At Grauer, the students stated:

"We use ones, tens and hundreds."

"We use the 0-9 digits in each place."

"1-9 in the ones, 10-99 in the tens, 100-999 in the hundreds and 1000-9999 in the thousands."

"Each spot has a value. Each number goes ten times bigger each time."

The students were able to demonstrate with the base ten blocks that the ten-block was ten times bigger than the ones block and the hundred-block was ten times bigger than the ten-block. Understanding this ten-timesness is a big idea in understanding our place value/base ten system.

I provided the value of 257 and asked the students to create an animal worth that much. The students created all sorts of creatures!

The students were asked to discuss each part of their animal - what part showed the 200, what part showed the 50, what part showed the 7 and expanded notation was introduced. It was interesting that in both classes, all the students used 2 hundreds, 5 tens and 7 ones for their materials, although both classes have been working on different ways to make large numbers. This made me wonder how I could have presented the task slightly different to make it a little more open so that students might have used different combinations of hundreds, tens and ones to make 257. Then again, it worked out well for introducing expanded notation!

The students then could create their own animal or other construction, as long as they could figure out what the value was. They used the camera on the iPads to take a photo of their creation and then used the Skitch app (a first time for both these classes) to show two other ways to represent the number or value of their creation.

In both of the above examples the students had to problem-solve around how to record their values in expanded notation as in both cases, the students used more than 9 ones. Carlo's butterfly used 2 hundreds, 3 tens and 12 ones so he (and others) decided to regroup his 12 blocks into 1 ten and 2 ones for the purposes of expanded notation.

~Janice

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