Diamond patterns III

Diamond patterns III

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

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

Number of diamonds

1

2

3

4

5

6

7

8

Number of matches

4

7

            
 
a)
 
Complete the table above to show the number of matches used, for each diamond pattern.
  
b)
How many matches would be needed for 20 diamonds? __________ matches.
You may show your working in the space below.
 
    

    

    

    

    

    
 
c)
 
What rule did you use to find the number of matches needed for 20 diamonds?
 

 
 
 
Task administration: 
This task is completed with pencil and paper only.
Level:
4
Curriculum info: 
Maths, Number and Algebra, Patterns and relationships
Keywords: 
rules, spatial patterns
Description of task: 
Students complete a table showing the number of matchsticks used in a spatial pattern, identify the number of matchsticks required for a given shape, and describe the rule for the pattern.
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 diamonds

3

4

5

6

7

8

Number of matches

10

13

16

19

22

25
easy very easy
b) 61 difficult moderate
c) For any 1 of: 

  • 3 times the number of diamonds and add 1 (m = 3n + 1);
  • m = 4 + 3(n - 1);
  • m = 4n - (n - 1);
  • add on 3 to previous diamond;
  • other rule which gives a correct sequence.
 very difficult difficult