Category: Geometry

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?”

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.

Continue reading “Dana’s Rectangle”

The Lawn Mower Problem

What happens when we let students write the questions?

Tyler opened the meeting by giving us a situation adapted from one he’d seen on Twitter posted by Fawn Nguyen. He then asked two questions: What do you notice? What do you wonder? Continue reading “The Lawn Mower Problem”

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”

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”

Resources from NCTM 2016

So many games, puzzles and problems from the NCTM annual meeting…

In April, along with some other CAMI members, Jane and Solange went to the National Council of Teachers of Mathematics (NCTM) annual meeting in San Francisco. In this meeting, they shared some of their favorite games, puzzles and problems from different workshops.

We started with the game Which Number is Closest? from Building Mathematical Thinking Through Number Games, by Linda Dacey and Jayne Bamford Lynch. We played a variation of the game where we each rolled a ten-sided die and then wrote down each number in the box of our choice. Continue reading “Resources from NCTM 2016”

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)”