In this meeting, we deconstructed a problem from NCTM’s Mathematics Teacher: Learning & Teaching PK-12, using a few ideas from The Art of Problem Posing, by Stephen I. Brown and Marion I. Walter.
Here’s the original problem:
Sequences of Fractions
Category: Number Patterns
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?
Function Diagrams
I decided to lead a meeting on function diagrams because I’m intrigued by the possibilities of teaching with them and because I wanted to introduce the resources that the math educator Henri Picciotto makes available. I have to admit that I haven’t spent that much time thinking about to teach with function diagrams, but I was interested to see what we can learn together by exploring this visualization.
Continue reading “Function Diagrams”What Comes Next?
Sarah and Eric have been teaching themselves how to code using Javascript, CSS, and HTML. The What Comes Next? game is the result of more than a year’s work. We are not fast coders! We used this meeting to share our game and to see if teachers might use it with their students.
To play the game: What Comes Next?
Continue reading “What Comes Next?”Sequences
Sarah and I have been meeting once a week to teach ourselves some basic coding. Our first project was a function game. We are currently working on another game involving sequences, which got us thinking about the sequences in this meeting.
Sarah started this meeting by asking the group to consider the following prompt.
Sums of Consecutive Numbers (follow-up)
In this meeting, we explored the sums of consecutive numbers (inspired by a CAMI meeting led by Usha Kotelawala in June 2017). The meeting is also based on a two-day lesson I led with the support of other teachers during summer 2020 problem-solving meetings with CUNY adult education students.
Before the meeting, I shared this post on the CAMI email list:
Number Pyramids
In this meeting, we explored Henri Piccioto’s number pyramid puzzles through notice/wonder, generating questions for problem-solving and additional puzzles for students.
At the beginning of the meeting, we shared some favorite sources of puzzles we like to use with students, include Which One Doesn’t Belong, Sometimes, Always, Never, and Open Middle.
Then I introduced Number Pyramids. Thank you to Henri Piccioto and his amazing web site of math resources. Here is the sequence we used:
Factor Graphs
Sarah Lonberg-Lew of the Adult Numeracy Network and SABES joined us from Gloucester, MA to lead this meeting with me (honestly, I did very little). We explored a diagram that Play With Your Math calls factor graphs. They got the idea from Things to Make and Do in the Fourth Dimension, by the mathematician and educator Matt Parker. (Check out Numberphile for some of his videos.)
The week before the meeting we sent out this teaser:
Math Art Challenges
Annie Perkins is a middle school/high school math teacher in Minneapolis, MN and she has been sharing a daily math art challenge every day since the governor’s made the call for everyone to stay at home. As I write this, we are going on Day 19.
Continue reading “Math Art Challenges”Decimal representations
Have you ever thought about why some fractions turn into decimal representations that go on and on, while others terminate?
Andrew started by describing two kinds of decimal representations of fractions:
