Game Play, Hands-On Math, Math, Teaching and Learning
As a novice teacher many years ago, I found that playing games in math class brought about high levels of engagement. My students loved it when they could play solo, partner, or group games, and they always begged for more. However, it wasn’t until several years later that I added individual accountability during game play, and this made a huge impact on student learning. I had learned that game play provides both motivation and practice, and yet with a slight twist to add individual accountability, it took students even deeper in their understanding.
For example, when students play “Double War,” I ask them to verbally state the sum (or product) of the two cards in front of them as a comparison statement. It sounds something like this: “14 is greater than 8.” By listening closely to my students, I can learn more about their thinking and mathematical precision.
This is exactly what was happened not too long ago in a first-grade classroom. As I walked around the class, listening in as students played Double War, I heard Travis proudly state, “14 is gooder than 8.” He was so confident and excited that he had won the round. And yet his statement revealed something I had not anticipated…he had interpreted the mathematical term “greater” as better than rather than more than. Because students were required to verbally state their comparisons, I was able to detect student misconceptions and weave that into my instruction just a few minutes later.
Accountability Leads to Learning
So, what can you do to emphasize individual accountability during game play? Here are five strategies I’ve picked up over the years:
1) Verbalize Thinking:
As described above, require that students verbalize their thinking using a sentence frame. This reinforces mathematical reasoning, precision, and vocabulary, and it provides opportunities for teacher observation.
2) Record Thinking:
Ask students to record the equations, comparisons, etc. on paper so you have evidence of learning. Don’t require this every time or it becomes a burden. However, used occasionally, it lets students know that game-play is so valuable that sometimes it counts towards a grade.
3) Record Observations:
Using checklists or post-it notes, record anecdotal observations based on pre-determined outcomes. Once again, this validates game-play as an authentic and measurable activity.
4) Take Photos:
You can use photos and video to record student thinking during game-play. Photos can be printed and placed in student files, and videos may be used as part of a digital student portfolio.
5) Complete Ticket Out the Door:
Once game play is completed for the day, ask students to complete a related task or problem, one that applies the concept(s) that were practiced during game-play. Collect these as evidence of student learning.
Accountability mechanisms such as these have made a huge difference in my classroom, and I’ll bet they will do the same for yours. We’d love to hear about your thoughts on game play in math class. What are your students’ favorite games? What do you do to maintain accountability? Please leave your comments below to continue the conversation.
BONUS: In last week’s post, we offered you a free game download for your class. The coupon is still good through June 1. If you haven’t yet claimed your free game, click here to go to the KP Mathematics Serious Play webpage. Use the code KPMathGame-Feb2026 when you check out.
Game Play, Hands-On Math, Math, Teaching and Learning
As we continue throughout quarter 3, you will likely be thinking about how to finish this quarter, and the year, strong. So as a third quarter surprise, KP Math is offering a gift to those of you who like to plan ahead with creative ideas for your classroom. Between today and March 1st, you may download a free math game of your choice by simply using this code: KPMathGame-Feb2026. Click here to select your Serious Play game.
Now, please understand that these are not ordinary games. They were designed specifically to incorporate three elements critical to games used for instructional purposes:
- Mathematical richness: Every game focuses on a single property of operations (or two related properties) for a range of grade levels, kindergarten through high school.
- Mental math fluency: The games’ contents, differentiated by operations and number sets (from sums within ten through rational numbers.) reinforce mental math strategies.
- The fun factor: Each game is designed with both chance and strategy in mind, making the game an exciting and challenging experience for students regardless of their math ability.
Whether you’re creating your own game or previewing a game to introduce to your students, it’s important that you ask yourself these questions:
- Does the game reinforce an important mathematical idea?
- Does the game allow students to connect the mathematical idea to important skills, such as mental math fluency?
- Does the game present an element of chance that makes it fun for all players, not just those who are fastest or most mathematically skilled?
Here’s your chance to have a model to examine and, at the same time, have a game to prepare for your incoming students. For the next ten days, you’ll have the opportunity to download one of our Serious Play games, each of which reinforces a property of operations, an operation, and facility with a grade-level-appropriate number set.
Download your game today, and please let us know what you think! You can leave your thoughts, questions, and suggestions in the comments section below.
Kimberly Rimbey, Ph.D., works with teachers and leaders to develop system-wide change in mathematics teaching and learning.
Game Play, Professional Learning, Teaching and Learning
In my last post, I shared the dangers of using imprecise language in the classroom – inadvertent mistakes we teachers make that can lead to student misconceptions down the road. I shared one way to ensure that teachers and students alike move toward a common mathematical language: establishing school-wide agreements around vocabulary usage. This week, we turn our attention to the classroom.
Academic vocabulary development often has limited utility. Our students are not likely to use words like “commutative property” and “Pythagorean Theorem” when they’re talking to their families over dinner. Math terminology tends to be used in math class and does not get a lot of mileage on the playground, in the cafeteria, or on the bus ride home.
So…it’s up to us to find ways to make it palatable, meaningful, and useful. Below you will find six tips for achieving this…strategies and activities that are supported by research and have been used in thousands of classrooms.
- Limit It: Students can retain only so many new words at one time. And yet we often introduce 20-30 new vocabulary words with each new math topic. Rather than holding students accountable for each word, select 5-7 high-leverage terms to concentrate on. These are the ones you will hold students accountable for using.
