|The Teachers' Lounge|
The basic MathDice dice game is lots of fun, and in itself does a great job of building and reinforcing math number skills. However, our belief – which has been reinforced by experience with students using the program in many classrooms – is that kids have more fun, play it more, and learn more when they are offered a variety of different games to play. We’ve done our best to deliver on this.
In this section, we describe all the different MathDice games that students can play in the Main Season Program.MathDice Dice Game
In MathDice Preseason, students learned the basic rules of MathDice and ended the season playing an in-class tournament.
As your students’ teacher, though, it is important for you to establish the principle that you have the right and the authority to introduce changes to the game as you see fit, to make it more fun for your class and also to advance your educational goals. Some of these changes would be minor, such as allowing students to use pencil and paper, and/or MathDice Training Tables when they play, or to give each student a chance to come up with their best answer, then everyone reveal their answers at the same time. (In this case, every student who gets an answer equally close to the target number gets a point, not just the first student.)
Some changes are more fundamental. A MathDice variant developed in the Arlington, VA school system uses chips as counters; players claim one chip for being first with their answer, two chips if they can get closer than this first answer, and three chips for hitting the target directly.
We have published a full list of ideas for rules adjustments and variations on the MathDice game in Appendix 4, and encourage you to read through these and encourage your students to experiment playing games with different rules. If you and your students invent a new way to play MathDice that is fun, please let us know so we can share your ideas with others.Solo Practice Games
We’ve developed four pencil-and-paper based “Solo Practice Games” for your students to play on their own. Three of these games: Soccer Shootout, Ski Patrol, and MathBowling – were introduced in the MathDice Preseason. The fourth game, which is slightly more sophisticated, is MathDice Mini-Golf.
In addition to being fun and providing variety, the value of these games is that they allow us to present specific challenges to your students that are clever, fun, and offer high educational content. We’ve worked very hard to find specific problems that will stretch your students, will call on them to problem solve as well as to practice their mental math skills.
We have developed these Solo Practice Games at three levels: Beginner (easier problems designed to build confidence), Intermediate (harder challenges, but not requiring the use of exponents) and Advanced (challenges that may require the use of powers to reach the best answer. Your students can choose the challenge level that suits them best; and you can encourage them to try to work their way up to the next challenge level.Soccer Shootout
This game is the easiest of the four and should be taught first. Since there’s a range of target numbers and not just one, it will reward students who may have a tough time reaching the target number when first learning MathDice.
It’s important to remember that you only score goals with different target numbers. Reaching the same target number with two different equations doesn’t count. Also, the student must find target numbers between the two defenders and not equal to their jersey numbers.
Each challenge has a perfect score of six goals, but the number of goals may differ from one goal to the next within the challenge. For example, the first goal may only have one answer, the second goal three answers, and the third goal two answers.Ski Patrol
Another simple game. The concept is similar to Soccer Shootout, but in this case, the goal is to find one number within a series of ranges, or gates. In the Main Season, the numbers on the gates will always increase, but that doesn’t mean the difficulty of the problems will increase as the student makes it down the slope.
This exercise shows the student the flexibility of numbers and how to best combine them to reach ever-increasing target numbers. Students will soon learn that certain combinations of numbers will always generate higher targets than others. As in Soccer Shootout, the answer cannot equal the number on one of the gates; it must fall within the two numbers. Also, in some of the easier problems, there might be more than one answer that works. Only one answer is needed.MathBowling
This game is slightly more involved than the first two. The goal is to knock down all ten pins by using two scoring balls. To knock down a pin, the student must pick a ball and then use the scoring numbers on that ball only. He/she may not mix the numbers on the two balls. However, one ball will not work for all the pins. The trick is to find out which balls can knock over which pins.
Some of the pins can be knocked down by either ball. As a bonus, challenge your students to find these pins.MathDice MiniGolf
With MiniGolf, players are presented with three different MathDice challenges, in the guise of a 3-hole golf course. Players putt their “ball” as close as they can to the “hole”; which really means that they use their three Scoring Numbers (printed on each ball) to get as close as they can to the Target (printed on the hole.)
For some challenges, it is possible to make an equation that reaches the target directly; for some challenges, the best answer may be several numbers removed from the Target number, or even further. A player’s score for each hole is the distance their equation is from the target number. For example, if the target “hole” is 16 and the player uses their Scoring Numbers to make an equation that equals 18, the score for that hole would be 2.
The score for each MiniGolf Challenge is the sum of the scores of the three individual holes.
Included with each challenge is a “best” score for all three holes combined. The twist to this game is that, if a student’s score for the challenge is higher than the Best published score, he or she may need to evaluate their answer for each of the three holes that make up the challenge. This introduces a level of abstraction and problem solving slightly more advanced than the other three games in this category. Our experience is that students tend to start MiniGolf with some trepidation, but quickly come to find this to be the most exhilarating of the games. (To help build confidence with this game, with most of the MiniGolf Beginner challenges, it is possible to hit all the target numbers exactly.)Cooperative Challenge Games
These games are simple to learn and to play, but they require a level of abstraction and decision making that is more advanced than the Solo Practice Games described above.
