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Unpacking 3D Shapes: The Power of Parallelograms

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Samantha Hansing

Tier 1
For Schools

Lesson Plan

Unpacking 3D Shapes Lesson Plan

Students will be able to calculate the area of a 2D parallelogram and identify parallelogram faces on 3D objects, understanding their role in forming these shapes.

Understanding 2D shapes is fundamental to comprehending 3D geometry and has practical applications in various fields such as design, engineering, and architecture.

Audience

6th Grade

Time

30 minutes

Approach

Review, visualize, and apply.

Materials

Slide Deck: Unpacking 3D Shapes, Worksheet: Parallelogram Puzzlers, and Answer Key: Parallelogram Puzzlers

Prep

Teacher Preparation

10 minutes

  • Review the Unpacking 3D Shapes Lesson Plan, Slide Deck: Unpacking 3D Shapes, Worksheet: Parallelogram Puzzlers, and Answer Key: Parallelogram Puzzlers.
    - Make copies of the Worksheet: Parallelogram Puzzlers for each student.
    - Ensure projector or smartboard is ready for the Slide Deck: Unpacking 3D Shapes.

Step 1

Warm-Up & Introduction: What are 3D Shapes Made Of?

5 minutes

  • Engage: Ask students: "What are some 3D shapes you see in our classroom or everyday life? What 2D shapes can you find on their surfaces?"
    - Introduce: Briefly introduce or review what a parallelogram is (a four-sided shape with opposite sides parallel and equal). State the objective for the day: to review how to find the area of a parallelogram and see how these shapes make up 3D objects.

Step 2

Slide Deck Presentation: From 2D to 3D

10 minutes

  • Present the Slide Deck: Unpacking 3D Shapes.
    - Review Area: Go through slides that review the definition and area formula for a 2D parallelogram (Area = base x height). Work through a simple example together.
    - Connect to 3D: Transition to slides that show how 2D shapes, like parallelograms, can be the 'faces' of 3D objects. Use a rectangular prism as an example, pointing out that its faces are rectangles (a special type of parallelogram). Emphasize that 'area' is for flat surfaces, and when we talk about 3D objects, we often discuss 'surface area' (the sum of the areas of all its faces) or 'volume' (the space it takes up). Clarify that there isn't an 'area of a 3D parallelogram' directly, but we can find the area of its 2D parallelogram faces.

Step 3

Guided Practice & Worksheet: Parallelogram Puzzlers

10 minutes

  • Distribute the Worksheet: Parallelogram Puzzlers.
    - Guided Practice: Work through the first one or two problems on the worksheet together as a class, demonstrating how to apply the area formula and how to identify parallelogram faces.
    - Independent/Pair Work: Have students complete the remaining problems on the worksheet individually or with a partner. Circulate to provide support and answer questions.

Step 4

Wrap-Up & Discussion: Reflecting on Shapes

5 minutes

  • Review: Go over the answers to the Worksheet: Parallelogram Puzzlers using the Answer Key: Parallelogram Puzzlers. Address any common misconceptions.
    - Discussion: Lead a brief discussion using the final slide: "What's one new thing you learned or remembered today about parallelograms or 3D shapes?" Encourage students to share their insights about the connection between 2D and 3D geometry.
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Slide Deck

Unpacking 3D Shapes: The Power of Parallelograms!

Have you ever noticed how many amazing shapes are all around us? Today, we're going to become shape detectives and unlock a secret about 3D objects!

Welcome students. Ask them to name some shapes they see every day (e.g., a book is a rectangle/rectangular prism, a cereal box, a pyramid). This helps activate prior knowledge and connect to the real world.

What's a Parallelogram?

A parallelogram is a four-sided shape where:

  • Opposite sides are parallel.
  • Opposite sides are equal in length.

Think of it as a 'slanted rectangle'!

Display an image of a parallelogram. Ask students to describe its features. What makes it different from a rectangle? (Slanted, but still has parallel sides). Emphasize that rectangles and squares are special types of parallelograms.

Finding the Area of a Parallelogram

How do we measure the space inside a parallelogram?

Area = base (b) x height (h)

Remember: The height is always measured straight up from the base, making a perfect right angle!

Clearly illustrate the 'base' and 'height' on a parallelogram diagram. Stress that height must be perpendicular to the base. Work through a very simple example: base=5, height=3, Area = 15 square units.

Parallelograms in the Third Dimension!

Many 3D shapes are made up of flat, 2D surfaces called faces.

Guess what? Parallelograms (like rectangles!) are often the faces of 3D objects!

We don't find the 'area of a 3D shape,' but we can find the area of its 2D faces!

