The Color Game

hundred yardsMotivating the students in my Problem Solving class – convincing them that they are capable of thinking critically and crafting solutions, and getting them to care about the quality of the work they submit – this is the challenge I face this term, a challenge with which I am familiar. I’ve been coming at this challenge since I began teaching – trying to motivate through classes in Personal Finance, Geometry, and now under the broad umbrella of problem-solving strategies. I really enjoy the students in these classes – the juxtapositions of attitude and self-deprecation, street smarts versus humble acceptance [sadly] of their mathematical deficits. These teenagers are honest – sometimes hilariously so, and, sometimes painfully. They are always interesting, and unpredictable.

by Sara

by Sara

Most of them don’t believe they can solve problems, and I face the dilemma of demonstrating solutions for them versus getting them to work independently. When I model, the students faithfully copy my work. When I toss the ball back to them, they stop. We use individual whiteboards, large vertical whiteboards around the room (I encourage the students to get up and work on the boards whenever they want), partners strategies, table work; my plan (read: my hope) is that eventually the most reluctant of students will become comfortable enough to dip their toe in the water. The problem sets I am using are well tiered, I think, and there will always be an entry point, somewhere, for everyone.


from Jeremy’s mathography

One of my first assignments of the year was a Mathography, an assignment I love to read. Again, these kids are honest. Unlike my ‘gifted’ students, they do not feel they need to present their best face, and the results are compelling. Sometimes they are just so sad, like Jeremy. And then there is Gabby, who admitted that the teacher she liked the least challenged her the most. There are big red flags that get raised. Rekindling this child’s faith in her education is a tall order, and I hope I am up to the task; I do believe that the beauty of the patterns in math can inspire the disenchanted.

Gabby and her nemesis

Gabby and her nemesis

It strikes me as I am writing this that perhaps I may have a staggering amount of chutzpah, thinking I can ‘save’ these students. But I don’t; I sort of despair at my own powerlessness to change anything. My class is 45 minutes out of a teenager’s day, when they leave my room, when they leave school, everything is more importantthan my math class. I would just like to give a student a sense that they are mathematically capable, that there is interest and value in solving a puzzling problem, just because. Many of these students are given repeated tacit messages that the only value of their high school education is the accumulation of credits required to achieve graduation in four years.   I would be thrilled if the experience they had in my classroom added a little “and yet…” to that message. I hope that doesn’t sound like too low an expectation for my students or me, because the effort can feel both Sisyphean and Herculean. (Sorry – I couldn’t help myself, former English major that I am.)

color gameThis isn’t at all what I meant to write about. I want to write about the Color Game we played today, the game that half the class wanted to ignore, only to end up shouting out answers, arguing with each other, hands shooting up the minute I gave clues. It’s a pretty simple game; I found it in the introduction to the Teacher’s Edition of Crossing the River with Dogs. Students need to prove the location of colored squares on a grid given minimal clues. They are only allowed to claim a square when they can justify that it can only be one color based on the information they have been given. At first, the kids wanted to guess my pattern and have me tell them whether it was correct, and many were annoyed that I wouldn’t consider their offerings. But one by one, they realized that ironclad proof was required, and we played as a whole class right up to the ringing of the bell.   Of course, they begged to play again – frequently and soon.


  1. Maya Quinn

    Instead of red, blue, and green: Can you play this game with red, blue, and yellow?

    If so, a nice question might be: What are the colors of the 12 “interior borders” (that is, the 12 line segments between adjacent squares)?

    With the color change, the answers would be among: red, blue, yellow, purple, orange, green.

    This version of the game assumes the colors overlap at the borders, but I think it might be a fun variation!

    (And it could be interesting as to whether information about any of the borders, perhaps obtained via other questions, turns out to be useful…)

    • Wendy Menard

      Maya -you can play with any three colors you like. First we did a 3-color grid, and then a 4-color grid (red, yellow, blue and green). I made two large grids and put them back to back in sheet protectors, 2 on each table. You can give the students dry erase markers to use, or, if you are so inclined (and have some volunteer student help!), you can make sets of colored squares out of paper for the students to use. I like your idea – thanks!!

  2. fractallyspeaking

    This is a great problem – can you pls tell m the book you sourced it from? I love the Mathography idea too – need to make sure I have mroe writing and reflecting in my maths class. Tracy

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