Student Sheet
Proportional Reasoning with Probability
Name:______________________
PART A: Understanding ratios
PART B:
Create three bags of marbles/blocks:
Bag X contains 1 white and 3 black marbles/blocks
Bag Y contains 2 white and 3 black marbles/blocks
Bag Z contains 2 white and 6 black marbles/blocks
Write your prediction in INK of the bag(s) with the best chance for picking a black marble/block: ________________
Explain your reasoning in words or mathematically: _____________________________________________________
_______________________________________________________________________________________________
PART C:
Design two more bags of different ratios, but proportionate to your answer from above.
Bag V: _________________________________________________________________________________________
Bag W: _________________________________________________________________________________________
Explain your reasoning in words or mathematically: _____________________________________________________
_______________________________________________________________________________________________
PART D:
Design a set of bags for a new problem with the goal of finding the one with the best chance for picking a WHITE
marble/block.
Bag A: _________________________________________________________________________________________
Bag B: _________________________________________________________________________________________
Bag C: _________________________________________________________________________________________
Write in INK your prediction for the bag(s) with the best chance for picking a WHITE marble/block. ______________
Explain your reasoning in words or mathematically: _____________________________________________________
_______________________________________________________________________________________________
Give your Bags A, B, & C to your neighbor and write in INK his/her prediction for the bag(s) with the best chance for
picking a WHITE marble/block. ________________
Have your partner explain his/her reasoning in words or mathematically: _____________________________________
_______________________________________________________________________________________________
If you did not predict the same or you have different reasoning make sure you understand why.
PART E:
Assume there are two bags of marbles/blocks:
Bag J has 4 black and 2 yellow marbles/blocks.
Bag K contains 5 yellow marbles/blocks, how many black marbles/blocks must be added to Bag K so that it has the
same chance of picking a black marble/block as Bag J?
Write in INK your prediction for the number of black marbles/blocks needed in Bag J. _________________________
Explain your reasoning in words or mathematically: _____________________________________________________
_______________________________________________________________________________________________
Probability extension
PART E for Bags X, Y, & Z above:
Selection
Bag X
Bag Y
Bag Z
1
2
3
4
5
6
7
8
9
10
Color selected
most often
Did this match your prediction? __________________
Why do you think it did or did not? __________________________________________________________________
Run this experiment as a simulation using technology, such as the Prob Sim app, Pick Marble simulation on the TI 84.
Run 50 trials, 200 trials, 500 trials.
List findings:
# of Trials
Bag X
Bag Y
Bag Z
50
200
500
Color selected
most often
Discuss and explain your findings: __________________________________________________________________
_______________________________________________________________________________________________
For additional information got to: http://www.probexplorer.com/Articles/StohlProbPR2002.pdf
Ideas and research on: Using Proportional Reasoning Appropriately: Lessons Learned Through Probability
Hollylynne Stohl, North Carolina State University
http://www.probexplorer.com/Articles/StohlProbPR2002.pdf
Compiled here by: Cathy Jones, Math Specialist
STEM Center for Math & Science Education University of Arkansas
cej001@uark.edu
The study of probability is rich in the use of rational numbers and proportions; however, the nature of probability as a
study of random phenomenon makes the use of proportional reasoning somewhat different than in many numeric,
algebraic, and geometric contexts.
There are three bags of marbles/blocks:
Bag X contains 1 white and 3 black marbles/blocks
Bag Y contains 2 white and 3 black marbles/blocks
Bag Z contains 2 white and 6 black marbles/blocks
Make a prediction of which bag you think has the best chance for picking a black marble/block and discuss a reason for
your prediction.
Identify the correct answer as Bags X and Z
To further see comprehension of the idea of proportionality:
1) Students each design two more bags that have the same proportion as Bags X & Z. Discuss their designs.
2) Students each design a set of Bags A, B & C as a new problem. Have the person who designed the bags write in INK
his/her answer for the bag which has the best chance for picking a WHITE marble/block. Exchange bags and the other
student will also predict. Discuss their designs and the reasons for the predictions.
3) Students will find the missing black marbles/blocks: Bag J has 4 black and 2 yellow marbles and Bag K contains 5
yellow marbles/blocks, how many black marbles/blocks must you add to Bag K so that it has the same chance of
picking a black marble/block as Bag J?
To further understand probability, actually do the experiment ten times from each bag with replacement and keep track
of the picks on a table. Did the findings match the predictions? Discuss the reports from the table. To more accurately
model the prediction use technology, such as the Prob Sim app, Pick Marble simulation on the TI 84. Run several
simulations of picking a marble from the bag with replacement. Did the data more accurately match the predictions?