Back in middle school the best day ever was when one of my teachers would wheel out the cathode ray TV and VCR combo on a wheely cart and pop in a sweet VHS tape. Time to turn my brain off and coast for an hour. Unless it was Bill Nye the Science Guy, I was automatically asleep at the wheel, and no learning was taking place. The one exception was when we watched Honey I Shrunk The Kids in elementary school as a “treat” and I was forever traumatized by the heroic ant being viciously stung to death by a scorpion (thanks, Mrs. Heath).
Perhaps you have a thought or emotion attached to the TV/VCR cart that comes to mind. It might be quaint nostalgia, or perhaps an endearing feeling attached to knowing you didn’t have to work hard for an hour.
Now, what feeling is attached to the teacher who wheeled out that cart? What words come to mind when you think of the educator who used it once in a while. What about every week? How about constantly? I suspect that the more it is used, the more negative those descriptors tend to be.
Whether correct or not, the TV cart usually indicated a teacher who was tired, lazy, or unmotivated. Aside from being the easiest sub plan ever (insert VHS, press play, relax), the TV cart showing up in class constantly was not a strong sign of an effective educator. Not much learning was going on in that classroom, I would surmise.
Even though TV carts are a relic of the past (if your school still has these in circulation, I’m sorry), there are modern equivalents that show up just as often. Obviously, firing up Disney + on your overhead projector is just a new technology form of the same thing, although there are many great documentaries and nature programs available that are of high value. Interactive quiz apps like Kahoot! and Blooket can be used effectively for review of a particular learning target, but often turn into “Name That Corporate Logo” or “Interesting Facts About Halloween” time wasters.
In my classroom my goal is to use every single minute for instruction and mathematical thinking. I don’t always succeed, but I’m always trying to maximize the learning. This means having the agenda and warm-up thinking task ready to go as the students walk in. Attendance is done within 30 seconds of the bell ringing. The main lesson starts no more than 5 minutes after class starts (after completing the warm-up task), and ends within 2 minutes of the bell ringing so students can organize their materials and get ready for the trek to their next class. Students are NEVER meandering around the room or standing by the door for minutes at a time, waiting for the bell to ring so they can sprint to the snack line (this is a huge classroom management pet peeve of mine).
So what do I do when the lesson ends early, or we have a few spare minutes left in class? Why, math games, of course! Over the years I have collected a few reliable math games that are effective in many situations, and require almost no materials or prep work. Here are some of my favorites:
The X Game
Time needed: Less than one minute.
Materials: Overhead Projector or Vertical Whiteboard Surface.
Directions in Google Doc format.
The perfect game for when you have less than a minute of class and you don’t want to waste it.
1. Think of any two integers (or fractions if you are feeling spicy). Draw an X on the board and write the product of the two numbers in the top space and the sum of the two numbers in the bottom space. For example, if I’m thinking of the numbers 3 and 5, I would draw this:
2. Have students silently study the drawing and determine what two numbers go on the left and on the right. For the above example, it could be 3 and 5 or 5 and 3. If they know the answer, they raise their hand. I never call on the first student, as my goal is not speed. I usually call on the 5th or 6th hand. If they get it correct, I make a new one. I can usually do 2-3 per minute once the students understand the game.
Note: I do not tell students how to figure out the blank numbers on the left and right. I just write it on the board and tell them to figure it out. Eventually they conclude that two numbers must multiply to get the number on top and add to get the number on the bottom. In 19 years I have never had to explain this game. I just write the x, the top and bottom numbers, and tell them to figure it out.
This game is great in middle school, as it secretly prepares them for factoring quadratic equations in high school later on.
Mental Pattern
Time needed: About 2-3 minutes.
Materials: Overhead Projector or Vertical Whiteboard Surface.
Directions in Google Doc format.
This game is my go to when I have only a few spare minutes left in class. This is great for developing number sense and function recognition. Here’s how it works:
1. Think of a function, any kind. Linear functions are best to start with before making things more complicated as your students get used to the game. Something like y = x + 7 or y = 3x is a great place to start.
2. Write a T-Chart on the board and complete two rows of the chart using random inputs. I usually do one positive integer and one negative integer to begin with. I never start with zero.
3. Give students some time to consider the pattern. If a student thinks they know the pattern being used, have them raise their hand. After a few hands are up (hopefully), call on one student and give them another x-value in the table and have them mentally compute the correct output. They are not explaining the pattern out loud, but simply giving the numerical output for the given input. If no students raise their hands at all, fill in another row with new values to give them more to think about.
Note: It’s important to stress that this is a mental math game and that students must try to figure out the pattern themselves. They are not sharing answers or telling other students how to do it. It is much more satisfying for a student to suddenly realize the pattern rather than have someone turn to them and tell them what it is. That’s no fun!.
4. If the answer is correct, fill in the table with that answer. If the answer is incorrect, just say that it is incorrect and call on another student. Many times students will be incorrect in the first round since the table does not have much information in it and they are thinking of many possibilities. Wrong answers are great, as they help narrow and focus other students’ thinking.
5. Continue this process, always calling on new students as you go, for about 5-6 different rows in the table. You will notice that more hands will go up each time you add numbers to the table. Sometimes students need a bit more time or a few more pieces of evidence for them to finally see the pattern. Once you have 5-6 rows complete, have a new student explain the pattern, or describe the pattern in terms of x.
6. Repeat the game with a new pattern if you have time. I usually just make one up in my head depending on the class I am teaching and the student population. If I know the class has been struggling with linear functions, I might focus on proportional equations or one-step linear functions. If they have mastered linear functions, I might start with linear functions with fractions or integers, then extend into simple quadratics such as y=x^2 + 3 or something with absolute value in it.
