87. To reinforce students' understanding of the properties of operations, a first-grade teacher writes the number sentences shown on the board. 7 + 8 = 15, 8 + 7 = 15, 15 - 8 = 7, 15 - 7 = 8. The activity reinforces students' understanding of which TWO of the following?
Answer: A,B
The activity reinforces students' understanding of the inverse relationship of addition and subtraction and the commutative property of addition.
The number sentences written on the board illustrate both the inverse relationship of addition and subtraction as well as the commutative property of addition. This activity demonstrates how addition and subtraction are interconnected and how changing the order of addends does not change the sum.
A) The inverse relationship of addition and subtraction
This option is correct because the teacher's number sentences show that addition and subtraction are inverse operations. For example, 7 + 8 = 15 and 15 - 8 = 7 demonstrate how adding a number and then subtracting it brings you back to the original number, reinforcing the concept that these operations undo each other.
B) The commutative property of addition
This option is also correct as the number sentences include both 7 + 8 = 15 and 8 + 7 = 15, which exemplify the commutative property of addition. This property states that the order of addends does not affect the sum, and the teacher's examples visually represent this concept.
C) The identity property of subtraction
This option is incorrect because the identity property is typically associated with addition or multiplication, not subtraction. In addition, the identity property states that a number plus zero equals the same number, which is not demonstrated in the provided number sentences.
D) The associative property of addition
This option is incorrect as the associative property refers to the grouping of numbers in addition. The examples provided do not illustrate this property, which states that the way numbers are grouped does not change the sum, such as (2 + 3) + 4 = 2 + (3 + 4).
Conclusion
The correct answers of A and B highlight essential mathematical principles being taught through the number sentences. Options C and D do not apply to the context of the activity, as they do not pertain to the concepts of inverse relationships or the commutative property, which are crucial for reinforcing students' understanding of operations.