Diamond patterns II

Diamond patterns II

Pencil and paper
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Further Resources
This task is about completing a pattern and writing a rule to describe the pattern.
a) Draw the next two patterns in this series of diamonds.
 
b)		  
Complete this table.
 

Shape number

1

2

3

4

5

Number of shaded squares

4

8

12

    
 
c)
 
How many shaded squares would there be in
 
i)     shape number 20? __________
 
ii)    shape number 50? __________
 
d)
Complete this rule to show how many shaded squares make up diamonds of various sizes.
 
The number of shaded squares = the shape number ... ___________________________

 

 
Task administration: 
This task is completed with pencil and paper only.
Level:
4
Curriculum info: 
Maths, Number and Algebra, Patterns and relationships
Keywords: 
spatial patterns, functional rules
Description of task: 
Students draw the next two patterns in a spatial pattern, complete a table and questions about the pattern, and write a rule to describe 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 (09/2000)
a)  
[Accept correct shape regardless of position or if more than 2 drawn correctly]		 very easy
b)  
Shape Number 1 2 3 4 5
Number of shaded squares 4 8 12 16 20
 
 
very easy
c) i)
ii)		 80
200		 easy
easy
d)   multiplied by 4
or any other rule which works.		 moderate