I can usually sneak one or two rounds in at the end of class. Some students will be packing up and organizing their belongings while others are playing the game. Nobody is just wandering around the room or waiting at the door.
Factor Clap
Time needed: 8-10
Materials: None
Directions in Google Doc format.
Warning: This game is exclusionary in nature, and may not be right for your class culture. I don’t play this game with every class. If you have fostered a growth mindset and students are ok with publicly getting math wrong, then it can be really fun. In most cases, students make fun of themselves and have a great time and are ok with messing up in front of others. We laugh a lot, but not at the expense of others.
This game is great to play outside if you have decent weather and just need the kids to move around a bit and be able to be loud. Here’s how it works:
Have all of your students stand in a circle with you in the middle. Explain the rules as follows:
- I will call out a factor number, point at a random student, and point either left or right.
- Starting at the number 1, each student must say the next number in order out loud.
- When you say the number out loud, you must either clap, or not clap, depending on what number you are on.
- If the number you yell out is a multiple of the factor number, you DO NOT clap.
- If the number you yell out has the factor number as one of its digits, DO NOT clap.
- If neither of the above is true, CLAP.
- If you clap when you shouldn’t, or don’t clap when you should, you are out and must either sit down or leave the circle.
- When a player gets out, the next student starts back at one.
- I can change the factor at any time, so pay attention!
For example, suppose you point at a student, yell out 4 as the factor number, and point to the left.
- The first student yells out 1 and claps.
- The student to their left yells out 2 and claps.
- The next student yells out 3 and claps.
- The next student yells out 4 and DOES NOT clap.
- Student 5 claps.
- Student 6 claps.
- Student 7 claps.
- Student 8 DOES NOT clap, since 8 is a multiple of 4.
- Students 9-11 clap.
- Student 12 DOES NOT clap, since 12 is a multiple of 4.
- Student 13 claps.
- Student 14 DOES NOT clap, since 14 has the digit 4 in it.
- Keep going until someone messes up.
I usually use the same factor for a few rounds and then change the number and the direction.
The last three students standing are the winners of the game.
A non-exclusionary variant of the game is to work as a class to see how high you can get without making a mistake. You can write down class records for different factor numbers and try to beat them as the year goes on. This way you are working as a team, rather than having individuals trying to win on their own.
D.U.C.K.S.
Time needed: 10-15 minutes
Materials: Overhead Projector or Vertical Whiteboard Surface, two number cubes, 1 quarter sheet of blank paper per student, 1 pencil per student.
Directions in Google Doc format.
I learned this game at a math conference about 17 years ago and cannot remember who taught it to me. Sorry, un-credited math educator. You are forever in my debt. I remember he called this game “SKUNK”, but I re-named it because I love the Anaheim Ducks, and it’s also easier for each round of the game to be represented by a different letter in the alphabet.
Hand out a quarter sheet of blank paper to each student and have them write D U C K S (or whatever word you like) at the top of the paper, like so:
Each letter represents a different round of the game. If you want a shorter or longer game, you can use a shorter or longer word. 4-5 rounds is usually the right amount.
Here are the rules of the game:
- At the beginning of each round, all students stand up at their seat (I provide red/green nesting cups for students who are unable to stand up due to physical differences. Green means standing, red means sitting).
- At the beginning of the round the game leader rolls two number cubes. I roll under a document camera for transparency.
- If neither number cube shows a 1, the values are added together and every student standing gains those points.
- For example, if I roll a 5 and 4, every student standing would write under the letter D that they got 9 points.
- If either number cube shows a 1, the round is over and anyone standing loses all of the points they collected that round.
- Optional rule: If the very first roll in a round has a 1 in it, ignore it and re-roll until you get a non-1 roll.
- After each roll, every student standing can choose to stay standing and continue playing, or sit down and be “safe”.
- Seated students cannot gain more points or lose any points. This is the only way a student can actually earn any points. If they stay standing, they are always risking their points.
- Once a student sits down during a round, that student cannot stand up again until the next round.
- A single round is over when one of two things happens
- A 1 is rolled on either number cube.
- Every student has chosen to sit down before a 1 is rolled (this rarely happens).
- At the end of the round, all students stand up again and begin the next round.
- Repeat this process until all rounds are complete.
- The winning student is the one with the most total points over all 5 rounds.
- This requires a level of integrity and trust that students are keeping score correctly.
- Verify the student’s score by confirming how many numbers they got for each round and that it all adds up.
- Optional Rule: Rolling two ones, or “snake eyes”, causes all students standing to lose all of their accumulated points for every round completed, not just their points for that round.
Here’s how a student’s score card might look at the end of a game:
- In round D the student stayed standing up for 4 consecutive rolls, then sat down. They earned 32 points.
- In round U the student stood up for two rounds, then was still standing during the third roll, which had a one in it, so they crossed out the points they had earned.
- Round C was tough, as a one was rolled on the second roll, so the student lost the 9 points they had.
- Round K was great, as they stayed standing for 5 straight good rolls and earned 37 points before sitting down.
- They got no points for Round S, as they were standing up when a one was rolled on the third roll.
This student would have a total score of 69 points. Nice.
Admittedly, there isn’t a whole bunch of skill involved in this game, but it does elicit good conversations about probability when rolling two dice. I love playing this in 7th grade after doing the Statistics & Probability unit.
Since this game takes longer than most, it’s great for a block day as a break between activities, or a fun way to close out a long class period.
Hopefully you can use one of these free math games in your own class and keep your students thinking until the very end of class.
What are some of your favorite math games to play in class that require little to no prep work or supplies? Let me know in the comments.
EZMath Blog 