Number machines

Number machines

Pencil and paper
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Further Resources
This task is about completing number pairs and writing equations for 'number machines'.
 
This is a machine that changes numbers. If you put 3 into the machine 16 comes out. If you put 2 into the machine 11 comes out. If you put 8 into the machine 41 comes out.
 
a)
Complete the following number pairs using the rule for the number machine.
 
(2, 11)   (3, 16)   (4, ____ )   (6, ____ )   (8, 41)   (9, ____ )
 
b) Write an equation to show the rule for the number machine. Use n to represent the number going in to the machine.
 

 
 
c)
Machine B produces different numbers. Complete the following number pairs to show the pattern for Machine B.
 
(2, 12)   (3, 19)   (4, ____ )   (6, ____ )   (8, 54)   (9, ____ )  
 
d) Write an equation to show the rule for Machine B. Use n to represent the number going in to the machine.
 

 
 
e)
Machine C also produces different numbers. Complete the following number pairs to show the pattern for Machine C.

(2, 7)   (3, 12)   (4, ____ )   (6, ____ )   (8, 37)   (9, ____ )  

 
f) Write an equation to show the rule for Machine C.  Use n to represent the number going in to the machine.
 

 
Task administration: 
This task is completed with pencil and paper only.
Levels:
4, 5
Curriculum info: 
Maths, Number and Algebra, Patterns and relationships
Keywords: 
functional rules, number machines, co-ordinates, linear equations
Description of task: 
Students complete number pairs, and write the equations for three 'number machines'.
Learning Progression Frameworks
This resource can provide evidence of learning associated with
Patterns and relationships, sets 5-6
Patterns and relationships, sets 6-7
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 
  

Y8 (11/1996)

Y9 (11/1996)
a) (4, 21); (6, 31); (9, 46) moderate easy
b) (n × 5) + 1 moderate moderate
c) (4, 26); (6, 40); (9, 61) moderate moderate
d) (n × 7) - 2 [other equations possible] very difficult difficult
e) (4, 17); (6, 27); (9, 42) moderate moderate
f) (n × 5) - 3 [other equations possible] difficult difficult