- Repeat It: Remember that mathematical terminology does not have much utility outside of math class. For any new vocabulary to stick, students should use the word(s) 5 times in the first day and 30 times in the first week.
- Sketch It: Helping students internalize new vocabulary requires more than memorization and spelling. Students must associate each word with its meaning. To help students access their spatial memories, ask them to focus on descriptions and drawings. One of my favorite things to do with students is to have them make vocabulary picture cards, where the pictures illustrate the word’s meaning. For example, students may write the word “parallel” by making the two large, thick “l’s” in the center. For other examples, check out the vocabulary cards on the Lone Star Learning website.
- See It, Say It, Draw It: This simple 3-5 minute “game” activates students’ understanding of selected vocabulary. From each math unit, introduce 5-7 high-leverage terms (see above). Each time you introduce a word, write it on a popsicle stick or strip of heavy paper and place it in a cup. This action is cumulative, so, over time, there will be dozens of strips in each cup. To play the game, pull a strip , read the word, and roll a die. If you roll a 1 or 2, students write the word. If you roll a 3 or 4, students explain (to a partner) the meaning of the word. If you roll a 5 or 6, students sketch a picture that represents the word. Students get one point for each correct response. You can also play this game in small groups –simply make a cup with strips for every 2-4 students.
- Math Term “Quiz”: For the quiz, have students number their papers to 5. Select a term and describe it without saying the word. Students write the words, in order, on their papers as you describe them — OR, to mix it up, you might ask students to make a quick sketch — OR you may use the agreed-upon hand gestures for each word and ask students to write the words. Make it quick and simple. Occasionally include a word from a previous unit for spiral review.
- Act It Out: Add one more dimension to the game above by having students create a hand gesture to represent each word. The game becomes a See It, Say It, Draw It, Act It game.
As we discussed in Part 1, mathematical precision requires a deep understanding and correct usage of appropriate terminology. Using strategies such as these, borrowed from the language acquisition world, may make all the difference as your students navigate the wonderful world of math.
What do you do in your classroom or school to help students grasp the concepts behind the words? Please continue the conversation by sharing your ideas 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, Math, Teaching and Learning
Serious Play-Part 1
Even before I had my own classroom, game play as a learning tool fascinated me. From the moment my favorite professor introduced me to the idea of using games to motivate students, I was hooked. And fortunately for my students, game-play became a serious part of my instructional repertoire.
You know that a classroom game is successful when students want to play it over and over again. A game with longevity is a game that students return to all year long, and sometimes over multiple years. One way to achieve longevity is to introduce games with multiple variations.
One of my favorite classroom games that has proven its longevity is the classic card game, War. This game, often played with very young children to reinforce the notion of “greater than” and “less than” for one-digit numbers, has utility well beyond the early years. Here are the basic rules and a few variations.
Instructions for Playing Basic War
Materials: one deck of card for two players, face cards removed; Ace = 1
Directions:
- Shuffle the cards well and distribute them evenly into two piles, one for each player.
- Each player flips over the top card in his/her pile.
- The player with the greater number wins both cards.
- When the numbers are the same, players repeat steps 2-3. The winner keeps all four cards.
- Play continues until all cards are used. The player with more cards wins the game.
Variation 1 – Less Than War: The player with the lesser number wins both cards.
Variation 2 – Addition War: Each player flips over the top two cards of his/her pile and adds the numbers. The player with the greater (or lesser) sum wins all four cards.
Variation 3 – Difference War: Each player flips over the top two cards on his/her pile and finds the difference between the two numbers. The player with the greater (or lesser) difference wins all four cards.
Variation 4 – Multiplication War: Each player flips over the top two cards on his/her pile and multiplies the two numbers. The player with the greater (or lesser) product wins all four cards.
Variation 5 – Integer War: Each player flips over the top two cards on his/her pile. Red numbers are positive, and black numbers are negative. Each player adds (or multiplies) the integers together. The player with the greater (or lesser) total wins all four cards.
As you can see, these variations provide a variety of differentiation opportunities within a classroom as well as options for playing across grade levels. In my experience, this game is revisited over and over, not just in kindergarten, but all the way up the grades as the rules change to incorporate new operations.
In the coming weeks, we will explore additional features that make game-play a valuable asset in the classroom. I’ve listed some of those characteristics below, adding some thoughts about how they apply to the game of War.
- Academic discourse development – students make a comparison statement prior to claiming the cards.
- Behavioral self-monitoring – students learn to be gracious winners and losers.
- Concrete – Pictorial – Abstract options – on occasion, I ask students to represent and/or record their solutions.
- Disciplined and positive social interactions – students learn how to interact in a social situation.
- Engagement with multiple math concepts – the variations, listed above, say it all!
- Fun-factors that keep students coming back – War has an element of chance that makes the game more accessible and unpredictable. It’s not necessarily the most-skilled student who wins each hand.
- Guided Math options – games such as War make for a great independent center during guided math group time.
Stay tuned for more on each of these Serious Play topics…and be watching for some exciting freebies from KP Mathematics in the coming weeks.
Question: What math games do your students play that have enough fun-factor and variation to stand the test of time? Please let us know by leaving 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, 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.
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.
