Students wrote some interesting division story problems today. We talked about making them real – though that can be tough – and we talked about making them meaningful – though that is certainly a challenge. I proposed to them that math should either be rather interesting or rather useful. Though story problems can fall into this category, they often don’t. For some senseless math check out what happens when we do stuff to numbers… because that’s what we do in math (not really). In the end they came up with a number of interesting and engaging problems that produced more to think about in their creation than in their solving. Here are a few:

There are 160 people at a party and there are 40 pies. Each pie is cut into 7 pieces. How many pieces would each person get?

Sasha made 117 cupcakes. She had platters that held 12 cupcakes each. How many platters does she need?

There are 157 students going on a field trip to Nisqually. There weren’t any buses, so they had to order “10 person” vans. One person brought their mom, dad, brother, and sister. Three teachers came as well. How many vans do they need to order?

The clock factory produces 20 clocks per hour. 143 clocks in the clock factory are finished. They are packed into creates that hold 44 clocks each. How many crates do they need? How many clocks are in the last crate? How long did it take to make the clocks in the first crate filled?

There were 260 3rd graders at a summer camp. Half of them were going to Great Wolf Lodge. A quarter of them were going swimming. The last quarter was staying at camp. The larger group took mini-buses that held 13 campers. The smaller groups took cars that held 5. How many buses and cars did they need?

I think some of these students could write for textbook companies! It’s interesting to see their worlds reflected in their math problems, and I was particularly happy to see how engaged they were in the process.

This month we are working on classifying quadrilaterals. Creating these overlapping hierarchies is  always a challenge. Relationships that work one way, don’t work the other way, and there is a lot of specific vocabulary that needs to be learned and applied in novel situations.

It’s a little like this: everyone who lives in Olympia lives in Washington, but not everyone who lives in Washington lives in Olympia. Bringing it back to the shapes – all squares are rectangles, but not all rectangles are squares.

To do this work, we need to know the defining characteristics of the quadrilaterals that we are classifying – and here we run into yet another difficulty… mathematicians don’t always agree on these! But the work of classification goes on. We just learn the specific characteristics and create the relationships accordingly. Here is a table that tries to communicate these overlapping relationships.

Under the inclusive definition of trapezoids, all six shapes a the top of this post are trapezoids, under the exclusive definition only three of them are… can you spot them?

What’s the first question that comes to your mind?

Dan Meyer, prolific blogger, high school math teacher, and current Ph.D. student at Stanford wants to know. Dan has decided that there are way too many artificial scenarios in his high school math texts that pretend to model the world. He wants to see the real world in his math class because he sees the math in the real world.

101qs.com is the brainchild of Dan Meyer. On this site, anyone can post an image or a short video and let the world ask the math questions that naturally arise from the scene.

From this, he and many of his followers have created lessons where the students can generate the questions (probably the ones that the teacher has in mind), ask for any relevant information they need, and solve real problems the way they would in the real world.

It’s fantastic – check it out, but don’t be surprised if you find yourself seeing math problems everywhere.

How about this one?

How many do you think there are? What number is just too many? What number is too few? Be brave.

What do you need to know?