Sixth Grade
Math Prep: Session 2
Note to Teachers:
This lesson will focus on geometry. Students will calculate area, surface
area, and volume of polygons and solids. Shapes can be deconstructed into
rectangles or triangles to find area. Students must represent 3D figures using nets.
Students will draw polygons on the coordinate graph and use them to solve real
world problems. Formulas are provided for your reference. However, students
should memorize them!
The session should be split up as such:
 Part I- 15 minutes computation
 Part II- 45 minutes of problem solving without a calculator
**Students in the sixth grade will not be permitted to use calculators on Book 1 of
the Assessment, but will be permitted to use them for Books 2 and 3.***
In problem solving sections, have students read the problems, think
carefully about each, and underline important math facts and information. When
students are finished, go over the correct answers, while providing explanations as
to why the problem may be solved in different ways.
Formulas
Volume = Length x Width x Height
Surface Area of a Triangular Prism=
2 (Triangle Base) + Rectangle + Rectangle + Rectangle
2 (1/2 B x H)
+ (L x W) + (L x W) + (L x W)
Surface Area of a Rectangular Prism =
2 (Small Rectangle) + 2 (Medium Rectangle) + 2 (Large Rectangle)
2 (L x W)
+ 2( L x W)
+ 2(L x W)
Area of a Trapezoid
Area of a Triangle
Area of a Rectangle
Grade 6 Lesson 2: Geometry
Part I: Computation
Find the area.
1.
2.
3.
4.
5.
Write the volume.
6.
Part II: Problem Solving –No Calculators
1. The volume of the cube below is 8 cm3. What is the length of h?
h
2. The figure below is a square with dimensions given.
3x – 5 inches
Part A: What is the perimeter of the square in terms of x?
Perimeter =___________________________________________________________
Part B: If the length of each side of the square is tripled, what would be the perimeter of the new
square, in terms of x?
Perimeter =____________________________________________________________
Part C: If x = 3, what would be the ratio of the area of the original square to the area of the new
square?
______________________________________________________________________________
3. Find the area of the octagon below.
Show your work.
Answer_________________________________________________
4. Find the area of the parallelogram below.
Show your work.
Answer_________________________________________________
5. Three vertices of a rectangle ABCD are given.
A (-6, 4)
B (-6, -1)
C (8, 4)
Part A: Find the location of the last vertex. Use the graph below.
x-axis
y-axis
Answer______________________________________________
Part B: What is the area of rectangle ABCD?
Show your work.
Answer______________________________________________
6. Find the volume, in cubic units, of the right rectangular prism pictured below.
Show your work.
Answer____________________________________________________________
7. Cereal boxes have the dimensions indicated in the illustration, below. The cereal box factory
is about to close for the weekend, and there are just 1,000 in2 of cardboard left. How many more
boxes of cereal can be produced at the factory with the remaining cardboard?
Show your work:
Answer________________________________________________________________
8. Triangle ADE is inside rectangle ABCD. Point E is halfway between points B and C on the
rectangle. Side AB is 8 cm and side AD is 6 cm.
B
E
A
C
D
Part A: What is the area of triangle ADE?
Show your work.
Part B: What is the ratio of the area of triangle ABE to triangle ADE?
Show your work.
Part C: What is the ratio of the area of triangle CDE to the area of rectangle ABCD?
Show your work.
9. A toy store needs boxes that measure 14 inches long by 6 inches wide by 4 inches tall.
Part A: Draw a net below for a box with these dimensions.
Part B: What is the surface area of the box?
Part C: A smaller box has measurements that are half the measurements of the original. Find the
ratio of the surface area of the original box to the surface area of the smaller box.
Show your work:
Answer:____________________________________________________________________
10. Renata bought a package of candy to give to her friend as a gift. The candy is shaped like a
triangular prism, with the dimensions below. She has 3 different sizes of wrapping paper to
choose from. Which will be the best wrapping for the candy—the paper that is 80 cm2, 130 cm2,
or 180 cm2.
Show your work.
Answer_______________________________________________
11. Mike is using cubes that measure ½ inch on each side to fill a box that has a height of 2 ½
inches, width of 2 inches, and length of 1 ½ inches. How many ½ inch cubes will Mike need to
fill the box?
12. On a coordinate plane, a line can be drawn between points A (-3,4) and Point B (3,4). What
are the coordinates of the point on the line segment that is half way between points A and B.
Show or explain how you found your answer. You may use the coordinate plane below to help
you find the answer.
13. The coordinates (-3, 5), (2, -3), (-3, -3), and (2, 5) are the vertices of a rectangle that is
graphed on a coordinate plane. What is the length and width of the rectangle? Show or explain
how you found your answer. You may use the coordinate plane below to help you find the
answer.
14. Create the net for the given prism or pyramid. Use the net to calculate the surface area.
15. What is the area of the polygon below? Show or explain how you found your answer
16. What is the area of the polygon below? Show or explain how you found your answer.
3 ft
7 ft
17. Lara is tiling the patio around her pool. The area of the pool is 960 square feet.
50 feet
25 feet
POOL
What is the area of the patio around the pool? Show or explain how you found your answer.
18. The vertices of a quadrilateral are the points: A(3, 4), B(3, 1), C(-1, 1), and D(-1, 4).
Part A: What is the length of side AB? _____________________________________
Part B: What is another name for this quadrilateral?___________________________
Part C: What is the perimeter of quadrilateral ABCD?___________________________
19. The net below can be folded on the dashed lines.
Part A: What 3-dimensional figure is made when the net is folded on the dashed lines?
Part B: What is the surface area of this 3-dimensional figure?
Show your work.
20. Find the volume of the rectangular prism below. Each unit cube is ¾ an inch.