Game Play, Math, Math Discourse, Problem Solving, Teaching and Learning
Serious Play, Part 2
We’ve all heard that “Every teacher is a reading teacher.” However, since learning is a social endeavor, “Every teacher is a communication teacher” makes more sense to me. Explicitly teaching children listening and speaking skills in the context of ones’ own discipline promotes the interactions that facilitate learning. In math class, math games present the perfect scenario for teaching children to talk math.
Below, I have listed four ways in which the speaking and listening standards interact with the standards for mathematical practice and connect to game play. For consistency, I’ve used in the previous post that referenced multiple variations of War as the context for each.
1) Communicate precisely – complete sentences.
I once had a middle school teacher say to me, “If you teach kids to speak in complete sentences, they’ll more easily learn to write in complete sentences.” That really spoke to me! I used that principle in oh-so-many ways. In the context of game play, I made sure that students communicated their thinking in complete sentences in each round.
For example, when students played Addition War, I asked them to use a comparison statement before taking the cards. It sounded something like this: “14 is greater than 8.” By listening to my students as they practiced their skills, I could learn more about their thinking and precision.
2) Communicate precisely – vocabulary.
By asking students to verbalize thinking while playing math games, I ensured that they also rehearsed using mathematical vocabulary. Math-specific vocabulary is rarely used outside of math class. So asking students to integrate these words into their game play increases their usage.
Listening carefully to students’ conversations and use of mathematical vocabulary pays off. When my students were playing Double War (addition, subtraction, or multiplication), I heard Travis proudly state, “14 is gooder than 8.” He was so confident and excited that he had won the round. His statement, however, revealed something I had not anticipated. He had interpreted the mathematical term “greater than” as “better than” rather than “more than.” Because students were required to verbally state their comparisons, I detected Travis’s misconception. I then wove this idea into my instruction just a few minutes later.
3) Construct viable arguments.
Another way to embed language use into the classroom includes teaching students a simple process for explaining their solutions. My favorite structure comes from a writing structure I used: “First – Next – Then – Last.” Students create a three- to four-sentence explanation that may sound something like the following.
“First, I wondered how many more I needed to add to 8 to make a 10 (it was 2). Next, I took 2 from the 6 and added it to the 8 to make a 10. Then, I noticed that there were 4 left from the 6. Last, I added the 10 and the 4 to get 14.”
By giving students a sentence frame or a language structure to use when playing math games, you increase the likelihood that their learning will be deeper and longer-lasting.
4) Critiquing the reasoning of others.
For children to learn to be good listeners , we must teach them what good listening looks and “sounds” like. In my classroom, we talk about looking at the speaker without fidgeting, about the inner “listener dialogue.” We learn how to respond when you don’t agree. We talk about what it means to be a respectful listener. We discuss that deep listening is more than just being quiet. It’s about thinking about what you’re hearing and asking questions inside your head. And, most importantly, it’s about listening to learn and to understand. A reply should not be formulated until you’ve listened and processed what you heard.
Stephen R. Covey said, “Most people do not listen with the intent to understand; they listen with the intent to reply.” Learning to listen serves our children well, and math games afford them time to practice. As Bryan H. McGill said, “One of the most sincere forms of respect is actually listening to what another has to say.” Wouldn’t our world be a wonderful place if all the adults learned to construct arguments worthy of being listened to, and then, in turn, listened with the intention to understand and to learn?
For now, I’m just happy if my students use their emerging speaking and listening skills to make math game-play richer in my classroom.
How about you? What do you think about this idea that speaking and listening can be taught in math class? Please share your thoughts in the comments box below.
Kimberly Rimbey, Ph.D., works with teachers and leaders to develop system-wide change in mathematics teaching and learning.
Hands-On Math
Serious Play, Part 3
Playing math games in the classroom offers so many benefits! Depending
on the game at hand, students engage in math practice, conceptual development,
mathematical discourse, logic, spatial reasoning…and more. In addition,
students use soft skills such as negotiation, emotional self-regulation, winning
graciously, and losing gracefully.
Today we take a look at the social-emotional benefits of using
math games in the classroom. These benefits include many of the interactions
and self-monitoring behaviors that students need for work and in life. Helping
children achieve them allows us, the teachers, to ascend to our highest calling
– to prepare our students for the world beyond our classrooms.
To set the context, let’s examine the game Race to $1.00. This game, which is described at the bottom of this post, is typically played in grades 2-3. In addition, I’ve included other variations, below, for extensions to other grades.
Once game play begins, the students interact with one another in
ways that require them to exhibit behavioral self-monitoring. For the sake of
this post, the examples below relate to Race
to a Dollar. However, they certainly apply to just about any game where two
or more students interact.
Negotiating
rules
When introducing the game, I provide the basic procedure, but I do
not explain every possible action that may occur. Here’s an example from Race to a Dollar. Let’s say that after a
few rounds, students once again roll a 5. They may realize that they can place
a nickel on the game board rather than five pennies. This is when they
excitedly raise their hands and ask me if it’s okay. The perfect teacher
response is, “What do you think?” Without exception, the students want to
create this new rule. The teacher responds with, “Do you both agree?” The
students quickly confer and nod their heads. “Then that can be your new rule.
As long as you agree that the rule is fair and makes sense, then you may use it.”
Later, the students share this new rule with the class when they come back
together. In my experience, the entire class negotiates and agrees that this
should be a permanent rule. All students walk away feeling oh-so-empowered.
Speaking
to clarify ideas
In last week’s blog post, we examined applying the speaking and listening standards while playing math games. Helping students learn to speak their minds clearly also helps them develop behavioral self-monitoring. Not only do students engage in math talk during game play, but they also express emerging thoughts and emotions. They may lose track of whose turn it is, disagree with their partner’s work, or want to negotiate rules. Whatever the case, “use your words” becomes a critical skill, and clarity is critical.
Listening
to understand
Due to the emotional nature of game play, learning to listen also plays a major role. As discussed in last week’s blog post, we humans frequently think about what we’ll say next rather than listening to understand. Playing math games provides a perfect opportunity for students to slow down their thinking and truly listen to their partner. Of course, both speaking and listening may occasionally require adult intervention. I find myself providing sentence starters to students as they learn to speak directly with one another. We also practice this during our opening mini-lesson or closing reflection so that all can benefit from the explicit intervention.
Being
a Good Sport
When the end of the game approaches, students typically realize
that there is going to be a winner and a loser. This can be a difficult
situation for children navigate, regardless of which label they’ve earned.
Helping children deal with losing gracefully and winning graciously sometimes
requires direct instruction. I engage
students in group conversations about what each looks, feels, and sounds like.
And then we rehearse appropriate words and body language. Students may also
benefit in this way when playing partner games such as Race to a Dollar. Partner games allow students to work in pairs,
both concurrently functioning as winners or losers. This give them the chance
to experience camaraderie when losing gracefully and winning graciously.
Race to a Dollar
Materials
for each pair of students:
Set up:
Students place the game board between them. They are playing as a team to race to $1.00.
Procedures
(students alternate turns):
- Player A rolls one 6-sided die to determine how many pennies to place in the penny column.
- Player B rolls again and places that many more pennies in the penny column.
- Players repeat steps 1 & 2 until there are five pennies. When appropriate, the active player trades five pennies for one nickel and places it in the nickel column.
- Players continue to roll for pennies.
- After each roll, the active player checks to see if any trades can be made. The possible trades include the following:
- Five pennies should be traded for one nickel.
- Two nickels should be traded for one dime.
- Two dimes and one nickel should be traded for one quarter.
- Four quarters should be traded for one $1 bill.
- Once the players have traded for a $1 bill, the race is won.
Variations:
- Backwards Race from $1.00:
Once players reach $1.00, they can play “Backwards Race to $0.” They take turns
rolling the die and subtracting that amount from the game board each time.
- Race to $100:
Play the same game with $1, $5, $10 and $20 bills for a whole-number version.
- Race to a Quarter:Play as described above, only play ends
when students reach 25¢.
- Race to 100:
Play as described above, only use base-ten manipulatives representing ones,
tens, and hundreds.
- Race to One: Play as described above, only use base-ten manipulatives representing
hundredths, tenths, and one whole.
Final Word
So…the next time you introduce math games to your class, take a few minutes to think through these four categories. How might you use this particular game, and every game, to afford your students opportunities to negotiate rules, speak clearly, listen graciously, and win/lose gracefully? The social-emotional benefits you help them develop extend well beyond game playing.
Please take a moment to let us know how you might use these ideas for a game you play in your classroom. You can leave your thoughts in the comments box, below.
Kimberly Rimbey, Ph.D., works with teachers and leaders to develop system-wide change in mathematics teaching and learning.
Hands-On Math
Serious Play-Part 4
Why is it that some games get played over and over while others remain on the shelf collecting dust? If you’re going to invest the time and resources into creating math games for your classroom, don’t you want to be sure that they’re going to get used? And even more so, don’t you want your students to want to play the games that will support their learning?
While designing the KP Mathematics games series, we discovered three characteristics that make for a great math game that gets played over and over:
- The game promotes challenging mathematical thinking that is accessible to students on multiple levels.
- The game primarily engages students in using mental math skills. Each turn would be too cumbersome if it required students to engage in complex tasks or computations.
- The game incorporates an element of chance. This is what makes the game fun. If the most-skilled student can (of course!) win most of the time, why would anyone else want to play?
