Recognizing and explaining mathematical relationships using reasoning means that we can understand how numbers and shapes are connected through logical thinking. Let's imagine you have a bunch of apples and you want to share them equally between you and your friend. You use reasoning to figure out how many apples each of you should get. This is like understanding division as a mathematical relationship. By recognizing the relationship between the total number of apples and the number of people they are shared with, you can explain why each person gets a certain amount. This helps in understanding how numbers can be divided and shared in a fair way.

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