Monday, December 10, 2012

Ada Lovelace

It is always good to hear about female mathematicians. Today, Google featured a graphic with the tag “Ada Lovelace’s 197th birthday”. Investigation revealed that Ada Lovelace was the daughter of the poet, Lord Byron, and lived in the 1800s.

A paragraph in the Washington Post caught my attention.

At the age of 17, Lovelace was among the first to grasp the importance of Babbage’s machines, Google noted. In her correspondence, as reported by New Scientist magazine, Lovelace said that “the Analytical Engine weaves algebraical patterns just as the Jacquard-loom weaves flowers and leaves.” She also noted that the Analytical Engine “does not occupy common ground with mere calculating machines” and had the potential to run complicated programs of its own.

Apparently, Lovelace wrote the first algorithm designed to be run by the Analytical Engine. Some say she should be considered the first computer programmer.

Here is another Lovelace quote to ponder (from Wikipedia:Ada Lovelace)

[The Analytical Engine] might act upon other things besides number, were objects found whose mutual fundamental relations could be expressed by those of the abstract science of operations, and which should be also susceptible of adaptations to the action of the operating notation and mechanism of the engine...

Supposing, for instance, that the fundamental relations of pitched sounds in the science of harmony and of musical composition were susceptible of such expression and adaptations, the engine might compose elaborate and scientific pieces of music of any degree of complexity or extent.[58]

The Wheel Shop

There’s a great website called Inside Mathematics. I learned about it at the Common Core Math sessions this year with Bob and Judi Laird, Sandi Stanhope, and Fran Huntoon, of the Vermont Mathematics Initiative.

Inside Mathematics is a treasure trove for teachers. It has problems of the month linked to Common Core standards. The best part about the problems is the fact that they begin with an easy level and progress to more difficult levels related to the same math and situation. It’s kind of like how the Bedtime Math website works.

Here’s one we tried today with Sandi Stanhope: The Wheel Shop. It starts innocently enough with Level A. There are 18 wheels in the shop that sells tricycles. How many tricycles are there in The Wheel Shop?

Then we went on. The Wheel Shop sells other kinds of vehicles. There are bicycles and go-carts in a different room of the shop. Each bicycle has only one seat and each go-cart has only one seat. There are a total of 21 seats and 54 wheels in that room. How many are bicycles and how many are go-carts?

Nick Mack had a lovely way to solve this one today at the workshop which involved doubling 21, then adding 2 wheels to bicycles until he had the right number of wheels. The bikes with the added wheels became the number of go-carts.

Nick said his second graders did a similar problem involving ducks and sheep. They drew a bunch of ducks then added 2 more legs to several of them in order to “turn them into sheep”. He said the sheep that began as ducks were fairly ugly, but the math worked out.

Today Sandi said, "Math should be hard. Let kids figure it out." 

Here is the Level C problem:
Three months later some vehicles have sold and new models have been brought into the Wheel Shop. Now, there are a different number of bicycles, tandem bicycles, and tricycles in the shop. There are a total of 135 seats, 118 front handlebars (that steer the bike), and 269 wheels. How many bicycles, tandem bicycles and tricycles are there in the Wheel Shop?

Today Nick started making a spreadsheet for this one and I did something similar tonight. My spreadsheet had columns for handlebars, seats, and wheels and did some multiplication and addition with formulas to get the totals. I guess-and-checked my way as the spreadsheet did the calculation. Setting this up took about 10 minutes, but my husband, Jim, had already gotten the answer and was eating muffins with the kids in the kitchen by the time I figured it out.

Jim had written his solution on an index card. He explained it as follows:

There are 118 total bikes (because there were 118 total front handlebars).
Multiply that by 2 and get 236 (so there must be 236 wheels).
But there are 269 wheels, so I subtracted. 269-236=33. There are 33 tricycles.
There were 135 seats but only 118 steering handlebars, so I subtracted. 135-118=17.
There must be 17 tandems and 33 tricycles. This left 68 regular bicycles because I subtracted 17 and 33 from 118 to get 68.

Enjoy the problems of the day! We did.