Our two performances of our play, “On Camera, Noah Webster” went off with any major problems. Everyone put it all out there to make it silly, serious, and — above all, as Dexter said — educational. Students learned challenging amounts of lines with a lot of new vocabulary and expressions, made rapid costume changes, interacted well with each other, and felt very pleased with the way the audiences (students and parents) responded. Thanks go to the parents who provided snacks and helped with cleaning up the Moore building at the end.

The alligator project has just about come to an end. We have finished all of the measurements and sent our ‘gators home. They will “grow” again if students put them back in water.

The final math activities involved making line graphs from our data: length, girth, and mass. Then we looked at the places on our graphs where we had not measured the critters because of weekends and snow days. We could see that the line passed through those blank spots and that the lines were fairly straight, which meant we could make a reasonable estimate of what the measurements would have been. We used colored pencils to differentiate between the data points that were from measurement and the ones we put on the non-measured days. Students added interpolate to their math vocabulary.

 

The only thing remaining for this project is the final editing and sharing of the stories students wrote about their alligators. We discussed what makes a good story — characters we can understand and some kind of central problem or goal that the main character(s) have to address. We mentioned that some of the signposts from our Notice and Note lists might help with the story, too. When we get back from Spring Break, we’ll share, revise and edit, and discuss these very varied “gator tales.” I must confess that I thought students would spend a day or two on creating a short fable, but our novelists have taken it to the next level (again!)

As part of our quick unit on the Celts and Romans, we started learning to play what is believed to be an ancient game from Ireland: brandubh (BRAN- doov, which means “black raven”). I really like games in which the opponents have different numbers and/or types of pieces and separate winning strategies . . . and this is one of those. What several of our students learned on the first day of playing it is that you have to play a new game a number of times before you can play strategically. We’ll get back to this game after the break.

We sent our “Roman” oil lamps home on the night of the play. Several students have worked on testing theirs already. They should all be tested and the experimental comment sheet completed and brought back to school on April 1. Here’s a photo that Jonah’s dad took of Jonah’s greatest success:

As we learn about the cultures of the Celts and Romans and what happened as the Romans brought their armies and engineering genius to more and more of the world, one of the things we are talking about  is the parallel we can find between that piece of history and what became of the indigenous peoples in North and South America when Europeans arrived.

The date of Pi Day this year was special: we not only had the month and day matching the first 3 digits of pi (3.14) but also had two more digits in the year: 3.1415.  I suspect that many of our students will always remember pi to at least 4 decimal places because of that. But what is pi? We used our math time to find out. Students were given tape measures and turned loose in the classroom to measure and record the circumference and diameter of as many things as they could. They were surprised to discover just how many round things we had. (A few wanted to measure people’s heads, but we were able to convince them that heads are not actually round.)

Then we got out our calculators and divided each circumference by its diameter. Just about everyone found that the quotients were somewhere around 3. We agreed that our measurements were not as precise as they would need to be in order to get a true value for pi, but the approximate values were pretty good. We then went to our computers, got Geometer’s Sketchpad going, and used the tools to create a circle and draw its diameter. After getting the built-in calculator to do the math, students changed the size of the circle and could see that C/D was equal to 3.14159 constantly, even though the numbers for circumference and diameter changed. Why did it stop at 5 decimal places? Just because that’s all the software was capable of providing.

So pi emerged as a relationship. Why does it have a name? Because it’s an irrational number — it cannot be precisely written as a decimal number or as a fraction. So any numerical naming would have to be approximate. (Compare this to 1/3. We can’t write it accurately as a decimal number because 0.33333 . . . goes on forever. But we can write it accurately as a fraction.) The best we can do with pi is give it a name.

We took the exploration a bit further by seeing if there was anything similar about measurements we could do with a square. So we drew squares of various sizes on Sketchpad’s grid. What else should we draw that would be comparable to the diameter of a circle? A few students suggested that one side would be right. But isn’t that part of the perimeter of the square? And is it the longest segment we can draw? Aha! A diagonal is what we need. So we measured the perimeter of a square, divided it by the length of its diagonal, and again found a constant relationship. No matter how we changed the size of the square, when we divided the perimeter by the length of the diagonal, we got the same result! It was an interesting extension of our traditional “discovering pi” activities.

We finally completed the students’ Life Skills 101 presentations just in time for our break. Network problems, weather, and students’ (un)readiness pushed us to the edge, but it all worked out.

The choices they made were delightfully varied: food preparation, doing laundry, cleaning up and organizing a space, redecorating a room, grocery shopping . . . all of them being things that are important to know about and that helped with some of the work that keeps a home and family comfortable.

