Two dice game II

Two dice game II

Pencil and paper
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
This task is about predicting, then recording, the outcome of a game of chance.
 
How to do this task

When two dice are thrown you can multiply the two numbers together to get a product.
 
   dice-3-md-12-ii.png  dice-5-md-120.png

Example: 3 x 5 = 15
a)
Predict the probability that the product of the two top numbers on the dice is less than 10 (i.e., 1-9) __________
 
b)
Now throw two dice yourself.
 
On the tally chart below, record whether the product of the two top numbers on the dice is less than 10, or 10 or more.
Repeat this 100 times altogether.  
 
 

Product of two dice

Tally

Frequency

i) Less than 10 (i.e., 1-9)

    

ii) 10 or more (i.e., 10-36)

    
 
c)
 
Use your results in b) to work out the probability of the product being less than 10. __________
 
d)
Comment on how accurate your prediction was.
 
 
 
 
 
 
 
 
Task administration: 
Equipment     
Two dice.
 
Administration of task
  • Model how to give the dice a thorough shake between throws.
  • Get students to make a quick intuitive prediction of the probability in a) and assure them there are no marks for their prediction. Remind them that probability is a number or fraction between 0 (impossible) and 1 (certain), or a percentage between 0% (impossible) and 100% (certain).
Level:
4
Curriculum info: 
Maths, Statistics, Probability
Key Competencies: 
Using language, symbols, and texts
Keywords: 
probability, prediction, fair games, experiments
Description of task: 
Students predict the probability about the product of two dice and test their prediction by conducting an experiment that estimates the probability.
Curriculum Links: 
This resource can be used to help to identify students' understanding of comparing experimental situations with predictions of  outcomes.
 
Key competencies
This resource involves communicating the findings of a probability experiment, which relates to the Key Competency: Using language, symbols and text.

For more information see https://nzcurriculum.tki.org.nz/Key-competencies

Learning Progression Frameworks
This resource can provide evidence of learning associated with
Interpreting statistical and chance situations, sets 4-5
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 

a)

  

b)

Results recorded in correct tally format (i.e., ) or some other 
systematic way of grouping. Do not accept .
Frequencies recorded and they sum to 100.

c)

Probability given consistent with b) as either a fraction, decimal, or percentage, i.e., frequency in b)i) ÷ 100.

d)

Sensible comparison, e.g., "My prediction was very close", etc.

NOTE:

  • The theoretical probability for c) is 17/36 = 0.4722.
  • The result in c) is most likely (95% sure) to be between 0.37 and 0.57 if the dice are fair and are thrown fairly.
  • Pool the results over 10-15groups who have each played the game 100 times. Most groups will have results between 0.44 and 0.50. Ths indicates the game is not fair.