PS, I’ve liked other posts – “problems” in Math Memos. My approach is “jump into a problem and try to swim” – so it’s great to have access to some doozies. Thank you and keep ’em coming!

Cheers,

Richard

]]>Eric

]]>The Name Race is an icebreaker and name activity I’ve been using with students the first time I meet them. It doesn’t require students to memorize each other’s names, so it’s low stakes, but it’s energizing and fun: http://www.collectedny.org/frameworkposts/name-race/

I didn’t get a chance to do the Handshake Problem with my class. It’s been a struggle to decide what I should do and what I don’t have time for, with only one class a week. I did give the class a visual pattern (http://www.collectedny.org/frameworkposts/a-collection-of-visual-pattern-handouts/) with a growth pattern that is the same as the handshake problem (1, 3, 6, 10, 15, 21, etc.) but we haven’t had a chance to go over it as a group and only one students figured out a generalization for it on his own. Similar to you, my goal at the time was for them to recognize patterns and not necessarily make a generalization. I think it takes a fair amount of guidance for most of our students to get to a generalization for the handshake problem.

Best,

Eric

We usually don’t give the answers as a way to encourage teachers to find their own strategies and approaches to engage with the math.

My strategy starts off similar to yours. I found the volume of both aquariums – 24,000 cubic cm and 81,000 cubic cm. Then I divided the volume of the larger tank (81,000) by the volume of the smaller one (24,000) to try to figure out how many times bigger the larger one is. I got 3.375, which meant to me that the larger tank is 3.375 times larger than the smaller tank. So I figured the price should be 3.375 times greater as well. Since the small one costs $24, the larger one should cost 3.375 times more than that. Or, as you found as well, $81. Thanks for your comment. How do you think your students might approach the problem?

]]>I am not the most confident math teacher, but this is how I did it:

I found the volume for both tanks – the small one is 24,000 cm and the large is 81,000 cm.

Then I set up a proportion: 24,000 over 81,000 and 24 over x.

Then I cross-multiplied and divided 81,000 times 24 divided by 24,000 and got 81 cm.

How did I do?

]]>I think what my students enjoy about these problems is that most of them can see that they have important ideas to contribute, so they become more confident and more engaged! ]]>

Thank you so much for the lovely comment. The icebreaker/classroom challenges at the beginning of class have been really helpful, I think, in helping form a group and generating empathy and collaboration among a multi-level, multi-age group. This time around, I’m making a point of asking the group to reflect after each of these activities: What was this like for you? What can we learn from this activity? There have been some lovely moments where students share their initial fears and express appreciation for each other.

I’ll be sharing other activities I have tried this semester, but they’re all listed in the icebreakers section in Framework Posts, if you’re interested: http://www.collectedny.org/fpsubjects/icebreakers/

Thanks again,

Eric