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.

illustration: calculator

Talia was using a calculator to make number patterns. If you keep pressing the equals button from a calculator 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     2 button          plus         7 button          equals button

 

a)

 
Pattern: 4, 20, 100, 500, 2500 …

Talia pressed     4 button          blank circle          blank square          equals button
 

b)

Pattern: 70, 62, 54, 46, 38 …

Taila pressed     7 button          nought button          blank cicrle          blank square          equals button
 

c)

Pattern: 45, 36, 27, 18, 9 …

Taila pressed     4 button          5 button           blank circle          blank square          equals button
 

d)

Pattern: 80, 40, 20, 10, 5 …

Taila pressed     8 button          nought          blank circle          blank square          equals button
Task administration: 
This task is completed with pencil and paper only.
Level:
3
Curriculum info: 
Maths, Number and Algebra, Patterns and relationships
Keywords: 
number patterns, recursive rules
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
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)

× 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).