Their presentations included descriptions of some unexpected problems — forgetting a key ingredient in a recipe, spilling the laundry detergent, setting fire to a kitchen towel that was left on the stove, putting things in the food processor without installing the blade, and more. We could all laugh about it because it worked out in the end.

Students came away with a deepened appreciation of the amount of time their parents spend on such jobs, and several are planning to keep their new skills sharp by continuing to do the tasks they have now mastered. They all are very proud of what they accomplished, and so are we.

should be up by Friday, March 20 — check back, please.

We’ll do a combined blog for this past week and the coming week. Check back after March 13.

A five day week . . . what a novelty!

Our alligator project that is part of our math unit on measurement is holding everyone’s interest and attention. The daily routine right now is: (1) remove alligator from water tank and dump the somewhat cloudy water; (2) dry the alligator gently; (3) measure and record its mass, length, and girth; (4) trace its outline on graph paper and record the approximate area; (5) add the measurement data to your spreadsheet; and (6) return the alligator to the tank and add cold water to cover.

It’s soon going to be time to remove them from their bath permanently and measure them as they shrink. We will be using our spreadsheets and hand calculation at the end of this entire activity to analyze our data in terms of mean, median, range, and mode(s) for each data category. We’ll also make some graphs.

On Friday, after students had struggled for several days with the challenge of estimating the areas of the tracings, we introduced Pick’s Theorem. Georg Pick was a mathematician who was a contemporary of Einstein, collaborated with him on some projects, and died in a concentration camp during WWII. Math should always have a human face, and we look for ways to bring people into our work with numbers and shapes.

No one knew what a theorem was and wondered if it were something like a theory. We explained that a theorem is a mathematical statement or process that comes from a chain of reasoning, such as the Pythagorean Theorem.  It has been proven to be true. A theory is a set of ideas or rules that is supported by all of the evidence we have. But it can also be disproved when new evidence comes along. It may be true, but it may also be incorrect or incomplete.

Pick’s Theorem is used to find the area of irregular polygons. It also works on regular polygons, too. The polygon is placed on a grid, or lattice. Then we count all of the places where its outline crosses intersections on the grid (let’s call them B) and also all of the intersection points that are inside the figure (call them I). The area equation is: B/2 -1 + I. We tried that with some rectangles drawn in Geometer’s Sketchpad for which we had already calculated the area by multiplying the length by the width. It worked! Then we tried it on an irregular polygon that didn’t have all of its vertices on grid intersections. Pick’s Theorem yielded an area of 12.5 square centimeters, which Sketchpad came up with 12.93 square centimeters. I’m not sure why there was a discrepancy, as my test of the polygon came out to be 12.5 both times. I think it had something to do with differences in the computers’ screen resolutions, but I’m not sure. We talked about it as a bit of a mystery but agreed that the two results were quite close to each other.

Students then went back to their alligator tracings to apply Pick’s Theorem and compare those results to their own visual estimates. Some were delighted to find that their own estimates were pretty close to the new results, while others laughed at how far off some of their calculations had been. We noted that the results were still going to be approximate because the alligator outline includes curves and is not a polygon.

Brooke Sexton came to school on Thursday to meet with both 5th/6th groups to give students some ideas about writing.  She’s the author of the play that our groups saw recently. It was a lot of fun as well as educational — we wouldn’t expect anything else from a Miquon graduate.

 

We’ll be using some of her ideas when we write stories about our alligators this coming week.

Our play (“On Camera, Noah Webster”) is coming along well. Everyone is just about solid with their lines, so we are now working on movement, expression, voice volume, and handling props. Students have been exposed to new vocabulary and phrases, including such things as prattle, mince your words, salty oaths, a well-turned phrase, and food for thought. We stop to review some of the new language from time to time. We’ll be setting a performance date as soon as we hear back from parents about their own schedules.

We’ve been researching aspects of pre-Christian Celtic life, primarily in Ireland. Students have used MindMup (a graphical organizer) to gather notes about such things as food, beliefs, and laws. We’re now going to spend a week getting an overview of ancient Rome, again gathering information about culture and social organization. Students have some information about that already that they have gleaned from reading Detectives in Togas. Our third week will bring the two groups together and focus on the expansion of the Roman Empire into the (mostly) Celtic territories of western Europe.  What happens when one group invades the lands of another? Who prevails, and why? We’ll learn a bit about two unsuccessful acts of Celtic resistance: one by the Gauls that was led by Vercingetorix and the other by Boudicca (the “warrior queen”) in England. This entire study is more compressed and superficial than I had originally planned because we devoted a lot of time in January to building and tinkering. It was time well spent, but it led to a reduction in the breadth and depth of this topic.