7. In a mathematical exercise, students are tasked with matching the appropriate strategy to simplify a set of given problems. The problems provided are: 73 + 55 = 120 + 8 = 128, 74 - 36 = 7 + 9 + 8 + 5 + 2 + 1 + 3 = 30 + 5 = 35, 44 - 6 = 40 - 2 = 38, and 24 + 4 = 28. The available strategies to choose from include taking away an extra ten then adding back ones, composing addends into tens and ones, taking away tens then taking away ones, and decomposing addends into tens and ones. The goal is to correctly assign a strategy to each problem based on the steps shown. Place the description of the strategy used to simplify the problem below the problem.
Answer: D
Decomposing addends into tens and ones
The strategy of decomposing addends into tens and ones is the most effective method for simplifying the given problems, as it allows for easier mental calculations by breaking down numbers into more manageable parts.
A) Taking away an extra ten, then adding back ones
This strategy is not appropriate for the problems presented, as it does not align with the operations being performed. For instance, simply removing ten and then compensating by adding back ones could complicate the addition and subtraction steps rather than simplifying them.
B) Composing addends into tens and ones
While this strategy involves organizing numbers into their tens and ones components, it focuses on the addition side of the problems rather than the subtraction processes involved. Therefore, it does not adequately address the requirements for all the problems presented.
C) Taking away tens, then taking away ones
This option suggests a method that is not directly relevant to the simplification of the problems. Taking away tens and then ones does not effectively facilitate the calculations shown in the exercise, which require a clear breakdown of numbers for easier manipulation.
D) Decomposing addends into tens and ones
This strategy effectively simplifies the calculations by breaking down numbers into their component parts, making it easier to compute sums and differences. For example, decomposing 73 into 70 and 3 helps to visualize the addition alongside other numbers in a straightforward manner.
Conclusion
The strategy of decomposing addends into tens and ones is clearly the most suitable choice for the problems given, as it simplifies calculations and enhances understanding of the number relationships involved. In contrast, the other options fail to provide the necessary clarity and efficiency needed for the exercises, making them less effective for the task at hand.