Exploration of Consecutive Numbers

In this meeting, Usha returned to lead an exploration of consecutive numbers through a low-entry, high-ceiling problem she recommends as an introduction to functions/algebra.

For our June meeting, we were lucky to have Usha Kotelawala, Director of Math Education for CUNY’s LINCT to Success, as a guest presenter. Usha started the meeting by talking a little about her thought process in choosing today’s problem. In discussing CAMI with Usha, Eric had raised the issue of how to order problems through a semester, so that the mathematics is sequenced and scaffolded for students and students learn through problem-solving. In response to this question, Usha brought us a problem she recommends as the first in a sequence on algebraic reasoning. Continue reading “Exploration of Consecutive Numbers”

CAMI Roadshow: 2017 COABE and NYC Adult Basic Education Conferences

CAMI did a few workshops in April, sharing our teaching circle’s work on exploring real-life math through three-act math tasks.

Eric and Mark did a workshop at the 2017 COABE Conference in Orlando called Mathematical Modeling: Questions from a Math Teachers’ Circle. A few weeks later at the NYC ABE Conference, Brian took the lead and together with Mark and Eric did a similar workshop called 3-Act Math Tasks: Let Students Build the Problem. Continue reading “CAMI Roadshow: 2017 COABE and NYC Adult Basic Education Conferences”

What Do You Do with a Dizzy Sailor?

CAMI often goes back and forth between problems that challenge us as problem-solvers and those which we could use to develop problem-solving in our students. At this meeting, Solange bridges the divide and does both.

Solange led us in an exploration of two problems – first, the Dizzy Sailor Problem and then the Perimeter of 18 Problem. The former was to challenge and deepen our own problem-solving. The latter was to have a discussion about how some of the math from the dizzy sailor connects to the perimeter of 18, which we all agreed was a problem we could do with our students. Continue reading “What Do You Do with a Dizzy Sailor?”

Carl’s Basketball Problem

With a simple set up, CAMI enters a rabbit hole of notice/wonder and number patterns.

At our meeting, we worked on two tasks that I got last summer at a gathering of teachers from the K-12 system called NYC Twitter Math Camp.

The first is an activity teachers can use to develop group problem-solving norms with students. Continue reading “Carl’s Basketball Problem”

CAMI Roadshow: NCTM 2016

CAMI celebrated its two year anniversary with a few founding CAMI members representing our teachers’ circle at this year’s regional NCTM conference in Philadelphia.

Our session began at 8 in the morning with a small but energetic and enthusiastic group of teachers from Maryland and New Jersey. We started with introductions and a brief introduction to CAMI including a discussion of the Diana Lambdin quote that went out with our initial invitation to CAMI in November 2014… Continue reading “CAMI Roadshow: NCTM 2016”

Making and Testing Conjectures: The Diagonal Problem

Draw a rectangle on grid paper and draw a diagonal. Is there a way to predict the number of squares the diagonal will pass through?

I have been thinking about MP3 from the Common Core, specifically about how to get students to make conjectures, to test those conjectures and to refine their conjectures when it turned out they were not always true. I was also thinking about student perseverance and helping them not get too frustrated. I’ve done some activities like Marilyn Burns’ consecutive sums problem (see additional resources below), but I want something that feels messier and a little more unwieldy. Continue reading “Making and Testing Conjectures: The Diagonal Problem”

Roller Derby (& probabilities in passing HSE exams)

April’s meeting was in two parts: First we played a dice game named Roller Derby, developing and analyzing game strategies. Then we discussed some of the odds of the TASC.

After introductions and a brief discussion of how we’ve each used dice in our classes in the past, Mark gave out a Roller Derby board – basically a sheet divided into twelve columns, numbered 1-12 – and twelve colored chips to each person and invited everyone to distribute their chips across their board any way they wanted.

Then he broke up the group into pairs, gave out a red and white die to each pair and gave out the rules: Continue reading “Roller Derby (& probabilities in passing HSE exams)”

CAMI Roadshow: COABE 2016

Facilitating a meeting in Dallas, while live-tweeting with teachers in NYC, we explored a visual pattern to model what our teachers’ circle is all about.

This CAMI Roadshow involved about 35 teachers in a ballroom at the Sheraton at the 2016 COABE conference and 3 additional teachers who were back in NYC, participating through Twitter.

We wanted to maximize teachers’ time working on the problem but we also wanted to convey some important norms about how we run CAMI meetings, so we began with an ice breaker. The instructions were simple. First, everyone sat down (including the facilitators). After that, the only goal was that there be 5 people standing and the only rule was we had to do it without talking. Continue reading “CAMI Roadshow: COABE 2016”

Keep it in the Family (with Pythagorean Triples)

Many of us are familiar with the 3, 4, 5 right triangle, and maybe the 5, 12, 13. Do you know any others? Is there a pattern to these triples?

As we came in the room, Eric asked us to place a post-it with our name on a voting spectrum he’d drawn on the board, ranging from “Never” to “This morning” under the statement, “The last time I thought about multiplication”.

As we settled in, Eric shared his goals for the meeting. He’s been working on a lesson for students combining some work he’s been doing on area models with a problem that has been consuming him for weeks. Continue reading “Keep it in the Family (with Pythagorean Triples)”

CAMI Roadshow: 2016 CUNY NYC Adult Literacy Institute

The CAMI Roadshow did a workshop at the CUNY NYC Adult Literacy Institute, January 22, 2016

Tyler and Solange facilitated a problem-posing with visual patterns activity, bringing the exploration from our February 2015 meeting to a wider audience.

Continue reading “CAMI Roadshow: 2016 CUNY NYC Adult Literacy Institute”