Calculator patterns

Calculator patterns

Pencil and paper
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Working with Students
Further Resources
This task is about finding rules for number patterns made on a calculator.


 

Talia was using a calculator to make number patterns. If you keep pressing the button
on Talia's calculator it keeps making the same change to the number.

Fill in the boxes with a number. Fill in the circles with an operation sign (+, ×, ÷, or –). An example has been done for you.
 

 
                         Pattern: 2, 9, 16, 23, 30 …

Talia pressed                                  

 

a)

 
Pattern: 4, 20, 100, 500, 2500 …

Talia pressed                                   
 

b)

Pattern: 70, 62, 54, 46, 38 …

Taila pressed                                             
 

c)

Pattern: 45, 36, 27, 18, 9 …

Taila pressed                                              
 

d)

Pattern: 80, 40, 20, 10, 5 …

Taila pressed                                             

Task administration: 
This task is completed with pencil and paper only.
Level:
3
Description of task: 
Students complete rules for number patterns generated using a calculator.
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 (03/2000)

a)

× 5

easy

b)

– 8

easy

c)

– 9

easy

d)

¸ 2

moderate

Diagnostic and formative information: 
 

Student response

Likely miscalculation

Likely reason

a)
d)

+ 16
– 40

4 + 16 = 20
80 – 40 = 40

Creates only the second term of the sequence.

a)
b)
c)
d)

+ 20
– 62
– 36
– 40

 

Enters the second number of the sequence with a + if the sequence increases and a - if it decreases.

b)

– 12 (or + 12)

70 – 62 = 12
because
7 – 6 = 1
2 – 0 = 2

Subtraction error (trying to get a rule for the second term of the sequence).