Objective:

Students will be able to predict what three-dimensional objects will result from folding a two-dimensional net and then confirm the prediction by folding the net.

Core Content:

6th grade

Domain: Geometry

Cluster: Solve real-world and mathematical problems involving area, surface area, and volume.

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

Materials:

Bell Work, Models of Three Dimensional Figures, Matching Game, Empty Pizza Box, Traditional Pizza Box Pattern,Geofix Activity Directions, Three Dimensional Objects (Models or Household items), Predicting Nets Activity Sheet, Geofix Shapes, Additional Nets Sheet, Predicting nets of 3-d objects without geofix shapes, Nets of cones and cylinders, Predicting Nets Discussion Questions, Chart Paper, White boards, Predicting Three Dimensional Objects, Nets and Three Dimensional Figures, Three Dimensional Sort Them, Traditional Questions

Time:

120-180 minutes (Time will vary depending on exploration time given.)

Vocabulary:

Circle / Congruent / Parallel / Polygon / Rectangle
Square / Cone / Cubic Units / Cylinder / Edges
Faces / Nets / Perimeter / Prism / Pyramid
Square Units / Vertices / Volume / Cube / Lateral Face

Internet Resources:

This is an interactive site that will have students predict which nets will form cubes.

This is a site that you can order geofix shapes.

Lesson Outline

  1. Bell Work (Bell Work)
  2. Review: Matching GameThree Dimensional Figures (Game Cards)
  3. Anticipatory Set (Pizza Box or Pizza Box Pattern)
  4. Activity : Geofix Activity- Geofix Activity Directions, Three Dimensional Objects (Models or Household items), Predicting Nets Activity Sheet, Geofix Shapes, Additional Nets Sheet, Predicting nets of 3-d objects without geofix shapes, Nets of cones and cylinders, Predicting Nets Discussion Questions, Chart Paper, White boards
  5. Practice: Worksheet- Predicting Three Dimensional Objects
  6. Homework: Nets and Three Dimensional Figures
  7. Assessments: Three Dimensional Sort Them, Traditional Questions
  1. In your own words, briefly describe what a two-dimensional shape is. Draw an example and identify the name of the example you drew.

Brief description in your own words. / Example Drawing / Name of Drawing
  1. Briefly describe what a three-dimensional object is. Draw an example and identify the name of the example you drew.

Brief description in your own words. / Example Drawing / Name of Drawing

Answer Key

  1. In your own words, briefly describe what a two-dimensional shape is. Draw an example and identify the name of the example you drew.

Brief description in your own words. / Example Drawing / Name of Drawing
(Answers will vary)
A two dimensional shape is a shape only have length and width, so it appears flat. / (Answers will vary)
Etc. / (Answers will vary)
Rectangle
Triangle
Square
Etc.
  1. Briefly describe what a three-dimensional object is. Draw an example and identify the name of the example you drew.

Brief description in your own words. / Example Drawing / Name of Drawing
(Answers will vary)
An object that has length, width, and height / (Answers will vary)
Etc. / (Answers will vary)
Rectangular Prism
Cube
Cylinder
Etc.

Anticipatory Set

(Have an empty pizza box to show to the class)

Say to the class:

Who has ever ordered pizza before? Who do you think makes the boxes the pizza comes in? How do you think they make the boxes? What do you think they have to take into consideration when designing a pizza box?

(Brainstorm ideas with your students. If no one thinks of surface area and volume, lead them to thinking of these considerations.Be sure to use specific vocabulary and review with students the units used to measure surface area (square units) and volume (cubic units).)

Say to the class:

Pizza Companies must hire packaging companies to design boxes for their pizzas. A packaging company will design a two dimensional pattern that will fold into the pizza box.

(Unfold the pizza box to reveal the two dimensional pattern that the packaging company used for your particular pizza box. If you are unable to unfold the box, show the pattern on the next page.)

Say to the class:

Why do you think they design a two dimensional pattern when they need a three dimensional pattern?

(Lead students to think of time, cost, convenience, etc.)

Say to the class:

In mathematics, a two dimensional pattern that can be folded to make a three-dimensional figure is known as a net. Today we will be predicting what three-dimensional objects will result from folding a two-dimension net, then confirming the prediction by folding the net.

