Flowers and trees

Flowers and trees

Pencil and paper
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Working with Students
Further Resources
This task is about working out probabilities from a tree diagram.

Rose-Anne went to a garden centre and bought a mix of seeds. She was told that the seeds would grow into plants which would have either red or yellow flowers and either round, oval, or diamond shaped leaves.

Below is a tree diagram showing the possible characteristics and the probabilities of a plant having these characteristics.

 
tree diagram

 
a)
Which combination of flower colour and leaf shape is least likely?
 
 
i)
 
ii)
flower colour: __________
 
leaf shape: __________
 
b)
Rose-Anne randomly picked out a seed. What is the probability that it will have ...
 
 
i)
 
ii)
 
iii)
 
iv)
red flowers? __________
 
round leaves? __________
 
red flowers and diamond leaves? __________
 
yellow flowers and oval leaves? __________
Task administration: 
This task is completed with pencil and paper only.
Level:
5
Curriculum info: 
Maths, Statistics, Probability
Keywords: 
tree diagrams, probability
Description of task: 
Students interpret a tree diagram to answer questions about the probability of selecting certain combinations.
Learning Progression Frameworks
This resource can provide evidence of learning associated with
Interpreting statistical and chance situations, set 5
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 
 
Y10 (10/1998)
a)
i)
ii)
 yellow
diamond		 easy
b)
i)
ii)
iii)
iv)
 3/4 or 0.75 or 75%
1/2 or 0.5 or 50%
3/24 or 1/8 or 0.125 or 12.5%
1/12 or 0.0833 or 8.3%
easy
easy
difficult
difficult
Diagnostic and formative information: 
  Common error Likely calculation Likely reason
b) i)

    ii)

 1/2
1/3		   Misreads probabilities.
b) iii)

    iv)

 11/12
7/12		 3/4 + 1/6
1/3 + 1/4		 Adding rather than multiplying probabilities.
b) iii)

    iv)

 4/10
2/7		 3/4 + 1/6 =
1/3 + 1/4 = 		Adding rather than multiplying probabilities and incorrect addition algorithm.
b) iii)

    iv)

 1/6
1/3		 Probability (Diamond)

Probability (Oval)

 Quotes only the last probability in a sequence of events.