Finding the rule for the pattern

Finding the rule for the pattern

Pencil and paper
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Working with Students
Further Resources
This task is about writing rules for spatial patterns.
a)
 
Shape 1 Shape 2 Shape 3 Shape 4
 

 
The number of dots in each shape follows the pattern: 4, 8, 12, 16, . . .
 
Complete this equation to describe the number of dots in this pattern:
 
dn = __________________
dn is the number of dots in shape n,
n is the shape number.
 
 
b)
 
Shape 1 Shape 2 Shape 3 Shape 4
 

 
The number of straight lines in each shape follows the pattern: 4, 7, 10, 13, . . .
 
Complete this equation to describe the number of straight lines in this pattern:
 
ln = __________________
ln is the number of straight lines in shape n,
n is the shape number.
 
 
c)
 
Shape 1 Shape 2 Shape 3 Shape 4
 

 
The number of crosses in each shape follows the pattern: 4, 6, 8, 10, . . .
 
Complete this equation to describe the number of crosses in the pattern:
 
sn = __________________ 

sn is the number of crosses in shape n,
n is the shape number.
Task administration: 
This task is completed with pencil and paper only.
Level:
5
Curriculum info: 
Maths, Number and Algebra, Patterns and relationships
Keywords: 
spatial patterns, number patterns, functional rules, linear equations
Description of task: 
Students complete equations that give the rule for the general term for a number of spatial patterns.
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) 4n moderate
b) 3n + 1 difficult
c) 2n + 2 difficult
 
NOTE: 
 		  
Accept any algebraically equivalent expressions for a), b) or c) especially
 
  b)
 
 
c)		 4 + 3(n-1)
4n -(n-1)
 
4 + 2(n-1)
4n - 2(n-1)
2(n-2) + 6
 
  Accept if the multiplication sign is included e.g., accept 4n, 4 × n or n × 4 etc.
Diagnostic and formative information: 
  Common error Likely reason

a)
b)
c)

n + 4
n + 3
n + 2

Writes "n plus the number of extra dots, lines or crosses required to get the next shape".