Machine rules

Machine rules

Pencil and paper
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Working with Students
Further Resources
This task is about using a rule to find numbers, and finding the rule from given numbers.

Three numbers go into each machine and come out changed by a rule. For example:

 

machine-rules-example.png

 

a) Use the rules below to find the three numbers coming out of each machine. Write the numbers that come out of each machine.
  i) machine-rules-add-10.png
  ii) machine-rules-add-4.png
  iii)
machine-rules-subtract-3.png
 
b)   Work out the rule for each of the machines below and write it on the machine.
  i) machine-rules-b-i.png
  ii) machine-rules-b-ii.png

 

Task administration: 
This task is completed with pencil and paper only.
Level:
2
Curriculum info: 
Maths, Number and Algebra, Patterns and relationships
Keywords: 
number machines, rules, functional rules, number patterns, addition
Description of task: 
Students use rules to find numbers and use given numbers to work out rules shown on number machines.
Learning Progression Frameworks
This resource can provide evidence of learning associated with
Patterns and relationships, set 3
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 
 

Y5 (05/2005)

a)

i)
ii)
iii)

30 18 25
6 13 21
6 8 12

very easy
easy
easy

b)

i)
ii)

+6
-5

easy
easy
Results are based on a trial set of 149 Y5 students.
Diagnostic and formative information: 
  Common error Likely calculation Likely misconception
b) i)
b) ii)		 6
5		 Omits the +
Omits the -		 Assumes the operation.
Next steps: 

Students who omit the operator required for the rule need to be made aware of the importance of providing a complete answer as part of successfully communicating mathematical ideas. The use of the "number machines" supports students in learning to write general rules. This can lead on to writing general rules for number patterns, spatial patterns, ordered pairs and/or simple graphs.

Figure It Out