Traditional Pizza Box Pattern


Geofix Activity

Part One: Making a Prediction

  1. Divide students into group of 2 or 3.
  2. Give each group a set of three-dimensional figures that will make the same shape as the Geofix manipulatives. (cube, rectangular prism, triangular prism, square pyramid, or triangular pyramid) You can use three-dimensional models or everyday items such as Kleenex boxes, food boxes, candles, etc.)
  3. Ask students to draw, identify the name of the three-dimensional figure, list characteristics of the figure, and predict the net of the three-dimensional figure you have given them on the Predicting nets activity sheet. (Stress the use of appropriate vocabulary, vertex, vertices, edges, faces, prism, pyramid, cube, base, lateral faces, etc. It is important to have students practice drawing the 3-D figures to work on spatial skills.)
  4. Rotate figures until every member in the group has made a prediction for each of the five figures.
  5. Ask students to share predictions on white boards or poster boards. Have students share why those predictions were made. Display all ideas to the class!!! (correct and incorrect)

Part Two-Testing the Predictions

  1. Give each group a set of Geofix shapes or use a set at the overhead and have them test their predictions.
  2. Challenge students to find different nets that work that they may not have thought of.

Part Three-Predicting Nets of Three Dimensional Objects That cannot be made with Geofix

  1. Give each studentPredicting nets of three dimensional objectsthat cannot be made with Geofix Shapes.
  2. Have students test their predictions. Students can create paper cut-outs of their own nets or you can provide the nets attached.

Part Four-Discussion Questions/Class Summary

  1. Have students individually answer predicting nets discussion questions
  2. Have students compare and discuss answers with a partner
  3. Have a class summary of the discussion questions and post the answers in the room

Predicting Nets Activity Sheet

Name:

Name of Figure / Sketch of Three-Dimensional figure / Identifying Characteristics / Sketch of Net Prediction
1
2
3
4
5
Name and Picture of Figure / Sketches of nets that work verified with Geofix shapes
1 / Cube
2 / Rectangular Prism
3 / Square Pyramid

4 / Triangular Pyramid

5 / Triangular Prism

Name and Picture of Figure / Sketches of nets that DID NOT work verified with Geofix shapes
1 / Cube
2 / Rectangular Prism
3 / Square Pyramid

4 / Triangular Pyramid

5 / Triangular Prism

Predicting Nets Discussion Questions

  1. What properties are common to all nets that will form a three-dimensional object?
  1. What type of nets will not work? Why not?
  1. Without folding, is there a quick way to determine whether or not a net will fold into a three dimensional object?
  1. How can you determine if two nets are identical?
  1. Compare and contrast properties of your three-dimensional figure to its net. Explain any commonalities and differences you find.

Predicting Nets Discussion Questions-Answer Key

  1. What properties are common to all nets that will form a three-dimensional object?

The nets have the same amount of two dimensional shapes as the faces on the corresponding three dimensional objects. Students may think of other properties.

  1. What type of nets will not work? Why not?

Nets with more or fewer two dimensional shapes than faces of the three dimensional objects will not work. In addition, many nets with the right amount of shapes cause two shapes to overlap. Examples would include cases when four shapes share a vertex; when two shapes lie on the same side of a center row of shapes; and when more than four shapes occur in a row.

  1. Without folding, is there a quick way to determine whether or not a net will fold into a three dimensional object?

If a net suffers from any of the problems noted above it will not form a three-dimensional object, and these problems can be determined by visual inspection.

  1. How can you determine if two nets are identical?

One of the nets will fit exactly on top of another net when flipped or rotated.

  1. Compare and contrast properties of your three-dimensional figure to its net. Explain any commonalities and differences you find.

Answers will vary. Examples could include: The surface area of the three-dimensional object is equal to the area of the net. The number of edges on the three-dimensional object is not equal to the number of sides on the net.

Predicting nets of three dimensional objects

that cannot be made with Geofix Shapes

Name:

Now that you are familiar with nets of three dimensional objects that can be made using Geofix shapes, let’s explore some objects that cannot be made using Geofix shapes.

Part One: Fill in the missing information in the chart below.

