AdministratorJanuary 22, 2022 at 7:22 am
So cool that you gave this a shot and you had some great engagement and sense making going on!
In every class I go into, students tend to estimate in decimals first – which I’m totally fine with as well – which suggests that they think in decimals. My hunch is because calculators spit out decimals and their understanding of the base 10 system works… however most can’t say what 0.7 is as a decimal (even though the place value name is ‘tenths’)!
As for what to ask or what I want from them convincing is just why they know what they know. I’m not really asking them necessarily to label (although that is helpful, too), but rather to tell me why each bar is constructed the way it is. For example, the student in the image is showing where “about” each worm went, but isn’t really telling us what those ‘notches’ represent as a fraction. If they verbally say “6 tenths” then I’m going to say “how do you know” and I’d expect them to show me by fully partitioning the bar into 10 and showing where the 6th bar is. Does that make sense?