Eric Appleton

Dividing a 2-digit number by the sum of its digits

Three very different visual solutions were shared in response to a problem about dividing 2-digit numbers.

This was our first online meeting (made necessary by the COVID-19 outbreak). It was a great distraction and made it possible for Adult Numeracy Network friends to join us from the Hudson Valley, Massachusetts, and Wisconsin. Our meetings for the next few months will almost certainly be online, so join us if you’re able.

The problem for this meeting came from Math with Bad Drawings and @mathsjem before that:

Nice little puzzle pic.twitter.com/qh7FCkcjLN

— Jo Morgan (@mathsjem) October 22, 2019

Open Middle equations

Ramon led the group into an investigation of a simple equation with many possible solutions.

Ramon Garcia brought a problem type called an Open Middle problem. He talked about how usually teachers give students problems that look like this:

1+2=?

There is one answer: 3. And you’re done. (It could be more challenging, but it would still have only one solution that makes the equation true.)

Card Puzzles and Tricks

Solange shared some card puzzles and tricks that she has been playing with. Our job was to figure out how they worked.

The first card “trick” (more of a puzzle, really) was from Marilyn Burns’ blog. It’s called the 1-10 card investigation.

“Reversed” Ages

A simple situation with a mother and daughter’s ages leads to many questions and interesting observations.

In August, at a summer board meeting of the Adult Numeracy Network, the fabulous Sarah Lonberg-Lew (@MathSarahLL) shared a problem. Well, it wasn’t really a problem, more like something she noticed. In the meeting, she asked what we noticed and what questions we might ask.

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…