Squares and matches

Squares and matches

Pencil and paper
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Marking Student Responses
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Further Resources
This task is about rules for spatial patterns.
Shape 1 Shape 2 Shape 3
 
Petra made these shapes out of matches.
The rule for the number of squares can be written as an equation like this:
 
  sn = 2n2 – 2n + 1
where n represents the shape number,
and sn represents the number of squares in shape n.
 
a) How many squares will there be in
 
 
i)
 
ii)
shape 6? __________
 
shape 10? ___________
 
The rule for the number of matches in a shape can be written in words as:  
  • Square the shape number.
  • Multiply this amount by 4.
b) Use this rule to work out how many matches would be needed to make
 
 
i)
 
ii)
shape 5? __________
 
shape 20? __________
 
c)
Write the rule for the number of matches as an equation.
 
 
Use n to represent the shape number, and
Use tn torepresent the number of matches in shape n.
 
Complete this equation for the number of matches needed for shape n.
 
tn = ____________________
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, functional rules, quadratic equation
Description of task: 
Students use rules to work out the number of shapes or matches in spatial patterns, and complete an algebraic rule from a word rule.
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) i)
ii)

61
181

moderate
difficult
b) i)
ii)

100
1600

moderate
moderate
c)   4n2 moderate
Diagnostic and formative information: 
  Common error Likely calculation Likely reason
a)   i)
      ii)

133
381

122- 12 + 1
202- 20 + 1

 Treats 2n2 as (2n)2.
b)   i)
      ii)

144
400

122
202

 Treats 2n2 as (2n)2 and ignores the other terms.