What’s going on here? What’s the misconception? What is there to build on?

Thanks to Nathan Kraft for the submission. Click on the blue words to check out his blog and this blue word to follow his tweets.

  • I love this question. I have used similar questions extensively when assessing comparing fractions, decimals and percents. I can only attribute this mistake as to a misconception with the number system, and wonder exactly how these students are being instructed when they are introduced to fractions and decimals.

  • In addition to the problem surrounding an infinity of 6’s, “rounding off” a 0.66 would make it 0.67 (as is done by most calculators). To build, will probably need to clarify “truncating” decimals first, showing how 0.666600 isn’t like 0.666666 before hitting with 0.6666666….

  • I think GregT makes a good point that we first want to follow up on the notion of truncating vs. rounding, but then also follow up on the notion of equals. What does it mean for two numbers to be equal? If I round or truncate a number do I get an equal number?