Pāua diving

Pāua diving

Pencil and paper
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Working with Students
Further Resources
This task is about constructing and interpreting a graph.
Te Hare loves pāua fritters, and dived for two weeks in her summer holidays to get some pāua. She kept a daily diary, as follows:

First week:
Dec 4, collected 6; Dec 5 – 6, didn't go out — water too murky;
Dec 7, got only 3; Dec 8, got 7; Dec 9, got 4; Dec 10, got 5.

Second week:
Dec 11 – 12, really great! — got 10 each day; Dec 13 – 15, wind blowing hard, didn't go out; Dec 16, collected 3; Dec 17, only got 1.

Te Hare started to draw a bar graph of the number of pāua she collected, but she didn't finish it.

a) Complete the graph, and answer the questions below.

 

bar graph of paua collected

 
b)
On how many days altogether over the two weeks did Te Hare dive for pāua?
 
__________ days
 
c)
On how many days did she collect more than 3 pāua? __________ days
 
d)
i)  Which was her best week? __________
 
ii)  How many more pāua did she collect in that week than in the other week? _________ more
 
e)
What was the average number of pāua she got per day over the 14 days? (Give to 1 decimal place) 
 
__________ pāua
Task administration: 
This task can be completed with pencil and paper only.
Levels:
4, 5
Curriculum info: 
Maths, Statistics, Statistical investigations
Keywords: 
bar graphs, graph construction, graph interpretation, mean, mode
Description of task: 
Students complete a bar graph from details about paua diving and answer questions interpreting the data, including finding an average.
Curriculum Links: 
This resource can be used to help to identify students' ability to construct and interpret bar graph.
Learning Progression Frameworks
This resource can provide evidence of learning associated with
Statistical investigations, set 5
Statistical investigations, set 6
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 
  

Y8 (10/1996)

Y9 (10/1996)
a) Correctly drawn graph (see below). easy very easy
b) 9 days very easy very easy
c) 6 days easy easy
d)
i) Best week was the first week,
ii) 1 more paua [She collected 25 paua altogether that week; the second week she only got 24.]
 moderate moderate
e) Average for the two weeks was 3.5
()		 difficult moderate


Diagnostic and formative information: 
  Common errors Likely calculation Likely misconception
d) 3 or 4

  

 Rounds 3.5 to nearest whole number.
d) 5.4 or 5r4 or 5 49/9 Calculates average number collected per day of diving.