Making triangles

Making triangles

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

Fill in the spaces below to show the next 2 triangular numbers in the sequence. Draw a diagram for these numbers.

3 is a triangular number: 

6 is the next triangular number: 

a)
__________ is the next triangular number. Diagram:
 
 
 
 
b)
__________ is the next triangular number. Diagram:
 
 
 
 
c)
Complete this sentence: "Each row is n + _____ of the row before it."
 
d)
In a supermarket Jane builds up a display of tins of soup like this:
patterns of stacked cans
If there were a total of 28 tins, how many tins high would the stack be?
 
(A) 6
(B) 7
(C) 14
(D) 28
(E) 56
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, recursive rules
Description of task: 
Student fills in spaces and draw diagrams to identify the next two triangular numbers. They also state 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)

easy easy
b)

easy easy
c) +1 moderate moderate
d) B moderate moderate