8th Grade EOG Review

1
8th Grade EOG Review

• Sandra Davidson, MaEd
• NBCT EA Math
• Lakeshore Middle School

2
Measurement

• Perimeter, Area, and Volume
• Changing Dimensions
• Indirect Measurement

3
Measurement of a Triangle

• The sum of the measures of the interior angle
  equals 180.
• Write an equation and solve for x
• 32 100 x 180
• 132 x 180
• -132 -132
• x 48

What is the value of x in the following triangle?
4
Perimeter and Circumference
P S1 S2 S3 S4 S5
C p d

• Perimeter is the distance around the outside of a
  plane figure.
• This distance is called the circumference when
  the figure is a circle.

5
Area the measure of square units inside a
plane figure.
A ½ bh
A bh
A bh
A p r2
6
Practice Area, Perimeter and Circumference

• 3. Carlos bought a pizza that had an area of 201
  in2. He paid 8.99 for the pizza. Tameka bought
  two pizzas, each of which had an area of 133 in2.
  She paid a total of 10.99 for the two pizzas.
• What is the approximate diameter of each pizza?
• Which pizza is the better buy based on the
  number of square inches per pizza?

• 1. Paul want to build a rectangular dog pen. He
  has 24 ft. of fencing in 1-ft. sections. What
  are the dimensions of the best dog pen he can
  build?
• 2. Paul decides to use a wall of the house as one
  side of the rectangular dog pen. If he uses the
  24 ft. of fencing for the other 3 sides, what are
  the dimensions of the best dog pen he can build?

( 6 ft. x 6 ft.)
( d 16 in. and 13 in.)
(Tameka, 0.04/sq. in. - while Carlos, 0.05/sq.
in.)
( 8 ft. X 8 ft.)
7
Practice Area, Perimeter and Circumference

• 3. Carlos bought a pizza that had an area of 201
  in2. He paid 8.99 for the pizza. Tameka bought
  two pizzas, each of which had an area of 133 in2.
  She paid a total of 10.99 for the two pizzas.
• What is the approximate diameter of each pizza?
• Which pizza is the better buy based on the
  number of square inches per pizza?

• 1. Paul want to build a rectangular dog pen. He
  has 24 ft. of fencing in 1-ft. sections. What
  are the dimensions of the best dog pen he can
  build?
• 2. Paul decides to use a wall of the house as one
  side of the rectangular dog pen. If he uses the
  24 ft. of fencing for the other 3 sides, what are
  the dimensions of the best dog pen he can build?

8
Volume - the measure of cubic units inside a
3-D figure.

• What is the volume of this rectangular prism?
• V Bh
• V l x w x h
• V 2.5 x 1.5 x 1.6
• V 6 m2

9
Surface Area the measure of square units of
the outside wrapping of a 3-D figure.

• What is the surface area?
• Find the area of the front
• 2.5 x 1.6 4
• and area of the right side
• 1.5 x 1.6 2.4
• and the area of the top
• 2.5 x 1.5 3.75
• Add these and multiply by 2
• 2(4 2.4 3.75) 20.3 m2

10
Practice - Volume and Surface Area

• What is the volume of this rectangular prism?
• V Bh
• V l x w x h
• V 8 x 8 x 7
• V 448 m3
• What is the surface area?
• front 8 x 7 56
• side 8 x 7 56
• top 8 x 8 64
• 2(56 56 64) 352 m2

11
Practice - Volume and Surface Area

• What is the volume of this cylinder?
• V Bh
• V p r2 x h
• V 3.14 x22 x 16
• V 200.96 in3 (or 64p)
• What is the surface area?
• top 3.14 x 22 12.56
• bottom 3.14 x 22 12.56
• label C x 16 (circumference x 16)
• pd x 16
• 3.14 x 4 x 16 200.96 in2
• 12.56 12.56 200.96 226.08 in2

12
Practice - Volume and Surface Area

• What is the volume of this triangular prism?
• V Bh
• V ½ (b x h) x h
• V ½ (6 x 4) x 8
• V 96 ft3
• What is the surface area?
• top/bottom ½ (6 x 4) 12
• 3 rect. sides 3(6 x 8) 144
• 12 12 144 168 ft2

13
Changing DimensionsPerimeter and Area
(Rectangles, Triangles, and Circles)

• When both the dimensions double, the perimeter or
  circumference doubles, and the area becomes 4
  times greater.
• When both the dimensions triple, the perimeter or
  circumference triples, and the area becomes 9
  times greater.

Change (action) Perimeter Area
When both dimensions...
double x2 x22 4
triple x3 x32 9
are multiplied by n xn x n2
14
Changing Dimensions Volume (Rectangular Prisms)

• Changing one dimension
• when one dimension doubles, the volume
  doubles... 21 2
• when one dimension triples, the volume
  triples... 31 3
• Changing two dimensions
• when two dimensions double, the volume becomes
• 4 times greater... 22 4.
• when two dimensions triple, the volume becomes
• 9 times greater... 32 9
• Changing three dimensions
• when all 3 dimensions double, the volume becomes
  
• 8 times greater... 23 8
• when all 3 dimensions triple, the volume becomes
• 27 times greater... 33 27

15
Practice - Changing Dimensions

• 1. If the length and width of the following
  rectangle are doubled, what will be the
  perimeter?
• 2. If the base and height of the following
  triangle are tripled, what will be the area?

16
Practice - Changing Dimensions

• 1. If the length and width of the following
  rectangle are doubled, what will be the
  perimeter?
• 2. If the base and height of the following
  triangle are tripled, what will be the area?

