## The Game

At first, Barnyard Bingo is a simple arithmetic game for kids just learning to add: cover spaces on your bingo board by adding cards from your hand, using at most one of each animal. The youngest kids (around 4+) can even simply count the legs on the animals.

To play, give each player a bingo board and 5 cards. Place the remaining cards in a draw pile, and turn over one card to start the discard pile. Players take turns. On your turn:

– Pick up 1 card from the deck or the top of the discard pile.

– Choose cards from your hand that add up to a number on your board. *Use at most one animal of each type.*

– Cover that number with a token.

– Place the cards face-up on the discard pile, with your choice of card on top.

– If you are unable to or choose not to cover any numbers, then play passes on to the next player.

The winner is the first to get four tokens in a row (across, down, or diagonally).

You can stop here and simply enjoy the game as addition practice. But for a child ready for a little more abstraction, there is plenty more to explore!

## Binary Notation

Now look again: each card is a power of two. So as kids are covering each number on their bingo board, they are in fact converting that number to binary notation. You can explore that connection further with these cards.

For example, you can record that 13 is made with 1 spider, 1 horse, and 1 snail. This shows that 1101 in binary notation equals 8 + 4 + 1 = 13 in our usual base-10 notation.

When introducing binary notation to children, make sure they read out the sequence of digits instead of pronouncing the number as a base-10 number. For example, “1101” should be pronounced as “one-one-zero-one.” Similarly, the numbers in the lower right of the game cards are in binary notation and should be pronounced as (for example) “one-zero-zero-zero” rather than “one thousand.”

You will also want to make sure that children understand that binary notation just gives new names for the same values. The number of legs on 1 spider, 1 horse, and 1 snail can be written as “13” in our usual base-10 system or “1101” in binary notation. It’s still the same number of legs either way.

## Adding

You can also explore adding numbers in binary notation. Remind children of the rule that at most one of each animal can be used. For example, when adding 1101 + 1 in binary notation, two snails must be exchanged for a rooster. The final answer is 1110 in binary notation.

Children can check that 1101 + 1 = 1110 (in binary) is correct by converting each number to base-10 notation. Indeed, this addition is the same as 13 + 1 = 14.

Now, how about 1101 + 11 ?

## A Note on Notation

People usually denote binary notation with a subscript “2,” so that 1101 in binary notation is written as 1101_{2} . This may be confusing for young children who are just learning to read numbers, as they may think that the 2 is part of the total value of the number. Because of this, I decided to leave off the subscript “2” in favor of specifying the context verbally instead. You can introduce a child to this notation and write it onto to the cards as they are ready.

## Further Reading

For more fun counting feet (without the restriction to powers of 2), try the book One is a Snail, Ten is a Crab . It’s great for investigating adding, multiple representations, skip-counting, repeated addition, and multiplication. Here are some ideas and more ideas and even more ideas for activities based on the book. You could also use the bingo cards to explore the uniqueness of a number’s binary representation vs. the multiple representations possible without the restriction to powers of two. Happy mathing!