Turbine patterns

Turbine patterns

Pencil and paper
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Further Resources
This task is about continuing a pattern and describing a rule for the pattern.
 
turbine patterns on a triangular grid
 
The shapes above are called turbines. Each turbine has 3 blades.
 
a)
Draw in the next two shapes in this series.
 
b)
Complete this table.  
 
Shape number (s)
1
2 
3
4
5
i)   Number of little triangles in each blade
1
4
      
ii)  Number of little triangles in the whole shape
3
12
      
 
c)		  
Complete the rule for each row of the table.
 
  i) 
The number of little triangles in each blade of shape number
 
s = ______________________________
 
  ii)
The number of little triangles in the whole of shape number
 
s = ______________________________
 
d) How many triangles would there be in shape number 8?   __________
Task administration: 
This task is completed with pencil and paper only.
Copyright: 
Graphic copyright: NZCER
Level:
5
Curriculum info: 
Maths, Number and Algebra, Patterns and relationships
Keywords: 
spatial patterns, functional rules, quadratic equation
Description of task: 
Students draw in the next two shapes in a spatial pattern, complete a table and rules about the pattern, then calculate the number of triangles in the 8th shape.
Learning Progression Frameworks
This resource can provide evidence of learning associated with
Patterns and relationships, sets 6-7
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 
 

   

Y10 (10/2000)

a)

  

2 correct - easy
 
1 correct - very easy

b)

i)
ii)

9, 16, 25 [Accept if consistent with a)].
27, 48, 75 [Accept if consistent with b)i)].

easy
easy

c)

i)
 
ii)
s2 [Accept if consistent with b)].
[Do not accept "number in a blade ¸ 3"].
3s2 [Accept 3 × c) i)].
[Accept "number in a blade × 3"].
[Accept i) or ii) if a different pronumeral than s is used or if "shape number" used instead of s].

difficult

 

 

difficult

d)

  

192 [accept if consistent with c) ii)].

difficult

NOTE:

Accept if another consistent pattern is given, especially if the blade lengths follow the pattern 1, 2, 4, 8, 16 ... The answers are then:
 

b)
 

i)
ii)

16, 64, 256
48, 192, 768 
  c) i) 4 (s-1)
    ii) 3 × 4 (s-1)
  d)
 		 49 152