Tossing A Die
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Approach:  One to one
ACCESS
Level: Year 8
Focus: Use probabilities for prediction  
Resources:
1 die, recording book
143kb
Questions/instructions:  
Table 1. Predictions
Number on Die How many times each number might come up in 30 tosses
1
 
2
 
3
 
4
 
5
 
6  
Imagine you threw a die 30 times.  
   
 
% responses
2009 ('05)
y4
y8
1. Fill in the table to show how many times you think each number would come up [Table 1].
Allow time.		    
Predictions: tick varied for each number but no number was given more than 10 49 (56)
prediction for each number was 5 42 (35)
any other response 9 (9)
2. Why do you think those numbers are reasonable?  
Explanation: tickshowed a clear understanding of variation in probability 3 (3)
showed expectation of an even distribution from throws 38 (34)
3. If someone put down that 12 out of the 30 would be sixes, would that be unusual or surprising?   
  yes 81 (70)
4. Why do you say that?  
Explanation: tickshowed a clear understanding of variation in probability, but indicated 12 out of 30 would be unusually high 3 (3)
showed a clear understanding of variation in probability, and thought 12 out of 30 was a reasonable possibility 4 (2)
showed an expectation that the distribution would be even 13 (8)
Table 2. Actual Amounts
Number on Die How many times each number might come up in 30 tosses

Tally Amount
1
    
2
   
3
   
4
    
5    
6    
 
5. Throw this die 30 times. Use this tally chart to record how often the numbers come up [Table 2].    
Allow time. Count the 30 throws for the student but don’t tally for them.  
Used tally system: yes, including clusters of five 79 (73)
  yes, not including clusters of five 18 (22)
Tallies totalled 30:   76 (76)
6. Why do you think there are differences between your predictions and what you actually got?  
Explanation:    
(extent to which the explanation
showed understanding of appropriate
variation in probability) 		strong 1 (1)
moderate 21 (23)
weak or no explanation 78 (76)


Total score:
 4–7
  5 (4)
3
6 (9)
2
48 (49)
1
33 (21)
0
8 (17)
Subgroup Analysis [Click on charts to enlarge] :
Year 8
Commentary:
The total score centred on understanding of randomness and probability, and few year 8 students performed well. All subgroups performed similarly.