Elementary Pull-Out: The Great Wall of China

The Elementary Mathematician, COMAP's award-winning K-6 newsletter is available for the first time in electronic format. Each issue contains a collection of K-6 mathematic lessons that are fun to teach and exciting to learn.

Each issue of The Elementary Mathematician contains a Pull-Out section which includes thematic lessons based on the national census, wildlife, other cultures, technology, and provides a practical way to bring the concepts and pedagogy of the NCTM Standards into your classroom. 

Note: The information below was created with the assistance of AI.

Level of Mathematics
This activity targets upper elementary to early middle school students. Specifically:

Grade Levels: 4–7

Mathematical Complexity: Moderate

Introduction and application of the Pythagorean Theorem (usually introduced in Grade 8, but simplified here for context)

Use of ratios and proportions for scale modeling

Unit conversion (inches to feet, feet to yards, miles)

Basic geometry and measurement (length, height, tapering widths)

Prerequisite Skills
Students should have familiarity with:

Basic arithmetic (multiplication, division)

Understanding of units of measure (inches, feet, yards, miles)

Simple fractions and decimals

Calculator usage for multi-step computation

Graph paper usage for scaling and layout

Understanding of right triangles and introductory geometry

Application Areas
The activity integrates mathematics with multiple domains:

History and Culture

Explores the architectural and historical significance of the Great Wall of China.

Engineering and Design

Students model a section of the wall to scale and evaluate its dimensions.

Encourages spatial reasoning and visualization skills.

Scale Modeling

Develops practical skills in drawing to scale and understanding proportional relationships.

Technology Integration

Use of calculators for precise calculations and to explore alternative scales.

Research and Analysis

Students compare the Great Wall’s dimensions to global landmarks (e.g., Moon distance, Earth's circumference).

Subject Matter and Key Topics
Mathematical Concepts:

Pythagorean Theorem (applied to slant height of the wall)

Scale Conversion: 1/4 inch = 5 feet

Ratio and Proportion

Measurement and Geometry

Estimation and Large Number Comprehension

Dimensional Analysis

Cross-Disciplinary Topics:
Geography & World Cultures: Facts about China and the Great Wall

STEM Connections: Using math to understand large-scale engineering

Correlation to Mathematics Standards
The activity aligns with several Common Core State Standards (CCSS) and National Council of Teachers of Mathematics (NCTM) content areas:

Common Core State Standards (CCSS) Examples:

CCSS.MATH.CONTENT.5.MD.A.1: Convert among different-sized standard measurement units.

CCSS.MATH.CONTENT.6.RP.A.3: Use ratio and rate reasoning to solve real-world problems.

CCSS.MATH.CONTENT.7.G.B.6: Solve real-world and mathematical problems involving area, volume, and surface area of two- and three-dimensional objects.

CCSS.MATH.CONTENT.8.G.B.6: Explain a proof of the Pythagorean Theorem and its converse.

NCTM Content Standards:

Measurement: Apply appropriate techniques, tools, and formulas to determine measurements.

Geometry: Analyze characteristics and properties of two- and three-dimensional geometric shapes.

Problem Solving: Solve problems that arise in mathematics and in other contexts.

Connections: Recognize and apply mathematics in contexts outside of mathematics.