Cups and saucers

Cups and saucers

Pencil and paper
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Further Resources
This task is about finding all possible combinations, and chance.

Questions/instructions:

a) Each cup can be paired with each saucer. How many different pairings of a cup and saucer can be made?
  (A) 2
  (B) 3
  (C) 5
  (D)
6
 
b)  
There is only one red marble in each of the bags shown below. Without looking, you are to pick a marble out of one of the bags.
Which bag would give you the greatest chance of picking the red marble?  

  (A) Bag with 10 marbles.
  (B) Bag with 100 marbles.
  (C) Bag with 1000 marbles.
  (D) It makes no difference.
Task administration: 
This task can be completed with pencil and paper or online (with auto marking).
These questions were NEMP trend tasks for the Year 8 students. They were trialled in both 1997 and 2001. The data for both years is on the scoring page.
Levels:
2, 4
Curriculum info: 
Maths, Statistics, Probability
Keywords: 
nemp, probability, combinations
Description of task: 
For this NEMP task students find the number of combinations of cups with saucers, and identify the most likely bag to contain a red marble.
Learning Progression Frameworks
This resource can provide evidence of learning associated with
Interpreting statistical and chance situations, set 3
Interpreting statistical and chance situations, sets 4-5
within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.
Answers/responses: 
 

Y4 (10/2001)
(1997 data is in brackets)

Y8 (09/2001)
(1997 data is in brackets)

a)

D

15%   (-)

56%   (56%)

b)

A

49%   (-)

76%   (74%)

Commentary
The results for Year 8 students were almost identical in 1997 and 2001. These tasks were not administered to Year 4 students in 1997.