Block patterns II

Block patterns II

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

Practical Task
The picture below shows how multi-link cubes have been used to build this growing sequence of steps.

Using multi-link cubes build the next 2 models in the sequence. When you have finished show them to your teacher.

   
Step 1 Step 2 Step 3 Step 4
Step 5
 
a)
How many cubes did it take to build each step model?
Write this information on the table below. The first one has been done for you.
 

Steps

1

2

3

4

5

Number of cubes

1

 

 

 

 
 
b)
 
Use the information you have recorded above to finish the table below.
 

Step

6

7

8

Number of cubes

 

 

 

c)		  
How many cubes would it take to build step model 26? __________
Task administration: 
This task is completed with pen and paper, and other equipment.
 
Equipment
40-50 multi-link cubes for each student.
  • This task assesses students' ability to identify and continue the pattern found in step models.
  • This assessment activity can be carried out with one student at a time or with a group/class of students working independently.

NOTE: Part c) could be given separately.

Copyright: 
Graphics: NZCER
Levels:
3, 4
Curriculum info: 
Maths, Number and Algebra, Patterns and relationships
Keywords: 
spatial patterns, model construction, recursive rules, quadratic equation
Description of task: 
Using multi-link cubes students construct and explore a growing sequence of step models, then they apply this information to continue the pattern without the cubes.
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) 3, 6, 10, 15
b) 21, 28, 36
c) 351