 # Operation ZERO

## Curriculum Goal

#### Primary: Number Sense

• Use the properties of addition and subtraction, and the relationships between addition and multiplication and between subtraction and division, to solve problems and check calculations.
• Determine whether given sets of addition, subtraction, multiplication, and division expressions are equivalent or not.

#### Junior: Number Sense

• Use the properties of operations, and the relationships between operations, to solve problems involving whole numbers and decimal numbers, including those requiring more than one operation, and check calculations.

## Context

• Students can play independently, cooperatively, or competitively.
• Students should have prior experience adding, subtracting, multiplying, and dividing.
• Students should understand how to perform more than one operation at a time (ex. adding and multiplying).
• Optional: Provide students with a calculator to check their calculations.

## Materials

In-person version

• Decks of Cards
• One deck of cards can make 3 arrays. This game requires one array per player/team.
• Score Card (
• Pencil
• Optional: Calculator

Online version

## Lesson

Introduction:

• The object of the game is to eliminate all 16 cards in the array by using mathematical operations, such as addition, subtraction, multiplication, or division to create equations that are equivalent to the target number.
• Indicate the value of the cards as follows:
• Aces have a value of one.
• Cards 2-9 have the face value listed on the card.
• Jacks have a value of 11.
• Queens have a value of 12.
• Kings have a value of 13.
• Optional: Remove face cards to simplify the operations.
• Provide each player with a score card (Appendix A), pencil and calculator (optional).
• To begin each round, one person from each group of players will shuffle the deck of cards and deal 16 cards to each player. Players will arrange their cards face up in a 4×4 array.
• If students are playing independently, they will need one 4×4 array.
• If students are playing cooperatively, they will take turns using one 4×4 array.
• If students are playing competitively, each player will have their own 4×4 array.
• Players are dealt two additional cards. These cards are kept separate from the array by placing them off to the side where all players can see them. Players add these two cards together and the sum becomes their ‘Target Number.’
• In the second column of the score card, each player or team will record their target number for that round.

Lesson:

• When round one begins, students will look at their array and ask themselves, “How can I use these numbers to form an equation that is equivalent to the target number?”
• Students can use any operation and as many cards from the array as possible to form their equation.
• Ex. The target number is 10. The player can use three cards from their array: 5, 6, and 3. With these cards, they could perform the operations (5 6) 3=10.
• Students record their equation on the score card and place the used cards in a discard pile.
• If students are playing competitively, the second player will take their turn. Players will continue to alternate turns throughout the round.
• On their second turn, students will look at their array and ask themselves “How can I use these numbers to form an equation that is equivalent to my target number?”
• Again, students can use any operation and as many of the remaining cards left in their array as possible to form their equation.
• Ex. The target number is still 10. The player can use four cards from their array: 9, King, 2, and 2. With these cards, they would perform the operations (9+13−2) 2=10.
• Students will record their equation on the score card (still round one) and remove the cards used from the array. Place the used cards in the discard pile.
• Students will repeat this process for as many turns as needed. Round one ends when all 16 cards have been eliminated or when the player cannot use the remaining cards in the array to form an equation that is equivalent to the target number.
• The students will record their score on the score card.
• If the student eliminated all 16 cards, they score ZERO.
• If the student was unable to eliminate all cards, they will score the sum of the remaining cards left in the array.
• Ex. If three cards remain, such as the 4, 1, and 2 cards, the student will receive a score of seven (e.g.,4+1+2=7).
• If students are playing independently, the goal is to score the lowest number possible. If playing competitively, the student with the lowest score wins the round.
• To play another round, return all the cards to the deck and repeat the introduction. Once new target numbers have been determined, round two can begin.
• When gameplay is finished, have each student calculate the sum of their scores from each round. The player with the lowest score wins the game.

## Look Fors

• What strategies do students implement to reach the target number (ex. do they use more than two cards per equation?)
• Can students effectively perform each operation: addition, subtraction, multiplication, division?
• Can students use multiple operations during the game?
• What strategies do students use to minimize their score (ex. do they use greater numbers first?)

## Extension

• Students can work cooperatively on a shared array to reach the target number (ex. Two players will take turns making equations to reach the target number, or for each turn, students alternate who picks the cards, and who picks the operations to form the equation).
• Specify the use of operations for a round (ex. Players must use multiplication to reach the target number).
• Specify the number of cards that must be used to reach the target number (ex. Use at least three cards per equation).
• Instead of adding the two “target number” cards, allow students to subtract, multiply, or divide the two cards to determine the target number in each round.
• Introduce a wildcard (use any card from the deck face down). Players get one wildcard per round. The player gets to decide the value of their wildcard and can use it as many times as they need to reach the target number in that round.
• If students are finishing the round quickly, play the game using a 5×5 or 6×6 array.