Initiatives

Math Investigations

Elementary School Investigations

Canada Counts
The 2001 Canada Year Book, published by Statistics Canada helps to tell the stories behind the numbers. Canada Counts is a collaborative project of Statistics Canada and The Galileo Educational Network created to facilitate Canadian's understanding of the social, economic and cultural forces that shape our nation. A Wintercount was one way that several Plains tribes recorded their history. Students can create their own version of a Wintercount.
 

Drilling For Oil
With this investigation you will entering the area of statistics. Engineers, geologists and Geophysicists in the oil industry are concerned with finding oil. They keep track of the number of times they drill for oil and the number of times that their drilling actually results in their finding oil. Keeping track of the data that they collect and the circumstances around each of the drilling instances is very important. One of the ways to analyze all the numbers that they collect is to use a mathematical tool that lets them stand back and average a whole lot of data. This tool is called the Central Limit theorem. It states that the average of a large bunch of measurements follows a normal bell-shaped curve even if the individual measurements themselves do not. A normal bell shaped curve is called a Gaussian curve in honor of the great nineteenth-century mathematician Karl Friedrich Gauss.

Secondary School Investigations

Financial Makeover
You are a financial planner who has just been given a new client. Her financial profile has been sent to you, and your client's name is Jennifer Russell. Your job will be to prepare a financial plan for Jennifer that considers her goals and considers her future. Jennifer wants a ten year plan that will will put her and her young son in good financial shape.

Open Investigations

Number
 
Just Zeros and Ones
This investigation can be entered into by children as young as 6 (particularly as it is structured in the game situation) and is entertaining for people who like to think about different number bases and find mathematical patterns. Playing with different number bases leads nicely into thinking about factoring and logarithms. The reason information theory makes such frequent use of logarithms base two is that the most fundamental unit of information is a bit, and a bit of information represents a choice between two possibilities.
 
The Vitruvian Man
Vitruvius wrote,
"In the human body the central point is naturally the navel. For if a man be placed flat on his back, with his hands and feet extended, and a pair of compasses centered at his navel, the fingers and toes of his two hands and feet will touch the circumference of a circle described therefrom. And just as the human body yields a circular outline, so too a square figure may be found from it. For if we measure the distance from the soles of the feet to the top of the head, and them apply that measure to the outstretched arms, the breadth will be found to be the same as the height ..." This investigation will allow students to explore their own proportions and eventually allow them to compare their own data against a database of other classes measurements.
 
Shape and Space

Area is a Square Deal
Some routine problems dealing with area and perimeter evoke unexpected responses. What to measure, how to measure it, and how to anticipate variations in area and perimeter are often difficult. "If we measure the area of rectangles by dividing them into squares, then what shape should we use to measure area for triangles?" Not such a bad question: Why don't we use "triangular units" to measure triangular areas?

 

Bean Pi
It's startling to discover the versatility of pi, crossing as it does the wide spectrum of geometry, calculus and probability.
 

Coming To Answers in Different Ways
Students and teachers from 3 schools in the Foothills School Division posed problems for each other to solve. They embarked on an online threaded discussion while investigation and solving these problems.

The purpose of this project was to sponsor mathematical conversation around good problems. We wanted to create more purposeful mathematical talk and activity. What do we know? What do we do when we don't know what to do? What do we need to know? How can we use models to help us? How do we know if we have a good model? What have we learned? How does math relate to our personal experiences?

 

Connect the Dots
A unicursal curve in the plane is a curve that you get when you put down your pencil, and draw until you get back to the starting point. As you draw, your pencil mark can intersect itself, but you're not supposed to have any triple intersections. You could say that your pencil is allowed to pass over any point of the plane at most twice. This property of not having any triple intersections is generic: if you scribble the curve with your eyes closed (and somehow magically manage to make the curve finish exactly where it began), the curve won't have any triple intersections.

 

Geometric Models
Have you ever built model airplanes, cars or boats? Models are often scaled-down versions of real objects. Physical models have many of the same features as the original but are often more convenient to study or to play with.

Theoretical or mathematical models are very common. Geometric ideas such as points, lines, planes, faces, edges, vertices, polygons, and diagonals can be used to represent physical objects. In the following investigation you will discover the rules that describe geometric situations.
 

Tiling
Determining what shapes tile a plane is not a simple matter. There are some polygons that will tile a plane and other polygons that will not tile a plane. For shapes to tile the plane edge to edge without gaps or overlaps, their angles, when arranged around a point, must have measures that add to exactly 360 degrees. If the sum were less, there would be a gap. If the sum were more, the shapes would overlap.
 
Statistics and Probability
 
Markov Process
Markov processes are among the most widely used models in probability. Recently, attention has focused on interacting systems which have applications from image processing, communications networks, models of spread of disease, etc.
 

Provincial Showdown
Statistics Canada has also supported Galileo Educational Network to create this investigation. You are part of a team of specialists that has been contracted by the Economic Development Department of one of the provinces or territories to help attract new businesses and investment to that province or territory. Your team is charged with the responsibility of creating a presentation that the province can use to persuade potential investors that a favourable business environment exists in the province or territory. What area of Canada would you represent?