Making triangle patterns II

Making triangle patterns II

Pencil and paper
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Further Resources
This task is about growing patterns with shapes.

Practical task

a)
Use sticks to continue the pattern below. Stop when you have made 5 rows of the pattern.
Draw each pattern row in the spaces provided.
 
Pattern row 1 Pattern row 2 Pattern row 3 Pattern row 4
   

Pattern row 5

 
 
 
 
 
  
 
 
 
 

Have your pattern checked by your teacher.
 
b)
Use your drawings in a) to complete the table below.
 
ONLY COUNT TRIANGLES THAT POINT UP ,  
DO NOT COUNT THE TRIANGLES THAT POINT DOWN .
 
 
Number of row(s) 1 2 3 4 5
i) Number of triangles 1 3      
ii) Number of sticks used 3 9      
Have your table checked by your teacher.
 
c)
Use your table to help answer the following question. 
How many sticks in total would you need to have 36 triangles () in your pattern?
 
______________________
Task administration: 
This task is completed with pen and paper, and other equipment.
 
Equipment:
At least 50 iceblock sticks (or matchsticks) per student.
  • This task assesses students' ability to continue a pattern and identify the rule.
  • The questions refer to upward pointing triangles only.
  • Teacher checks are set to ensure that students have completed parts a) and b) correctly before doing part c).
Levels:
3, 4
Curriculum info: 
Maths, Number and Algebra, Patterns and relationships
Keywords: 
spatial patterns, recursive rules, quadratic equation, practical, model construction
Description of task: 
In this task students continue a triangular shape pattern with sticks to explore the rule used in the pattern. Students then use their understanding of the pattern rule to continue the pattern without the sticks.
Learning Progression Frameworks
This resource can provide evidence of learning associated with
Patterns and relationships, sets 4-5
Patterns and relationships, sets 5-6
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 
a)  
Pattern row 3

 Pattern row 4
Pattern row 5
b) i)
 
 
 
 
 
ii)
Number of row(s) 1 2 3 4 5
Number of triangles 1 3 6 10 15

 
 

Number of rows 1 2 3 4 5
Total number of sticks used 3 9 18 30 45

NOTE: The rule for this pattern is "multiply the number of triangles by 3 to get the number of sticks used".
c)   108