The following conversation occurred during a second-grade mathematics lesson. Teacher: 'Solve 36 plus 24 using mental math.' Veronica: 'The answer is 60.' Teacher: 'How did you get your answer?' Veronica: 'I knew that 4 and 6 made a 10, so 10 plus 30 plus 20 would be 60.' Veronica is demonstrating which of the following strategies in solving the problem?

Rationale

Veronica is demonstrating decomposing and composing in solving the problem.

Veronica effectively breaks down the numbers 36 and 24 into manageable parts (30 + 6 and 20 + 4) to simplify the addition, showcasing her understanding of decomposing numbers and then composing them back together for the final answer.

A (Compensation and counting up) YOUR ANSWER

This strategy involves adjusting one of the numbers to make the addition easier, often by rounding. In this case, Veronica did not adjust the numbers but instead broke them down into smaller components, which is not aligned with the compensation strategy.

B (Decomposing and composing) CORRECT

Veronica's method involves breaking down the numbers into tens and ones: she separates 36 into 30 and 6, and 24 into 20 and 4. She then adds these parts together (10 + 30 + 20) to reach the total of 60. This clearly illustrates the decomposing and composing strategy, making this the correct choice.

C (Front-end estimation and rounding) YOUR ANSWER

Front-end estimation typically involves using the leading digits of the numbers for a quick estimate, often ignoring the less significant digits. Veronica did not apply this strategy; her approach was based on exact decomposition rather than estimation.

D (Using doubles and counting on) YOUR ANSWER

This strategy typically involves using known doubles (like 4 + 4) to assist with addition and then counting on from there. Veronica’s method did not utilize any doubles; instead, she focused on breaking the numbers down, which makes this choice incorrect.

Conclusion

Veronica's strategy of decomposing the numbers into tens and ones and composing them back together highlights her understanding of addition through the decomposing and composing method. This approach is fundamental in early mathematics education, helping students develop flexible thinking and a solid foundation for more complex calculations. Her ability to see the relationship between numbers in this way is crucial for their mathematical development.

Veronica is demonstrating decomposing and composing in solving the problem.

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