# Cross Sections of 3D Figures Prisms & Pyramids Lesson Plan

## Overview

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.

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## Learning Objectives

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.

## Prerequisites

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

## Key Vocabulary

• Cross sections

• Three-dimensional figures

• Two-dimensional figures

• Right rectangular prisms

• Right rectangular pyramids

• Plane sections

• Base

• Vertical slices

• Horizontal slices

## Procedure

### Introduction

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.

### Practice

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.

### Real-Life Application

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:

1. 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.

2. 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.

## Extensions

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: