Addition Strategy Game

Cats and Dogs is a traditional ‘Chase and Capture’ board game combined with the learning of Basic Addition Facts.


Addition Game

Strategy Cats & Dogs – Printables and VIDEO GAME

addition game 19

Addition Games – Cats & Dogs – A Traditional Chase & Capture Game… with Addition

Addition Game: Cats and Dogs is a two-player abstract strategy game thought to have originated in Northern Europe. In this version of the game, a sly elderly cat is trying to outsmart three playful puppies.

What You Need:

2 players
1 Cats and Dogs board game
1 counter to be the cat
3 counters to be the dogs 

How to Play:

  1. The student with the longest hair is Player One.
  2. Player One reads and answers each algorithm aloud on the dogs’ side of the board. They then place their counters on the ellipses as shown.
  3. Player Two reads and answers the algorithm where the cat is on the board above or below then places their counter over it ready to start the game.  
  4. The dogs make the first move by sliding one of their counters along the lines of the game board. Both cats and dogs can only move one space on each move.  Dogs may NOT move backward.
  5. Player Two then makes a move. The cat can move one space in any direction along the lines of the game board.
  6. Players take turns moving their counters using these rules.
NB there is no capturing of pieces and no jumping over the opponent

How to Win:

  • If the cat makes it passed the three dogs or reaches the other end of the board then they are declared the winner.
  • If the dogs trap the cat so it has no legal moves available then the dogs win.
NB If a dog repeatedly moves vertically it is considered ‘stalling’ & results in a win for the cat – not a draw. Traditionally this has to happen 10 times but in my classroom, it is 3 times. This keeps the game moving.
       7. Swap roles for the next game.

Addition Games


– The cat begins the game on the ellipse shown.
– The cat can place their counter on any empty position on the board.
– Cat goes first.

Before the Game Possibilities:

– Ensure students have a good understanding of what ‘equals’ really means.
– Quick pre-game quiz question. ‘What does “equals” really mean?’ Think Pair Share Answers.
– Equals means ‘the same as’. 5+6=11 really means 5 put with 6 is ‘the same as’ 11. –  So… 11=5+6 really means 11 is the same as 5 put with 6. This is an important mathematical concept. Explore examples.
– Explore and reinforce the need for using efficient mental strategies when playing the game. – Explore the strategies that will help the students do well and this game and keep it flowing.

During the Game: 

– Encourage students to plan a move ahead and to anticipate their opponent’s move. ‘If she does that then I will…’ ‘If I go here then they will go…’
– Encourage children to predict the options their opponent has and what moves they may choose to make.
– Ensure students continue to say the algorithms and their answers aloud throughout the game.

Possibilities for After the Game:

– What do you feel you still need to work on after playing this game?
– Games like this are designed to ‘balance out’ by giving each player a different set of rules to move by. In this game, the puppies cannot go backward plus there are three of them. There is only one cat but it can move backward. Do you think this game is balanced or does one player have an advantage?  Explain your answer.
– Mathematicians believe with ‘perfect play’ the game will always result in a win for the puppies.  Explain how you think they would have figured this out?.

Possible Extensions:

– Investigate the origins of the game.
– Argue For or Against – ‘Chase and Capture’ board games such as this one have gone by many names over the centuries. The British called it a ‘Fox and Hound’ or ‘Fox and Hare’ and as part of the game the hare ends up ‘dead’. In Napoleonic Times soldiers enjoyed playing this type of game. To them, it was known as ‘The Soldiers’ Game’ or ‘The French Military Game’. In their version, 3 soldiers chased an escaped prisoner or spy and things did not end well for the ‘chasee’ when captured.
– In this classroom version, the game’s author has chosen to have 3 playful puppies chase a wise elderly cat and no blood is spilled. Write a brief argument, either for or against, the author taking the ‘inferred violence’ out of the game.
– Create your own chase and capture game using computer software of your choosing. Play your game with friends.
– Teach another class in your school how to play ‘Cats and Dogs’
– A famous mathematician once stated this ‘chase and capture game’  “combines extreme simplicity with extraordinary strategic subtlety”. What could this mean?

Possible Gifted & Talented Extension:

– Combinational Game Theory is a new branch of Mathematics you might like to check out simply because it is interesting. What is it and how does it work?

Included in this Download:

7 Full-Color Boards
7 Low-Color Boards
1 PowerPoint file of ALL the color Boards
1 Video Game Version (Windows Only)

Addition Fact Families Covered:

Doubles + 1
Doubles + 2
Facts to 10
Facts to 20