Category: Visual Patterns

What do you see?: Attention & imagination in math

Sometimes CAMI meetings have a mind of their own. This one followed a direction we didn’t expect!

We started with a question about this image:

The catch? We wanted to spark our creativity by exploring the world of wrong answers. 

What is the Area? WRONG ANSWERS ONLY

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Sarah’s Passing Drill

In another edition of revisiting problems from the CAMI vaults, at this month’s meeting we went back to further explore a number pattern we first looked at in January 2017 (Carl’s Basketball Problem).

We started off discussing WHAT IS SIMILAR? WHAT IS DIFFERENT? looking at these four expressions:

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Diagonals in Rectangles

2024 marks the 10th anniversary of CAMI (!) and to honor all we have learned and all the ways we have grown as a group, we are going into the vaults for a few CAMI meeting, to reopen and revisit some of our early explorations together. This month’s meeting was a new take on a problem we explored in June 2016 at Making and Testing Conjectures: The Diagonal Problem.

We started with a Which One Doesn’t Belong?

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Why are maintenance covers round?

In the December evening meeting, Amy Vickers led us through a new exploration that was loosely inspired by last month’s meeting on some circles.

As a warm-up, Amy presented us with this question: Why might a manhole cover (or, in the gender-neutral, maintenance cover) be round? One of the central ideas that came up in the resulting discussion was that a circle won’t fall through its own hole, no matter which way you turn it. It has a constant diameter, or constant width.

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A Pattern With Circles

In CAMI Meetings and in class with students, we often want a prompt to get students generating their own mathematical questions to answer, rather than giving them a predetermined math problem that everyone needs to solve. In the November evening meeting, we started off by considering some prompts and sentence starters to get students asking questions that will lead to math explorations.

Here are a sentence-starters that we came up with:

  • How many…?
  • How many ways…?
  • Is this always true?
  • Could this pattern continue?
  • Would it be possible to…
  • What would happen if…?

And a few questions we can ask to get students thinking mathematically:

  • Why would I show you this? 
  • What’s the point?
  • What do you see that relates to math?
  • How do you see this?

What questions do you ask students to get them thinking? What kinds of questions do you want them to ask themselves?

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