Navy Beans – a way into magnitude and place value

A great deal of emphasis has been given to subitising small groups of objects. The visual image of a group of objects provides a foundation for the ideas of quantity and conservation of quantity. For example, five counters set out in different arrangements is still five counters.

But less emphasis is given to magnitude of larger numbers. If the only image a student has of, say, 365 (see Question 1 on NAPLAN 3, 2013) is a structured form then it is likely that their place value concept will be poorly developed. Seeing the magnitude of a large quantity is as important as subitising a small quantity

Susan Prince from Auburn Primary School took a recent opportunity to explore magnitude with her class. The school had decided to hold a “How many navy beans in the jar” competition.

Susan's class took on the job of actually finding out. It took two whole maths lessons for students in small groups to count small dishes of beans, first in tens and then in hundreds. Running totals were kept which provided purposeful situations for learning how to number split and add hundreds, tens and ones. 

When the total 8,632 was arrived at there was no doubt but that these students understood the magnitude and the place value aspects of 8,632.
But for the Grade 3s in this class, the final step was to consider what 100,000 would look like. It would take more than 10 jars of beans and and at least 20 more days to check that many beans ... and they asked "What would happen if we tried to eat them?"