Continue the shape patterns

Continue the shape patterns

Pencil and paper
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Working with Students
Further Resources
This task is about continuing and explaining the rule for growing shape patterns.
a) i) Draw the next two shapes in this pattern. 
   
  ii) Explain how you worked out what shapes to draw.

 
 
 
 
 
b) i) Draw the next two shapes in this pattern. 
   
shape 1 shape 2 shape 3 shape 4 shape 5
stick pattern stick pattern
stick pattern		 stick pattern
stick pattern
stick pattern		    
  ii) Explain how you worked out what shapes to draw.

 
 
 
 
Task administration: 
This task is completed with pencil and paper only.
Level:
2
Curriculum info: 
Maths, Number and Algebra, Patterns and relationships
Key Competencies: 
Using language, symbols, and texts
Keywords: 
spatial patterns, growing patterns, rules, functional rules, recursive rules
Description of task: 
Students find the next three shapes in several growing shape patterns and explain how they worked out the shapes.
Curriculum Links: 
Key competencies
This resource involves describing how to continue a spatial pattern. This relates to the Key Competency: Using language, symbols and text.
For more information see http://nzcurriculum.tki.org.nz/Key-competencies
Learning Progression Frameworks
This resource can provide evidence of learning associated with
Patterns and relationships, set 3
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 
      Y4 (06/2009)
a) i) and    very easy
  ii) Functional rule:
An explanation that links the shape number with the number of spikes.
or Recursive rule:
Any 1 of:

  • "Add 1 more spike each time";
  • "Add 1 more each time" but doesn't mention the actual shape (spike)
  • Worked it out by counting

Both shapes drawn correctly and a correct explanation.

 moderate
b) i) very easy
ii) Functional rule:
An explanation that links the shape number with the number of squares or "" shapes.		 moderate
Recursive rule:
Any 1 of:

  • "Add 1 more square (or ) each time";
  • "Add 1 more each time" but doesn't mention the actual shape.
  • Worked it out by counting.

Both shapes drawn correctly and a correct explanation.

 very difficult
Teaching and learning: 
  Common error Likely misconception
a) i) Comprehension
Student does not follow the instructions.
a) i)

b) i)

and

and
             

 Repeats pattern
Student does not recognise the repeating part ("set" or "chunk") of the pattern and repeats the pattern from the beginning of the sequence that is given.
b) i)
Functional rule:
An explanation that links the shape number with the number of squares or "" shapes.
or 
Recursive rule:
Any 1 of:

  • "Add 1 more square (or ) each time";
  • "Add 1 more each time" but doesn't mention the actual shape.
  • Worked it out by counting.

Both shapes drawn correctly and a correct explanation

 Sees two extra pieces as a square
Student sees the "set" or "chunk" as a square, but omits the "" under the squares, or sees it as a complete square.
a) ii)
b) ii)		 Statements such as: "Seeing the pattern";
"Carrying on the pattern"; or "Doing the same".		 Cannot adequately write the rule for the pattern
Student may be able to see the pattern, but cannot write a description of how the pattern progresses.
a) ii)
b) ii)		 Statements about couting. Counting
Gives the pattern of the shape numbers rather than the actual shape; e.g. I just counted the first 3 shapes then kept on going to shape 5. There was a pattern to 5. It went 1, 2, 3, 4, 5

For more information about algebraic patterns, see the Algebraic Patterns Concept Map.