Black and white
0
Overview
Using this Resource
Connecting to the Curriculum
Marking Student Responses
Working with Students
Further Resources
This task is about comparing probabilities.
The arrow on this spinner has an equal chance of stopping on black or white when it is spun.
Task administration:
This task is completed online and has auto marking displayed to students.
Level:
4
Curriculum info:
Keywords:
Description of task:
This task sees what a students understanding of probability is.
Curriculum Links:
This resource can be used to help to identify students' understanding of ordering probabilities.
Learning Progression Frameworks
This resource can provide evidence of learning associated with within the Mathematics Learning Progressions Frameworks.
Read more about the Learning Progressions Frameworks.Answers/responses:
Y8 (11/2015)  
a)  C  Each of these two options are equally likely.  easy 
b)  C  The arrow points to black once and white once.  moderate 
c) 
All 5 correct

moderate

Based on a sample of 100 Year 8 students
Teaching and learning:
The key element in this task is recognising which outcomes of a chance event are more probable that others.
Diagnostic and formative information:
Equiprobabily misconception
b) Students tick "Each of these three options are equally likely."
The student sees events as equally likely, even when the events have different probabilities. This error involves either:
The student sees events as equally likely, even when the events have different probabilities. This error involves either:
 ignoring the different probabilities of events; or
 ignoring that 1 black and 1 white can occur two different ways, and is therefore twice as likely as 2 blacks (which can only occur one way).
See Throwing a coin for a resource that also has this as a common misconception.
Next steps:
Equiprobabily misconception
Get the student to record the results for a game with equal probabilities by making a spinner. Click on Making spinners for instruction on how to make a fair spinner. With a large number of spins, students should observe that 1 black and 1 white is twice as likely as 2 blacks or 2 whites. The results of this could be discussed, and students encouraged to note that black followed by white, and white followed by black both lead to a total of 1 black and 1 white.
Students could also write down the 4 possible options using either:
 a list, e.g.: B B; B W; W B; and W W;
 a tree diagram: See Combinations of marbles
 a table, e.g.
B  W  
B  B B  B W 
W  B W  W W 
For more information click on the Probability concept map
Two dice game and Throwing a coin both provide more information about sequences of events with a probability of ^{1}/_{2}.
 Combinations of ties and socks
 Spinner for a board game
 Colour a spinner
 Library books
 Farm helicopter
 Missing cat
 Pick an item
 Speed trap
 Probability number lines
 Cup of marbles
 Fun run prizes
 Dice combinations III
 Speed camera
 Draw of socks
 Dice combinations IV
 Scrabble tiles
 Flowers and trees
 Kī o rahi tournament
 One dice chances
 Prize wheel
 Two coin game
 Four spinners
 Prize draw
 Summer births
 Scrabble
 Five coin throws
 Netball tests
 Two zone spinner
 Two dice game IV
 Target arrows
 Complementary probabilities
 Candle combos
 Three coin throws
 Board game
 People in cars
 Making spinners
 Coloured spinner
 Three dice game I
 Two dice game III
 Four dice game I
 Three coin game I
 Five dice game I
 Two dice game II
 Two dice game I
 Cups and saucers
 Throwing a coin
 Describing probabilities
 Coin throws
 Probability Concept Map