George is in New York and Martha is in Washington. They leave at the same time and follow the same road to meet each other on the way. The distance between New York and Washington is 229 miles. George has a fast horse and averages 16 miles/hr. Martha has a slow carriage and averages 7 …
This picture made the front page of the New York Times this morning. It is not very often that a science experiment makes the headlines in a great newspaper, particularly above the fold. It is a thrilling discovery. “The First Image of a Black Hole.” The concept of black holes, hundred years old, came out …
Exploring Mathematical Concepts with Dynamically Linked Multiple Representations Using Spreadsheets Fri, 10/4: 11:00 AM – 12:00 PM 1448 Session 60 Minutes Music City Center Room: 207 AB Description How can we build multiple representations into teaching and learning activities? This can be a challenging task, but technology provides the means to do this effectively and …
Adding to 10 is but on example of a large number of spreadsheets that could be developed to practice addition. We give students two number lines (number bars) to 10, and have them copy a number from each to build a pattern of all the sums to 10. We suggest you encourage students to extend …
We introduce students to more complex patterns and rules in hundreds tables. In particular, we have students look at diagonal patterns and develop rules to fill them. This spreadsheet hundreds table practice is designed to build numbersense, the primary building block for a strong math education. We encourage students and teachers to develop more spreadsheets …
We use rules to build new numberlines. For example we can start in the middle and go both forward or backward using adding and subtracting rules. You can even generate and experiment with negative numbers by subtracting below 0. As you build numberlines on spreadsheets you are building them in your mind. And by thinking of numberlines in terms of rules you are getting ready for algebra.
Our number system inherited from India and from the Medieval Arab world enables us to use just 10 symbols to write any number we can imagine. Students learn in this spreadsheet to enter numbers, to compare compact and expanded forms of those symbols and to add units to any number. Students who like to explore …
We can use these proportions to compare two ratios with different denominators by finding a denominator that their proportions have in common. Thus the common denominator of 2/3 and 3/4 is 12. We then can use the common denominator to add/subtract and divide common ratios (fractions). This approach to division is quite different from the …
Linear functions are the most important family of functions. They pervade our everyday lives and our work. Their graph is a line, and their general form is f(x)=mx+b where m is the slope of the function and b is the y-intercept, the value where the line crosses the y-axis. This Lab is designed to give …
One of the most powerful aspects of the mathematics of functions is our ability to treat them as abstract quantities (essentially numbers) and then combine them with standard operations. But with functions we can go further and develop a new operation we call composition or taking a function of a function. We give students the …
