Temperature is Cool

How do the functions for converting between Celsius and Fahrenheit work? Temperature talk during the coldest week of 2019 thus far.

At our evening CAMI meeting earlier this month, Kevin Winkler from CUNY Start led us in an exploration of the conversion between Celsius and Fahrenheit based on something strange he noticed while crossing the Brooklyn Bridge.

I wanted to bring that idea to the afternoon CAMI meeting, and also try to scaffold the exploration a bit, so that we could extend the invitation to our students. It also just happened to be the week where the Midwest was experiencing such cold weather that friends in Minnesota kept making the same joke over and over again about the temperatures there being colder than they were in Antarctica.

Optimizing Social Security Benefits

Steve brought us a problem in the form of a financial decision most of us will have to make at some point: When is the best time to start collecting social security benefits?

Warm-Up Discussion

Steve started the session by asking the group what we knew about social security benefits. It turned out that some people knew a LOT about social security benefits and others (like me) didn’t know too much.

Pedaling a Bicycle

Bicycles are everywhere. Most of us know how to ride them. Many ride a few times a week. But have you thought about how the gears of a bike work? It’s stranger than you might think.

A little bicycle history…

I started the meeting with a notice/wonder on some images from the history of the bicycle. Here are the images, with some of the things the group noticed and wondered, followed by some comments from me.

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The Mysterious Bicycle Tracks

Audrey led the group through a classic problem which allowed us to use sidewalk chalk and ride bikes.

August’s CAMI meeting began with the following story:

You are brought to a crime scene. You are told that a thief just made off with a bag full of diamonds, escaping on a bicycle. You come across the following pair of bicycle tracks in the snow, no doubt made by the fleeing thief. But which way did the thief go?

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Exploding Dots

Sophie gave us an introduction to the strange world of Exploding Dots, which can be used to represent all kinds of math. We started with place value.

In July’s evening CAMI meeting, we met an interesting machine, the “two one” machine, written like this: 1<–2 machine.

Here’s how the machine works:

We can add dots to the box on the far right – as many as we want! Whenever there are two dots in the same box…

…they EXPLODE!

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Skellzies!

Ramon had his students work on research projects, sharing their cultural backgrounds and relating them to mathematics. He shared the results of one student’s project and then led us into an exploration of the New York City street game called skellzies, skully caps, skellies, etc. (depending where and when you grew up in the city.)

When we walked into the room, this was on the board:

Teaching Problem: For three consecutive semesters, an adult education teacher began classes with roughly 36 students and ended with roughly 12 students. What can the teacher try that will help to reduce attrition?

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A Strange Algorithm

In our first evening meeting, Eric shared a web site that turns pairs of numbers in diagrams. But how does it work?

(This meeting was based on an underground mathematics lesson, Fawn Nguyen’s post and Michael Lawler’s videos. Thank you all!)

I started the meeting by showing the group the Picture This! web site that turns pairs of numbers into a diagram visualization. I asked for a volunteer to give me two numbers, each less than 10. The first suggestion was 3 & 7. I entered the number into Picture This and this diagram was returned.

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Factor Towers

Eric shared activities from a draft lesson on factors, multiples, primes and composites. The lesson is linked in the post if you are interested in using the materials from the meeting. He would love feedback if you use it with a class.

Launch

To start off the meeting, Eric put us into groups and gave each group a bag of paper tiles. He asked us to spend a few minutes looking at them and discussing anything we noticed.

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The Wet Iphone Task

We explored a problem related to volume and surface area with multiple solutions. But wasn’t one of them more right than the others?

–Updated April 2, 2021 to remove the Wet Phone task published originally in Middle Grades Geometry and Measurement (Steele, 2006). Our apologies to the author Michael Steele for posting your intellectual property.–

Cynthia started today’s meeting by saying that she would be sharing a problem from a recent workshop she attended on multiple solution tasks (MSTs). These problems are designed so that there are multiple correct solutions. In our math circle, we have grown accustomed to seeing multiple strategies for solving a problem, but usually there is one correct solution. Even after we saw different solutions later on, there was something nagging at me. Are they both equally correct? Really? Continue reading “The Wet Iphone Task”

CAMI Roadshow: 2018 NYC Adult Basic Education Conference

NYC CAMI revisited the Grid Power problem and modeled the collective problem-posing/problem-solving process of CAMI meetings.

At this year’s NYC ABE Conference, Jane, Eric and Mark brought back the Grid Power problem from the summer 0f 2016.

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