Target Grade: 4^th \ 5^th (However, easily adapted to other grade

Concept: Operations 

Procedures: Addition, Subtraction, Multiplication, and Division

Common Core State Standard Targeted:

CCSS.MATH.CONTENT.4.OA.A.2

Use the four operations with whole numbers to solve problems: Multiply or divide to solve word problems involving multiplicative comparison

While playing this game, students are using all four operations, with an emphasis on multiplication and division, to solve a real world problem. By definition, a real world problem is something that is concrete, not abstract, and uses a concept in a real setting or application. To students, a game qualifies as such. Therefore, this game targets and helps students to meet this standard. The game could be used to teach and practice the standard or assess the mastery of it.

Mathematical Practices Used:

• Make sense of problems and persevere in solving them: The students are given a situation where they are asked to problem solve as there is no one “right” way to solve the problem. The students are also asked to work through situations in which a pre-described method or set of steps is not provided to them. They must utilize strategy when playing against themselves or a partner, and must make adjustments to that strategy, in order to use the most cards and ultimately win the game.
• Model with mathematics: The students are modeling the situation as they create number sentences (with the cards) that represent the given situation (product number), which exemplifies the use of modeling with mathematics. By modeling, the students are taking an abstract concept of operations and are turning it into a concrete and tangible representation. This transfer from ideas on a page to the tangible real world, in the form of a game, can solidify knowledge in students. It can also give the students a reason why it is important to learn, adding motivation for the students to master the concept. Lastly, modeling can make the concept come alive, leading to better retention, higher ability to transfer the knowledge, and allowing for higher thinking skills to occur in regards to the concept.
• Look for and make use of structure: The students are taking a general idea of operations and using it in a specific situation, using the structure of the operations as their guide to solve the problems.
• Construct viable arguments and critique the reasoning of others: The students will engage in dialogue about their mathematical reasoning as they explain to their partner how they arrived at their target number. The partners will have discussion about whether or not they agree as well as what modifications would need to be made to make the equation true.  

Technology

A use of technology that could be included in this activity would be the use of a calculator. However, the purpose behind the activity was to practice mental math and quick access of math facts. This purpose would not be served if the use of a calculator was permitted.

Mathematical Modeling Aspects Present in the Activity

•  Realizing when revisions need to be made: Students must realize when their answers are incorrect and make the necessary changes in order to make their equation equal their targeted number.
•  Make improvements on their model or strategy: Students will choose a strategy that gives them the most cards. However, as the game is continued and more time is spent playing the game, students may change their strategy in order to receive more cards. Strategy may also change when playing with a partner versus themselves. This idea of strategy and how it changed is discussed during the wrap up period.
•  Interpret their mathematical results in the context of the situation and reflect on whether the results make sense: Students will evaluate their answers through self-check and peer discussion to establish of their results makes sense and are correct.

Objective: Students will be able to use multiple operations (addition, subtraction, multiplication, and division) to create equations that equal specific answers.

Time: 25 – 30 minutes (with an additional discussion and wrap-up for an extension, if applicable or time permitting)

Players: One or two

Materials: Deck of cards (with jokers and face cards removed), two dice, one tally sheet* per partner (if playing in partners), one board* per partner (optional)

*Tally Sheet Master           *Board          Directions

How to Play – Individual:

1. If not already done, remove the jokers and face cards from the deck of cards.
2. Shuffle the cards.
3. Roll the two dice and multiply the numbers together. This is your target number for this turn.
4. Take the first seven cards of the deck and flip them face up, placing them in a row (on the board spots if using one).
5. Using the seven up facing cards, add, subtract, multiply, and\or divide the numbers to achieve the target number. The object of the game is to use as many cards as possible of the seven facing up. (Note: Ace cards are worth 1)
6. After the target number is achieved, place the used cards in a pile to the side (or on the board where labeled) and leave the remaining, unused cards in the row.
7. Replace the used cards so seven cards are facing up again.
8. Roll the dice again for a new target number and complete steps 3-7 until the deck is gone.

How to Play – Partners:

1. If not already done, remove the jokers and face cards from the deck of cards.
2. Shuffle the cards.
3. Determine which partner will go first.
4. Distribute seven cards to player one. Player one will take the seven cards and flip them face up, placing them in a row (on the board if using one).
5. Player one will roll the two dice and multiply the numbers together. This is their target number for this turn.
6. Using their seven up facing cards, player one will add, subtract, multiply, and\or divide the numbers to achieve the target number. The object of the game is to use as many cards as possible of the seven facing up. (Note: Ace cards are worth 1)
7. After the target number is achieved, player one will explain to player two what operations and steps they used to get to their target number.
8. Player two has the opportunity to challenge any flaws they see in player one’s explanation at this point.
9. Once the two players have agreed on the equation and the target number was achieved, player one will place the used cards in a used card pile on the table (or board), tally how many cards they used, and leave the remaining, unused cards in the row.
10. Now it is player two’s turn. Player two will place the next seven cards in the deck on their board.
11. Player two will follow the same steps listed in direction number 5-9.
12. At the start of each players next turn, they will need to replace the cards so that seven cards are facing up at the start of each turn.
13. The players will alternate turns, following directions 5-9, until the deck is gone. Once the deck is gone, a winner will be determined based on which partner has the most tallies.

Adaptations:

For students who need a change of some kind, rules can be set that changes what operations the students can use. The rules can limit, expand, or include all operations to meet the student’s needs.  Rules can also be made that set a minimum in the number of cards that must be use in order to challenge the student with how many operations they use in order to use that many cards and still achieve the target number.

For example, students who are below the fourth grade level, the game can be adapted to use only addition and subtraction for both the target number operation, and the operations used to achieve that target number.

An example for students who are above the fourth grade level would be to set a minimum of four cards to be used each turn so that the student must challenge their thinking in order to use more cards.

Discussion Questions

1. What was a strategy that got you the most cards?
2. Was the strategy that you used different when you played against yourself than when you played against a partner? If so, how was it different?
3. Did you and your partner have any disagreements about their reasoning or mathematical equations? If so, what were they? How were they resolved?
4. Which operation did you use the most? Why do you think that was?
5. Which operation did you use the least? Why do you think that was?
6. How are these skills used in real life?
7. Why are these skills important to learn?

Wrap Up

By allowing the students to engage in math talk about the game that they just played, mathematical connections can be drawn and the students can really dive deep into the embedded concepts as well as the mathematical practices that are included in the game. This discussion can serve as a reflection and a time for further and deeper mathematical learning to occur. Of course, these questions can be used as a quick debrief or a more extensive conversation starting point.

Game Adapted from:

Currah, J., Felling, J., & MacDonald, C. (1992). All hands on deck, math games using cards and dice. (Vol. 2). Alberta, Canada: Box Cars & One-Eyed Jacks