making roadbed

Now this is not a complicated procedure, but for a group of youngsters with minimal experience working with their hands to make things, it has plenty of opportunities to apply some of the math they’re learning and to solve problems related to sizes, shapes, and working cooperatively. I’m no longer surprised that tasks that should take about 15 minutes often stretch out to several hours, but I still marvel at the level of energy and enthusiasm that kids can sustain when they feel like they’re really doing something for a change.

The plan was to lay the homosote on the floor, spread a layer of white glue on it, position the plywood, then put weights (upside down tables) on the sandwich while the glue sets. To protect the floor from glue oozing out of the joint, we needed a craft paper barrier.

putting math to work

I had the end of a roll of 36” wide craft paper, just about 9 feet long. At first, the kids were stumped for how to make that work. It was long enough, but not wide enough. One very mathematically minded student declared that it was impossible, we had 27 square feet of paper but 32 square feet of sheet material. After letting them stew on that for a while, I pointed out that we didn’t really need to protect the middle of the sheets, just the edges. Lightbulbs. We can cut the paper into strips!

Most of the kids immediately understood how that solved the problem, but a few still needed a diagram to see where we were headed.

Jeff Allen

making it happen

Of course, some kids aren’t familiar with the “measure twice, cut once” wisdom and were reaching for the scissors. My question “How wide are you going to make the strips?” met with stunned silence.

Now, it may well be that the result of their impulsive approach would have been perfectly satisfactory, but that’s far from a sure thing and I’d like them to become accustomed to a more precise approach to things. So I handed them a tape measure and a yardstick, both of which for them are alien technologies. While two of them started measuring the width of the paper, the rest of us discussed whether we needed four long strips or two long and two short as in the diagram. The kids like the idea of four long strips because it avoided the complication of having to think about multiple lengths. I liked that idea because it meant more measuring and cutting, good practice.

When the measurement team announced that the paper was 36” wide there was an astonishingly long and agonizing silence while they determined how wide each of the four strips would be. My impression was that they were slightly incredulous that they were using math to solve an actual real-world situation. Slowly, they started to murmer “nine inches.”

Jeff Allen

the fun part

Positioning the homosote and spreading the glue was very satisfying.

Jeff Allen

meanwhile, across the room

The four kids on the Inglenook were also deep in problem solving mode.

Jeff Allen

I think it's great that

these kids are learning some real world applications for basic problem solving.  I was astounded when a high school senior whom I was working with didn't know what a yard stick was when I asked him to get it.  He asked how big it was and I replied "REALLY?"  He played on the football team.

The yard

It took me a while to appreciate the irony of that story (on first reading I only considered the stereotypical "football player," not the individual for whom yards are a matter of high concern). 

As a math teacher in the United States, I have my work cut out for me. On the one hand, it really does make for more flexible mathematical thinking to be using a system of measurement in which things might be divisible by 3, 10, 12, or powers of 2, but kids find it infuriating and quickly smell the rat in any such rationalization for what is really just a legacy of political cowardice. 

On the other hand, it is certainly a vivid example of the contrast between the elegant clarity of theory and the messy tangle of reality! That's a chasm I want my students to feel equipped to bridge. 

Jeff Allen

I think it’s great you’re

I think it’s great you’re tying real world problem solving in!

If they smell a rat, maybe the next generation will be the one that actually finishes the switch to metric 

Switch to metric

It makes so much sense Australians switched in 1968.  Only 50 years ago.

US Standardization

The USA "officially" went metric in the late 50's (Eisenhower Administration), but left it up to industry to do the conversion. The move was made in response to the International Standards Bodies changing the length of the inch to be exactly 25.4 mm. Although the change was only a few thousands of and inch, we had a great time at a town bonfire where we burned a many of our "obsolete" wooden rulers. Of course that's what a town full of Nerds (National Laboratory Engineers and Scientists) who used metrics daily would do as a teaching moment for the kids in town.

Industry did a bang-up job with the conversion. I know of one project which specified that all "external" threads would be Imperial and all "internal" threads would be metric. Since there were no clear definitions of internal and external the product never made past the prototype stage.   

Parents

I think this is great, but I wonder how parents react to the students reply of what did you do in math class today when they say ran trains.

Curious if you have gotten any irate parents calling and/or email asking what you are you teaching?

Conversion to metric

I don't understand by now why they have not, I mean seems like all the companies that do worldwide business would see a cost savings it they used half litter bottles everywhere instead of half litters some places, others places 20 oz bottles. 

There may be an advantage to

There may be an advantage to using different units for the smaller bottles - it makes it hard to do a price comparison and see just how much you’re paying for the convenience of a small bottle vs. a large one.

Any irate parents?

I try to balance all the fun with enough grueling calculations on the homework to be sure kids do a lot of moaning and groaning around the house to keep parents feeling satisfied. 

Seriously, parents appreciate that their sometimes math-phobic kids are enthusiastic about taking on tasks that they used to shy away from. And, students who have graduated give testimonials about how well prepared they've been for high school, so parents are very supportive. 

More commonly, parents recall their own experiences in middle school and like what they see in comparison. 

Jeff Allen

re: Any irate parents?

Glad to read they realize the value of teaching practical applications of math, I have always believed there should be more practical math taught, like having a home budget.

what type of learning is the best!

Having to deal with students of any age, and having learning a trade of profession, HAND"S on TRAINING beats a book any day. A book gives the correct procedure to the text issued. But a person ,now having to use their brain and hand's, now has to put the book to the test. A another way to solve the text issue , the person might have a total and better way to deal with the text. Like hobby of model railroading many many magazines, book's ,and every person having to deal with the text has their way of dealing with it. Mike