Smita’s Worksheet
by a80e00d3_admin
Q12: The Beehive Pattern Builder
Look Smita, they’re trying to throw you off with shapes. But a shape is just a number sequence wearing a disguise. Use the simulator below to build the chain and prove the pattern yourself.
The Setup: We only care about the outer perimeter sides of the final shape. When hexagons connect, the sides in the joint get covered.
Hexagons: 1
Outer Sides: 6
a) Complete the table.
Hint: Use your findings from the visual simulator above. Once you know the jump between 1 and 2 hexagons, apply it to 10 and 100!
| Number of hexagons | 1 | 2 | 3 | 10 | 100 |
|---|---|---|---|---|---|
| Number of sides |
b) Find the formula for $x$ hexagons.
Hint: You saw it visually. The first hexagon starts with 6. Every new hexagon covers 2 sides and adds 4 new outer edges. How do we turn “+4, starting from 6” into a formula?
