Pythagoras in Space – Applying the Theorem in 3D Contexts

Description:

Pythagoras in Space is a collaborative worksheet that introduces students to the application of the Pythagorean Theorem in three-dimensional geometry, specifically in calculating a space (body) diagonal of a 3D shape.

Through hands-on exploration with a physical wire model and guided steps, learners:
- Identify and draw the 3D shape using parallel projection
- Measure and annotate edge lengths
- Use multiple 2D projections to break down the 3D problem
- Apply the Pythagorean Theorem twice to first find a face diagonal, then the full space diagonal
- Compare their calculated results with a real-life measurement for validation

The activity links to Kerndoelen 24 and 26:
- Understanding and applying measurements and dimensions
- Visualizing and calculating with 2D and 3D figures

From a CLIL perspective, this task:
- Builds mathematical language fluency (e.g. face, diagonal, edge, measurement, length)
- Supports structured reasoning and step-by-step explanation

Encourages the use of functional language for collaboration, such as:
"We still need to find the length of..."
"According to the Pythagorean Theorem..."
"Let’s compare the calculated length with the string measurement."

It also promotes interactive learning, spatial reasoning, and oral and written language production in English — making it a strong example of task-based CLIL in mathematics.