6 Grade Geometry Project€¦ · Geometry Project Part B 1. Graph the vertices to create each rectangle listed below. Color the rectangles as indicated. Find the perimeter and area

6th Grade Geometry Project Activity Guide

With this project, students must identify nets and 3D figures along with

calculating surface area, perimeters, and volume. It is great way to

practice several sixth grade standards!

Students get hands-on experience working with nets, surface area, and

volume. Not only is this activity engaging, but it will help create a

conceptual understanding of 3D figures and their attributes.

The project has 4 parts and 2 Follow Up practice worksheets. The parts can be assigned

to individual students or partners.

Part A: Students graph points to create a net of a rectangular prism. They cut out and

create the 3D figure, find volume and surface area, and answer questions. This is a

good one to do as a whole class so students get the idea.

Part B: Next students create a rectangular polygon whose net is configured differently.

They create the 3D figure by cutting it out and folding it, and then answer questions.

Part C: Then students graph points to create the net of a pyramid. They cut it out and

work with the 3D figure to answer questions.

Part D: Finally students create the net of a triangular prism. They work with the 3D figure

to answer questions.

A large graph is included if you would like to print it for each part. Or, students can

draw their own graphs on graph paper. Students will need a graph, colored

pencils/markers, scissors, and tape for each part.

Follow Up: Two practice sheets are provided after the project. These extend students’

thinking about surface area and volume. They could be assigned as homework or

classwork.

Answer Keys are included.

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Details

Common Core Standards:

6.G.A.1 Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.

6.G.A.3 Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems.

6.G.A.4 Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.

6.NS.C.8 Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.


Page Item

3 Large Graph (Print 1 copy for each part or use graph paper instead)

4 Part A and Part B (Rectangular Prisms)

5 Part C (Pyramid) and Part D (Triangular Prism)

6 Project Scoring Checklist Rubric

7 Follow Up #1

8 Follow Up #2

9 – 18 Answer Keys

Name _________________________________________________

Geometry ProjectY

X


Part A1. Graph the vertices to create each rectangle listed below. Color the rectangles as indicated. Find the perimeter and area of each rectangle.

2. Cut around the outside of the figure you created so that it is one piece. Fold along the lines and create a rectangular prism. Tape it to hold it together.

3. Calculate the volume of your rectangular prism in unit cubes. Show your work below.

4. Calculate the surface area of your rectangular prism. Show your work below.

5. How many cubes measuring 2 units in all dimensions would fit inside your rectangular prism?

Yellow

(1, -3)

(1, 5)

(-3, 5)

(-3, -3)

Perimeter:

Area:

Blue

(1, 5)

(3, 5)

(3, -3)

(1, -3)

Perimeter:

Area:

Purple

(1, -5)

(1, -3)

(-3, -3)

(-3, -5)

Perimeter:

Area:

Orange

(-3, 5)

(-5, 5)

(-5, -3)

(-3, -3)

Perimeter:

Area:

Red

(-5, 5)

(-9, 5)

(-9, -3)

(-5, -3)

Perimeter:

Area:

Green

(-3, 5)

(-3, 7)

(1, 7)

(1, 5)

Perimeter:

Area:

Name _________________________________________________

Geometry ProjectPart B1. Graph the vertices to create each rectangle listed below. Color the rectangles as indicated. Find the perimeter and area of each rectangle.


3. Calculate the volume of your rectangular prism in unit cubes. Show your work below.

4. Calculate the surface area of your rectangular prism. Show your work below.

5. How many cubes measuring 2 units in all dimensions would fit inside your rectangular prism?

Green

(0, 10)

(0, 6)

(5, 6)

(5, 10)

Perimeter:

Area:

Purple

(0, 6)

(0, 0)

(5, 0)

(5, 6)

Perimeter:

Area:

Orange

(0, 0)

(0, 6)

(-4, 6)

(-4, 0)

Perimeter:

Area:

Blue

(0, 0)

(-4, 0)

(-4, -5)

(0, -5)

Perimeter:

Area:

Red

(-4, 0)

(-4, -5)

(-10, -5)

(-10, 0)

Perimeter:

Area:

Yellow

(-10, -5)

(-10, -9)

(-4, -9)

(-4, -5)

Perimeter:

Area:


Part C1. Graph the vertices to create each polygon listed below. Color the polygons as indicated. Find the area of each one.

2. Cut around the outside of the figure you created so that it is one piece. Fold along the lines and create a 3D figure. Tape it to hold it together.

3. What is your 3D figure?

4. Calculate the surface area of your figure. Show your work below.

5. Explain how to calculate the surface area of a 3D figure.

Name _________________________________________________

Geometry ProjectPart D1. Graph the vertices to create each polygon listed below. Color the polygons as indicated. Find the area of each one.