Name of Figure / Sketch of Three-Dimensional figure / Identifying Characteristics / Sketch of Net Prediction
1 /
2 /

Part Two: Answer the following questions.

  1. Why can’t we make these objects using Geofix shapes?
  1. What are some possible ways or items we could use to test our predictions.?

Predicting nets of three dimensional objects

that cannot be made with Geofix Shapes

Name:Answer Key

Now that you are familiar with nets of three dimensional objects that can be made using Geofix shapes, let’s explore some objects that cannot be made using Geofix shapes.

Part One: Fill in the missing information in the chart below.

Name of Figure / Sketch of Three-Dimensional figure / Identifying Characteristics / Sketch of Net Prediction
1 / Cylinder / / A three-dimensional figure with two parallel and congruent circles as bases and no vertices / Answers will vary
2 / Cone / / A three-dimensional figure with one circular base and one vertex. / Answers will vary

Part Two: Answer the following questions.

  1. Why can’t we make these objects using Geofix shapes?Geofix shapes only are made up of polygons, not circles.
  2. What are some possible ways or items we could use to test our predictions? Answers will vary: roll a piece of paper, birthday hats

Name:

This problem gives you the chance to sort the name of a three dimensional object with its pictorial, verbal, and two dimensional (nets) characteristics.

Seven different objects are given on the following pages, and each object is presented in four ways:

  • Name
  • Picture
  • Net
  • Verbal Description

Each set of cards on the following pages is grouped incorrectly. It is your job to sort the cards into equivalent sets.

Directions:

  1. Cut out all of the cards.
  2. Decide how they should be sorted.
  3. Glue or tape the equivalent sets on paper under the titles Picture, Net, Description and Name.
Picture / Net / Description / Name
/ / A three-dimensional figure that has triangular bases that are congruent and parallel / Cube
/ / A three-dimensional figure whose base is a triangle and whose lateral faces are triangles that share a common vertex. / Cylinder
/ / A three-dimensional figure that has 6 congruent squares as faces. / Triangular
Prism
/ / A three-dimensional figure that has rectangular bases that are congruent and parallel / Cone
Picture / Net / Description / Name
/ / A three-dimensional figure whose base is a square and whose lateral faces are triangles that share a common vertex. / Rectangular
Prism
/ / A three-dimensional figures with two parallel and congruent circles as bases and no vertices / Square
Pyramid
/ / A three-dimensional figure with one base and one vertex. / Triangular Pyramid

Answer Key

Picture / Net / Description / Name
/ / A three-dimensional figure whose base is a triangle and whose lateral faces are triangles that share a common vertex. / Triangular Pyramid
/ / A three-dimensional figure with one circular base and one vertex. / Cone
/ / A three-dimensional figure that has 6 congruent squares as faces. / Cube
/ / A three-dimensional figure whose base is a square and whose lateral faces are triangles that share a common vertex. / Square
Pyramid

Answer Key

Picture / Net / Description / Name
/ / A three-dimensional figure that has triangular bases that are congruent and parallel / Triangular
Prism
/ / A three-dimensional figures with two parallel and congruent circles as bases and no vertices / Cylinder
/ / A three-dimensional figure that has rectangular bases that are congruent and parallel / Rectangular
Prism

Formative Assessment

Name:

  1. Nathan folded and taped a piece of cardboard to form the figure shown below. Which of the following nets shows the unfolded figure?

A. B. C. D.

  1. Which figure shows the net for a rectangular prism?
  2. B. C. D.
  3. Darren made this net of a shape. Which three-dimensional shape can he make from the net?

AB. C. D.

  1. A net of a three-dimensional shape is shown. Which three-dimensional shape can be made from the net?

  1. Ray found the paper cut-out shown. Which 3-dimensional object is formed when the cut-out is assembled?
  1. Cone
  2. Cylinder
  3. Prism
  4. Sphere

6.

7. Which figure does not show the net for a cube?

A. B. C. D.

8. If a triangular pyramid were lay flat on a plane, which of the following would represent its net?

A. B. C. D.

  1. Nicole made several paper cut-outs of what she predicted would be the net of a cylinder. Which paper cut-out will actually make the cylinder?
  1. B. C. D.