Kauri trees

Kauri trees

Pencil and paper
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Working with Students
Further Resources
This task is about reading information from a data table.

A scientist measured the height of 50 young kauri trees.

The table below shows how many of the trees were at different heights.

Height of Trees (cm)

 Number of Trees
65   1
66   5
67   3
68   6
69   8
70 10
71   7
72 10
TOTAL 50

a)		  
How many kauri trees are:
   
i)
 
ii)
 
iii)
 
iv)
 
exactly 66 cm tall? __________
 
more than 70 cm tall? __________
 
less than or equal to 68 cm tall? __________
 
less than 71 cm, but more than 66 cm tall? __________
 
b)
What percentage of kauri trees are:
 
 
i)
 
ii)
exactly 70 cm tall? __________ %
 
less than 69 cm, but more than 65 cm tall? __________ %
Task administration: 
This task is completed with pencil and paper only.
Level:
4
Curriculum info: 
Maths, Statistics, Statistical investigations
Keywords: 
frequency tables, table interpretation, percentages, bi-variate data
Description of task: 
Students answer questions and calculate percentages from a frequency table of tree heights.
Curriculum Links: 
This resource can be used to help to identify students' ability to interpret a table, and answer questions about the distribution of the data.
Learning Progression Frameworks
This resource can provide evidence of learning associated with
Statistical investigations, set 5
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 
 

Y8 (05/1998)
a) i)
ii)
iii)
iv)		 5
17
15
27		 very easy
easy
easy
moderate
b) i)
ii)		 20
28		 difficult
difficult

 

Diagnostic and formative information: 
   Common error Likely calculation Likely reason
a) ii)
    iii)
    iv)		 27
9
32
34
39		 10 + 7 + 10
1 + 5 + 3
5 + 3 + 6 + 8 + 10
3 + 6 + 8 + 10 + 7
5 + 3 + 6 + 8 + 10 + 7		 Confuses either with > or with <.
a) i)
    ii)
    iii)
    iv)
b) i)
    ii)		 1
2 (or 3)
4 (or 3)
4 (or 5 or 6)
12.5%
37.5%		   Uses number of categories rather than number of trees.
a) ii) 6   Gives number of trees = 70 cm.
b) i)
    ii)		 10
14		   Gives number of trees rather than percentage.