Download “The Locker Game” Performance Task

“The Locker Game”
Performance Task
4.OA.4  Find all factor pairs for a whole number in the range 1-100. Recognize that a whole
number is a multiple of each of its factors. Determine whether a given whole number in the
range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number
in the range 1-100 is prime or composite.
Math Practice Standard 7: Look for and make use of structure.
Math Practice Standard 8: Look for and express regularity in repeated reasoning.
Performance Task: The 20 students in Mr. Wolf’s 4th Grade Class
are playing a game in a hallway that is lined with 20 lockers in a
row.
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2
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10 11 12 13 14 15 16 17 18 19 20
The 1st student starts with the first locker and goes down the hallway and OPENS ALL
the lockers.
The 2nd student starts with the second locker and goes down the hallway and SHUTS
EVERY OTHER locker.
The 3rd student stops at every third locker and opens the locker if it is closed AND closes
the locker if it is open.
The 4th student stops at every fourth locker and opens the locker if it is closed AND
closes the locker if is open.
This process continues until all 20 students in the class have passed through the
hallway.
Questions:
1. Which lockers are still open at the end of the game? Explain your reasoning.
2. Which lockers were touched by only 2 students? Explain your reasoning.
3. Which lockers were touched by only 3 students? Explain your reasoning.
4. Which lockers were touched the most?
Scoring Rubric
4.OA.4  Find all factor pairs for a whole number in the range 1-100. Recognize that a whole
number is a multiple of each of its factors. Determine whether a given whole number in the
range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number
in the range 1-100 is prime or composite.
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2
3
4
Recognize that whole
Determine whether a
Find factor pairs for
Identify specific
numbers have countgiven whole number in whole numbers in the
features of a pattern
by’s and/or multiples.
the range of 1-100 is
range of 1-100.
in a problem with
a multiple of a given
reasoning and
one-digit number.
Identify apparent
explanation.
features of a pattern
Generate a shape
in a problem with
pattern that follows a
scaffolding.
given rule.
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