This page presents two numerical games appropriate for students
at the upper elementary grade levels -- 3rd to 6th grades.  In each
game, use of calculators is presumed to be part of the setting, mostly
to speed up play and to guarantee greater accuracy of the computations
involved.  It has been my observation that many students at this level
lack the necessary familiarity needed with this technology.  So these
games are merely intended to give the students an environment in which
they can use calculators in an enjoyable way, yet build up their skills
at the same time.

The Product Game

There are two players for this game; each one needs a pencil, paper and a calculator.


1. Each player forms a pair of numbers using the digits 1, 2, 3, 4, and 5, once and only once. This is done simultaneously and out of sight of each other. One number thus formed will contain three digits; the other will contain two digits. Example: 2 4 1 × 3 5 2. Each player computes his own product. 3. Then the difference of the two products is found. 4. Points are awarded in the following manner: a. If the difference between the products is 1000 or more, the player who made the larger product scores 5 points. b. If the difference between the products is less than 1000, the player who made the smaller product scores 10 points. 5. The first player to score 50 or more points is declared the winner. 6. NOTE: To make the game more challenging and fair, no number formed should ever be used twice. So keeping a record of what numbers have been used is important.
* *** *


A: 235 × 14 = 3290 Difference = 5134 B: 351 × 24 = 8424 B gets 5 points A: 423 × 15 = 6345 Difference = 135 B: 432 × 15 = 6480 A gets 10 points The game may be varied in different ways. One is by changing the digits used to another set of five: (2, 3, 4, 5, 6) or (1, 3, 5, 7, 9) for example. Another might be to change the scoring of points to something like "15 points go to the player with the larger product whenever the difference is greater than 5000". [This is added to the previous two scoring rules, however.] Or dream up your own adaptions.

The Sum-of-Squares Game

This game is similar to, yet different from, the previously described game. It is similar in its scoring system, i.e. the big vs. small aspect. The differences are that addition is the operation to be used and the squares of the numbers from 10 to 31 are numbers that will be added. The reason I have selected these particular squares has already been discussed in my page
It's a Square, Square World. Prior to playing this game, a deck of 3-by-5 cards need to be prepared with the twenty-two squares written on one side. It is recommended that each card carry the information written in this form:
122 = 144
After that, the same equipment as for the other game are required.


1. The cards are placed face down spread out on a table; perhaps they may be shuffled as well before doing this step. 2. Each player takes turn in selecting two cards. 3. The sum of the two squares is then calculated. 4. Next, the difference of the sums is calculated. 5. Points are awarded in the following manner: a. If the difference between the sums is 500 or more, the player who made the larger sum scores 5 points. b. If the difference between the sums is less than 500, the player who made the smaller sum scores 10 points. 6. These cards are put aside and the process is repeated with the remaining cards. This would mean three more rounds before the cards need to be collected and reshuffled. [This is to promote familiarity for each player with as many of the squares as possible throughout a game.] 7. The first player to score 50 or more points is declared the winner.
This game can likewise take on different variations. One is that three cards at a time could be selected to form the sum. Another is that all (or some) of the cards could be dealt to each player in typical "poker" style, giving the player the opportunity to select which cards he/she desires to use in given round of play. Again, you may be the designer of your own variation.
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