3. What is your 3D figure?

4. Calculate the surface area of your figure. Show your work below.

5. What is the difference between surface area and volume?

Red

(-2, 4)

(1, 10)

(4, 4)

Area:

Purple

(4, 4)

(4, -2)

(-2, -2)

(-2, 4)

Area:

Yellow

(-2, -2)

(-8, 1)

(-2, 4)

Area:

Green

(-2, -2)

(4, -2)

(1, -8)

Area:

Orange

(10, 1)

(4, -2)

(4, 4)

Area:

Green

(-6, 6)

(4, 6)

(4, 1)

(-6, 1)

Area:

Purple

(4, 1)

(-6, 1)

(-6, -3)

(4, -3)

Area:

Yellow

(4, -3)

(4, -6)

(-6, -6)

(-6, -3)

Area:

Blue

(-6, -3)

(-9, -3)

(-6, 1)

Area:

Orange

(4, 1)

(4, -3)

(7, -3)

Area:


Name _____________________________

Scoring Rubric

Part A

❑ Net drawn correctly

❑ Rectangular prism created

❑ Area calculations

❑ Perimeter calculations

❑ Volume calculation (#3)

❑ Surface area calculation (#4)

❑Question #5

Part B







❑Question #5

Part C


❑ 3D figure created


❑ 3D figure identified (#3)


❑Question #5

Part D






❑Question #5

Name ______________________________

Scoring Rubric

Part A







❑Question #5

Part B







❑Question #5

Part C






❑Question #5

Part D






❑Question #5

Name _________________________________________________

Follow Up #1Some of the figures drawn below are nets and some are not nets. If a figure can be

folded to create a 3D figure and enclose all sides, it is a net. If it cannot, it is not a net.

Use the figures to answer the questions below.

1. Which is the net of a cube?

What is the surface area? What is the volume?

2. Which is the net of a rectangular prism with a volume of 9 unit cubes?

What is the surface area?

3. Which is the net of a rectangular prism with a volume of 30 unit cubes?

What is the surface area?

4. Explain why the remaining figures are not nets.

A B

C

ED

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Name _________________________________________________

Follow Up #2Some of the figures drawn below are nets, and some are not nets. If a figure can be


Draw an X over the figures that are not nets.

For each net, identify the 3D figure it forms. Then calculate the surface area.

/

2 in.

2 in.

2 in

.

2 in.

2 in

.2

in

. 20 ft

20 f

t6 ft

8 f

t6 ft

5 m

3 m

3 m

2 m

4 m3 m

3 cm

12 c

m

12 cm

3 cm

3 c

m3

cm

3 c

m

10 yd

10 y

d

12 y

d1

2 y

d

12 yd 12 yd

9 in.

9 in.

9 in

.

9 in

.10 in. 7 in.

7 in

.2

2 in

.

1 m

1 m

1 m

1 m

1 m 1 m

11 cm

7 c

m

2 cm 2 cm

2 c

m2

cm

A

B

C

D

E

F

G

H1 m

7 c

m


Part A1. Graph the vertices to create each rectangle listed below. Color the rectangles as indicated. Find the perimeter and area of each rectangle.


3. Calculate the volume of your rectangular prism in unit cubes. Show your work below.64 units3

4. Calculate the surface area of your rectangular prism. Show your work below. 112 units2

5. How many cubes measuring 2 units in all dimensions would fit inside your rectangular prism?8

Yellow

(1, -3)

(1, 5)

(-3, 5)

(-3, -3)

Perimeter:

24 units

Area:

32 units2

Blue

(1, 5)

(3, 5)

(3, -3)

(1, -3)

Perimeter:

20 units

Area:

16 units2

Purple

(1, -5)

(1, -3)

(-3, -3)

(-3, -5)

Perimeter:

12 units

Area:

8 units2

Orange

(-3, 5)

(-5, 5)

(-5, -3)

(-3, -3)

Perimeter:

20 units

Area:

16 units2

Red

(-5, 5)

(-9, 5)

(-9, -3)

(-5, -3)

Perimeter:

24 units

Area:

32 units2

Green

(-3, 5)

(-3, 7)

(1, 7)

(1, 5)

Perimeter:

12 units

Area:

8 units2

Answer Key

Geometry ProjectPart B1. Graph the vertices to create each rectangle listed below. Color the rectangles as indicated. Find the perimeter and area of each rectangle.


3. Calculate the volume of your rectangular prism in unit cubes. Show your work below.120 units3

4. Calculate the surface area of your rectangular prism. Show your work below. 148 units2

5. How many cubes measuring 2 units in all dimensions would fit inside your rectangular prism (without cutting the cubes)?12 (There would be space left, but extra whole cubes would not fit.)

