What is hidden inside the bottle?
Summary
School level
Generating questions
Mathematical domain
Duration
Material
Grade 7 or 8
What is hidden inside the bottle? How balls of each color are there?
Informal inferencial statistics; hypotheses formulation; frequencies is, absolute and relative freqüències; percentages; sample variability.
4-5 sessions of 50 minutes (or equivalent)
Opaque bottles numbered and filled with coloured balls, a blackboard for collective recording, activity booklets, and sheets for individual and group reports.
Motivation
Through an experiment involving opaque bottles, students formulate hypotheses about their contents, collect data through systematic observation, and analyse sample variability. This process enables the informal introduction of key concepts in statistical inference, while promoting reasoning, argumentation, and data-based decision-making.
A first look
What is hiddent inside the bottle? (in Catalan with English subtitles available)
Video of the implementation at Col·legi Natzaret and interview to Berta Barquero, researcher of Labinquiry project.
Observation and empirical exploration
A group of students carefully observes the colour of the balls through the small hole in the bottle, initiating a key process of empirical exploration. This seemingly simple moment marks the beginning of statistical reasoning: they learn to generate hypotheses, collect data, and recognise uncertainty as an inherent part of mathematical analysis.
Data collection
Data collection is a fundamental stage in the investigative process. It allows students to experiment with different strategies, compare results, and develop their own criteria for interpreting them. This active engagement fosters autonomy and consolidates key learning around sampling, frequencies, and the validity of hypotheses.
Planning
PHASE
1
First hypotheses
2
Validation of hypothese with increasing N (sample size)
3
Joint collection and final report
CENTRAL QUESTIONS
What is the bottle content? What information can we get? How to organise the statistical study? How to formulate hypotheses and collect data in a systematic way?
What is inside the bottle? What can we know and what can’t we know by observing the bottle? How is a statistical study organised? How can we formulate hypotheses and collect data systematically?
Do all bottles have the same composition? What are there variation in the collected data? What results will we get if we pool all the data? What final hypothesis is more coherent and justified?