Building patterns

Building patterns

Pencil and paper
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Further Resources
This task is about continuing a spatial pattern and writing a rule.
Shape 1 Shape 2 Shape 3

Here are the first three shapes in a pattern.
a)
b)		 Use the cubes to build Shape 4.
Complete the table below for Shape 4.
  

Shape number (n)

1

2

3

4

Number of cubes (c)

1

4

9

 
   

Check with your teacher if your model is correct, and your table is correct for Shape 4.
 
c)
 
How many cubes would be needed to build
 
 
i)
 
ii)
 
iii)
 
Shape 5? __________
 
Shape 6? __________
 
Shape 20? __________
 
d)
Explain in words or symbols how to get the answer for shape 20 above.
 
 
 
 
 
e)
Use your model of Shape 4 to show your teacher how this works.
 
 
 
 
Task administration: 
This task is completed with pencil and paper, and other equipment.
 
Equipment:
About 20 cubes per student.
Levels:
4, 5
Curriculum info: 
Maths, Number and Algebra, Patterns and relationships
Key Competencies: 
Using language, symbols, and texts
Keywords: 
spatial patterns, model construction, functional rules, rules, quadratic equation, practical
Description of task: 
Students use cubes to construct part of a spatial pattern and answer questions on how to continue it.
Curriculum Links: 
Key competencies
This resource involves describing how a non-linear rule is obtained. This relates to the Key Competency: Using language, symbols and text.
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: 
 

a)

   Fourth shape correctly built.

Shape 4

b)

  

16

c)

i)
ii)
iii)

25
36
400

d)

  

Any 1 of:

  • Square the shape number
  • c = n2
  • Equivalent explanations

e)

   Shows how the cubes can fit together to make a square, i.e.,

(left-hand side)      (right-hand side)
Multiplies the height (4) by the width (4) without showing how the unshaded blocks complete the square.

NOTE: This resource spans Level 2 to Level 5.
Part a) is Level 2; Parts b) and c) i) are Level 3; Parts c) ii) and iii) are Level 3-4.
Part d) is Level 4-5; and Part e) is Level 5.