Green

(0, 10)

(0, 6)

(5, 6)

(5, 10)

Perimeter:

18 units

Area:

20 units2

Purple

(0, 6)

(0, 0)

(5, 0)

(5, 6)

Perimeter:

22 units

Area:

30 units2

Orange

(0, 0)

(0, 6)

(-4, 6)

(-4, 0)

Perimeter:

20 units

Area:

24 units2

Blue

(0, 0)

(-4, 0)

(-4, -5)

(0, -5)

Perimeter:

18 units

Area:

20 units2

Red

(-4, 0)

(-4, -5)

(-10, -5)

(-10, 0)

Perimeter:

22 units

Area:

30 units2

Yellow

(-10, -5)

(-10, -9)

(-4, -9)

(-4, -5)

Perimeter:

20 units

Area:

24 units2


Part C1. Graph the vertices to create each polygon listed below. Color the polygons as indicated. Find the area of each one.


3. What is your 3D figure?Pyramid

4. Calculate the surface area of your figure. Show your work below. 108 units2

5. Explain how to calculate the surface area of a 3D figure.Answers may vary. Calculate the area of each face, and then add all the areas together.

Name _________________________________________________

Geometry ProjectPart D1. Graph the vertices to create each polygon listed below. Color the polygons as indicated. Find the area of each one.


3. What is your 3D figure?Triangular Prism

4. Calculate the surface area of your figure. Show your work below. 132 units2

5. What is the difference between surface area and volume?Answers may vary. Surface area measures the flat 2D space on each face of a figure. Volume measures the 3D space inside a figure.

Red

(-2, 4)

(1, 10)

(4, 4)

Area:

18 units2

Purple

(4, 4)

(4, -2)

(-2, -2)

(-2, 4)

Area:

36 units2

Yellow

(-2, -2)

(-8, 1)

(-2, 4)

Area:

18 units2

Green

(-2, -2)

(4, -2)

(1, -8)

Area:

18 units2

Orange

(10, 1)

(4, -2)

(4, 4)

Area:

18 units2

Green

(-6, 6)

(4, 6)

(4, 1)

(-6, 1)

Area:

50 units2

Purple

(4, 1)

(-6, 1)

(-6, -3)

(4, -3)

Area:

40 units2

Yellow

(4, -3)

(4, -6)

(-6, -6)

(-6, -3)

Area:

30 units2

Blue

(-6, -3)

(-9, -3)

(-6, 1)

Area:

6 units2

Orange

(4, 1)

(4, -3)

(7, -3)

Area:

6 units2


Answer Key

Follow Up #1Some of the figures drawn below are nets and some are not nets. If a figure can be


Use the figures to answer the questions below.

1. Which is the net of a cube? B

What is the surface area? 24 units2 What is the volume? 8 units3

2. Which is the net of a rectangular prism with a volume of 9 unit cubes? D

What is the surface area? 30 units2

3. Which is the net of a rectangular prism with a volume of 30 unit cubes? C

What is the surface area? 62 units2

4. Explain why the remaining figures are not nets.

A does not have enough faces to enclose a rectangular prism. One side would

be open. E would have two faces overlapping if folded and one face open. It is

not configured correctly to create a cube.

A B

C

ED

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Answer Key

Follow Up #2Some of the figures drawn below are nets, and some are not nets. If a figure can be


Draw an X over the figures that are not nets.

For each net, identify the 3D figure it forms. Then calculate the surface area.

/

2 in.

2 in.

2 in

.

2 in.

2 in

.2

in

. 20 ft

20 f

t6 ft

8 f

t6 ft

5 m

3 m

3 m

2 m

4 m3 m

3 cm

12 c

m

12 cm

3 cm

3 c

m3

cm

3 c

m

10 yd

10 y

d

12 y

d1

2 y

d

12 yd 12 yd

9 in.

9 in.

9 in

.

9 in

.10 in. 7 in.

7 in

.2

2 in

.

1 m

1 m

1 m

1 m

1 m 1 m

11 cm

7 c

m

2 cm 2 cm

2 c

m2

cm

7 c

m

A

B

C

D

E

F

G

H

Triangular Prism528 ft2

Triangular Prism36 m2

Cube6 m2

1 m

Pyramid340 yd2

Rectangular Prism226 cm2


Geometry Project A

Y

X


Geometry Project BY

X


Geometry Project C

Y

X


Geometry Project DY

X


Geometry ProjectAssembled Examples


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6 Grade Geometry Project€¦ · Geometry Project Part B 1. Graph the vertices to create each rectangle listed below. Color the rectangles as indicated. Find the perimeter and area