Assessing Division Concepts and Remainders: World's Trickiest!

Okay, you think this is just one big joke:

"Want a Hurtz Donut?"
"Sure!"
"Ouch!"

Promise: hand your students a calculator and this assessment and you'll find out all sorts of things about what your students DON'T know about a concept they learned in 3rd grade: Division!

This is a fun and non-threatening away to assess what your students actually know about division without having them do some dumb algorithm which they'll never use for the rest of their lives (except for some assessment created by someone who uses calculators and spreadsheets to do division...)

This assessment address these four common issues that students misunderstand about division:

1) Small into big, or big into small? Students often judge division problems by the relative size of the numbers: if you sell 4 donuts for $2, then divide 2 into 4 and end up with $2 per donut. Uh, nooooooo......

2) This number doesn't go "into" this number: Contrary to what is shown in cruddy textbooks and even cruddier worksheets, most division problems do not work out evenly. In fact, students often look at problems like 22 ÷ 5 and refuse to complete it because "5 doesn't go into 22...." This assessment has no problems where the divisor goes into the dividend evenly.

3) What should I do with the remainder? Students often do not understand that there are no "rules" about how to leave a remainder: sometimes it can be a whole number, sometimes a decimal, sometimes a fraction, sometimes it tells us to round up, sometimes it tells us to round down, sometimes it has to be discarded entirely. This assessment looks at different ways of expressing remainders.

4) What does the remainder mean? Our students have almost no clue about what a remainder means; it's a complete and utter disaster. In this activity, remainders have to be interpreted in different ways.

This is a 2 page assessment that should be used with a calculator to facilitate assessing concepts rather than proficiency with a dumb algorithm. It has very specific explanations of the answers as well as "hot tips" on how to raise the understanding of division among your students. I promise this will provoke very thoughtful discussions about how well your students actually understand a simple operation like division...