Mental Math


Continuing the process of letting some ideas breath on the blog this summer. Here’s another.

It’s a simple activity for those few unexpected extra minutes near the end of the period…or if I just want to hit them with some quick mental stimulation. I picked it up from my fourth grade teacher: mental math.

I simply call out a sequence of operations with a pause between each operation. For example, I might say “2 plus 5 (pause)…times 8 (pause)…minus 10 (pause)…divided 13…what’s the answer?

Students can’t allowed to say anything out loud and, obviously, any electronic device is prohibited. I don’t require that everyone plays (most do). The students must wait until I say ‘What’s the answer?’ before raising their hands. I call on a different student each time and if that person’s answer is wrong, someone else gets a chance. Because it’s a terribly simple idea, it’s always engaging. The trick is to make it challenging to the point where they get hooked and want more.

Some tidbits: I’ll usually start with one that’s pretty straightforward with long pauses – especially at the beginning of the year. Things get interesting when I start to call out the operations lightning fast or the sequence contains something like 15 operations. Make things fun by using numbers in the millions – or even billions. Also, depending on the class, the level of the math can vary from basic arithmetic to roots and exponents to evaluating trig functions. It’s endless. And fun.



I always hear about Trashketball. I thought I’d briefly share the version I play with my students.

I set up the room with 1, 2, and 3 point distances, one of each. I use duct tape and white out for this. 

I post a question. Each group works on it and I randomly select one student to answer. Before answering, the chosen student can confer with their group members, but he must able to explain or justify his answer. Here are the guidelines for the game:

  • If a student gets the question correct, he earns three shots to make a basket. All shots must be taken from the same location.
  • Each group is allowed to passed earned shots to another group member once during the game.
  • Groups can use any resource but a non-calculator, electronic device to aid them in answering the questions.
  • If a student gets the question incorrect, I earn one shot to make one basket. I can earn a maximum of three shots per question. Each shot is separate from any others and can be taken from any distance.
  • Groups cannot communicate with other groups. If they do, I earn a bonus shot.
  • The game is the entire class versus me. Whoever has the most points at the end of the class period wins.

Here is what we use to shoot.

The trash basket is the typical, run-of-mill classroom trash receptacle.

My record as of today is 83-0-1. No kidding. Despite what my record may reveal about my utter dominance, my students LOVE playing. This is due in part because each class desperately wants to hand me my first loss. Hey, students need motivation, right?

Oh, and how have I amassed such an impeccable record? You’ll have to ask my students.



Mystery Prize Game

This simple game is fun on many levels. I play it a few times a year and it’s a hit every time. And, after reading this, if someone can give me a catchy name for it, thank you in advance.

I give every student a set of 8-10 problems. Usually review and stuff that can completed somewhat quickly. Most recently, it was using the discriminant to determine the nature of the roots of a quadratic equation. The kids are in groups of 2-4 and, since class is 43 minutes, I give them 20-25 minutes to complete the problems. I foreshadow and mention that their group may earn an awesome prize based on correct answers.

Here’s where the fun comes in, especially the first time we play it. After working out the problems, I reveal three prizes. They are written on index cards and sealed with staples inside a folded piece of paper; a poor man’s envelope.

Prize Game Sealed Envelopes

For each round of the game, I use a random name picker to select a student. The selected student’s group gets an opportunity to answer a question from the handout. I usually go in sequential order. Correct answer = choice of prize. When choosing their prize, they have the right to any prize, even if that means stealing one from another group. We repeat this process for the remaining problems. To keep it fun for everyone, I limit the number of prizes per group to one, but groups can swap prizes with another group if they already have a prize. If a group gets a question wrong, we spin again to find another group. 

The game gets heated. I, of course, totally encourage stealing prizes from other groups. It’s fun and I love the instant rivalry that’s created when a prize is heartlessly taken. From a teacher’s point of view, this also provides high levels of motivation to earn correct answers!

With a few minutes left, we stop and the three sealed envelopes are opened by the groups that possess them. After a hard-fought game earning prizes, the anticipation behind opening them up is palpable. You would think it was Christmas morning. 

Here they are from the most recent game:

IMG_0198            IMG_0200

The kids always go crazy. 

I suppose you could play this with “real” prizes like candy or bonus points, but the kids always get an extra special kick out of these types of prizes – especially after competing for it throughout the game. They are just as motivated the next time we play. It’s all about good-natured competition and the mystery behind the prizes that make it fun. 

The prizes are different every game, but I usually stick with the Smile & Handshake each time we play. It’s become my trademark.