( P 116 m )
( A 810 ft2 )
17
Practice - Changing Dimensions

• 5. Kasey drew a circle that has a circumference
  of 13 cm. If he draws another circle with a
  radius that is 4 times greater, what will be the
  circumference?
• 6. A small pizza at Petes Pizza has an area of
  29 in2. A large pizza has a radius that is
  triple the radius of a small pizza. What is the
  area of a large pizza?

• 3. Gary had a triangular dog pen with a perimeter
  of 12 ft. He made it bigger by doubling the
  dimensions. What is the perimeter now?
• 4. Tara has a rectangular table with an area of 2
  m2. She is going to buy another table that has
  dimensions that are double the first table. What
  is the area of Taras new table?

18
Practice - Changing Dimensions

• 5. Kasey drew a circle that has a circumference
  of 13 cm. If he draws another circle with a
  radius that is 4 times greater, what will be the
  circumference?
• 6. A small pizza at Petes Pizza has an area of
  29 in2. A large pizza has a radius that is
  triple the radius of a small pizza. What is the
  area of a large pizza?

• 3. Gary had a triangular dog pen with a perimeter
  of 12 ft. He made it bigger by doubling the
  dimensions. What is the perimeter now?
• 4. Tara has a rectangular table with an area of 2
  m2. She is going to buy another table that has
  dimensions that are double the first table. What
  is the area of Taras new table?

( C 52 cm.)
( P 24 ft.)
( A 8 m2 )
( A 261 in2 )
19
Practice - Changing Dimensions

• 8. Claires old aquarium has a volume of 27,000
  cm3. She bought a new aquarium in which the
  length and width are 5 times those of her old
  tank. What is the volume of Claires new
  aquarium?
• 9. The swimming pool at the park is shaped like a
  rectangular prism. The volume of the pool is 800
  yd3. The city is going to make the length of the
  pool twice as long. What will be the volume of
  the new pool?

7. If the length, width, and height of
the rectangular prism are tripled, what will be
the volume?
Practice Buckle Down ( pp. 160 162 )
20
Practice - Changing Dimensions

• 8. Claires old aquarium has a volume of 27,000
  cm3. She bought a new aquarium in which the
  length and width are 5 times those of her old
  tank. What is the volume of Claires new
  aquarium?
• 9. The swimming pool at the park is shaped like a
  rectangular prism. The volume of the pool is 800
  yd3. The city is going to make the length of the
  pool twice as long. What will be the volume of
  the new pool?

( V 675,000 cm3 )
7. If the length, width, and height of
the rectangular prism are tripled, what will be
the volume?
( V 1512 m3 )
( V 1600 yd3 )
Practice Buckle Down ( pp. 160 162 )
21
Indirect Measurement

• Apply the concepts of similar figures to find the
  unknown measurement of an object that is nearly
  impossible to measure with a common measuring
  tool.
• What is the distance across the lake?

22
Indirect Measurement

• Apply the concepts of similar figures to find the
  unknown measurement of an object that is nearly
  impossible to measure with a common measuring
  tool.
• What is the distance across the lake?

( 48 ft.)
23
EOG Grade 8 Math Sample Items-Goal 1(released
by NC DPI)

• 1. If the length of a rectangle is doubled, what
  will happen to its area?
• A. the area will be the same
• B. the area will double.
• C. the area will triple.
• D. the area will quadruple.

• 2. The side measurements of a cube are tripled.
  What is the ratio of the surface area of the
  original cube to the larger one?
• A. 13 C. 19
• B. 16 D. 112
• 3. The shadow of a flagpole is 19 ft. long. The
  shadow of a 12 ft. wall is 4 ft. What is the
  height of the flagpole?
• A. 48 ft. C. 62 ft.
• B. 57 ft. D. 75 ft.

24
EOG Grade 8 Math Sample Items-Goal 1(released
by NC DPI)

• 1. If the length of a rectangle is doubled, what
  will happen to its area?
• A. the area will be the same
• B. the area will double.
• C. the area will triple.
• D. the area will quadruple.

• 2. The side measurements of a cube are tripled.
  What is the ratio of the surface area of the
  original cube to the larger one?
• A. 13 C. 19
• B. 16 D. 112
• 3. The shadow of a flagpole is 19 ft. long. The
  shadow of a 12 ft. wall is 4 ft. What is the
  height of the flagpole?
• A. 48 ft. C. 62 ft.
• B. 57 ft. D. 75 ft.

1. (B)
2. (C)
3. (B)
25
EOG Grade 8 Math Sample Items-Goal 1(released
by NC DPI)
The diagram below shows a companys current
packaging of its plant food.

• 4. The company doubles the radius but keeps the
  height the same. What effect will this change
  have on the volume of the container?
• A. the volume will be 1 ½ times the original
• B. the volume will be twice the original
• C. the volume will be three times the original
• D. the volume will be four times the original

26
EOG Grade 8 Math Sample Items-Goal 1(released
by NC DPI)
The diagram below shows a companys current
packaging of its plant food.

• 4. The company doubles the radius but keeps the
  height the same. What effect will this change
  have on the volume of the container?
• A. the volume will be 1 ½ times the original
• B. the volume will be twice the original
• C. the volume will be three times the original
• D. the volume will be four times the original

4. (D)
27
EOG Grade 8 Math Sample Items-Goal 1(released
by NC DPI)

• 5. Jake wanted to measure the length of the pond,
  so he drew this diagram of two similar triangles.
• What is the approximate length of the pond?
• A. 25 ft.
• B. 19 ft.
• C. 18 ft.
• D. 13 ft.

28
EOG Grade 8 Math Sample Items-Goal 1(released
by NC DPI)

• 5. Jake wanted to measure the length of the pond,
  so he drew this diagram of two similar triangles.
• What is the approximate length of the pond?
• A. 25 ft.
• B. 19 ft.
• C. 18 ft.
• D. 13 ft.

4. (D)