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 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
Description of task: 
Students identify the missing part of equations shown as number machines.
Curriculum Links: 

Links to National Standards (Patterns and relationships Level 3)
This resource can provide one source of evidence of students' ability to continue number patterns based on multiplication and addition.
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: 

 

Y8 (03/00)

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.

Figure it Out 
  • Follow that arrow and Crunch machine Algebra L2-3, pages 4 & 7, and 
  • Operation time Algebra L3, pages 10-11.