I don't know if you have seen my performances before, so today is your opportunity to see it. Basically, I spend the show doing very big multiplication and squaring problems, create magic squares, tell people the day of the week they were born on, and more. Here is a compilation of some of my performances.
If you liked it, you can see me live at the Chicago Toy and Game Fair in November, and many other possible shows. These are listed on my website, www.EthanMath.com.
In this video, you saw me square numbers. This is a method like the close-together method, but even easier than squaring numbers, and even the things I've taught you all along is squaring a two-digit number ending in five. A crowd of fifth graders could understand it, so hopefully, you guys are smarter than those fifth graders!!
Let's take the number 35. In order to square it, you need to remember two things:
1) The last two digits are always 25.
2) The start of the number is the first digit times the first digit plus one.
So, first, we take the first digit, or 3. Three times four (3 + 1) is equal to 12. Since the last two digits are always 25, 35^2 is 1225.
Let's look at, say 85^2. 8 x 9 = 72, so the answer is 7225. Very simple, right.
Let me make it a tad harder on you. Try 145^2. All we need to do is think of it as a two-digit number, with fourteen as the first digit and five as the last one. So, 14 x 15 isn't too bad, as you remember from the first post. If you try it yourself, you will get the number 210. Since it always ends in 25, the answer is 21025.
With very little practice, you will be able to square two-digit numbers ending in five. If you practice the close-together method I taught on August 20, you will be able to square three-digit numbers ending in five. Have fun!!
August Problem of the Week Answers:
Easy:
b = 35
Explicit Formula: n - 1
Recursive Formula: an-1 + 1
g = 34
a = 908
p = 5%
Hard:
z = 42.5
a = 1/2
b = 1/2
c = 1
y = 55
x = 10
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