Block patterns

Block patterns

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

Practical task
Here are the first 3 patterns of a sequence of step models.

1 2 3

 
Use multi-link blocks to build a set of 6 step models to use in your investigation.
Show your models to your teacher before you start your investigation.
Each block in a step model has a number of faces showing.
 
a) i)
Using your models, count the number of faces on each cube that can be seen in models 4, 5, and 6.
Record your information in the table below. Models 1, 2, and 3 have been done for you.
 
  ii) Have your work checked by your teacher.
   
 
  iii)
Now use the information you have gathered to complete the tables for models 7 and 8.
 
  iv)
Have your work checked by your teacher.
 
b) Now use the pattern from your table above to help you complete the table for models 9 and 10.
Task administration: 
This task is completed with pen and paper, and other equipment.
Equipment:
60 or more multi-link cubes for each student; recording sheets photocopied for each student.
  • This task assesses students' ability to identify and continue a pattern.
  • This assessment activity can be carried out with one student at a time or by observing a group or class of students working independently.

NOTE: The definition of the phrase "faces showing" may need explaining.

Level:
3
Description of task: 
Using multi-link cubes students investigate the number of faces visible in a sequence of step models, then they use this information to continue and record the pattern in a table.
Learning Progression Frameworks
This resource can provide evidence of learning associated with within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 
a)

i)
 
 
ii)

Model 4 – 2, 3, 4, 1
Model 5 – 2, 4, 6, 3
Model 6 – 2, 5, 8, 6
Model 7 – 2, 6, 10, 10
Model 8 – 2, 7, 12, 15

b)

 

 

Model 9 – 2, 8, 14, 21
Model 10 – 2, 9, 16, 28