The big ideaDoubling starts small and grows very fast, one square after another.
How it works
Doubling means twice as many each time: 1, 2, 4, 8, 16.
Sissa asked the king for rice on a chessboard: one grain on the first square, and each square holding double the one before.
It starts so small, and then it grows so fast. All ten squares held 1023 grains, about a handful of rice, but the board has 64 squares.
By the twentieth square the pile would fill a sack, and by the fortieth it would be as big as the palace.
Grains on the first eight squares.Doubling is not adding two.
Example 1: Double 4
The third square holds 4 grains.
Double 4 is 4 + 4 = 8.
So the fourth square holds 8 grains.
Example 2: Climbing the squares
Square 5 holds 16 grains, and 16 + 16 = 32.
Square 6 holds 32 grains, and 32 + 32 = 64.
Square 7 holds 64 grains.
Example 3: The tenth square to the eleventh
The tenth square holds 512 grains.
Double 512 is 512 + 512 = 1024.
The eleventh square holds 1024 grains, not 513.
Example 4: Empty squares
The board has 64 squares.
Ten are used, so 64 − 10 = 54.
Fifty-four squares are still empty.
Words to know
double
Twice as many.
doubling
Twice as many each time: 1, 2, 4, 8.
grain
One tiny piece of rice.
square
One of the 64 places on the board.
Watch out
Doubling is not adding two each time. Adding two goes 2, 4, 6, 8, but doubling goes 2, 4, 8, 16.
Doubling is not adding one: after 512 comes 1024, not 513.
A small start can fool you. Ten squares were only a handful of rice, but the board has 64.
This is a folk tale about grains of rice. There is no money in it.
Try it
The fourth square holds 8 grains. How many go on the fifth?
Does 2, 4, 6, 8 double each time?
The tenth square holds 512 grains. How many on the eleventh?
The board has 64 squares and ten are used. How many are empty?
Answers: 1. 16 · 2. No · 3. 1024 · 4. 54
Try at homeWith a grown-up, fold a paper in half again and again and count the layers. That is doubling!
For grown-upsTry it with paper: fold a sheet in half again and again, and count the layers together. This is a story about growing very fast. There is no money in it.
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