Solving systems of equations sometimes called simultaneous equations with graphs is simply a matter of finding out where they intersect. One of the most valuable things students can learn is to be able to visualize linear equations and systems of equations so that they can tell the quadrant where the intersection and therefore the solution is. This develops the valuable ability to estimate solutions. We suggest students practice picturing and then graphing systems with a variety of slopes and intercepts. Significant relationships like perpendicular lines should be another focus.
Tag: graphs
Composition of Functions
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 opportunity to explore composition by using different functions and by seeing their result on graphs. This is very powerful and great fun to push imaginations.
Inverse of a Function
Spreadsheets make it very easy to switch axes and add graphs. They enable students to play with what may have been difficult and abstract concepts like the inverse of a function. You may want to approach the inverse of a function by challenging students to fill in a table of values with a rule that creates a mirror of that function. So you can approach the inverse of a function either as the interchange of axes or as a symmetry issue. Either one works well on spreadsheets.
Rule of 72
The rule of 72 is an old banker’s rule of thumb to find out how long it will take to double your money at different interest rates. Financial literacy has become an increasingly important topic for K-12 education and we believe spreadsheets and headmath or mental estimation should be central to it. Rule of 72 combines both and gets students calculating compound interest. They can also see how expensive high credit card interest rates can be to them.
Polynomial Functions
Polynomial functions are not limited to the highest term and while that term is most important in determining the shape of its graph, additional terms play a role. Try out additional terms to see how they affect the shapes of the graph. Focus on the patterns!