**1. Make sense of problems and persevere in solving them. **

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### Proficient students explain to themselves the meaning of a problem and look for entry points to its solution.

*To develop these mathematical practices in students using Who’s Counting, the teacher should encourage/model/demonstrate/expect students to:*

- Organize the cards in his/her hand to create a coherent and reasonable expression.
- Think of a ‘path’ to take, whether deciding what blue or red card to use to increase his/her score or to negatively impact their partner’s score, instead of doing whatever operation they “see” first. They ‘think ahead’ to make sense of what the best next move may be.
- Use a ‘trial and error’ or ‘guess and check’ strategy as he/she perseveres in finding an expression to represent.
- Use ‘self-talk’ to think through a reasonable expression or next move.

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**2. Reason abstractly and quantitatively. **

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### Proficient students make sense of quantities and their relationships. They understand the meaning of quantities and math symbol, not just how to compute quantities.

*To develop these mathematical practices in students using Who’s Counting, the teacher should encourage/model/demonstrate/expect students to:*

- Create coherent expressions using math symbols. (This is representing the problem.)
- Understand the meaning of each quantity on each number card and how the operation cards impact the quantity.
- Reason why certain quantities should or should not be used based on the operation cards available to him/her.
- Use patterns from previous math encounters to apply it to his/her current situation.
**Example:**“When is another time we had to multiply with ten, what did we learn?”

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**3. Construct viable arguments and critique the reasoning of others. **

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### Proficient math students understand and use stated assumptions, definitions, and previously established results in constructing arguments.

*To develop these mathematical practices in students using Who’s Counting, the teacher should encourage/model/demonstrate/expect students to:*

- Answers questions during play or after play such as, “Why did you choose only one operation each time?” Students should be able to explain why they did use a card, why they didn’t use an alternate card and argue why his/her decision was the better decision.
- Construct, justify, and communicate why certain operations or moves were made in the game. Each partner must explain the expression and how he/she chose to solve the expression.
- Critique opponent’s logic in making various moves during the game by identifying flawed logic, computational fluency, etc.
- Offer expressions, suggestions, and/or ways to solve expressions to partner if partner struggles with either of these during play.

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**4. Model with mathematics. **

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### Proficient students can apply the mathematics they know to solve problems arsing in everyday life, society, and workplace.

- Estimate to make more complex expressions easier to solve.
- Change the next move based on assumptions made by his/her partner or moves anticipated by his/her partner.

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**5. Use appropriate tools strategically. **

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### Proficient students consider the available tools when solving a mathematical problem.

- Know when the use of a math tool (paper and pencil, hundreds chart, multiplication table, etc.) is necessary and appropriate to solve a particular operation or to calculate what the total will be when a blue, red, or operation bonus is applied. Student must also know how to use these math tools.

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**6. Attend to precision. **

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### Proficient students communicate precisely to others.

- Calculate accurately when finding totals, creating expressions, applying blue/red cards, etc.
- Calculate efficiently (teacher intercedes if methods students use to calculate are not efficient).
- Use correct and accurate math vocabulary/terminology when explaining a move made, or why a card was played.
**Example:**“I chose to multiply by my sum of 12 by 2 when I played my double blue card and I ended up with a product of 24.” - Use correct symbols to represent the intended expression.
**Example:**Uses the multiplication sign when multiplication is intended, not the division sign.

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**7. Look for and make use of structure. **

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### Proficient students look closely to discern a pattern or structure.

- Identify a pattern such as noticing that the commutative property is applicable in this game.
**Example:**If 3+5=8, then 5+3 must also equal 8. Teachers can use this game to help student partners identify when the commutative property is used incorrectly (such as with division). Repeated practice with numbers will help develop this understanding.

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**8. Model with mathematics. **

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### Proficient students notice if calculations are repeated and look for both general methods and for shortcuts.

- Notice when a particular card was played previously and remember the outcome, so that similar reasoning, calculation methods, etc. may be applied to the new or similar situation/expression.

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