Planting trees

Planting trees

Pencil and paper
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Further Resources
This task is about constructing and reading information from a back-to-back stem-and-leaf graph.

The kaitiaki of Kaituna Reserve planted akeake and kōhūhū trees. After 3 years they were finding out whether the akeake were taller than the kōhūhū.

They chose 30 akeake and 30 kōhūhū at random. Here are their results.  

 

Akeake (height in cm)

146       160       166       171       175
149       160       167       171       178
151       162       167       171       179
153       163       168       173       181
155       165       170       173       184
157       165       170       174       185
Kōhūhū (height in cm)

143       153       159       162       169
147       154       160       165       170
149       156       161       166       171
151       157       161       166       173
152       157       162       167       176
153       158       162       169       178
 
a)
 
Draw a back-to-back stem-and-leaf graph for this data.
The graph has been started for you.
 
 

Akeake

Height (cm)

 Kōhūhū

 

 
b)
What is the most common range of heights for the kōhūhū?
 
 
(A) 140-149 cm
(B) 150-159 cm
(C) 160-169 cm
(D) 170-179 cm
 
c)
Make a statement which compares the heights of the akeake with the kōhūhū.
 

 
 
 
Task administration: 
This task is completed with pencil and paper only.
Levels:
4, 5
Curriculum info: 
Maths, Statistics, Statistical investigations
Key Competencies: 
Thinking, Using language, symbols, and texts
Keywords: 
composite graphs, stem-and-leaf graphs, graph construction, graph interpretation, distribution
Description of task: 
Students construct a back-to-back stem-and-leaf graph for heights of trees. They then answer a question on range and make a statement comparing the heights of akeake and kōhūhū.
Curriculum Links: 
This resource can be used to help to identify students' ability to construct and interpret a back-to-back stem-and-leaf graph.
Key competencies
This resource involves comparing distributions visually to identify patterns variations and relationships and explaining their rationale. These relate to the Key Competencies: Thinking and Using language, symbols and text.
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: 
    

Y10 (07/1998)
2 marks
(all correct)
or
1 mark
(1-3 errors or stem not ordered)		 a)
NOTE: accept commas between numbers.		 moderate
1 mark b) C very easy
1 mark c) On average, akeake are taller than kōhūhū (or similar statement that compares the groups in general).
NOTE: No mark for argument based on range.		 easy