For today, let’s use the game One-Two-Switcheroo as an example. You can download a free copy of the game by clicking here, choosing an option, and using the code kpmathgame-nov2025 when you check out. Note that there are many versions of the game. Although the rules remain the same for all, you can choose either addition or multiplication and a number set (0-10, 0-18, 0-100, beyond 100, fractions, integers, rational numbers).
Basic Rules for One-Two Switcheroo
- Players decide who takes the first turn.
- Player 1 places a card from his hand on a Sum/Product Spot, saying aloud the correct addition/multiplication statement: for example, “5 + 9 = 14.”
- Player 2 takes the next turn, following the same procedure as Player 1.
- When a player has a card that makes a Switcheroo Pair (a commutative pair), s/he places that card on the Game Board on top of the other card of the pair.
- Then, s/he places his/her marker on the pair of cards and says aloud the commutative statement: for example, “9 + 5 = 5 + 9, One-Two Switcheroo.”
- Players alternate turns. The game is over when all the cards have been played.
- The winner is the player with more Switcheroo Pairs.
Let’s take a closer look at this game to examine how it addresses the three characteristics we’re exploring today.
Does One-Two Switcheroo promote challenging mathematical thinking that is accessible to students on multiple levels?
Yes! First, this game is layered with two separate concepts: the commutative property and basic addition facts within 10 (or other numbers/operations, depending on the version you chose). In each turn, students will attend to both the property and to the mental math. It’s important to note that multiple versions of this game may be offered concurrently (feel free to download a couple of versions if that will help you in your work). While one pair of students is working on multiplication within 100, others may be working on multiplication with fractions or integers. Although the game directions are identical, the mental strategies will vary tremendously.
Does One-Two Switcheroo primarily engage students in using mental math skills?
Yes! Every version of this game requires that students use mental math strategies rather than paper-pencil strategies. This allows the game to flow smoothly so students don’t get bogged down with complex arithmetic. If students appear to be struggling with the version they’re playing, they can switch to a different version. You may even want to give students the opportunity to create their own versions of the game!
Does One-Two Switcheroo incorporate an element of chance?
Yes! Students draw cards from a shuffled stack that contains some chance cards (such as “take a card from another player”) that add to the game’s unpredictability. Such cards help balance the chances that all students may win the game, regardless of the skill-level they bring to the table.
Please take a moment to download the free game we offered above and examine it closely. Do you see how these three components were woven into the game, regardless of the version you selected?
Next Step for Teachers: Try out One-Two Switcheroo with your students. Do you see how those same three characteristics lend to the appeal of this game? Examine other games used in your classroom. Do they exhibit these three characteristics? Finally, ask your students which math games they play and why. Use their responses to shape how you select math games in the future.
Next Step for Leaders: Encourage your teachers to use game play to reinforce math skills. During grade-level or department meetings, discuss the characteristics of a “winning” math game. You may even want to make copies of One-Two Switcheroo to use as a basis for these discussions. And finally, make time for walk-throughs during game play to interact with students and to hear their thoughts on which math games are fun and why.
Let’s continue the conversation! What math games do you your students love to play? Do they exhibit any or all of the three components I mentioned? What makes them fun and keeps the kids coming back? Please share your thoughts in the comments box below.
Kimberly Rimbey, Ph.D., works with teachers and leaders to develop system-wide change in mathematics teaching and learning.
Game Play, Hands-On Math, KP® Ten-Frame Tiles, Teaching and Learning
Serious Play #5
Imagine this…you walk into a noisy, bustling classroom where students are spread out in small groups at tables, on the floor, at the counter. They’re everywhere, really. They’re huddled around game boards and decks of cards, playing mathematics games that engage them in mathematical thinking, discourse, and strategy.
As you reflect on what you’ve witnessed, what did you notice? What math concepts were being reinforced? Were all the students playing the same games, or was there a variety? Did you see evidence of different levels of thinking?
After several years of using mathematics games in my own classroom, I noticed that that most of my games centered on arithmetic and math-fact practice, almost always at the abstract level (e.g., using the symbols of mathematics). It was at this time that I started looking for games that included representations other than numerals. Could I find games that incorporated concrete manipulatives? Were there games out there that incorporated pictures, diagrams, or other graphic representations? It turns out that there are plenty of options if you know what you’re looking for! These days, when selecting great mathematics games, I look for a balance in concepts, DOK (Depth of Knowledge), thinking strategies, and representations.
For today’s post, let’s look at representations that promote thinking at different levels. Below you will find three games, each addressing one of the C-P-A levels: concrete – pictorial – abstract. Notice that they all exhibit the characteristics described in last week’s blog post that make mathematics games fun.
