Question 90

Veronica is demonstrating decomposing and composing in solving the problem.

Veronica's approach to solving 36 plus 24 illustrates the strategy of decomposing and composing numbers. By breaking the numbers down into more manageable parts, she effectively simplifies the addition process.

A) Compensation and counting up

This option is incorrect because compensation involves modifying one of the numbers to make the addition easier, often by rounding. Veronica did not use this strategy; instead, she decomposed the numbers into parts that she added together.

B) Decomposing and composing

This option is correct as Veronica decomposed the numbers 36 and 24 into parts: she recognized that 4 and 6 make 10, and then composed the sums of 10, 30, and 20 to arrive at the total of 60. This method clearly demonstrates her understanding of how to break numbers down to facilitate mental math.

C) Front-end estimation and rounding

This option is incorrect because front-end estimation involves rounding the leading digits of the numbers to estimate a sum. Veronica did not round any numbers; she used exact parts of the numbers to derive the total.

D) Using doubles and counting on

This option is also incorrect as it describes a strategy where students use known doubles (like 2+2 or 3+3) to aid in addition and then count on. Veronica's method did not involve doubles; instead, she relied on the decomposition of the numbers.

Conclusion

Veronica's method of breaking down 36 and 24 into smaller, more manageable components exemplifies the strategy of decomposing and composing. This choice is the only one that accurately reflects her mental math process, while the other options describe different strategies that do not apply to her specific approach. Thus, option B is the definitive correct answer.