Pyramid
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Approach:  One to one  
Level: Year 8
Focus: Patterns/spatial relationships  
Resources:
Ball pyramid, recording book
152kb
Questions/instructions:  
Have a look at this pyramid made of balls. You can pick it up if you want to. You can use pencil and paper if you need to.
   
 
% responses
2009 ('05)
y4
y8
1. How many balls make up the pyramid? 30   54 (63)
2. How many balls are hidden in the middle? 1 25 (25)
3. If another layer is added to the bottom of the pyramid, how many more balls would be needed to make the new layer? 25 37 (41)
4. Describe how you got that answer.  
clear explanation with 5 × 5 calculation 32 (27)
clear explanation of thinking process 3 (9)
some explanation but not clear 4 (5)

Total score:
4
  24 (24)
3
9 (11)
2
3 (5)
1
28 (29)
0
36 (31)
Subgroup Analysis [Click on charts to enlarge] :
Year 8


Commentary:
The instruction for question 2 was interpreted in various ways by students so the results for that question were not included in the total score. Performance was similar in 2005 and 2009.