Friday, November 29, 2013

looking at our world through a mathematical lens

On Tuesday at Grauer, I worked with Ms Poon and her class of grades 4 and 5 students. We began our session together with a short discussion about what math is…all the different areas of mathematics. We then explained that we were going to go outside of the school with the iPads and use the camera to see what mathematics we might notice. The students were a bit hesitant at first but soon began to see math in all sorts of places. The students worked in partners for this task.

When we got back to the classroom the students went through their photos and chose one that inspired them mathematically. We discussed what the photograph made them wonder about (and many of these questions had emerged when we were outside) and what kind of mathematical problem they could ask based on the photograph. During our discussion of problems we discussed how a problem really isn't a problem if you know how to solve it right away which helped students move on from the more standard word problem format (ie. There were 43 leaves on the ground and 26 blew away. How many leaves were left?).

How many pieces of garbage can fit in the garbage can?
How many squares are in this window?

How many triangles are there? How many lines are in the wheel? Is the shape symmetrical? 
As students posed their problems, they began to think about how they might solve them. Some students used the screencasting app ShowMe to share their photograph, state their problem and explain how they might start to figure it out.

The students emailed their photos and problems to me and during our next session together we are going to compile the photos and problems into a photo book, possibly using Book Creator on the iPads.

place value constructions in grade 3

This week two grade 3 classes in Richmond played around with some place value concepts as they built animals using base ten blocks. At both Grauer in Mrs. Partridge's class and at Cook in Mrs. Verkade's class, the students shared with me what they knew about place value.

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.