Matchstick patterns

Matchstick patterns

Pencil and paper
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Further Resources
This task is about patterns and rules.
Christine began making the pentagon pattern below with matches.

She noticed a relationship between the number of pentagons and the total number of matches used, which she recorded on a chart.

 

 Number of pentagons

1

2

3

4

5

6

7

8

 Number of matches

5

9

            

  
a)
Complete the chart above to show the number of matches used.
 
b)
How many matches would be needed for 30 pentagons? __________ matches
 
c) Complete the rule below which you could use to find the number of matches needed for any number of pentagons.

Rule: "The number of pentagons × ___________ + ___________ = the number of matches."
Task administration: 
This task is completed with pen and paper only.
Level:
4
Curriculum info: 
Maths, Number and Algebra, Patterns and relationships
Keywords: 
functional rules, spatial patterns
Description of task: 
Students complete a table showing the number of matchsticks used to build a series of pentagons. They identify the number of matchsticks required for a given pentagon and state the rule as an word equation.
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 (06/1996)

Y9 (06/1996)
a)

Number of pentagons

3

4

5

6

7

8

Number of matches

13

17

21

25

29

33
very easy very easy
b) 121 difficult moderate
c) 4, 1,
or others which are equivalent, e.g., 
5p - (p - 1), or 5 + (p - 1) × 4,
where p is the number of pentagons
or "Add 4 each time" with a correct answer of 121.		 difficult difficult