Thirteen Ways of Looking at Multiplication Tables

Looking for the surprising in the familiar, we see what happens when you look, really look, at the multiplication table and tumble through the looking glass.

I once taught a poem by Wallace Stevens called “Thirteen Ways of Looking at a Blackbird” to a class of adult literacy students. Before I gave out the poem I put the title on the board and asked students what they thought the poem was going to be about. They had all kinds of ideas about looking at blackbirds. Then I asked them, “What about the first part? What does that mean Thirteen ways of looking at a blackbird?”And they said things like:

• “Thirteen ways to understand the bird is better than one… but you have to take time to see the bird.”
• “If you look at the bird you will find all the different things it does, but you have to look closely.”
• “We don’t pay attention to these things and he wants us to focus.”
• “He stopped to pay attention to something so maybe we will too.”

Mondrian Art Puzzle

CAMI plays around with a way to practice multiplication, think about area and extend into algebra and generalizations. Through art!

For our final CAMI meeting of 2017, I wanted to spend some time at a CAMI meeting doing some math that would create some thing visual and beautiful. As I was looking around for activities to bring to the group, I came across the website, Math Pickle (as in “Put your students in a pickle”). They had a trove of math problems that I look forward to exploring in future CAMI meetings. The one I chose for this one is at its core an opportunity for students to practice multiplication in a way that is much more engaging than just memorizing facts and doing worksheets. And it builds works of art. As I started to play around with it, I started to notice different ways to think about how to make designs with the best score. Continue reading “Mondrian Art Puzzle”

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.

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 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?”