Matchstick patterns II

Matchstick patterns II

Pencil and paper
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Working with Students
Further Resources
This task is about completing and describing rules for growing patterns.
1 2 3
a) i) Here are the first three shapes in a pattern. Finish the table to show the number of matches you would need to make the next four shapes in the pattern.
 

Shape number

1

2

3

4

5

6

7

Number of matches

5

9

13

       
 

ii)

Use words or an equation to explain how you worked the pattern out.

 

 

 

 
 
1 2 3
b) i)  Finish the table to show the number of matches you would need to make the next four shapes in this pattern.
 

Shape number

1

2

3

4

5

6

7

Number of matches

3

6

8

       
   
ii)
 
Use words or an equation to explain how you worked the pattern out.

 

 

 

 
Task administration: 
This task is completed with pen and paper only.
Level:
3
Description of task: 
The start of spatial matchstick patterns are shown and described in tables. Students complete the tables and show the rules in either words or equations.
Learning Progression Frameworks
This resource can provide evidence of learning associated with within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 

   

Y8 (03/2000)

a)

 

i)
ii)

17, 21, 25, 29.
Either:

•   Multiply the shape number by 4 and add 1.
•   Add on 4 each time.

easy
easy

b)

i)
ii)

11, 13, 16, 18.
Add 3 and 2 alternately.

moderate
moderate

Diagnostic and formative information: 
 

Common error

Likely reason

a) i)
    ii)

18, 23, 28, 33 or 20, 25, 30, 35
"add on 5" or "times by 5"

Forgets that one match is shared between adjacent squares.

b) i)
    ii)

11, 14, 17, 20
"add on 3"

Forgets that one match is shared between adjacent triangles on the odd shape numbers.

b) i)
    ii)

10, 12, 14, 16
"add on 2"

Assumes a match is shared between adjacent triangles at each shape number.