Grade 8
Mathematics
Unit: 07 Lesson: 01
Geometric Gravel Garden
Tina, Andrea, Joel, and Luis are designing a meditation area for school called Geometric Gardens. The
garden is a joint project between the student council and the PTO. The plot for the garden is
rectangular. The students will use white, yellow, green, and blue gravel to create pathways and
geometric designs in the garden. The students plan to use approximately five tons of gravel to fill the
garden.
1. Shade each region of the gravel garden the color indicated in the diagram below.
II
18 ft
4 ft
18 ft
I
white
white
bl
ue
blue
green
yellow
yellow
13 ft
4 ft
? ft
blue
4 ft
5 ft
6 ft
? ft
yellow
blue
5 ft
4 ft
blue
bl
ue
green
blue
4 ft
? ft
green
6 ft
yellow
yellow
yellow
6 ft
4 ft180
13 ft
yellow
blue
6 ft
green
blue
4 ft
white
III
©2012, TESCCC
4 ft
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white
IV
Grade 8
Mathematics
Unit: 07 Lesson: 01
Geometric Gravel Garden
2. Use the diagram of the gravel garden from page 1 to calculate the area in the chart below for each
specified region of the gravel garden:
Location
Figure
a) Entire grid
Rectangle
overall garden
b) Positive y-axis
Rectangle
yellow walkway
c) Negative y-axis
Rectangle
yellow walkway
d) Positive x-axis
Rectangle
green walkway
e) Negative x-axis
Rectangle
green walkway
f) Origin: axes
intersection
Square
center blue walkway
g) Quadrant I
Right triangle
blue
h) Quadrant I
Right triangle
blue
i) Quadrant I
Trapezoid
yellow
j) Quadrant II
Circle Sections
blue
k) Quadrant II
Right triangle
green
l) Quadrant II
Right triangle
yellow
m) Quadrant III
Semi-circle
blue
n) Quadrant III
Rectangle
yellow
o) Quadrant IV
Trapezoid
blue
p) Quadrant IV
Isosceles Triangle
green
q) Quadrant IV
2 Right Triangles
yellow
©2012, TESCCC
Calculations
Area (ft2)
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Grade 8
Mathematics
Unit: 07 Lesson: 01
Geometric Gravel Garden
3. Complete the chart below to determine the amount of gravel needed for each color.
Color of Gravel
Total Area of Gravel in
Specified Color
% of Specified Color of
Gravel
in the Garden
Amount of Gravel
Needed of
Specified Color
White
Yellow
Green
Blue
Totals
4. Use a written description in conjunction with math symbols to describe how to calculate the area of
the blue sections of the circle in quadrant II from the diagram on page 1.
©2012, TESCCC
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Grade 8
Mathematics
Unit: 07 Lesson: 01
Geometric Gravel Garden
5.
a) Complete the table below.
Rectangle 1
length
5 cm
Rectangle 2
width
9 cm
length
8 yds
width
12 yds
Scale Factor
3
Original Perimeter
Scale Factor
0.5
Original Perimeter
New Perimeter
New Perimeter
Original Area
Original Area
New Area
New Area
b) Describe the effects of the dimensional change on the perimeter of each rectangle.
c) Write an equation that shows the effects of the dimensional change on the perimeter of each
rectangle.
d) Describe the effects of the dimensional change on the area of each rectangle.
e) Write an equation that shows the effects of the dimensional change on the area of each
rectangle.
f) Use the equation from part c to determine the new perimeter of a rectangle whose dimensions
are changed proportionally by a scale factor of 1.5 units if the perimeter of the original rectangle
is 20 units.
g) Use the equation from part e to determine the new area of a rectangle whose dimensions are
changed proportionally by a scale factor of 0.6 units if the area of the original rectangle is 15 u 2.
©2012, TESCCC
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