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?
Category: Number Theory
Happy Numbers
For this month’s meeting, we returned to explore some numbers we first encountered in CAMI back in 2015 (Happy Numbers and the Melancoil).
After some community building, we started our exploration with a notice/wonder of this diagram.
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?
Ring-a-Ding Numeration
We started this meeting with a notice and wonder with this image of the numbers 1 through 6 in a numeration system created by professor emeritus at Smith College Jim Henle. The system (a piece of mathematical art!) is called Ring-a-Ding Numeration. The rings are the circles and the dings are the dots.
Number Visuals
The session opened with a wonder and notice of this image:
Participants noticed that the number of dots in each figure is increasing by one as you look left to right in each row. One person said they see certain groupings of dots repeated in other groupings. Another noticed that the dots are arranged in a circle for some numbers and someone else wondered if that was because those numbers are prime.
Continue reading “Number Visuals”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:
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:
