Title – Certain or Impossible "less than" Logic Problem
Idea

By – Shantal Turner

Primary Subject – Math

Grade Level – 3th

Definitions:

• An event is something that
  
  may
  
  happen
• An event is
  
  certain
  
  if it will
  
  always
  
  happen
• An event is
  
  impossible
  
  if it will
  
  never
  
  happen.

Problem:

• Daniel made this spinner for a game.
• Is it impossible or certain that he will spin a number less than 5 on his
  spinner?
  =

Solution:

• Ms. Turner did not offer a solution to her problem and only titled it "Certain
  or Impossible." How fun! Be sure to find your own solution before looking
  at what we came up with below, which may not be the intended solution at
  all!

Possible Solutions (offered by LessonPlansPage.com):

• Whoops:
  • 
    Impossible
    
    : "This" spinner? What spinner? You can’t
    actually spin a number on an imaginary spinner.
  • 
    Neither
    
    : Without knowing what numbers are on the spinner, it
    is impossible to determine if the event is "certain" or "impossible".
    You need to know what number the spinner landed on in order to determine
    if that number is less than, greater than, or equal to the number 5.

• If you make an actual spinner to show the kids with
  
  numbers 1-4
  
  on
  it:
  • Neither: it is not actually certain that he will ever spin the spinner,
    but if he did…
  • Neither: if he spins the spinner, it could actually hit the line.
  • 
    Certain
    
    : if he spins the spinner and it doesn’t hit the line,
    it will always hit a number less than 5, because 1, 2, 3, and 4 precede
    5 on a number line and stand for a value that is less than 5.

• If you make an actual spinner to show the kids with
  
  numbers 5-8
  
  on
  it:
  • 
    Impossible
    
    : It will never hit a number less than 5.
    
  • Note: even if it hits a line or he never spins, it still can never
    hit a number less than 5, because 6, 7, and 8 are greater numbers and
    stand for greater values than 5.

• If you make an actual spinner to show the kids with
  
  numbers 1-6
  
  on
  it:
  • 
    Neither
    
    :
    • It is not impossible, because it could land on 1, 2, 3, or
      4 if he spins an actual spinner with the numbers 1-6 on it.
    • It is not certain, because it could land on 5, 6, 7 or 8 which
      are equal to or greater than 5.
    • It is also not certain, because it could land on the line or
      he could choose to throw away the spinner and never use it.

• If you make an actual spinner to show the kids with all spots labeled with
  the
  
  number 5
  
  on it:
  • 
    Impossible
    
    : It will never hit a number less than 5, because
    5 equals 5, it can never be less than itself.
    • Note: even if he never spins or it hits the line, it will still
      never hit a number less than 5.

• If you make an actual spinner to show the kids with all spots labeled with
  the
  
  number 1
  
  on it:
  • 
    Certain
    
    : If he spins the spinner and it never hit the line,
    he will always hit a number less than 5, because 1 is less that 5.

Notes from LessonPlansPage.com:

• This is a great logic problem if your students have a great grasp of number
  sense and the concepts of less than, greater than, and equal to.
• It would make a great extension for gifted learners.
• If less than, greater than, and equal to is the concept you are trying
  to teach, be sure to draw an actual spinner on the board and then put on
  the numbers that you want them think about. Also, be sure to say that the
  spinner never hits the line (because the line is too thin and the pointer
  is very big).

E-Mail

Shantal Turner

!