Math Memos

The Multiples of Nine Problem

I recently discovered this problem, and I really like it for a number of reasons. First, it requires a little bit of vocabulary in order to get started. Students will have to know what a multiple is, they will have to know what digits are—and more specifically, how digits can differ from numbers—and they’ll have to understand the difference between even and odd numbers. I also like how nonintimidating it looks at first glance. “How hard could it be to find a multiple of 9 that has only even digits? I shouldn’t have to count up very far.” Because the problem doesn’t look lengthy or challenging, it comes as a surprise when the correct answer is actually the 32nd multiple of nine. I anticipate a lot of students writing out 9, 18, 27, 36, 45, 54, etc, and then getting frustrated or giving up when they don’t get to the answer fairly quickly.

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The Cookie Problem

The cookie problem does not require any advanced mathematics techniques, but it is quite challenging nonetheless.  Thus, it is a “problem” for my students, but it has few barriers to entry and is approachable for everyone in my classes.  Without giving any parameters for a solution, students can come up with a variety of ways to solve the problem.  In the end, those various representations present a verdant opportunity for discussing algebra, algebraic thinking, diagrams, as well as mean and median and central tendency, and arithmetic series.  So, altogether, it is a simple but rich problem.

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The Banquet Table Problem

I was really excited about using this problem in my class because I felt that students with little knowledge about functions or algebra would still be able to answer it. Students would be able to use pictures and charts to get to the answers, and once different students had the answers, we could use that to lead into a discussion about functions. Often times students ask the question, “When will I ever use this?” By using different methods to solve these functions before we talk about functions, students will already know at least one scenario where they would use it.

Continue reading how Randy Raux used The Banquet Table Problem in class »

Zip Zap Zowie

I like Zip Zap Zowie because I thought the language was catchy, it lends itself to using visual representations, and it requires algebraic thinking. It’s also open-ended in that it has multiple solution pathways, which is important in my classroom. I need activities that everyone has a shot at, as the prior knowledge and ability levels of my students are all over the place. It is also a nonroutine problem that requires strategic thinking and reasoning. It has a low-entry point but a high ceiling, so students at all levels in the classroom can potentially solve this problem. It also requires that students persevere and make multiple decisions and take multiple steps to solve the problem.

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The Gold Rush Problem

I love the Gold Rush Problem because it is similar to a problem that I had used in my class before; the version I used involved maximizing the area of a garden given a limited amount of available fencing to surround the garden. What I liked about the gold rush problem is that it took the garden problem a step further by asking students to analyze what happens to area when perimeter is doubled, tripled, etc, and I like how it invites different strategies for solving.

Continue reading how Tyler Holzer used The Gold Rush Problem in class »