A Strike on the Carrom Board
Carrom, the game behind this number line.
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A strike sends a coin a certain distance in one direction. That distance and direction is what we write as an integer.
Turn each carrom strike into a positive or negative number, find where the coin lands with P = a + b, and read jump diagrams.
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How each carrom strike becomes a number with a direction.
A carrom coin starts at 0. The first strike moves it 4 units right. The second moves it 3 more units right.
It ends at .
Carrom, the game behind this number line.
A strike sends a coin a certain distance in one direction. That distance and direction is what we write as an integer.
The book's example: where does the coin land after +5 and −7?
Problem. The coin is at 0. The first strike moves it 5 units right. The second strike moves it 7 units left. Where does it stop? (Textbook p. 26)
P = a + b, with signs for direction.
Work out the second movement from the first move and the final position.
Textbook p. 26, Question 1: the first movement is −4 and the final position is 5. What is the second movement?
Use P = a + b: 5 = −4 + .
Check: −4 + 9 = .
So the second strike moved the coin units to the .
Quick coin questions, including a long chain of strikes.
Strikes move the coin in the order . Where does it end? (Textbook p. 27, Q2)
A movement like −4 tells you two things: how far and which way.
When we write a movement as a positive or negative number, it carries two things:
For , the magnitude is 4 and the direction is left. For , the magnitude is 7 and the direction is right.