Explain that 3D shapes are built from 2D 'faces.' Show a simple rectangular prism or a box. Point to its rectangular faces and explain that rectangles are a type of parallelogram. Clarify that we don't find the 'area of a 3D shape' but rather the 'surface area' (the total area of all its 2D faces) or 'volume' (the space it takes up). The focus here is on identifying the parallelogram-shaped faces.

Time to Practice Our Shape Skills!

Now that we've reviewed parallelograms and seen them in 3D, let's put our knowledge to the test!

We'll work on finding the area of parallelograms and identifying them on some 3D figures.

Introduce the worksheet. Explain that students will first practice finding the area of individual parallelograms, and then they'll identify parallelogram faces on 3D objects.

Quick Check: What's Your Big Idea?

What's one new thing you learned or remembered today about parallelograms or 3D shapes? Share with a partner or the class!

Facilitate a brief discussion. Encourage students to share their 'aha!' moments or any lingering questions. This serves as a quick formative assessment.

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Worksheet

Parallelogram Puzzlers!

Name: ____________________________

Part 1: Finding the Area of Parallelograms

Directions: Calculate the area for each parallelogram below. Remember, Area = base x height! Show your work.

  1. Parallelogram A

    • Base = 7 cm
    • Height = 4 cm
    • Area =


  2. Parallelogram B

    • Base = 10 inches
    • Height = 3 inches
    • Area =


  3. Parallelogram C

    • Base = 6.5 meters
    • Height = 2 meters
    • Area =


  4. Parallelogram D

    • Base = 8 feet
    • Height = 5.5 feet
    • Area =


Part 2: Parallelograms in 3D Shapes

Directions: Look at the 3D shapes below. Answer the questions.

(Imagine a standard rectangular box)

  1. What kind of parallelogram makes up the faces of a typical rectangular box (also called a rectangular prism)?




  2. How many faces does a rectangular box have?




  3. If a rectangular box has a front face with a base of 10 cm and a height of 5 cm, what is the area of that front face?

    • Area =


  4. Can you think of another real-world object that has parallelogram-shaped faces (even if they are rectangles)? Describe it!







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Answer Key

Parallelogram Puzzlers Answer Key

Part 1: Finding the Area of Parallelograms

Directions: Calculate the area for each parallelogram below. Remember, Area = base x height! Show your work.

  1. Parallelogram A

    • Base = 7 cm
    • Height = 4 cm
    • Thought Process: The formula for the area of a parallelogram is base multiplied by height. I will multiply 7 cm by 4 cm.
    • Area = 28 cm²

  2. Parallelogram B

    • Base = 10 inches
    • Height = 3 inches
    • Thought Process: Using the formula, I multiply the base (10 inches) by the height (3 inches).
    • Area = 30 inches²

  3. Parallelogram C

    • Base = 6.5 meters
    • Height = 2 meters
    • Thought Process: I will multiply the decimal base (6.5 meters) by the height (2 meters).
    • Area = 13 meters²

  4. Parallelogram D

    • Base = 8 feet
    • Height = 5.5 feet
    • Thought Process: I multiply 8 feet by 5.5 feet to find the area.
    • Area = 44 feet²

Part 2: Parallelograms in 3D Shapes

Directions: Look at the 3D shapes below. Answer the questions.

(Imagine a standard rectangular box)

  1. What kind of parallelogram makes up the faces of a typical rectangular box (also called a rectangular prism)?

    • Thought Process: A rectangular box has flat sides that are all rectangles. Rectangles are a special type of parallelogram because their opposite sides are parallel and equal, and all angles are 90 degrees.
    • Answer: Rectangles (which are a special type of parallelogram).

  2. How many faces does a rectangular box have?

    • Thought Process: I can visualize a rectangular box (like a tissue box) and count its sides: top, bottom, front, back, left, right.
    • Answer: 6 faces.

  3. If a rectangular box has a front face with a base of 10 cm and a height of 5 cm, what is the area of that front face?

    • Thought Process: The front face is a rectangle, which is a parallelogram. I use the area formula: base x height.
    • Area = 10 cm x 5 cm = 50 cm²

  4. Can you think of another real-world object that has parallelogram-shaped faces (even if they are rectangles)? Describe it!

    • Thought Process: I need to think of objects that are 3D and have flat, four-sided faces where opposite sides are parallel. Many common objects fit this description.
    • Answer (Examples):
      • A brick: It's a rectangular prism, and its faces are rectangles.
      • A book: Its cover and sides are rectangular (parallelogram) faces.
      • A dresser drawer: The front panel is a rectangle (parallelogram).
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