All Activities U High Ground
for parents
for teachers

High Ground

Write numbers in a twisting, branching path. Whoever writes the highest number wins.

Ages: 5+
Players: 2
Time: Under 10 Minutes
Type: number games
Location: tabletop
Share This Activity
Ages: 5+
Players: 2
Time: Under 10 Minutes
Type: number games
Location: tabletop

Instructions

First draw a 5x5 grid. (See Learning Notes below for tips.) Player 1 starts the game by writing a 0 in any space in the grid. Then, using a different color, Player 2 writes a 0 in any space.

5 by 5 grid on a piece of paper with 0 written in the center
Player 1 (Red) writes a 0.
5 by 5 grid with a red 0 and a blue 0
Player 2 (Blue) writes a 0.

Next, starting with Player 2, take turns writing numbers in the grid. Pick any number in your color, then write the next number in a neighboring square (above, below, left, right, or diagonal).

5 by 5 grid with blue and red numbers
Blue writes a 1 next to their 0.
5 by 5 grid with blue and red numbers
Then Red writes a 1 next to their 0.

Note that Player 1 always writes the first 0, but Player 2 always writes the first 1. After that, players take turns, picking a number, then writing the next number in a neighboring square.

5 by 5 grid with blue and red numbers
5 by 5 grid with blue and red numbers

You can choose your highest number to build from, or you can branch out from a lower number. For example, first Red chooses their highest number, 3, and writes a 4 in a neighboring square. In the next turn, though, Blue chooses to block Red's progress by starting a new branch from their 1 instead of continuing from their 3.

5 by 5 grid with blue and red numbers
5 by 5 grid with blue and red numbers

Sometimes it's better to build from your highest number, but sometimes it's better to block your opponent.

Once the grid is full, the player with the highest number wins.

5 by 5 grid with blue and red numbers
Red has the highest number. Red wins!

As you play more games of High Ground, take turns as the first player to write 0.

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.

This game is adapted from "Sequencium" by Walter Joris.

Variations d

New Zeros:

Players are allowed to use a turn to place a new starting 0 anywhere on the board at any time.

Add 'Em Up:

Once the board is full, add all the numbers of each color. The player with the higher sum wins.

Skip-Count:

Instead of adding 1 when you write a new number, add 2, 5, 10, or whatever number your child is learning to skip-count by.

Classroom Tips d

Play High Ground to practice strategic thinking, or addition or skip-counting (see Variations). This is another great game for students who finish an assignment early.

Discussion Questions

  • Does it matter who makes the first play? Does one player have an advantage?
  • Where is the best place to write your first zero?
  • Is it better to think about blocking your partner or trying to get the biggest number?
  • What is the best way to make a 5x5 grid? How many vertical lines will it have? How many horizontal lines will it have? How many smaller squares will be inside?
  • How many squares (of any size) are in a 5x5 grid?

Alignment with Beast Academy Curriculum

  • Level 2, Chapter 12: Problem Solving
  • Level 4, Chapter 6: Logic
  • Level 3, Chapter 2: Skip-Counting (see Variations)

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

Learning Notes d

Writing Numbers:

At its simplest, High Ground is a good chance for the very young to practice counting and writing numbers.

Drawing the Grid:

Drawing the grid can itself be a good learning opportunity, and a chance to practice spatial reasoning. One way to do it is to first draw two lines across the middle. Then, draw a line across the middle of the top and bottom sections to split them each in half.

Drawing the grid
Two lines down the middle
Drawing the grid
A line through the top and bottom sections

When drawing the first two lines, you want the space on the top and bottom to be twice as large as the space in the middle. That way, when you split the top and bottom sections, you have 5 equal rows.

While you're at it, you can ask questions like "How many lines do you think we'll need to draw to split this square into 5 rows?" or "How many little squares will there be when we've drawn all the lines?"

Strategic Thinking:

One way to investigate the strategy of a game is to play with a specific focus in mind. Before you play, decide if you will focus on offense (reaching as high a number as possible) or defense (trying to block your opponent). Let your opponent choose what their focus will be, too, but don't tell each other before you play. Afterward, see if you can guess what your opponent was focusing on. Ultimately, of course, both offense and defense are important.

What do you think of this activity?

We're always looking to improve. Submit your feedback to us below.

Share This Activity
Materials
  • markers
  • paper
Learning Goals
  • strategic thinking
  • counting
  • spatial reasoning
  • writing numbers
  • skip-counting
Common Core Standards
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

Recommended Videos

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