The Mathematics of Gomoku

 

Over the last several months, I have been sharing a series of five in a row games called Gomoku.  The rules of the game are simple: roll two dice, perform the given operation, find a square with the answer, and the winner gets five squares in a row first.

This is also a way to introduce the number system to students.  The first three games use whole numbers: Addition, Subtraction, and Multiplication.  The next two games use rational numbers: Simplifying Fractions and Improper Fractions.  I included an enrichment game with integers to introduce negative numbers.

 

Gomoku Games: Five in a Row is available for free at Teachers Pay Teachers and Teacher's Notebook.

Gomoku with Integers

To download the game board for Gomoku with Integers, click here.

This is the last in my Gomoku series.  I included integers because I always have those students who want to do something more advanced than the rest.  The rules of the game are the same: roll two dice, perform the operation, place a marker on the square.  Try to get five in a row before your opponent.  This version of the game includes negative numbers.

I would provide a number line like the one below to support my students' conceptual understanding of negative numbers.  I would explain that they could start with either number on the dice and subtract the other.  I would teach this at an exposure level to students who want a "challenge."

 

 

Gomoku Games: Five in a Row is available for free at Teachers Pay Teachers and Teacher's Notebook.

Gomoku with Improper Fractions

To download the game board for Gomoku: Improper Fractions, click here.

Like Gomoku: Simplifying Fractions, students play this game by rolling two dice and dividing the answers.  This game board has whole numbers and improper fractions, because the larger number is divided by the smaller number. 

Students place a marker on an open place with the answer.  The winner is the one who places five markers in a row.

Gomoku Games: Five in a Row is available for free at Teachers Pay Teachers and Teacher's Notebook.

Gomoku -- Simplifying Fractions

 To download the game board for Gomoku Simplifying Fractions, click here.

Frequent readers of this blog know I love creating math games for my students to practice their facts.  I created Gomoku Games, a freebie in my Teachers Pay Teachers store where students can follow a few basic directions to play different versions of the game.  The change in difficulty comes in the operation performed on the numbers rolled.  For example, I have introduced addition, subtraction, and multiplication versions of this game. 

When I got to division, I wanted my students to work with fractions.  For this version, have the students roll two dice.  The smaller number becomes the numerator, the larger number becomes the denominator.  (There is another game board where this pattern is reversed.)

If your students haven't learned how to simplify yet, I would recommend a "cheat sheet": a list of possible fractions with their simplified forms.  As you can see from the list below, their aren't that many of them that need simplifying.

1 = 2/2 = 3/3 = 4/4 = 5/5 = 6/6
1/2 = 2/4 = 3/6
1/3 = 2/6
2/3 = 4/6

Once a player has figured out the answer, he/she places a marker on a square with that answer.  The objective is to get five markers placed in a row.

Gomoku Games: Five in a Row is available for free at Teachers Pay Teachers and Teacher's Notebook.

Gomoku Multiplication

To download the game board for Gomoku Multiplication, click here.

My fourth grade students need all the practice they can get with math facts.  This five in a row strategy game is one of many I have to get them to automaticity.  Students roll two dice, multiply them together and place a marker on a square with the answer.  The objective is to place five markers in a row.

This is one of a series of games I am sharing on my blog with my teaching tips.  If you want to download the whole set for free from my Teachers Pay Teachers store, click here.  Gomoku Games is also available in my Teacher's Notebook store.

 

 

Gomoku Subtraction

A couple of weeks ago, I introduced Gomoku with Addition, the simplest level of my new freebie Gomoku Games.  This week, I am featuring Gomoku with Subtraction. (Click here to download from Google Drive.)

In this game students roll two dice and subtract the smaller amount from the larger.  Students place a marker on a square with the answer.  The winner is the one who places five markers in a row.

When we introduced this game to our first grade buddies, my students noticed the wide range of math abilities in the class we were visiting.  Right next to each other there was a student who was ready for the multiplication version and another who struggled to count the dots on the dice.

I spend time talking with my students about how they learn, because I want them to take responsibility for their own education.  This experience was a good one for all of us.

Gomoku -- Addition

To download the Gomoku with Addition game board from Google Drive, click here.

Today I am starting a series of posts about a set of five-in-a-row game, I created for my classroom.  I went a little crazy with the seven different versions, and I have since shared this game with my colleagues at different grade levels.  Gomoku with Addition is the easiest level.

Students roll two dice, add the numbers together and put a marker on a square with the answer.  The goal is to get five markers in a row horizontally, vertically, or diagonally.  I introduced the multiplication version to my fourth graders.  I had them teach this version to our first grade buddy class.

If you can't wait to get the whole set of game boards, Gomoku Games is a freebie in my Teachers Pay Teachers store.  Gomoku is also available in my Teacher's Notebook store.

Gomoku on the 100s chart

There are many versions of Gomoku online game.  Two players take turns claiming squares and the goal is to get five squares in a row.  Rows can be horizontal, vertical, or diagonal.

Here is a free 100 chart with larger squares so many math materials will fit as markers. 

To use this game to practice number sense, students must claim their number with an equation.  For example, when the red player chooses the space 45, he must claim it by telling the other player 9 X 5 = 45.  The blue player verifies that this equation is correct.

Students may use any process we have learned in class to claim their number.  I have each pair turn in a paper with the two names and a list of the equations they used to play the game.

Update November 2: Now available as a set of seven games in my Teachers Pay Teachers store. Gomoku Games is also available in my Teacher's Notebook Store.