Patterns and rules

Patterns and rules

Pencil and paper
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Working with Students
Further Resources
This task is about using different rules to continue number patterns.
 

a)

 

 i)

 
Work out the rule and fill in the boxes to complete the number pattern below.


 4,
8,
 ,
 ,
 ...
  ii)

 

 How did you complete the pattern?
 

 
 
b)

 

 i)

 

 Using a different rule to question a), fill in the boxes to complete another number pattern below.


 4,
8,
 ,
 ,
 ...
  ii)

 
How did you complete this pattern?
 
 
 
Task administration: 
This task is completed with pencil and paper only.
Level:
3
Curriculum info: 
Maths, Number and Algebra, Patterns and relationships
Keywords: 
number patterns, rules
Description of task: 
Students complete number sequences, and identify different rules for sequences that begin with the same numbers.
Learning Progression Frameworks
This resource can provide evidence of learning associated with
Patterns and relationships, sets 4-5
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 
    Y6 (09/1998)
a)
 		 i) 12, 16, 20
ii) add four		 very easy
easy
b)

 

 i) 16, 32, 64
ii) multiply by two (or double)
Accept:

  • 13, 19, 26 and +4, +5, +6, +7 (increasing by an incrementing amount); and
  • 12, 20, 32 and 4+8=12, 8+12=20, 12+20=32 (Fibonacci pattern);
  • Other sequences with a rule stated and consistently applied.
 moderate

Based on a representative sample of 192 students.

NOTE: Answers for a) and b) are interchangeable.

Next steps: 
Encourage students to find a general rule that applies to all numbers in the sequence/pattern, and explore the use of operators other than addition when identifying rules for sequences.