Visiting Moa Island

Visiting Moa Island

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 flowchart to find a general rule.
 
 
 
Use the flowchart to answer the following questions about visiting Moa Island.
a) The table below lists the next four groups to visit the island. Calculate the total cost for each group to visit Moa Island and write your answers in the spaces provided.
 

Group number Total number visiting Number wanting tour Number wanting lunch on tour Total Cost
i)   Group 1 4 4 4 $__________ 
ii)  Group 2 5 3 2 $__________ 
iii) Group 3 12 12 2 $__________ 
iv) Group 4 16 16 16 $__________ 
 
b)
 
Let C = "total cost", and p = "the number of people". Write down an equation to show how much it costs
 

i) 

4 to 9 people to visit Moa Island, with all of them wanting a tour, but nobody wanting lunch provided.
 
__________________________________________________________________
 

ii)

15 or more people to visit Moa Island, with all of them wanting a tour and lunch provided.
 
__________________________________________________________________
Task administration: 
This task is completed with pencil and paper only.
Level:
5
Curriculum info: 
Maths, Number and Algebra, Equations and expressions, Patterns and relationships
Key Competencies: 
Using language, symbols, and texts
Keywords: 
linear equations, tree diagrams, flowcharts
Description of task: 
Students use a flowchart to find solutions and generate rules from them.
Curriculum Links: 
Key competencies
This resource involves interpreting a flow chart and using it to formulate a linear equation. This relates to the Key Competency: Using language, symbols and text.
Learning Progression Frameworks
This resource can provide evidence of learning associated with
Using symbols and expressions to think mathematically, sets 6-7
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 
   

Y10 (11/2002)

a)

i)
ii)
iii)
iv)

$180
$155
$310
$460

very easy
moderate
easy
moderate

b)

 i)
ii)		 C = 35p
C = 30p - 20		 moderate
difficult
Diagnostic and formative information: 
 

Common error

Likely calculation

Likely misconception

a) ii)

195

(3 × $35) + (2 × $45)

Includes all people under 'wanting a tour'.

a) iv)
b) ii)

480
c = 30p

16 × $30

Does not 'take $20 off the total cost'.

a) i)

    ii)

    iii)

    iv)

64
12
30
10
288
26
4096
48

4 × 4 × 4
4 + 4 + 4
5 × 3 × 2
5 + 3 + 2
12 × 12 × 12
12 + 12 + 12
16 × 16 × 16
16 + 16 + 16

Does not relate question to flowchart and just multiplies or adds number in table.

a) i)-
    iv)

45, 35, 15, etc.

  

Quotes per person costs not total costs.