Playing the game of Dominoes is an excellent way to introduce and practice problem solving. I’ve used this game for several years in my 3rd grade classroom, and now I am introducing it to my gifted students.
This past week was the first week that I met with my elementary (K-5) gifted students. Obviously, the various grade levels were in different places when it came to math concepts. Second grade is working with word problems. Third grade will be tackling multiplication soon. Fourth grade is focused on geometry right now. And, 5th grade is preparing to use formulas to solve for volume.
Tuesday morning’s second grade gifted lesson began with my typical introduction to Dominoes. I told the students that each tile is called a “Bone” and the pile of unused tiles is the “Boneyard.” They learned that there are always 28 Bones in a game, and that every single Bone is different. Each one has two numbers on it, even the ones that look empty! “What number is on this side?” I asked holding up a Bone with a six on one side while the opposite was blank. They didn’t skip a beat in guessing “Zero.”
It took a little longer to explain adding the ends of each Line of Play. “You add up any number that is at the tip of an arm, no matter how long or short the line is,” I told them. We practiced some play. The adding wasn’t a problem. We discussed using the cumulative property to switch up the order of numbers, so that the mental math was easier. “Look for combinations that create ten,” I told them. “Rather than adding 4 + 5 + 4 +2 equals fifteen, combine the 4, 4, 2, first. Then you instantly know that the five makes fifteen.”
“Points are only awarded when the sum is a multiple of five. The ends of all of the lines of play add up to ten. Is that a multiple of five?” They knew that ten was made up of two fives. “How many fives are in 15? 20? 50? 500?” Flawless computation… Multiplication, here we come!
“Whenever you earn points, you say, ‘Give me ten…’ or however many points you earned.” I learned this from a fun video that taught me how to play ages ago, and elementary students LOVE this aphorism.
“Give me ten!” one of my second graders beckoned. I put 10 on the board, and we played a couple more sets before moving on to our Self Portrait project. Even though I only have my gifted students for 40 minutes at a time, I found doing more than one mini lesson to be helpful in keeping their interest.
After school, I came up with a word problem for Wednesday using Dominoes. I typed it into a Jamboard. Even though I tried to word it in such a way that you could visualize the game in your mind, I went ahead and used Domino tiles (Bones;) to make a model of the hypothetical game on a table and took a photo. I imported the picture on the Jamboard slide with the word problem text.
When Wednesday arrived I was excited to try out my word problem. The first group of students that I met with was 5th graders. Because I do car duty, I get to my room at the same time as my students. This morning I had placed a note on the open door, instructing them to try to work out the answer to this problem while they waited for me to show up. The word problem was presented on a giant Google Jamboard that I’d rolled in front of the entrance to the room.
The group was crowded around the screen when I got to my room. I enjoyed listening to their discussion of possible moves. From what I heard, a couple students were aware of the general concept of matching numbers. They didn’t quite understand adding all of the numbers from the end of each line of play, but that was okay.
When one of the students decided the trick to solving the problem was to simply take a new Bone from the Boneyard, I invited the 5th graders into the room. Before talking Dominoes, I praised their persistence and told them that I was proud of how hard they worked. I purposefully pointed out the failure to solve the problem as an example that not everything will come easily to them. It is my job to come up with challenges that stretch their thinking, and I intend to make not only their intellects but also grit grow.
As I explained the solution to the puzzle, I used it as a teaching tool. When I informed them on how the points work, they noticed that placing the Bone with the two on one side at the end of one of the lines of play would bring the total sum of all of the arms to 20, a multiple of five, and thereby an opportunity to earn points. “Good. But, there is a third and less obvious option,” I told them. “This one,” I said, pointing to the Double that had a six on both sides, “Is a Double. It is special. Not only can you play it with one six touching the line of play (also a six), but you can set it perpendicular to the line, thereby creating an extra arm.” I waited for someone in the group to notice the new sum.
It didn’t take long for a fifth grader to notice that all of the sixes add up to 30 points. “Turning the Double on its side, created a fifth number to add. Since all of the numbers were the same, you can’t help but have a multiple of five! It is literally five of the same number.”
Next, it was 2nd grade’s turn. These kiddos had just learned how to play the game for the first time the day before. I used the word problem to reteach some of the ideas. More than focusing on problem-solving, I walked my second graders through the mechanics of writing a word problem. We discussed the details of Dominoes that I included in my little story. “Why did I mention multiples of five?” I prompted. “The goal is to earn points.”
I had toyed around with the idea of only having words. When I originally crafted the word problem, I didn’t have the Dominoes laid out on a table. I tried to provide just the right amount of text for students to be able to visualize all of the details necessary for solving the problem in their heads. At the last minute I decided to include a photo with the problem. This was only the third day I was teaching these students! Watch out, though. Word problems, here we come!
Pride flooded my person when fourth grade arrived in my room and crushed this problem within seconds. I’d taught all but two of these students how to play Dominoes last year. When I saw how quickly they solved the puzzle, I wished I’d hidden the photo.
I pointed out the verbiage at the end of the word problem. “Why is it okay that I didn’t say what numbers were on the Double in the word problem?” I asked them. I had left out this vital information on purpose, and I wanted to see if they could find the puzzle within the puzzle. I did this kind of trick with them all last year. They understood that it had to be two sixes because the word problem stated that “You have two bones that you can play.” If the double were any number other than six, you couldn’t play it.
Here’s a question I failed to float: “Is it possible that the player has more than two Bones?” And, this is where a photo is limiting. Because you can see only two Bones on the table, it is difficult to imagine there being more than two. But, yes, the parameters of the problem leave that detail open. You have two that are “able to play,” but you may have more. I’ll have to work that riddle into a future problem!
My last group of the day was third grade. Here, I used the word problem differently. After exploring the numbers and solving the puzzle, plus revisiting how to play the game, I drew their attention to the structure of the word problem. It was a story, providing characters (you and a friend), a setting (a game of Dominoes), and a conflict. “This word problem has a plot,” I pointed out. (Plot is the language arts concept that third graders are learning right now.)
The problem of which Bone to play is the climax of our story. The resolution is a mystery. You could use either Bone. Which one is better? What is the third, less obvious option? How will the story end?
And, this is the end of my blog about this amazing word problem. But, is it? Through the process of fleshing out the many lessons that coated these Bones, I have come up with some additional puzzles. Here is a taste: “What is the highest score that can be collected in one play of Dominoes? What would the Bones look like at the ends of each line of play?” I think I’ll provide manipulatives; Bones; for pupils to push around when solving this. Good luck!
The Captain of Class 
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