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, 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.
Hands-On Math, KP® Ten-Frame Tiles, Math, Teaching and Learning
Becoming a teacher-turned-inventor never crossed my mind earlier in my career. However, since founding KP Mathematics, this is the path I’ve traveled. KP Ten-Frame Tiles, an embodiment of the base-ten number system, came to life as we searched together to find a solution to the problems presented with pre-grouped manipulatives such as base-ten blocks.
As physical and pictorial models, base-ten blocks do an adequate job of illustrating place-value-based quantities. However, everything falls apart when using base-ten blocks to demonstrate the action of grouping and ungrouping tens and magnitudes of ten.
In her article, Choosing the Right Tool, Stacy Boote explains that base-ten blocks have a static form that renders them less useful when demonstrating operations such as division due to the need to group and ungroup. In contrast, when used to demonstrate the area model of multiplication, they will suffice because the action of grouping occurs after the model has done its job.
“When using the area model, exchanges between place values do not occur in the creation of the rectangle or when finding the areas of the four inner rectangles. Renaming occurs at the end of the process, when calculating partial products. Therefore, using materials that can be easily manipulated is not an area model requirement” (Boote, p. 479).
This regrouping issue that exists for long division also appears when representing the operations of addition and subtraction. The need to manipulate the materials for exchanges between place values is an important process. And when using base-ten blocks, the trades that must take place for grouping and ungrouping (aka, carrying and borrowing) obstruct student understanding rather than support it.
Using groupable manipulatives, such as KP Ten-Frame Tiles, craft sticks, or unifix cubes, requires less cognitive load because the actions children demonstrate are relevant to the mathematics they are learning. When students are “regrouping,” they literally group and ungroup rather than “trade,” which is the only option with pre-grouped manipulatives such as base-ten blocks.
So, you may ask, how do we resolve this issue? The answer is simple…use groupable manipulatives when the mathematics being modeled requires the action of grouping and ungrouping. KP Ten-Frame Tiles, craft sticks, or unifix cubes are a few options. It’s okay to use pictures of base-ten blocks to help kids visualize quantities, especially given this is the most common model used in testing situations. But when students need to manipulate to represent the movement between places, groupable models are the way to go.
If you’d like to learn more, I recommend reading the groupable vs. pre-grouped manipulatives section in Teaching Student-Centered Mathematics, or the article linked above, Choosing the Right Tool. And take a look at Peggy’s series of journal entries, Beyond Base Ten Blocks.
Kimberly Rimbey, Ph.D., works with teachers and leaders to develop system-wide change in mathematics teaching and learning.
After reading this post, please join in on the conversation! What have been your experiences with pre-grouped manipulatives such as base-ten blocks? What have been your successes and challenges? We always love to hear from you!
Math, Math Content, Math Discourse, Math Standards, Professional Learning, Taking Care of Teachers, Teaching and Learning
Equal Sign Means Relationship
Blog post #1 in the series, Lies We Tell Our Students
The Story
A while back, I was working in a fifth-grade classroom, and as a warm-up, I put the following equation on the board:
8 + 4 = 1 + 11
I then asked the students, “Is this statement true or false?” After waiting several seconds, I asked them to raise their hands to indicate their votes. At that point, two students voted for true, and the other 22 students voted that the statement was false.
Being the good teacher that I am, I asked the students to discuss their thinking, believing that those two students who said it was true would quickly convince the others. However, when I brought the class back together and once again asked my questions, 24 hands went up stating that the answer was false.
“Yikes!” I said, “What’s going on here? This statement is actually true. Can you tell me what you’re thinking?”
“Mrs. Rimbey,” started one of those original two students, ”8 + 4 does not equal 1.”
The Lie
I’ve since come to learn that this is not an isolated case. Many students across the grade levels believe that the equal sign is a symbol that indicates the action of finding the answer, when, in fact, it actually signals a relationship between the expressions on each side. In the vast majority of classrooms, students develop this misconception because virtually every equation they see in the early grades follows the same format: 3 + 3 = 6; 4 x 4 = 16; 20 – 13 = 7; and so forth. The “answer” appears last.
The Truth
So, what do we do about this? We can be sure to provide students with multiple daily opportunities to see equations written in different formats, pointing out that the equal sign indicates an equal relationship, not the action of finding the answer. Provide examples with the “answer first” (e.g., 6 = 2 + 4), with “nothing to do” (e.g., 1000 = 1000), or with “no answer” (e.g., 32 + 42 = 20 + 5).
The Series
This blog post is the first of a series that addresses the lies we tell our students. It’s important to note that these lies are not deliberate untruths. Rather, they are rules, procedures, mnemonics, and tricks we teach kids in an effort to make math easier for them. Sometimes, the lies come in the form of omission, such as the example of the equal sign shared above, where we don’t provide enough varied examples. Sometimes, they come in the form of half-truths, such as addition and multiplication, which always make bigger, which is only true with natural numbers (not including 0).
In Summary
To sum up this week’s Lies We Tell Our Students:
- The inadvertent lie: The equal sign indicates the action of finding the answer.
- The truth: The equal sign indicates relationship, not action.
As always, we love hearing from you! Do you think your students fully understand the meaning of the equal sign? Have you tried any of these (or other) strategies with your students? Please share your thoughts in the comments box below.
Next Steps for Teachers: Use a variety of equation structures with students on a daily basis (see examples above). Consider making a set of 4-6 “true-false cards” each day to show the class. Simply write one equation on each card, using a variety of formats, making some true and some false. Then ask the students whether each is true or false and to justify their answers.
Next Steps for Leaders: Discuss the meaning of the equal sign with grade levels, focusing on the notion that the equal sign indicates a relationship, not the action of finding the answer. Although this concept typically appears in the K-1 math standards, this misconception continues to exist in middle school and beyond. Discuss ways to avoid this misconception in each grade level, and then share their ideas across grade levels.
Kimberly Rimbey, Ph.D., works with teachers and leaders to develop system-wide change in mathematics teaching and learning.