These games are designed to be played either solo or cooperatively in teams. They work extremely well as a classroom challenge: divide your class into teams, offer the same challenge to everyone, and when the challenge is completed have each team announce their score and then discuss the results as a class.ChipAway
With ChipAway, players are presented with an initial set of Scoring Numbers and eight Target Numbers. To play, you place eight chips, or markers, on the board next to each Target Number, and place three dice in the indicated positions at the bottom of the board.
Players start by creating MathDice equations with their scoring numbers to equal as many target numbers as possible. Each time they find an equation, they place the chip associated with that Target Number at the bottom of the board in the indicated position. When they can’t find any more equations, players are allowed to turn one of their scoring dice to a new number, and make new equations to equal as many of the remaining Target Numbers as they can.
For all Target Numbers they reach with this number combination, they place the chips associated with these targets and place them in the indicated position for this turn. When they can’t find any more equations, players can then turn a second die to any new position they choose, and then repeat the process; and if there are still Target Numbers remaining, they turn the third die to a new position and repeat the process. If there are still Target Numbers remaining after all three dice have been turned, players may turn the dice to any position they wish to find equations to reach the remaining target numbers.
To score a ChipAway challenge, players determine the number of Target Chips they solved each turn, and multiply this number by the bonus number associated with this turn. In a standard game, for example, players would multiply the number of targets they hit in the first turn by five, the number of targets they reached after turning one die by four, the number of targets they hit after turning two dice by three, the number of targets they hit after turning all three dice by two, and the number of targets they reached once they could turn the dice at will by one. Add all these numbers together to reach the total team score for the challenge.
Allowing players the choice to turn different dice to different numbers creates a great deal of variability. Because of this, different teams will rarely follow the same path or reach the same score as other teams. This can make for wonderful class discussions as teams discuss the reasons behind their choices.Scavenger Hunt
With Scavenger Hunt, players must travel from the Start Position to two different Scavenger Stations and then continue on to the Finish Line. Each Scavenger Station consists of a Target Number and a Replacement Number. To travel to a Scavenger Station, players use their Scoring Numbers to create an equation that comes as close as they can to the Target Number for that station.
Once they have traveled to that station, they must pick up the Replacement Number from that station and swap it in for one of the Scoring Numbers they used to get to that station, and then use that combination of Scoring Numbers to travel to the second Scavenger Station. At the second station, they must pick up the Replacement Number from that station, and create a new equation to reach a number as close as they can get to the Target Number represented at the Finish Line.
Players may travel to the Scavenger Stations in either order.
To score, players calculate the distance that their equation was from each of the Target Numbers in the two Scavenger Stations and the Finish Line, and then add these three distance numbers together.
In practice, players will find that the choices they make about which station to visit first and which die to swap out at each station can quickly lead to widely divergent paths. This quality makes Scavenger Hunt an ideal game to be played by cooperative teams.Competitive Board Games
Four in a Row is played on a board 7 by 7 units square; a Target Number is printed on each of the 49 squares. The object is for players to place colored tokens on the board, and to get four of their tokens in a row before their opponent does so.
Play starts with one of the players rolling the three scoring dice and placing them in the indicated position at the base of the board. The first player creates an equation with the three scoring numbers that equals his/her chosen target number, and places a colored chip or token over that number. The second player must then turn any one of the dice to a new number, and uses those Scoring Numbers to create an equation to reach a target number of his/her choice, placing a different colored chip on that target number. Play goes back and forth, with each player turning one die to a new face each turn, until one player gets Four in a Row.
The value of this game, aside from being a lot of fun, is that it places such an emphasis on the strategic thinking necessary to either extend your own line or block the other player’s line, that the mental math skills necessary to accomplish one’s goals start becoming just a skill necessary to play well at the game. Once students make the shift to thinking this way, their understanding of basic math facts start to take on a new dimension, integrated into their thinking process rather than isolated facts simply held in memory.A Word on Levels of Play
We have designed all of the printed game variations of MathDice, the Solo Practice Games, the Cooperative Challenge Games, and the Competitive Board Game, to have challenges at different skill levels; Beginner, Intermediate and Advanced.
As you work with your students, it’s important for you to take this into account. Spiral learning works extremely well with the MathDice program; you might want to start your students out with Solo Practice Games at the Beginner level, then move on to play Beginner versions of ChipAway and Four in a Row, then move back to Intermediate challenges with the Solo Practice Games, etc. You’ll be amazed at how much fun your students will have with this program as they gain confidence and rise up to new challenges… we promise!