Penny Collection

Solange led us in a meeting about teaching mathematics with a focus on discovery, investigation, and student thinking.

In this meeting, Solange presented us with the following problem:

Consider a collection of pennies with the following constraints:
When the pennies are put in groups of 2 there is one penny left over. When they are put in groups of three, five and six there is also one penny left over. But when they are put in groups of seven there are no pennies left over. How many pennies could there be?
Thank you to YouCubed.org for the problem.

Can you help us out? Can you find a solution? Can you find more than one? What strategies are you using?

Civic Statistics and Statistical Literacy

Usha and Iddo led us through an approach to exploring statistics.

A number of us were part of a lovely meeting a while back on statistics. Iddo Gal started the meeting by sharing an overview of a guide he and a few colleagues created for teaching civic statistics and statistical literacy. Iddo is presented at the U.S. Conference on Teaching Statistics in Pennsylvania a few weeks after the CAMI meeting.

The Secretary Problem

Audrey introduced the group to a classic problem from optimal stopping theory (whatever that is). 🙂

If you’re on the search for a new secretary, how would you choose who to hire? For June’s evening CAMI meeting, Audrey shared a classic problem with the group:

The Popular Secretarial Problem!

There are N applicants for a secretarial position. The applicants are interviewed in random order, and you must accept or reject a candidate immediately after interviewing them.
After you reject someone, there is no way to bring them back.
There is only one position available. So as soon as you accept a candidate, you’re done. What strategy should you use in order to maximize the likelihood of hiring the best candidate out of the N applicants?

Some of the assumptions we used when exploring the problem:

There is one best candidate.
If you could see all the candidates at one (you can’t), you would be able to rank them all from best to worst.

Pentominoes!

We moved shapes around a 100-grid to find patterns that lead to algebraic generalizations.

Today’s problem was from this year’s annual meeting of the Adult Numeracy Network (ANN) at the COABE conference in New Orleans. Christin Smith, Patricia Helmuth, and Heidi Schuler-Jones led the group through a series of activities over the course of the day. The theme of the ANN annual meeting was the idea of revealing algebra in basic mathematics. In our CAMI meeting, we explored an activity that starts with adding on a 100-grid and finding patterns and then moves towards generalization.

Return to the Fold

Usha and Sophie led a frenzy of folding, observing, counting, and predicting at Fashion Industries High School.

Update: Check out these related videos —> Numberphile | Doodling in Math Class | Wrong Turn on the Dragon

It was a beautiful spring day when Usha and Sophie represented CAMI at the 40th anniversary of the New York City Adult Basic Education Conference. Sophie gave a little history of CAMI…

CAMI was founded in November 2014
There have been 61 CAMI meetings
104 teachers have attended at least 1 meeting
15 different teachers have run a meeting
Average attendance at a meeting is 7.8 teachers

Celtic Knots

We learned how to draw interlocking knots and investigated mathematical questions related to counting features of the knots.

We started by looking at a few Celtic knots and thinking about what we noticed and wondered.

Maybe you’ll take a few notes before you move to the next page…

Playing with Prime Factors

Starting with a colorful visual representation of numbers, we looked at a series of problems based on prime factors.

For the last few months, I’ve been working on study materials on exponents and roots. While doing research for the packet, I started to get interested in factors and especially prime factors. It turns out that they are really useful for thinking about lots of different kinds of math that we have been looking recently. For example, the mathematics of bicycle gears or Spirograph both have to do with factors, as do fractions, place value, exponents and other math that is relevant to math teaching in adult literacy.

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.

Continue reading “Pedaling a Bicycle”

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?

Continue reading “Skellzies!”