Document 8k

This software, after compilation, allows a student to practice simple to fairly sophisticated arithmetic. It does provide feedback to the...

Document 8k

This software, after compilation, allows a student to practice simple to fairly sophisticated arithmetic. It does provide feedback to the...

Subtraction Method "Borrow" vs. "Shift" Most can remember subtraction using the classic "borrowing" method, such as, 63 - 28 = (50 + 13) - (20 + 8) = (50 - 20) + (13 - 8)* = 35. Here we "borrowed" from the 60, adding 10 to the 3 for 13, and leaving 50 behind to subtract the 20 from. This all looks more familiar... read more

We’ll start with the easy stuff. Multiplying by 4: (1) Double the multiplicand you want to multiply 4 by (2) Double it one more time e.g. 8 * 4 = 32 8 * 2 = 16 16 * 2 = 32 Why does this work? 4 can be broken up into 2 * 2 8 * 4 = 32 8 * (2 * 2) = 32 Thanks to the associative property of multiplication,... read more

Welcome back to the school everyone! I hope you all had a great summer. For all those whose summer was maybe a little too great, maybe those who’ve forgotten even the basics, we’re going to take it all the way back to arithmetic a.k.a “number theory”. A review of number theory is a perfect place to start for many levels. Calculus and a lot of what you learn in pre-calculus is based... read more

Summary: Mental math teaches students to see short, efficient solutions—rather than to blindly follow the brute-force, cookie-cutter, one-size-fit-all, show-all-your-work procedures taught at school. To my youngest students, I lie—by omission—that vertical arithmetic does not exist. I can usually get away with it for about a year. Until the school shows them the light... read more

Dazzling pocket PCs are aplenty for the children of today. Kids roll into the classroom with iPhones, Blackberries, and various Android devices capable of supporting myriad complex applications. We are living in a wonderful age where handheld computers help us tremendously and continuously. Alongside all of the fancy apps (that allow us to manage everything from our finances to our fantasy football... read more

In elementary school, mathematics is often taught as a set of rules for counting and computation. Students learn that there is only one right answer and that the teacher knows it. There is no room for judgment or making assumptions. Students are taught that Arithmetic is the way it is because it's the truth, plain and simple. Often students go on to become trapped in this view of the universe... read more

When working with fractions, I find it effective to require students to convert each fraction that we work with to its decimal equivalent, to convert that decimal equivalent back into the original fraction, to convert that decimal into its percentage equivalent, to work a simple percentage problem using that percentage and finally to work the same problem using the initial fraction. This... read more

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