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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, we can multiply factors in whatever grouping or order we chose and still get the same answer. We start by multiplying multiplicand we want to multiply 4 by 2 because this computation is easy for most people to do in their heads. (8 * 2) * 2 (16) * 2 We then multiply our product by the remaining multiplicand, which is 2. 16 * 2 = 32 Multiplying by 10: Stick a zero behind whatever number you wish to multiply 10 by 988 * 10 = 9880 Why does this work? Consider what we’re doing in terms of place value. When... 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, we can multiply factors in whatever grouping or order we chose and still get the same answer. We start by multiplying multiplicand we want to multiply 4 by 2 because this computation is easy for most people to do in their heads. (8 * 2) * 2 (16) * 2 We then multiply our product by the remaining multiplicand, which is 2. 16 * 2 = 32 Multiplying by 10: Stick a zero behind whatever number you wish to multiply 10 by 988 * 10 = 9880 Why does this work? Consider what we’re doing in terms of place value. When... 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.  Say, how to add 25 and 8 vertically, with the carry-over 1 carefully written on top of the 2.  By that time, my students are proficient in mental addition and subtraction of 3-digit numbers: carrying, borrowing, and all.  My goal though is by no means to turn them into human calculators.  So then, why bother? Vertical arithmetic is a convenient method for computing numerical answers.  Especially when the numbers to manipulate are multidigit.  But it is a procedure, requiring—once learned—little thought.  The entire process is delegated to the... 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 teams) is a standard utility application that accompanies every smartphone: the basic calculator. Need to carry out some quick arithmetic to figure out how much money you owe your buddy? Pull out your phone and type away. It’s that simple. So why the heck do kids need to memorize the multiplication table? Because it is still crucial to a successful math career and a promising life thereafter. Don’t believe me? Here are four reasons why mental math is still tremendously important and absolutely foundational. 1. Confidence Is Key You have likely heard people utter the following... read more

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