Mariana, a vibrant young girl, embarks on a mathematical adventure with her prized collection of marbles. This seemingly simple scenario unfolds into an engaging exploration of numerical expressions and problem-solving, perfectly suited for young learners eager to grasp the fundamentals of arithmetic.
Unraveling Mariana's Marble Story
Mariana begins her day with an impressive stash of 25 marbles, each one a tiny sphere of color and potential. The allure of the playground beckons, where friendly competition and the thrill of the game await. As Mariana engages in spirited rounds of marbles with her friends, the dynamics of her collection shift. The give and take of the game introduce the concepts of subtraction and addition, weaving a narrative that resonates with real-life experiences.
The Initial Marble Count: Setting the Stage
The story commences with a precise figure: 25 marbles. This number serves as the bedrock upon which the subsequent events unfold. It's the starting point, the known quantity from which gains and losses will be calculated. For young learners, this concrete number provides a tangible reference, a foundation for understanding the numerical manipulations that follow. 25 marbles represent a substantial collection, hinting at the potential for both exciting wins and perhaps, some disappointing losses.
The First Setback: Losing Marbles
The playful atmosphere of the game takes an unexpected turn when Mariana experiences her first setback. In the heat of competition, seven marbles slip from her grasp, becoming casualties of the game. This loss introduces the concept of subtraction, the act of taking away from the initial quantity. The number 7 assumes significance, representing the magnitude of Mariana's loss. It's a concrete reduction in her collection, a tangible demonstration of how subtraction works in a real-world context. The subtraction of 7 from 25 sets the stage for the next phase of the marble adventure.
A Turn of Fortune: Gaining Marbles
However, Mariana's spirits are far from dampened. The ebb and flow of the game bring a welcome reversal of fortune. In the subsequent round, her luck changes, and she triumphs, winning an impressive nine marbles. This victory injects the concept of addition into the narrative, the act of adding to the existing quantity. The number 9 becomes the symbol of Mariana's gain, representing a boost to her collection. This addition not only recoups some of her earlier losses but also propels her beyond her initial count. The addition of 9 to the diminished marble count marks a turning point in Mariana's marble journey, showcasing the dynamic nature of mathematical operations.
Part A: Deciphering the Mathematical Expression
The heart of the challenge lies in translating Mariana's marble saga into a concise mathematical expression. This step bridges the gap between a narrative and its symbolic representation, a crucial skill in mathematical literacy. The task involves scrutinizing the sequence of events and selecting the expression that accurately mirrors the changes in Mariana's marble collection.
The Art of Expression: Choosing the Right Symbols
The options presented offer a glimpse into the world of mathematical notation. Each symbol carries a specific meaning, dictating the operation to be performed. The plus sign (+) signifies addition, the act of combining quantities. The minus sign (-) indicates subtraction, the act of taking away from a quantity. The equals sign (=) asserts equivalence, stating that the expression on one side yields the value on the other. Selecting the correct expression requires a careful consideration of how these symbols interact to represent the story's events.
Option 1: 25 + 7 + 9 = ?
This expression suggests a scenario where Mariana gains marbles in both rounds, adding 7 and then 9 to her initial 25. However, the story clearly states that Mariana lost 7 marbles in the first round. Therefore, this expression fails to capture the initial loss, making it an inaccurate representation of the situation. The plus signs incorrectly depict the loss as a gain, leading to a flawed calculation of the final marble count.
Option 2: 25 - 7 - 9 = ?
This expression paints a picture of continuous loss, where Mariana loses 7 marbles and then loses another 9. While the initial subtraction of 7 aligns with the story, the subsequent subtraction of 9 contradicts the narrative. Mariana wins 9 marbles in the second round, indicating an addition, not another subtraction. The consistent use of minus signs misrepresents the gain, resulting in an underestimation of the final marble count.
Option 3: 25 - 7 + 9 = ?
This expression emerges as the most accurate representation of Mariana's marble journey. It meticulously captures the sequence of events: starting with 25 marbles, losing 7 (subtraction), and then gaining 9 (addition). The order of operations mirrors the chronology of the story, ensuring that the expression reflects the true dynamics of Mariana's marble collection. The combination of subtraction and addition accurately portrays the losses and gains, providing a solid foundation for calculating the final marble count. This expression successfully translates the narrative into a symbolic form, paving the way for the next step: solving for the unknown.
Part B: Solving the Expression Unveiling the Final Marble Count
With the correct expression identified, the next step involves solving for the unknown, determining the final number of marbles in Mariana's possession. This calculation reinforces the understanding of arithmetic operations and their application in problem-solving.
The Order of Operations: A Step-by-Step Approach
To solve the expression 25 - 7 + 9, we adhere to the standard order of operations, performing subtraction and addition from left to right. This systematic approach ensures accuracy and consistency in calculations. Following the order of operations is crucial for arriving at the correct solution.
Step 1: Subtraction The Initial Loss
The first operation is subtraction: 25 - 7. This step reflects Mariana's initial loss of marbles. Subtracting 7 from 25 yields 18. This intermediate result represents the number of marbles Mariana has after the first round, setting the stage for the subsequent gain. The result of the subtraction, 18, becomes the new baseline for the next calculation.
Step 2: Addition The Triumph
The next operation is addition: 18 + 9. This step captures Mariana's victory in the second round, where she wins 9 marbles. Adding 9 to 18 results in 27. This final result represents the total number of marbles Mariana possesses at the end of her marble adventure. The addition of 9 to 18 completes the calculation, revealing the ultimate outcome of Mariana's marble journey.
The Grand Finale: Mariana's Final Marble Count
Therefore, after the losses and gains, Mariana concludes her marble adventure with a total of 27 marbles. This number encapsulates the entire journey, reflecting the initial count, the setback, and the triumphant comeback. The final answer, 27, represents a concrete solution to the mathematical problem, solidifying the understanding of how arithmetic operations can be used to model real-world scenarios. 27 marbles is the ultimate answer to the question.
Conclusion: Marbles and Math A Winning Combination
Mariana's marble adventure serves as a compelling illustration of how mathematical concepts can be interwoven with everyday experiences. The story highlights the importance of translating narratives into mathematical expressions, applying arithmetic operations, and solving for unknowns. This exercise not only reinforces mathematical skills but also fosters problem-solving abilities, empowering young learners to approach challenges with confidence. The combination of marbles and math creates a winning formula for engaging and effective learning.