What'll they think of next?

Ann has been working at North Ingle Primary School with students in Grades 5, 6 and 7. She had set them a problematised situation that they were successful in solving, Then she decided it was time to turn the tables.
"I want you to think up some problematised situations for me. Do you think you could do that?"
She was overwhelmed by the range and quality of the responses. Here are a couple of the problems that the students thought up but it was hard to choose from the great ideas that came forward,

Problem 1

Do you want to hear about the time that I went to my nanna's two weeks ago and helped her run her egg store. She has chickens and had an order for 3 1/2 dozen eggs. Every other day I had to collect the eggs. On my first day, which was a Monday, the hens had laid 8 eggs. After that I only collected 6 eggs each time. After two weeks, I had to come home on the Sunday. Do you think there were any eggs left over?

Problem 2

One day Dr Phil was looking for a new studio to record in.

He had a few options.

Option 1 is 15m × 18m for $7829 with a 10% discount.

Option 2 is 16m × 17m for $8792 with a 13% discount.

And Option 3 is 28m × 13m for $11829 with a 23% discount.

Which option do you think Dr Phil should choose and why?

The students are really looking forward to working on each others' problems.

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?"