One of my favourite open questions we present to teachers:
Extend the pattern Ann, Brad, Carol, … , in as many ways as you can.
That’s it. Simple, but brings out some big ideas.
So what’s next? Daniel gets a lot of early votes: starts with D, male, six letters. At some point, the increasing pattern–start at three letters and add one each time–becomes challenging. Take Elizabeth. Starts with E? Check. Female? Check. Seven letters? Crap. Extending the pattern in this way eventually means hyphenated names.
After exhausting Ann, Brad, Carol, … as an increasing pattern–Eleanor!–teachers get creative with repeating patterns.
For example, looking at one attribute:
- Aaron, Blake, Caleb (ABC)
- Olivia, Jackson, Isabella (female-male-female)
- Max, Liam, Jacob (3-4-5)
Looking at two or more attributes:
- Andrew, Brooklyn, Christopher (ABC & female-male)
- Ava, Bono, Chloe (ABC & female-male-female & 3-4-5)
What if Ann-Brad-Carol wasn’t the core of the pattern?
- Ann, Brad, Carol, Connor, Amy, Bryn, Caden, Carter (ABCC & 3-4-5-6)
A different attribute:
- Ann, Brad, Carol, Elijah, Genevieve (1-1-2-3-5 vowels)
Not mathy enough for you? Remember, not all teachers will have a positive attitude towards mathematics. This is a safe icebreaker. You can always follow it up with the mathier “Extend the pattern 5, 10, 15, … in as many ways as you can.”
The big idea? Patterns involve something that repeats. Sometimes items repeat, sometimes its the rule that repeats.
Ann, Brad, Carol, … can focus teachers/students on another big idea: the way you show information can make patterns easier to see. Moving from names to SET, spot the pattern in the photos below:
When I last posed the Ann, Brad, Carol, … problem, I encouraged teachers to rearrange the names to highlight patterns. One teacher connected this to 100 charts–an aha moment for her.
Big ideas above paraphrased from Marian Small’s Big Ideas.
This is part of this.
Chris Hunter 
I love this! I loved the Fibonacci vowels! You mentioned that you did this with teachers. Is this for a professional development? I think I’m going to use this in my next math team meeting! Thanks for the share and for blogging with MTBoS!
I love the game SET. When my colleague first introduced the game to me, I could not see the patterns. The students would find the set quicker than me. I had to learn to be okay with the fact that they will find the patterns before me. I had to learn that my role is not to know everything but to facilitate the learning with my students.
I agree with you that not all teachers have a positive attitude towards math. It is frustrating to be at an elementary school where math is not valued as much as reading/ELA. How can we change the culture of math within a school?
Brandon Yes, for pro-d. A quick warm-up (<15 minutes to answer and have a "classroom" discussion). In addition to the big ideas above, there's much to talk about from the teaching side: multiple solutions, low floor/high ceiling, justifying answers, etc. Let me know how it goes if you use it in your meeting. BTW, the problem isn't mine. I just don't know the source. Given that it's Ann not Ann and Carol not Chloe, I'm going to say it's been around for awhile.
Siobhan Yeah, my youngest daughter (5) often finds them quicker than me. It’d be kinda cool to collate math activities across the grades that are based on SET. @NatBanting, for example, uses SET in a HS math classroom: http://musingmathematically.blogspot.ca/2013/02/sorting-sets.html
Changing the culture? That’s a big question. I have discovered a truly marvellous solution to this, which this blog comment is too narrow to contain. Short answer: have teachers experience mathematics themselves in non-threatening, engaging ways (who, in turn, will want this for their kids); relationships among teachers that allow for open and honest conversations.
I think you’re right; the key lies in reducing the teachers’ math anxiety. Maybe you will talk more about this solution in a future blog? 😉
“have teachers experience mathematics themselves in non-threatening, engaging ways (who, in turn, will want this for their kids); relationships among teachers that allow for open and honest conversations.”
This is so true! I think not only in talking about math, but also in how to teach math. Before teachers will be comfortable doing open ended problems with their students, and inquiry based learning, I think they need to experience those types of problem and that time of learning too. Lately, most of our PD seems to be Data, Data, Data and missing the mark on this!
What a great icebreaker! It may not look “mathy” at first (which is ideal for math-anxious students as well as teachers), but can be turned into something quite deep, as you have shown above. I also love the game SET, though my children are ever-so-much faster at seeing the patterns than I am! I never thought about using the cards to illustrate a sequence; thanks for that great idea! I will definitely use it (and Ann, Brad, Carol…) in the future.