Tag: triangular numbers

Thirteen Ways of Looking at Multiplication Tables

Looking for the surprising in the familiar, we see what happens when you look, really look, at the multiplication table and tumble through the looking glass.

I once taught a poem by Wallace Stevens called “Thirteen Ways of Looking at a Blackbird” to a class of adult literacy students. Before I gave out the poem I put the title on the board and asked students what they thought the poem was going to be about. They had all kinds of ideas about looking at blackbirds. Then I asked them, “What about the first part? What does that mean Thirteen ways of looking at a blackbird?”And they said things like:

  • “Thirteen ways to understand the bird is better than one… but you have to take time to see the bird.”
  • “If you look at the bird you will find all the different things it does, but you have to look closely.”
  • “We don’t pay attention to these things and he wants us to focus.”
  • “He stopped to pay attention to something so maybe we will too.”

Continue reading “Thirteen Ways of Looking at Multiplication Tables”

Exploration of Consecutive Numbers

In this meeting, Usha returned to lead an exploration of consecutive numbers through a low-entry, high-ceiling problem she recommends as an introduction to functions/algebra.

For our June meeting, we were lucky to have Usha Kotelawala, Director of Math Education for CUNY’s LINCT to Success, as a guest presenter. Usha started the meeting by talking a little about her thought process in choosing today’s problem. In discussing CAMI with Usha, Eric had raised the issue of how to order problems through a semester, so that the mathematics is sequenced and scaffolded for students and students learn through problem-solving. In response to this question, Usha brought us a problem she recommends as the first in a sequence on algebraic reasoning. Continue reading “Exploration of Consecutive Numbers”

Keep it in the Family (with Pythagorean Triples)

Many of us are familiar with the 3, 4, 5 right triangle, and maybe the 5, 12, 13. Do you know any others? Is there a pattern to these triples?

As we came in the room, Eric asked us to place a post-it with our name on a voting spectrum he’d drawn on the board, ranging from “Never” to “This morning” under the statement, “The last time I thought about multiplication”.

As we settled in, Eric shared his goals for the meeting. He’s been working on a lesson for students combining some work he’s been doing on area models with a problem that has been consuming him for weeks. Continue reading “Keep it in the Family (with Pythagorean Triples)”

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”

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”