1. “Changing Garden”
    2. 5. Do all the possible gardens that use the 30 feet of wire fencing have
    3. the same perimeter? _____________ Why, or why not?
    4. the same area? ______________ Why, or why not?
    Navigating through Measurement in Grades 3 – 5, NCTM, 2005
    1
    “Changing Garden”
    FENCE
    LENGTH
    (Feet)
    WIDTH
    (Feet)
    PERIMETER
    (Feet)
    AREA
    (Square Feet)
    A
    1
    14
    30
    14
    B
    2
    13
    30
    26
    C
    3
    12
    30
    36
    D
    4
    11
    30
    44
    E
    5
    10
    30
    50
    F
    6
    9
    30
    54
    G
    7
    8
    30
    56
    2. What does
    area
    mean?
    Area is the number of square units that cover a two-dimensional figure or
    shape.
    3. What does
    perimeter
    mean?
    Perimeter is the distance around a two-dimensional figure or shape.
    4. In the space below, use words, pictures, or numbers to describe how
    you
    would find the perimeter of a rectangle of any size.
    Students’ responses will vary but should suggest the idea that they would (a)
    add the lengths of all four sides, or (b) add the length and width of the
    rectangle and multiply this sum by two, or (c) multiply the length by two and
    width by two and add these two products.
    5. Do all the possible gardens that use the 30 feet of wire fencing have
    the same perimeter? _____________ Why, or why not?
    Yes, all the gardens have the same perimeter. The changes in the
    dimensions of each arrangement do not affect the total perimeter since at no
    point does the total
    amount
    of fencing change.
    6. Do all the possible gardens that use the 30 feet of wire fencing have
    the same area? ______________ Why, or why not?
    No, all the gardens do not have the same area. As the dimensionsl change,
    square units are either “pulled into” or “pushed out of” the garden, changing
    its area/ As the length and width approach each other in value (i.e. as the
    garden becomes more nearly square), the space inside the garden, or its
    area, increases.

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