# Short activity: nearest to the gnarly number.

Provide students with opportunities to practise addition strategies whilst enhancing their estimation skills through this highly tactical, absorbing card-based game. Nearest to the Gnarly Number is designed for two players and can be easily modified to allow for participation by primary school students of all ages and abilities (see Differentiating the game). The goal of the game is to be the player who finishes nearest to a designated target number (the 'gnarly number') at the end of the round. The first player to win five rounds wins the overall game.

Before beginning the game, sort the playing cards and remove all picture cards and tens from the deck.

As a variant on the game, Jacks (or tens) can be left in the deck to represent the number zero.

Example of a game: Nearest to the gnarly number targeting 100

A Year 3 class plays a game of Nearest to the Gnarly Number targeting 100. Lucy (Player One) and Aaryan (Player Two), begin their game.

Lucy, as Player One, begins by turning over five cards: 2, 3, 7, 4 ,5. Lucy needs to create a two-digit number through choosing two of these cards; one card to place into the tens column of her gameboard and one card to place into the ones column. She decides to take the cards 7 and 4, and create the number 74. Aaryon, as Player Two, now has to create a two-digit number from the remaining three cards. Left with the cards 2, 3 and 5, he decides to create the number 35, and places these cards on his gameboard. The leftover 2 is placed back into the bottom of the deck (see Figure 1, top photo).

It is now Aaryan's opportunity to turn over five cards and be the first to create a two-digit number. He turns over five new cards: 5, 8, 4, 2, 4. He chooses the 5 and the 8 to create the number 58. This time, Lucy is left with having to create a two-digit number from the remaining three cards. With the 4, 2 and 4 left over, Lucy creates the number 24 (see Figure 1, bottom photo).

Each player now adds their two numbers together, using a strategy of choice, to work out their total. Lucy uses a 'number splitting' strategy to work out her total ("74 + 24 = 98 because 70 + 20 = 90, and 4 + 4 = 8"). Aaryan uses a 'pay it back' strategy to work out his total ("35 + 58 = 93 because 35 + 60 = 95, but I have to pay back the 2, so it is 93"). Both players immediately realise that Lucy is closer to the gnarly number (i.e., "98 is closer to 100 than 93"), and therefore that she has won the round.

Although Aaryan chose to create the number that would bring him closest to the target, he made a tactical error by leaving the 2 card available for Lucy to use. Which number do you think Aaryan should have created to win the round?

As the winner of the previous round, Lucy begins the next round by turning over five new cards. Given that Player Two is tactically advantaged, ensuring that the winner of the previous round always acts as Player One serves to even out the game.

Post-activity discussion

What strategies did you use to work out which player was closest to the gnarly number?"

* "How did you decide which cards to choose and which place value column to place them into?"

* "Why is it important to keep track of your opponent's cards, as well as your own cards?"

* "Would you change your game tactics next time you play? If so, how?"

Differentiating the game

The game can be easily differentiated to cater for different year levels and abilities by choosing lower (e.g., 10) or higher (e.g., 1000 or 10 000) gnarly numbers and altering the number of cards accordingly.

* To increase the level of challenge, get players to turn over seven cards on each turn, and allow them to create three-digit numbers targeting 1000. The level of challenge can obviously be further increased by involving additional cards (e.g., nine cards and four-digit numbers) and further increasing the size of the target number (e.g., 10 000).

* To reduce the level of challenge, players turn over three cards on each turn, and create a one-digit number targeting 10. For example, Player One might turn over 7, 3 and 4, and choose the number 7. Player Two may then choose the number 3 from the remaining two cards. It is now Player Two's chance to turn over three cards: 8, 9 and 1. Player Two might select the 8, making a total of 11 (3 + 8 = 11). Player One might select the 1, making a total of 8 (7 + 1 = 8). Player Two would win the round because they are nearest to the gnarly number.

Caption: Figure 1. Example of a game with 100 as the gnarly number.
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