pieces; 1/6 means it's split into 6 smaller pieces. So 1/4 > 1/6, even though 4 < 6. The fraction ordering runs opposite to the denominator ordering for unit fractions.
Question 5 Short Answer
A classmate wants 1/8 of the cake instead of 1/6 because '8 is bigger than 6, so I'll get more.' How do you explain the error?
Think about your answer, then reveal below.
Model answer: A bigger denominator means more cuts, which makes each piece smaller, not bigger. If the cake is divided into 8 equal pieces, each piece is smaller than if it were divided into only 6. So 1/8 is actually less than 1/6. The denominator counts the number of cuts, not the size of each piece.
The denominator's role is to state how many equal pieces the whole is divided into. More pieces means the same whole is split further, giving smaller slices. A large denominator signals a small fraction: 1/8 < 1/6 < 1/4 < 1/3 < 1/2 < 1. This ordering contradicts the natural ordering of whole numbers, which is why the misconception is so persistent and explicit instruction is essential.