Non-Intuitive Answers

Multiplication of Fractions: Fractions get smaller and students are used to multiplication answers (products) being larger than whatever they started with. Mathematics Teaching in the Middle School has an excellent article update ("The Future of Fractions" was first published in 1978) by Zalman Usiskin from the University of Chicago -- the driving force behind the K-6 Everyday Math curriculum.

One of the features in the article was a NAEP (National Assessment of Educational Progress) items from 1978 for thirteen-year-olds.

Estimate the answer to: 12/13 + 7/8
You will not have time to solve the problem using paper and pencil (let alone a calculator!!)

The choices given -- and percents responding were

1 (7%)
2 (24%)
19 (28%)
21 (27%)
"I don't know" (14%)

Fractions have always been a sore spot for many and it is that foundational upper elementary/lower middle school Math that enables students to succeed in high school and beyond. It also contributes greatly to Math confidence or lack thereof.