For this meeting, Sarah invited us to explore the weird and wonderful world of numbers between 0 and 1. We started with a notice/wonder on this set of equations (suggested by Eric):
What Would I Think If I Didn’t Know?
Tag: patterns
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:
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?
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.
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.
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.