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Sim

Take turns connecting dots, but try not to make a triangle in your color.

Ages: 5+
Players: 2
Time: Under 10 Minutes
Type: shape games
Location: tabletop
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Ages: 5+
Players: 2
Time: Under 10 Minutes
Type: shape games
Location: tabletop

Instructions

Draw six dots in a hexagon shape.

Six dots drawn on a piece of paper

Each player has their own color of marker. Take turns drawing a line connecting any two dots with your color.

A blue line connecting dots
A red line connecting dots

Try not to complete a triangle with all three sides in your color. Whoever makes a triangle in their color loses.

A triangle with all sides red
Red completes a triangle with all red sides. Blue wins!

Only triangles with all three corners on dots count.

A small triangle with all sides blue
This blue triangle doesn't count, since only one of its corners is actually on a dot.

For younger players, first draw pencil lines connecting all of the dots. This makes it a bit easier to see what lines are still available to draw in your color.

Six dots drawn on a piece of paper with pencil lines connecting them

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

More Dots:

Try Sim starting 7 or 8 dots.

One-Color Sim:

Both players draw in the same color. The first to make a triangle (with all three corners on dots) loses.

Triangles in Triangles:

Make a triangle with 6, 10, or 15 dots.

Ten dots drawn in a triangular grid

In this variation, both players use the same color. Take turns connecting a pair of neighboring dots. The first player to connect a pair of dots that completes a triangle of any size loses.

A line connecting two dots
First move
A second line connecting two dots
Second move
Lines connecting dots on a piece of paper
One player is forced to draw a line that completes a triangle. The other player wins!

Classroom Tips d

Play Sim when learning basic geometric shapes, or to practice thinking about sides and diagonals of polygons. (Or just play for fun!) This is a great game for students who finish a task early.

Discussion Questions

  • Is there always a winner? Can a game end in a tie?
  • Does it matter who plays first?
  • How many lines can be drawn to each dot? How many of these make up the "sides" of the shape? How many are "diagonals"? (see Learning Notes)
  • Use a finished game of Sim as a puzzle: At the end of the game, how many total triangles can you find with all vertices on a dot (ignoring different colors)? What if you also count triangles "inside" the shape, whose vertices aren't on dots?
  • For more advanced students: Assuming the dots are equally spaced around a circle, can you find any triangles you know are equilateral? How many? How do you know they are equilateral? What about scalene triangles? Or right triangles? Obtuse? Acute?
  • At the end of the game, what other polygons can you find and name?

Alignment with Beast Academy Curriculum

  • Level 3, Ch. 1: Shapes (A variation of this game is on page 25 of the guidebook.)

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

Learning Notes d

Sides and Diagonals:

Say you've got 6 dots arranged in a circle, like at the start of Sim. These dots can be connected to make a hexagon.

Six dots on a piece of paper with lines connecting them to make a hexagon

Each of these lines connects a pair of neighboring dots. These are called, unsurprisingly, the "sides" of the hexagon. Lines that connect non-neighboring dots are called the "diagonals" of the hexagon.

Six dots on a piece of paper with lines connecting them to make a star

A hexagon has 6 sides and 9 diagonals. Draw 5 dots in a circle. Can your child figure out the number of sides and the number of diagonals? What about for 7 dots, or 8? Don't give away the answers, but in case you need to check your work: 5 dots form a 5-sided shape with 5 diagonals (a pentagon), 7 dots form a 7-sided shape with 14 diagonals (a heptagon), and 8 dots form an an 8-sided shape with 20 diagonals (an octagon).

Ties:

Can Sim end in a tie? In other words, is it possible for both players to run out of moves without anyone making a triangle in their color? Give it a try! See if, using two colors, you can fill in a game of Sim with no triangles of a single color. Don't look ahead at the next two Learning Notes until you've tried.

5-Dot Draw:

Okay, have you tried drawing a Sim game with no ties? If not, go back to the last bullet point and give it a try before reading ahead! The answer is... 6-dot Sim can't end in a tie. When all the lines are drawn using two colors, there will always be at least one triangle of a single color. But, 5-dot Sim can end in a tie. Can your child draw a tie-game of 5-dot Sim? In other words, challenge your math beast to connect every pair of dots in a pentagon, using two colors, without creating a triangle with all sides of the same color (and with corners on the original dots).

14 Lines, No Triangle:

Regular 6-dot Sim can't end in a tie, which means when all 15 lines are drawn in there must be at least one triangle with all sides of the same color. But, it's possible to draw 14 lines in a Sim game, using two colors, without making a single losing triangle (that is, without drawing a triangle with all sides the same color). Can your child (or you) draw these 14 lines? One answer is shown below. Don't peek if you haven't tried yet!

Six dots connected with two colors of lines

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Materials
  • paper
  • markers
  • pencil
Learning Goals
  • shapes
  • spatial reasoning
Common Core Standards
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Image of Ms. Q

Ready to level up?

Keep problem solving with Beast Academy’s full math curriculum for students ages 7–13. Check out our captivating comic book series and immersive online platform.

LEARN MORE

Bring problem-solving to your classroom

Keep your entire class engaged with a full book and online math curriculum, for students ages 7–13. 98% of teachers say they’re satisfied with Beast Academy.

LEARN MORE
Image of a BA book