Mark’s Metrocard

Have you ever noticed the money left over on a Metrocard when you have “insufficient funds” to ride the train? Is it possible to break even? It seems to be part of an MTA conspiracy.

In this meeting on our third anniversary, I tried out a 3-Act Math Task I’ve been planning for a while. It’s got to do with the 5% bonus the MTA gives us on non-unlimited MetroCards and the odd remainders I often find when I run out of funds on the card.

Continue reading “Mark’s Metrocard”

Multiple Factors

Several engaging activities for exploring factors. Which would you use for HSE math classes and how would you use them?

I puzzled over what to bring to today’s meeting for days. I have a couple unfinished problems that I’ve been thinking to bring to a CAMI meeting, but in the end I chose to go with a few activities on factors, mostly from Fostering Algebraic Thinking, by Mark Driscoll. A group of us read the book last summer and loved the problems. There were so many good ones that we weren’t able to solve them all while reading the book. I went into this meeting hoping that the surprise of the central problem wouldn’t be ruined. Continue reading “Multiple Factors”

Can you fit more boxes in a shipping container than Jane can?

Exploring some of the mathematics in packing a shipping container.

For today’s CAMI meeting, Mark was trying out a draft of a lesson that he wrote with Eric involving volume and units in a workplace context. The problem we explored involves trying to fit rectangular boxes into a shipping container.  Continue reading “Can you fit more boxes in a shipping container than Jane can?”

Tropicana Cash Wheel

In this meeting, Steve challenged us to figure out the best of some bad choices at the casino.

Steve started today’s meeting by sharing that he had recently noticed that the Tropicana Casino in Atlantic City has a game called the Cash Wheel. Steve took notes on what he saw and presented us with a representation of the Cash Wheel. Continue reading “Tropicana Cash Wheel”

Exploring Algebraic Thinking in a Math Teachers’ Circle

How to use an inquiry-based exploration of visual thinking to develop algebraic thinking in our adult numeracy and hse classes.

Eric, Solange and Mark led a webinar called “Exploring Algebraic Thinking in a Math Teachers’ Circle”, revisiting a workshop that we gave at the 2015 National COABE Conference. This webinar focuses on an inquiry-based process of algebraic thinking through use of visual patterns and multiple strategies for problem solving, including drawing, different ways of seeing, making charts/tables, and making predictions using rules. Facilitators model an open approach, having students generate their own problems and also discuss how to help students analyze and connect different solution methods and how to bridge visual thinking into algebraic thinking.

Continue reading “Exploring Algebraic Thinking in a Math Teachers’ Circle”

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”

Growing Rectangles

This task, from Mathematical Mindsets, by Jo Boaler, asked us to explore how area and volume are affected when shapes are scaled up in size. For example, if you double the dimensions of a square, how is the area affected? What if you triple the dimensions?

We used this meeting to explore a problem from Mathematical Mindsets by Jo Boaler. I had worked on it a few weeks ago as part of an online book group with LINCS. I decided not to give out all the questions in the task at once, but you can look at the problem URL above to see the whole thing. Continue reading “Growing Rectangles”

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”

Making Trains from Cuisenaire Rods

Inspired by Mathematical Mindsets, by Jo Boaler, we explored questions related to “trains” made out of Cuisenaire rods.

A few of us are reading Mathematical Mindsets, by Jo Boaler, as part of a book group on LINCS that will start this coming Monday, April 17th. The book is similar to Boaler’s other writing in that it cites evidence of recent work in brain science to show that everyone can learn, that the brain is plastic and grows like a muscle when used, and there is no such thing as math people and non-math people. Boaler also argues for an approach to developing growth mindsets that is rooted in mathematics. The book  includes examples of low-entry, high ceiling problems that can be used to develop mathematical mindsets. Continue reading “Making Trains from Cuisenaire Rods”

Multiple Ways of Multiplying

We explored multiplication through a number talk and alternative algorithms for calculating products.

Before the meeting, Davida showed Rachel and me a multiplication method a student had showed her earlier in the day. The student said that she only knew how to do multiplication using the method on the right and wanted to learn the method on the left. What a coincidence! This is exactly what I was planning to explore today.

Continue reading “Multiple Ways of Multiplying”