Period:
Date:
Relationships to Count On and Graph II
1) Complete a table to show the relationship between the length of a square's side and the length
of the perimeter of.the square.
Perimeter of Square
Process
Length of Side of Square
2 cm
a) What do the variables S and P represent?
b) Write an equation for the relationship between the length of the side and the perimeter of the
square.
c) What does your equation mean in words?
2) Complete the table to determine the relationship between the length of a side of a square and
the area of the square. (Use the same lengths you used to find the perimeter.)
Length of Side
Process
S
a) Write an equation for this relationship?
b) What does this equation mean in words?
Area of Square
A
---•-----3) Look at the table below. Complete the process section to help you determine an equation for
the relationship
Number of Sides
of a Regular
• ' Pcdygon •
Process
Perimeter of
Polygon
16.5m
49.5m
27.5m
55m
38.5m
22m
33m
8
44m
y
a) Write an equation for the relationship?
b) What is the relationship between the number of sides of a regular polygon and the perimeter?
Period:
Name
Review the table below and complete the process column.
Process
Date:
9
3
12
10
30
4) Which of the following could be a possible relationship displayed in this.table and described by
your eqnation? Answer yes or no and explain your thinking for each
a) The perimeter of a pentagon given the length of its side.
b) The perimeter of a scalene triangle given the length of its side.
c) The volume of a rectangular prism given its height.
d) The perimeter of an equilateral triangle given the length of its side.
e) The length of a side of an equilateral triangle given its perimeter. '
f) The volume of a cube given the length of its edge.
5) Based on this table, what could the x and the y represent?
Each of the relationships you discovered was displayed in table format. Another way to display
relationships between two quantities is on a graph. Place the data from the previous tables (#1 and
following-graphs.- (Remember, good graphs always have titles-and axis labels as well
#2)
as an appropriate scale to match the data )
5) Square's side to perimeter (Use the information from #1)
Name
6) Square's side to area (Use the information from #2)
a) Compare the graphs for # 5 and # 6. What is the same?
What is different?
b) Which graph shows a greater increase?
Explain your thinking.
Period:
Date:
7) Study the graph below. Use the information from the graph to complete the table and
write the rule/equation for the relationship that is displayed in the graph.
Perimeter of a Regular Hexagon (cm)
•
40
•
36
32
•
28
24
20
•
16
12
8
•
4
0
1
2
Length of Side
(cm)
3
6
4
5
Length of Side (cm)
Process
7
Perimeter (cm)
8
10