Number machines II

Number machines II

Pencil and paper
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Working with Students
Further Resources
This task is about finding the rules for some number machines.
This is a number machine. It makes the same change to every number.
 


     
 

What changes do these number machines make?

Fill in the box on each machine with an operation sign (+, ×, ÷, or -), and a number.
 

a)

     
 

b)

     
 

c)

     
 

d)

    
Task administration: 
This task is completed with pencil and paper only.
Level:
3
Curriculum info: 
Maths, Number and Algebra, Patterns and relationships
Keywords: 
relationships, functional rules, number machines, addition, multiplication
Description of task: 
Students identify the missing part of equations shown as number machines.
Learning Progression Frameworks
This resource can provide evidence of learning associated with
Patterns and relationships, sets 4-5
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 

 

Y8 (03/2000)

a)

× 2

very easy

b)

÷ 4

easy

c)

– 12

easy

d)

÷ 8

moderate
Diagnostic and formative information: 
  

Common errors

Likely calculation

Likely misconception

a)
b)
c)
d)

 ÷ 2
× 4
+ 12
× 8		 4 ÷ 2 = 2
5 × 4 = 20
2 + 12 = 14
2 × 8 = 16

Gives the rule for the right-hand numbers to turn into the left-hand numbers (rather than vice versa).

a)
b)
c)
d)

 + 2
– 15
÷ 7
– 14		 2 + 2 = 4
20 – 15 = 5
14 ÷ 7 = 2
16 – 14 = 2

Gives a rule than only works for the first pair of numbers.