The House (Symbol)
In the poem, the house can be interpreted as a symbol for the speaker's childhood. The further the speaker gets from his mother, the older he becomes. Starting on the ground floor, the "acres of the walls" and the "prairies of the floors" show how big the house seems to the speaker. This line also shows how a child can see the world through a filter of magic and adventure. As the speaker travels up the stories of the house, he reports measurements back to his mother. It is not until the speaker reaches the top floors of the house that he begins to depart from his childhood.
In general, a house symbolizes shelter and comfort. At the end of the poem, the speaker reaches toward a hatch that opens on the "endless sky" of adulthood. It is implied that the speaker is ready to leave the shelter of his childhood and take on the risks and freedoms that come with adulthood.
The Measuring Tape (Symbol)
The measuring tape symbolizes the connection between the speaker and his mother as the speaker walks through the house (a symbol of his childhood). The tape is reminiscent of an umbilical cord, the tube that connects a mother to her baby in the womb. The speaker travels through the house with the measuring tape, reporting measurements back to his mother and unreeling the "years between [them]." The further the tape is drawn out, the more distance there is between the speaker and his mother. The connection between them is also referred to as an anchor and a kite, both of which rely on a chain, string, or rope.
The top level of the house is defined as "the breaking point, where something / has to give" in the relationship. In other words, the speaker is ready to cut the cord that connected him to his mother. This does not necessarily mean that he wants to cut off the connection entirely, just that he is ready to be treated as an adult rather than as a child. Once the speaker exits the house, he is free "to fall or fly" without his mother waiting at the other end.
The Sky (Symbol)
The "endless sky" symbolizes the vast world of adulthood that exists beyond the scope of the speaker's experience. At first, the walls and floors of the speaker's house seem expansive—they are described in terms of acres and prairies. However, as the speaker travels upward through the house (with each story symbolizing different stages of development) he becomes more eager to encounter the vast trials and tribulations of adulthood. The acres of the walls (and everything else) in the house are measurable, but the "endless sky" is not. This echoes the common phrase "the sky is the limit," which means that anything is possible. The speaker's act of reaching toward the hatch that will open to the sky shows that he is ready to embark on the journey of adulthood.