L Patterns

This task is about continuing a spatial pattern and finding the rule.

Suli is playing with counters, making letter Ls of various sizes, like this:


   

a) Complete this table, giving the total number of counters in letter Ls of different sizes:


Height of letter L (counters)
 
3 4 5 6 7 8

Total number of counters
 
4 6 8        
 
b)
 
How many counters in total would be needed to make a letter L that is ...
 

  

i)

ii)

iii)

 

10 counters high? __________ counters
 
16 counters high? __________ counters
 
37 counters high? __________ counters
 
c)
Explain or write a rule that describes how to work out the total number of counters needed from the height of an L-shape.
 
 
 
 
 
d) If the total number of counters was 40, how many counters high would the letter L be?
 
____________ counters