90. 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?
Answer: B
Veronica is demonstrating decomposing and composing strategies in solving the problem.
Veronica's approach illustrates the use of decomposing numbers into more manageable parts and then composing them back together to find the total. By breaking down 36 and 24 into 30 plus 6 and 20 plus 4, she effectively simplifies the addition process.
A) Compensation and counting up
This option is incorrect as compensation involves adjusting numbers to make calculations easier, typically by rounding, which Veronica did not demonstrate. Counting up is a method where one number is incremented towards the other, but her strategy was more focused on breaking down the numbers rather than counting up.
B) Decomposing and composing
This option is correct because Veronica broke down the numbers into their component parts (30, 6, 20, and 4) and then recombined them to arrive at the total of 60. This method allows for easier mental calculations, showcasing her understanding of number relationships.
C) Front-end estimation and rounding
This option does not apply to Veronica's method since she did not round numbers to the nearest ten or hundred for estimation. Instead, she utilized the exact values of the numbers after decomposing them, which contradicts the concept of rounding.
D) Using doubles and counting on
This option is incorrect as it refers to a strategy where one uses known doubles (like 2 + 2 = 4) and then counts on from that point. Veronica’s method focused on breaking the numbers apart rather than relying on doubles, making this option irrelevant to her approach.
Conclusion
Veronica's strategy of decomposing and composing numbers effectively demonstrates her understanding of addition by simplifying the components before combining them. The other options do not accurately reflect her method, as they involve different strategies that she did not employ in her calculation. Thus, option B stands out as the only correct representation of her mathematical thinking.