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Ever wondered how to teach cross sections of 3D figures in an engaging way to your 7th grade students?

In this lesson plan, students will learn about slicing prisms and pyramids and their real-life applications. Through artistic, interactive guided notes, check for understanding, a practice coloring worksheet, and a maze worksheet, students will gain a comprehensive understanding of cross sections of 3D figures.

The lesson culminates with a real-life example that explores how this math skill is used in real-world situations.

- Standard: CCSS 7.G.A.3
- Topic: Surface Area & Volume
- Grade: 7th Grade
- Type: Lesson Plans

$4.25

After this lesson, students will be able to:

Identify different two-dimensional figures resulting from slicing three-dimensional figures.

Recognize and describe plane sections of right rectangular prisms and right rectangular pyramids.

Connect the concept of cross sections to real-life applications in various fields.

Before this lesson, students should be familiar with:

Basic geometric shapes such as squares, rectangles, triangles, and circles

Understanding of three-dimensional shapes such as prisms and pyramids

Pencils

Colored pencils or markers

Cross sections

Three-dimensional figures

Two-dimensional figures

Right rectangular prisms

Right rectangular pyramids

Plane sections

Base

Vertical slices

Horizontal slices

As a hook, ask students why it is important to understand cross sections of three-dimensional figures. Invite them to think about the ways in which cross sections are used in real life. For example, ask them to consider how geologists use cross sections in studying rocks or how doctors use cross sections in medical imaging.

Use the first page of the guided notes to introduce the concept of cross sections and plane sections of 3D figures. Explain that a cross section is the shape that is created when a three-dimensional figure is cut by a flat surface, or a plane. Emphasize that cross sections can be vertical or horizontal, parallel or perpendicular plane, and that they can result in different two-dimensional figures depending on the orientation of the cut.

Walk through the key points of the topic of the guided notes, highlighting the vocabulary and important concepts. Show examples of different types of cross sections, such as slicing a triangular prism parallel to the base to create a triangle or perpendicular to the base to create a rectangle. Explain that the shape of the cross section depends on the shape of the original 3D figure (base and lateral faces) and the orientation of the cut. Then, move onto the second page of the guided notes to have students complete the practice examples in groups.

Refer to the FAQ section below for a walk through on how to respond to common student questions. Anticipate questions and misconceptions that students may have, such as whether all cross sections of a prism are rectangles or whether a vertical cross section of a pyramid will always be a triangle.

Based on student responses, reteach any concepts that students need extra help with. If your class has a wide range of proficiency levels, consider pulling out students for reteaching while more advanced students begin work on the practice exercises.

Have students practice identifying two-dimensional figures resulting from slicing three-dimensional figures using the maze (page 3 of the guided notes). Walk around the classroom to answer any student questions and provide support as needed.

Fast finishers can then complete the color by number activity (page 4 of the guided notes) for extra practice. You can assign it as homework for the remainder of the class.

Bring the class back together, and introduce the concept of real-life applications of cross sections of 3D figures. Explain that understanding how to identify plane sections of 3D figures has practical uses in various fields and industries.

Some examples of real-life applications of cross sections include:

Medical Imaging: Medical professionals use imaging techniques such as CT scans and MRI to produce cross-sectional images of the human body. These images help doctors diagnose diseases, plan surgeries, and monitor the progress of treatments.

Geological Studies: Geologists use cross sections to analyze the layers and structures of the Earth's crust. By studying cross sections of rock formations, geologists can determine the history and composition of different geological features.

These are just a few examples of how cross sections of 3D figures are used in real-life applications. Encourage students to think about other areas where cross sections might be important. Refer to the FAQ section of the resource for additional ideas on how to teach this concept in a real-life context.

If you're looking for digital practice to reinforce the concepts of slicing 3D solids, try these Pixel Art activities in Google Sheets. Every answer is automatically checked, and correct answers unlock parts of a mystery picture. It's incredibly fun and a powerful tool for differentiation.

Here are some activities to explore:

A fun, no-prep way to practice cross sections of 3D figures is Doodle Math — they’re a fresh take on color by number or color by code. It includes multiple levels of practice, perfect for a review day or sub plan.

Here are some activities to try:

Cross sections of 3D figures are two-dimensional shapes that result from slicing or cutting through a three-dimensional object with a flat surface called a plane.

To identify cross sections of 3D figures, you need to examine the shape that is formed when a plane intersects the 3D figure. Look for the resulting two-dimensional shape.

Cross sections help us understand 3D figures by giving us a way to visualize and analyze different parts of the figure. They allow us to see the internal structure and shape of the object.

Some examples of cross sections of 3D figures include circles, rectangles, triangles, and irregular shapes. The specific shape of the cross section depends on how the plane intersects the 3D figure.

The type of cross section formed depends on the orientation of the plane in relation to the 3D figure. Here are some common types of cross sections:

If the plane slices through the figure parallel to the base, the cross section is a similar shape to the base.

If the plane slices through the figure at an angle, the cross section is an irregular shape.

Vertical cross sections are formed when a plane intersects a 3D figure in a vertical direction, while horizontal cross sections are formed when a plane intersects the figure in a horizontal direction. The resulting cross sections will have different shapes and orientations.

Cross sections are frequently used in architecture, engineering, and manufacturing to understand how 3D objects will be cut, assembled, or analyzed. They are also used in medical imaging to visualize internal structures of the body.

To teach students about cross sections of 3D figures, you can use hands-on activities, visual aids, and guided notes. Engage students with real-life examples and encourage them to explore and analyze various cross sections.

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