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Hexagon vs. Triangle

Slide coins to make your shape before your opponent can make theirs.

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

Instructions

Make the game board by tracing a coin.

Circles drawn on a paper

Then arrange seven coins as shown.

Coins arranged on a paper

Before playing, decide which player will attempt to make a 6-coin triangle, and which will attempt to make a 6-coin hexagon.

A hexagon of coins
A triangle of coins

Players take turns moving a coin one space, or jumping a single coin to an empty space. (Either player can go first.) Whoever makes their shape first wins!

Play multiple rounds, alternating who plays triangle and who plays hexagon.

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

Continuous Play:

In this variation, as soon as one player forms their shape, they must select a coin from their shape and move it to any other position on the board (not necessarily just one space or jumping another coin). Play then continues. Keep track of how many of their shapes each player has made. First to make 3 wins.

Classroom Tips d

Play Hexagon vs. Triangle when learning basic geometric shapes, or just for fun. This is a great game for students who finish a task early.

Discussion Questions

  • See the questions listed in Solitaire Puzzles below.
  • What other shapes can you make with coins?
  • What's the next square number? (see Learning Notes)
  • What's the next triangular number? (see Learning Notes)
  • Can you make other sequences of numbers with coins? (see Learning Notes)

Alignment with Beast Academy Curriculum

  • Level 3, Chapter 1: Shapes

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

Learning Notes d

Solitaire Puzzles:

After kids are familiar with the game, have them investigate the following:

  • How many different triangle positions are there on the game board? (4)
  • How many different hexagon positions are there on the game board? (3)
  • From the initial coin setup, what is the fewest number of moves needed to make a hexagon? (3)
  • From the initial coin setup, what is the fewest number of moves needed to make a triangle (4)?
  • Make a triangle, then place the remaining coin anywhere on the board. What is the fewest number of moves needed to make a different triangle? (As few as 2, depending on the setup.)
  • Make a hexagon, then place the remaining coin anywhere on the board. What is the fewest number of moves needed to make a different hexagon? (As few as 3, depending on the setup.)
  • Make a triangle, then place the remaining coin anywhere on the board. What is the fewest number of moves you can make to form a hexagon? (As few as 1, depending on the setup.)

Triangular Numbers:

The triangle formation above uses 6 coins, so 6 is one of the "triangular" numbers. Let kids try forming larger and smaller triangles with their coins to determine the sequence of triangular numbers: 1, 3, 6, 10, 15, 21, etc. (Note that the triangular numbers are "solid," without a hole in the middle.)

The first five triangular numbers

Triangular numbers are found arithmetically by adding consecutive counting numbers: 1 = 1, 3 = 1 + 2, 6 = 1 + 2 + 3, 10 = 1 + 2 + 3 + 4, and so on.

Hexagonal Numbers:

6 is also a "hexagonal" number. Let kids use their coins to find the hexagonal numbers: 1, 6, 15, 28. (Note that hexagonal numbers form only the outline of a hexagon, leaving a hole in the middle, and each hexagonal number is built by adding a larger hexagon to the previous.)

The first four hexagonal numbers

Can they find the list of hexagonal numbers within the list of triangular numbers? The first, third, fifth, and so on, triangular numbers are hexagonal numbers! This means that every hexagon can be formed into a triangle, but there are triangles that can't be formed into hexagons.

Children can explore other figurate numbers. Ask them to guess what the first few "square" numbers are.

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Materials
  • 7 coins (all the same type)
  • paper
  • pencil
Learning Goals
  • shapes
  • strategic thinking
  • 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