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”

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”

Signed Number Pyramids

Using number pyramids to practice adding signed numbers leads to a surprising discovery.

Jane started the meeting by telling us that her class has been studying signed numbers recently. She has been looking for creative ways for them to understand adding and subtracting signed numbers. One example was to imagine taking away negativity as the same thing as making someone happier.

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Pascal’s Triangle

A big thank you to Turning Point for hosting us this month and raising the bar for all future hosts. We started with a tour of TP”s building and saw their classrooms, offices, and rooftop deck (!). Evidence of great student work is everywhere with student posters and presentations on the diverse topics of supply and demand, classified ads for housing, and dice and probability. It was wonderful to see such a beautiful, well-established community-based education program with full-time staff. And they provided refreshments!

For this meeting, we looked at Pascal’s Triangle, since it came up in discussion at the end of the October craps meeting Continue reading “Pascal’s Triangle”

Happy Numbers and the Melancoil

Our work on this month’s problem led us to the beginning of a larger exploration of a very curious repeated loop in a certain sequence of numbers.

This month’s problem comes from the 2015 Stanford-Math League Tournament Individual Questions for grades 6 & 7.

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Problem-Posing with Visual Patterns

We can get conditioned to approach visual patterns in a particular way and jump immediately to the problem of looking for the nth figure (# of squares, for example). Beginning with an open, problem-posing approach can help break us out of that habit and really open up the mathematics.

Usha led us through an exploration of a visual pattern, building off of the work we’ve done at the last two meetings. She used problem posing to enable us to have greater ownership on the problem and to widen options to explore.

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Toothpick Patterns: Growing Squares, Growing Triangles, Growing Stairs

We wanted to build off the problem from last meeting, exploring visual patterns, with a focus on different ways of approaching these problems and how can we bring them into the classroom.

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Pentagon Patterns

Still looking for a name for our group, we went around introducing ourselves and each offered one word for our group vision:

Fun, Math, Community, Community, Building, Sharing, Other People’s Thoughts, Resources, Escape, Learning, Ideas, Adult/Young Adult, Inspiration

Continue reading “Pentagon Patterns”