All entries for Wednesday 22 December 2010
December 22, 2010
I used this page for teaching "divide in ratio" and "an introduction to algebraic expressions". The "divide in ratio" was introduced using the multi-buy discount offer. The question was how many items to pay if the shop offers a discount of "buy N get M free". The emphasis was on how the sum was worked out. The students were encouraged to explain their methods of working out the division. Their tasks were not about working out the sum, but to write the expression of the sum. The worksheet prints the expression for the total. The objective was to show the commutative law of addition and subtraction and the distributive law of multiplication using a shopping list. The amount of money to pay is independent of the order by which the items and the loyalty discount were counted.
I constructed the simple harmonic motion page for a physics lesson. I had this dynamic image in my mind when I learnt the topic years ago! However, I could only stare at the equations and mentally register the interdependencies of different terms. I suppose that most students would have done the similar mental and manual exercise: plot a few different versions of the oscillation corresponding to different sets of controlling parameters. It was the process of training to be a mathematician or physicist. Now, it is a wonderful experience to see the instantaneous response of the changes graphically.
"The simple harmonic motion with damping" page is not a simulation. Actually, the analytic solution to the second order linear differential equation was entered into the page directly. Geogebra simply plots the graph. The spring was a locus of a point on a small circle rolling up the y-axis! I certainly have done a lot of thinking on the topic of "constructions and loci".
The pages that I created can also be viewed and downloaded from http://sites.google.com/site/huivictorc/geogebra.
The projectile explorer was prepared for a mechanics lesson. The construction is general enough such that the page could be adapted into a Geogebra tool. Then two or more projectiles could be put together in a single page to enable the exploration of interception.