Misconceptions & Reasoning
📋 What it is
The big traps: adding denominators, thinking a bigger denominator means a bigger fraction, and forgetting equal parts.
🗣️ Coach says
Everybody hits the same fraction traps. Adding the bottoms. Thinking 1/8 > 1/3 because 8 > 3. Forgetting that parts must be equal. Knowing the traps by name means you catch yourself before you fall in.
🧠 Memory hook
Bottoms don’t add. Bigger bottom = smaller piece. Parts must be EQUAL.
😂 Giggle
Why did the pizza go to math class?
To learn how to be divided into equal slices!
😲 Whoa!
Research shows the “bigger denominator = bigger fraction” trap is so strong that even many adults fall for it under time pressure.
✅ Quick check: A classmate writes 1/4 + 1/4 = 2/8. Name the trap and give the right answer.
Say your answer out loud first — then reveal.
The “add the bottoms” trap — the bottom stays 4, so it’s 2/4 = 1/2.
The denominator names the piece size and does not add.
🧪 Try it! (2 minutes)
Catch the trap: for 1/3 vs 1/5, predict which is bigger, then draw both. Notice the pull to pick 1/5 because 5 is bigger.