By Tom

Note: this is part 2 of a three part series. For part 1, click here.

So we’re at the midpoint in this canoe project. The students have built the canoe, along with their 1/10 scale models and they’ve been able to prove that it will actually float. It has been an absolute blast so far, with total student engagement and wonderful, cross-curricular learning. I want to focus here on one learning activity we did that encapsulates about half of what fourth graders are supposed to do in math. First look at this excerpt from the Common Core Math Introduction for Fourth Grade:

“In Grade 4, instructional time should focus on three critical areas: (1) developing understanding and fluency with multi-digit multiplication, and developing understanding of dividing to find quotients involving multi-digit dividends; (2) developing an understanding of fraction equivalence, addition and subtraction of fractions with like denominators, and multiplication of fractions by whole numbers; (3) understanding that geometric figures can be analyzed and classified based on their properties, such as having parallel sides, perpendicular sides, particular angle measures, and symmetry.”

After we finished building the canoe, I explained that in order to prove that it would float, it was necessary to measure the boat’s mass and volume. From there, we could find something called “density,” and compare the canoe’s density to the density of water, which would tell us whether it would float or not. But first we needed to find out how much it weighs and how much volume it has.

Finding the weight was pretty easy. They told me to stand on a scale and then stand on a scale holding the canoe. OK, so it wasn’t that easy. But I managed. Then they subtracted the two numbers to find the mass. (23 Kg., in case you’re wondering.)

The volume was trickier. First we measured the volume of the model canoes. It turns out that each one holds 500 ml of water. A nice, round number. Then we predicted how many model canoes would fit into the large canoe. Their numbers were all over the place, even after I reminded them that we made the model canoes by dividing every measurement for the large canoe by 10.

So I had them line up model canoes inside the large canoe like you see in the picture. (There’s only nine along the bottom, but we figured ten would fit along the top.) Then we lined ten across the bottom. They were quick to figure out that one hundred model canoes could fill up one layer inside the large canoe. After that we started stacking them up, like you see in the second picture. They discovered that ten layers of 100 model canoes would completely fill the boat. “One thousand canoes!” they shouted.

From there, they were quick to realize that if their models have a volume of 500ml, then the volume of the large canoe must be 500,000 ml.

So let’s take another look at that excerpt from the common core. This time I’m going to underline every idea supported in just this one lesson:

“In Grade 4, instructional time should focus on three critical areas: (1) developing understanding and fluency with multi-digit multiplication, and developing understanding of dividing to find quotients involving multi-digit dividends; (2) developing an understanding of fraction equivalence, addition and subtraction of fractions with like denominators, and multiplication of fractions by whole numbers; (3) understanding that geometric figures can be analyzed and classified based on their properties, such as having parallel sides, perpendicular sides, particular angle measures, and symmetry.”

All of this is goes to show a very simple truth: teaching to the Common Core does not have to be boring work out of a boring textbook.

It can, and should, inspire us to be creative and have fun.

### Tom White

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Lindsey Stevens says

Tom, this makes me jealous of you in three (more) ways (than I already was), one, I do not even understand the math well enough to have designed a fourth grade lesson like this, two, you were not MY fourth grade teacher, and three, as a secondary teacher I am not called on to do these types of integrated units of study, but I am going to figure out how to get as close as possible.

Hallie says

Great work Tom! Your students are always going to remember their 4th grade year and this project. I wholeheartedly agree that CCSS does not confine us to a box. There is, and should be, a lot of room for teacher creativity.

Doug says

Tom, you are a brave man! I love the cross-discipline application and am hoping to take on some similar projects with our students. I really appreciate how you are taking abstract concepts and making them concrete: mass, volume, density, buoyancy, ratio, and all of the math standards that you listed. I think I mentioned this before, but I am definitely planning on using your posts as an example during our problem-based learning training this summer. Looking forward to the third and final installment!

Chris Gustafson says

I love the way students predicted and then used their models to model answers to the volume question. But I feel like I missed out on a very important part. Are you planning to post about construction? I’m envisioning saws and, I don’t know, glue? Really skinny nails? And the bent sides? Inquiring minds do want to know. Thanks for taking us on this journey with you and your students.

Kelly Pruitt says

Tom, this is just an amazing example of combining, science, math, engineering, and art (yes, I said art). Your students are lucky to have you as a teacher who, not only helps them meet the standards, but also makes it meaningful. :)

Kelly