## 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.

## 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”

## 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”

## 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.

## Gerrymandering Math

Can math save us from dark depression?

Among the thoughts racing through our minds on election night was the realization that we had decided to have a CAMI meeting on the next day. What were we thinking? Solange and I spoke before the meeting. We briefly considered scrapping our plans to explore gerrymandering math and do something to get our minds off the election, but eventually decided that we should take the opportunity to talk with other teachers about this moment. Continue reading “Gerrymandering Math”

## Dana’s Rectangle

Inspired by the work of the Navajo Math Circle, CAMI explores the area of rectangles and their borders, testing conjectures and making generalizations.

Eric started the meeting by talking about the Navajo Math Circles, which is a joint project of the Navajo Nation and mathematicians from Math Teachers Circle Network. A recent documentary tells the story. This meeting’s problem is from an article about the Navajo Math Circle (see Further Reading pdf link above) by Tatiana Shubin, whose video Grid Power was the subject of this past July’s CAMI meeting.

## Grid Power

What mathematical questions can you ask of a blank piece of grid paper?

After CAMI was recently accepted as a member of the Math Teachers’ Circle Network, a few of us started exploring their resources, which include a series of videos of mathematicians leading teacher circles. Eric was inspired to share today’s problem after watching Tatiana Shubin’s Grid Power.

Eric started the meeting by asking participants to look at a blank piece of graph paper for 7 minutes and write down questions that came up. 7 minutes?! Yes, 7 minutes. Continue reading “Grid Power”

## Millions and Billions

I need your help visualizing millions and billions.

In a recent interview on Innovation Hub, the mathematician and educator Steven Strogatz reflected on math education (specifically the requirement for students to study algebra) and the level of number in the general public:

“We don’t do a very good job of teaching what you might think of as numeracy, that is, the use of arithmetic [in the real world]. So, here’s an example: In current political discussion, there is a lot of talk from Senator Sanders about millionaires and billionaires, right? Continue reading “Millions and Billions”