1) Mathematics Games That Use Concrete Representations
Since students often manipulate objects when exploring a concept, games in this category typically include a game tboard or concrete materials. Race to 100 provides a concrete way for students to focus on grouping (and ungrouping) tens as they build numbers to 100.
Click here to download Race to 100.
When playing this game, students work as partners rather than as competitors. As they repeatedly group ten ones into one ten, the “concreteness” of the game promotes visualization of place value.
2) Mathematics Games That Use Pictorial Representations
Ruler Races involves the use of a 12-inch ruler marked in fractional parts of inches. Students are encouraged to think of the ruler as a number line marked in fractional parts. They physically identify different points on the fractional number line as they explore flexible ways to think of fractions and fraction addition.
Click here to read the directions for Ruler Races.
Although one may think of a ruler as a concrete object, it is not mathematically concrete. It really is a pictorial representation of the 1-inch units (or 1-cm, or whatever unit is being used) used to measure objects. Some teachers even use rulers as number lines, which is the case in this game.
3) Mathematics Games that Use Abstract Symbols
Salute has been a favorite in my classroom for years! Students practice inverse operations (addition/subtraction OR multiplication/division) during game play. Students alternate between finding sums/differences and related missing addends/factors.
Click here to read the directions for Salute.
This game uses the numbers (abstract representations) on the playing cards to generate new problems for each round, and the students use mental math strategies to determine the missing values.
So…think about the games you use in your classroom. Do they offer students the opportunity to engage in mathematics beyond math-fact practice? Do your mathematics games include various levels of representations? How might you incorporate more concrete and pictorial games into your repertoire? Please share your thoughts in the comments box, below.
Next Steps for Teachers: Set up the games in this blog post (and others) and provide them for students to play. Also, take inventory of the games you already have in your classroom – do they provide concrete and pictorial opportunities as well as abstract practice?
Next Steps for Leaders: Lead your teachers in a conversation about this post. Have them list the mathematics games available in their classrooms and categorize them by C-P-A. Then walk through the classrooms to see how students are responding to the math games that use different levels of representation.
Kimberly Rimbey, Ph.D., works with teachers and leaders to develop system-wide change in mathematics teaching and learning.
Hands-On Math, KP® Ten-Frame Tiles
Spoiler Alert: If you haven’t already read John Van de Walle’s Teaching Student-Centered Mathematics, you’re going to want to get a copy right away!!!
Several years ago, I had the amazing opportunity to meet and work with John Van de Walle for a brief time. Subsequently, as I read the original version of his Teaching Student-Centered Mathematics, I was awed by the compilation of so many ideas I had read, heard, and discovered during my years as a classroom teacher and math coach. Honestly, I couldn’t put the book down. It brought together so many incredibly important ideas I had discovered over the years, all in one place!!!!
Perhaps one of the most impactful messages in the book was the reference to groupable vs. pre-grouped base-ten manipulatives. It was only a two-page spread, but it sent me on a journey that has forever changed my professional life.
It turns out that pre-grouped physical models, including the most-commonly-used base ten blocks, can obstruct student understanding rather than support it. I had heard some of my favorite researchers, such as Constance Kamii and Pat Thompson, make similar claims in their talks, and it was in this moment that their words came to life for me.
You see, in this very brief section, the authors stated that the potential is great for children to use pre-grouped manipulatives to demonstrate operations “without reflecting on the ten-to-one relationships or without really understanding what they are doing – this is especially true if children have not had adequate experience working with groupable models.” The added cognitive load increases dramatically when students must think about the structure of the manipulative in addition to representing numbers and operations (more on this next week).
The authors suggest that we use objects that can be grouped into tens, such as popsicle sticks, beans, or unifix cubes. They go on to suggest that an organizing structure such as the ten frame might further help students internalize the grouping-by-tens structure.
After reading this, my head started to spin with possibilities. What if we could somehow use ten frames in every place in our base-ten numbers to represent quantities, both large and small. How might this help children understand and internalize numbers and operations???
Well…that journey continues to this day. Peggy Akin and I joined forces a decade ago when we created Ten Frame Tiles, a groupable manipulative that helps children view mathematics in entirely new ways. This tool has the potential to transform the teaching of elementary mathematics.
Interested in learning more? Check out Peggy’s series of journal entries, Beyond Base-Ten Blocks: The Search for a Better Solution. Each entry visualizes the contrasting ways base ten blocks and Ten-Frame Tiles address a common base ten standard and then speculates on the contrasting impacts on children’s learning — and, ultimately, on the way children think about mathematics.
Kimberly Rimbey, Ph.D., works with teachers and leaders to develop system-wide change in mathematics teaching and learning.
After reading this post, please share your thoughts in the comments box below. Have you faced frustration with base-ten blocks the way I did? Have you gone looking for alternatives? Have you found any that worked?
