Study Guide: Pattern Problems

These web-based activities were developed, during summer sessions from 1997 through 1999, by students at Mainland High School, located in Daytona Beach, FL. As part of Mainland's CCTT grant, the students were given permission by the book's publisher to convert the ancillary materials of the County's adopted Algebra 1 textbook (Glencoe Algebra 1 — ISBN: 9780028253282) into html format.

Study Guide:

Some problems have a pattern in them. To solve the problem, you need to recognize the pattern and read the directions carefully. Study the example below.

Question: Dan is playing on a ladder. He takes four steps up and then 1 step back. The ladder has 19 rungs on it. How many times will Dan go up the ladder until he reaches the top?

Solution: The pattern is up 4, down 1, up 4, down 1 etc. To work this problem, start at 0, and follow the pattern.

	15	+ 4	= 19	Dan reaches the top
	16	- 1	= 15
	12	+ 4	= 16
	13	- 1	= 12
	9	+ 4	= 13
	10	- 1	= 9
	6	+ 4	= 10
	7	- 1	= 6
	3	+ 4	= 7
	4	- 1	= 3
Dan starts at the bottom	0	+ 4	= 4

Answer: He went UP (+4) 6 times to reach the top.

Follow the pattern in the following three problems to find each solution.

1. Two men were digging a well. Each day they dug down 10 feet. Each night wild dogs would come by and push 2 feet of dirt back in. How many days did it take them to dig a 50 foot well?

2. Tim was running up an escalator that was moving down, UP the DOWN staircase! Every time he ran up 5 stairs, the escalator brought him down 1. How many extra stairs did he have to climb to get as high as the 21st step had the escalator been shut off?

3. Emilio had his boat anchored 30 yards from shore while he lay on the beach. When he tried to swim back to his boat, the tide was coming in. Every time he swam 5 yards forward, the waves brought back 3 yards toward shore. How many yards does he have to swim to reach his boat?