Students learn about random events, and the patterns and variations occurring in such events. The context is a jube machine that randomly packages jubes of different shape and colour. The jubes in the machine make up a sample space based on an even distribution of 1:1 or 1:1:1 or an uneven distribution of 2:1. The focus throughout the series is the notion of long-run data being more reliable than short-run data due to random variation.
Random or not: explore and Random or not: analyse
At the Fantastic Fruit Jube factory, a machine packages jubes in random order into packets, each holding 12 jubes. The jubes are dispensed from a container holding different types of jubes in different proportions (depending on the learning object).
Two approaches underpin the learning objects in the series.
- In the explore subseries of learning objects students make a packet of jubes for the comparison of results against five machine-made packets and explore the variation in jubes from packet to packet.
- In the analyse subseries of learning objects the machine randomly generates all packets for the comparison of data. Students observe that the jubes vary from packet to packet and notice the patterns in successive batches (samples) of 1000 packets.
In both the explore and analyse subseries, the various learning objects allow students to investigate:
- the most commonly occurring type of jube (numbers of jubes)
- the longest run or sequence of jube (runs of jubes)
- the length of the longest alternating sequence of jubes (alternating jubes).
In addition, both the explore and analyse subseries allow students to investigate different outcomes when the sample space contains different ratios of jube types, including 1:1; 1:1:1; and 2:1.
Each of the 17 Random or not learning objects automatically collates experimental results and displays them as frequency graphs.
Random or not: open investigations
This is an open-ended exploratory tool for teacher and student use. Students can explore relationships between ratios, sample size, uneven distributions and random variation.