Chain of numbers

Chain of numbers

Pencil and paper
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
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Further Resources
This task is about continuing number patterns and finding a rule.
A chain of numbers begins: 1  3
This could be continued several ways.
 
a)
1  3  5  7  9
 
What is the rule for continuing this chain? ____________________________________
 
b)
1  3  9  27  81
 
What is the rule for continuing this chain? ____________________________________
 
c)
1  3  7  15  31  63
 
What is the rule for continuing this chain? ____________________________________
 
d) i)
Make up a different chain by writing down the next three numbers.
The chain starts with: 1  3 and keeps getting bigger.
 
1 3      
 
  ii) Write the rule for the chain you have written.

 
 
 
 
Task administration: 
This task is completed with pencil and paper only.
 
Level:
4
Curriculum info: 
Maths, Number and Algebra, Patterns and relationships
Keywords: 
number patterns, recursive rules
Description of task: 
Students identify the rule for continuing number patterns then develop their own pattern and write it as a rule.
Learning Progression Frameworks
This resource can provide evidence of learning associated with
Patterns and relationships, sets 5-6
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 
  Y8 (09/2000)
a) Any 1 of:

  • Add on 2.
  • Next odd number.
  • Other rules which work.
 very easy
b) Any 1 of:

  • Multiply the last number by 3.
  • Other rules which work completely.
 easy
c) Any 1 of:

  • Multiply last number by 2 and add 1.
  • Add 2, add 4, add 8, add 16, ...
  • Other rules which work completely.
 moderate
d) i) Any sequence different from a), b) or c). Most likely ones are:

  • 6, 10, 15 (add 2, add 3 add 4 etc).
  • 7, 13, 21 (add 2, add 4, add 6 etc).
  • 11, 43, 171 (times 4 and minus 1).

ii) Correct rule given that works completely.

 difficult
Diagnostic and formative information: 
 

Common error

Likely reason

d) i)
    ii)

6, 9, 12
add 3

Uses rule that does not work for first two members of the sequence (i.e., 1, 3)