Question

1. make a table representing the relationship between the length of the side of a square flower bed and the perimeter of the flower bed. explain how the pattern in your tabular representation relates to the concrete models.

Explanation:

Step1: Recall the formula for the perimeter of a square

The perimeter \(P\) of a square is given by \(P = 4s\), where \(s\) is the length of the side.

Step2: Choose values for the side length

Let's choose \(s = 1\), \(s=2\), \(s = 3\), \(s=4\)

Step3: Calculate the corresponding perimeters

When \(s = 1\), \(P=4\times1 = 4\)
When \(s = 2\), \(P=4\times2=8\)
When \(s = 3\), \(P=4\times3 = 12\)
When \(s = 4\), \(P=4\times4=16\)

Step4: Create the table

Side Length (\(s\))	Perimeter (\(P\))
\(2\)	\(8\)
\(3\)	\(12\)
\(4\)	\(16\)

Step5: Relate to concrete models

In a concrete model (e.g., using square - shaped tiles), if each side of the square tile (representing the side of the flower - bed) is of length \(s\), the number of unit lengths around the square (perimeter) is \(4s\). For example, if the side of a square tile is \(1\) unit, the perimeter is \(4\) units (counting the lengths of all four sides). If the side is \(2\) units, each of the four sides has length \(2\), so the total perimeter is \(2 + 2+2 + 2=8\) units.

Answer:

The table is as shown above and the pattern in the table (\(P = 4s\)) is consistent with the physical interpretation of perimeter as the sum of the lengths of all four sides of a square in a concrete model.