All Activities U Circuit Breaker

# Circuit Breaker

Ages: 4+
Players: 2
Time: Under 10 Minutes
Type: abstract games
Location: tabletop
Ages: 4+
Players: 2
Time: Under 10 Minutes
Type: abstract games
Location: tabletop

## Instructions

First, draw the grid of dots. Start by drawing 4 horizontal lines and 5 vertical lines.

Draw a blue dot where the lines cross. This should make a blue grid 5 dots wide and 4 dots tall. Then draw a red dot in the middle of each of the squares (and above the top squares and below the bottom squares, as shown). This should make a red grid 4 dots wide and 5 dots tall.

Finally, draw a blue line down the left and right columns of dots, and draw a red line across the top and bottom rows of dots. These are your circuit boards.

Now start the game. Each player plays a color: one red, one blue. The younger player goes first. On your turn, connect any two adjacent dots of your color. You can't cross a line that your opponent has already drawn.

Whichever player connects their circuit boards wins.

Don't forget: it's Beast Academy Playground, not Beast Academy Study Hall. Change the rules, be silly, make mistakes, and try again. The Variations and Learning Notes are here for you if you want to dive deeper, but not all of them apply to learners of every age. The most important thing is to have fun.

## Variations d

### Larger Grid:

Use a larger grid for a longer and more-difficult-to-predict game. Start with 5 horizontal and 6 vertical lines, or even more. Or try drawing the grid of dots without first drawing lines.

### Smaller Grid:

Use a smaller grid for younger players. Draw 3 horizontal and 4 vertical lines. The youngest math beasts might enjoy playing on a grid drawn from 2 horizontal and 3 vertical lines.

### Hex:

This classic math game is normally played on a grid of hexagons, but a diamond drawn with coins works just as well. Players label opposite sides of the diamond in their color. Then they take turns filling in circles in their color. The player who is able to make a path that connects their opposite sides wins.

Alternatively, one player places dimes and the other player places pennies on the circles, rather than coloring. This has the added benefit that you won't need to redraw the grid each time.

## Classroom Tips d

Play Circuit Breaker (or any of our abstract strategy games) after a test or quiz. Once students know these games, they can play them together in pairs or groups if they finish a task early.

Discussion Questions

• Does it matter where you start your path?
• What is the least amount of moves to win? What about the most?
• Is it possible to tie?
• When you set up your gameboard, how can you calculate the total number of dots?
• How many blue columns of dots are there? How many red columns of dots are there? How many total blue dots are there? How many total red dots are there? How do we get the same number of dots in each color?

• Level 2, Chapter 12: Problem Solving
• Level 3, Chapter 3: Perimeter & Area

See Variations and Learning Notes for more ideas on how to adapt this activity and incorporate it into your classroom.

## Learning Notes d

### Game Theory:

After playing a few rounds of Circuit Breaker, try a variation. Play the game as described above, but instead of trying to win, both players try to work together so that the game ends in a tie. Before long, you'll notice that ties are impossible in Circuit Breaker. Now let your child try on their own to draw any game board that ends in a tie. Even when you allow there to be more of one color than the other, this is impossible.

Why can't a tie occur? One way to visualize this is to imagine that one player is cutting a piece of paper (rather than drawing, say, red lines), while the other player draws blue lines that cannot be cut through. The cutter's goal is to split the piece of paper in half (dividing the two circuits of the other player), while the drawer is trying to prevent the paper from being entirely divided. Thinking of the game this way, we can see that it wouldn't make sense for a game to end with the paper cut in half and not cut in half at the same time. By the end of the game, the paper is either still one piece, or it isn't.

### Strategy:

What is the best strategy for Circuit Breaker? To improve your play, try different things and see what works. Play a game focusing only on offense, for example, then a game focusing only on defense. Or try playing from the center outward, then from the outside inward.

Another way to understand the basics of the game is to start with a smaller grid (see Variations). Even a 2x3 grid can help you understand why the game can never be tied.

Trying things to see what works, starting with a simpler version: these are some of the same problem-solving strategies we want young math beasts to use when confronting a new math problem!

### Math History:

Circuit Breaker is also called Gale, after mathematician David Gale who invented it, and is related to Hex, a classic math game invented independently by mathematicians Piet Hein and John Nash. Mathematician Claude Shannon made a mechanical version of Hex that used actual changes of voltage within a circuit so an early computer could beat a human player!

## What do you think of this activity?

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Materials
• markers
• pencil
• paper
Learning Goals
• spatial reasoning
• strategic thinking
Common Core Standards
• MP1
• MP7
• 2.G.A.2

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