Diamond patterns

Diamond patterns

Pencil and paperOnline interactive
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Further Resources
This task is about patterns and their rules.
 
Loretta made some patterns using green and white diamonds.
 
  diamond pattern 1
Pattern 1
  diamond pattern 2
Pattern  2
  diamond pattern 3
Pattern  3
  diamond pattern 4
Pattern  4

Question 2Change answer

a) Complete the table below to show the number of green and white diamonds that each pattern would have.  
 
Pattern Number (n) 1 2 3 4 5 6 ... 10 25
Number of Green Diamonds, (b) 3 4  
Number of White Diamonds, (w) 4 6  

Question 2Change answer

b)  i)  the number of green diamonds (b) to the pattern number (n).
          b = 
     ii)  the number of white diamonds (w) to the pattern number (n).
           w = 
c)  What pattern number would Loretta have painted if the pattern had a total of 86 white diamonds?
     Pattern number
Task administration: 
This task is completed with pencil and paper or online with some auto-marking.
Levels:
4, 5
Curriculum info: 
Maths, Number and Algebra, Patterns and relationships
Keywords: 
spatial patterns, functional rules, linear equations
Description of task: 
Students continue two number patterns of diamonds in a sequential pattern, state the general rule for the number sequences and use the rule to find the pattern number with a given number of diamonds.
Learning Progression Frameworks
This resource can provide evidence of learning associated with
Patterns and relationships, sets 5-6
Patterns and relationships, sets 6-7
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 
 

Y10 (08/2001)
a)  
12, 27 
22, 52		 very easy
 
 
 
 
very easy
moderate
b)

i)
ii)

n + 2
Accept any 1 of: 

  • 2n + 2
  • 2(n + 1)
  • n + b
  • n + answer to b)i)
  • other algebraically equivalent answers

easy
moderate
c)   42 [Accept answer which correctly uses the formula given in b) ii)]. moderate