The Apparatus

The Decimal Checkerboard & Color Hierarchy

The Mirror Kingdom

The Unit is the King. Everything reflects out from the center.

Whole #
"Colors Darken" (Spheres)
Decimal
"Colors Lighten" (Cubes/Disks)

The Board

1k
100
10
1
0.1
0.01
0.001

"The colors guide the child. Blue always means 'Ten-ness', whether it's 10 or 1/10."

0.2 × 0.3

"I have 2 tenths. I need to multiply it by 3 tenths. But... I don't think I can do that with my materials. I would have to cut my cubes into pieces."

🔪🧊

PHYSICAL LIMIT

"We can't cut the beads!"

The Guide's Simulation

Follow the script & actions

Action

"Move the decimal card to the right."

0.6 → 6

Guide's Script

"If we multiply our multiplier by 10, we make it a whole number. But to keep the problem fair, we must divide our multiplicand by 10."

Why? To allow us to use whole beads instead of cutting them.

Multiplying 6 Thousandths (x6)

"Count with the children. Do not pre-count!"

0 / 6

The Exchange

"Let's follow our rule of 10. Ten thousandths can be exchanged for..."

Wait for the child to answer! Point to the Green beads and trace the line to the Red beads.

10 Thousandths → 1 Hundredth

Trainer's Warning: The "Pre-Counting" Trap

"In the video, I pre-counted the beads to save time. Do not do this."

"Counting out the beads is where the child builds the memory of the quantity. If you prep it for them, you steal the learning moment."