I like ratios. All the introductory skills are performed using whole numbers. Therefore, I think this is a topic/concept that should be taught in primary schools. I have found that, when properly introduced, children adapt quite well to this kind of thinking.
I start by calling it sharing. Every child is familar with the concept of sharing … one for me, one for you, two for you … and can predict how many items each person will have after a given number of cycles. They do this when dealing cards, for example.
Many students have watched concrete being made. When I explain how a labourer will have a pile of blue metal (aggregate), a pile of sand, and a supply of cement powder, and how they load the mixer, most of them readily understand the process and can calculate what a labourer would need to do for a double load. Most can even suggest two methods/sequences for loading the mixer.
In my opinion, it is vital that students learn to set their work out clearly in columns and that, except for the most elementary problems, the first line should consist of column headings. You will see more of this when I begin adding material here.
Rates compare measurements of ‘like’ quantities, for example two distances or two times or two money amounts. They are normally written side-by-side separated by colons (:). All will be revealed as I add material to this page!
Your method is perfect, I couldn’t imagine a better way to find derivatives with the chain rule. Thank you! Regards from France
CopainVG (on CCM YouTube video about the Chain Rule)
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