Geometry: Circles & Discovering Pi

Calculating the Ratio of Diameter to Circumference (Pi)

This week we made a big discovery — the number π (pi)

We began with a question: How many times does the diameter of a circle fit around its edge?

First, we reviewed the parts of a circle using our three-part geometry cards — radius, diameter, and circumference. The children recorded what they learned in their geometry notebooks, sketching circles and labeling each part.

We collected circles of different sizes — lids, and a wagon wheel. The children rolled each one, marking how far it traveled in one complete turn. That distance represented the circumference.

Next came the measuring and comparing: how many “diameters” long was that rolled-out distance? After careful observations, we discovered — no matter the size of the circle, it always took three diameters... and a little bit more to go all the way around. That “little bit more” is what mathematicians call pi (π) — about 3.14.

Exploring Prefixes

The Prefix

Word study this week involved prefixes — those small but powerful parts added to the beginning of root words that change their meaning.

Some of us took on a self-directed challenge, finding as many prefix–root word combinations as they could from the books they’re reading. Others researched the meanings of different prefixes or used the hands-on prefix matching material to build and decode new words.

Exploring Energy: Mechanical: Gears

This week we shifted our focus from our study of matter to energy. We explored different forms of energy and watched a short film on mechanical energy, discovering that potential energy is stored energy (like pausing at the top of a roller coaster) and kinetic energy is the energy of motion. We also examined how energy can be transformed from one form to another.

Later in the week, we studied gears as an example of mechanical energy in action. We watched a film with the lock system on the Ottawa canals, looked at bike gears, and discussed how gears transfer motion between parts. Ignatius extended this study by analyzing different gear ratio combinations (1:2, 1:3, etc.) to calculate and observe how the rotation of one gear affects another. Through this exploration, we discovered that common multiples are used to determine gear ratios.

Energy Classification

Since we didn't have a 3D printer to make our own gears, some students watched this video to discover the gear ratio formula https://youtu.be/idqq_VPChic?si=aIJ9FTI7fTVR5fQy

The 5 Layers of the Atmosphere

The children were interested to learn how temperature changes direction as we move farther from Earth and to discover what exists in each layer — from weather and clouds in the troposphere to satellites orbiting in the exosphere. Students created definitions and illustrated their work to show their understanding of each layer.

Layers of the Atmosphere