Tag: patterns

What do you see?: Attention & imagination in math

Sometimes CAMI meetings have a mind of their own. This one followed a direction we didn’t expect!

We started with a question about this image:

The catch? We wanted to spark our creativity by exploring the world of wrong answers. 

What is the Area? WRONG ANSWERS ONLY

Continue reading “What do you see?: Attention & imagination in math”

Sarah’s Passing Drill

In another edition of revisiting problems from the CAMI vaults, at this month’s meeting we went back to further explore a number pattern we first looked at in January 2017 (Carl’s Basketball Problem).

We started off discussing WHAT IS SIMILAR? WHAT IS DIFFERENT? looking at these four expressions:

Continue reading “Sarah’s Passing Drill”

Diagonals in Rectangles

2024 marks the 10th anniversary of CAMI (!) and to honor all we have learned and all the ways we have grown as a group, we are going into the vaults for a few CAMI meeting, to reopen and revisit some of our early explorations together. This month’s meeting was a new take on a problem we explored in June 2016 at Making and Testing Conjectures: The Diagonal Problem.

We started with a Which One Doesn’t Belong?

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Story Tables

In this meeting, Amy introduced the story table, which is a teaching tool for solving algebraic equations. Story tables allow us to use guess and check and then analyze patterns in the results, in order to find values of x that make equations true.

To get us started, Amy shared the following algebraic equation:

3x - 2 = 10

And asked us to tell the story of x. To find a solution in this story, Amy asked us for the moment not use other ways of solving equations.

Getting started with story tables
Continue reading “Story Tables”

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”