Can't get much closer. Maybe that's why the Police sang Don't Stand So Close to Me.
Can't get much closer. Maybe that's why the Police sang Don't Stand So Close to Me.
How many sides does a paragon have?
Reality doesn't work that way. Ninety percent of the leaves accumulate in the gaps between cans. And that's assuming someone move the birdbath in the middle of the garden, which doesn't jibe with a plan born out of laziness.
By the way, the mat is actually written in English. It has not been translated from, say, Klingon for the benefit of the viewer.
It's like sinking a free-throw without even putting down the broom. Which is impressive if you've ever tried to throw a leaf.
To give them a more thoughtful question than just what is the sum of SQRT(75) + SQRT(48), where the only "thought" is to get past thinking that it's SQRT(123), I decided to pull out Right Triangles and that Old Favorite, the Pythagorean Theorem. Now, I didn't want them to just simplify the irrational number, I wanted some kind of addition in the problem. That brings us to Perimeter of a Right Triangle.
There are basically two types of problems you can offer up for consideration: problems with one radical number, and problems with two radical numbers. Three is just being mean, and overly complicates things -- on the other hand, it could make it interesting. Give the students the length of the legs (the base and the height), establish that there is a right angle between them, and let them go to work.
In the first kind of problem, you can pick any two numbers and you'll most likely have an irrational hypotenuse. Okay, but boring. It's more interesting if you make one of the legs irrational in such a way to make the hypotenuse rational. Surprise them.
It keeps it interesting when you consider these two problems, which look very similar, but are very different.
Consider the square root of 13 triangle first. If we square 6, we get 36. If we take the square of the square root of 13, we get 13. 36 + 13 = 49, which is the square of the hypotenuse. Therefore, the hypotenuse is 7.
Finding the perimeter is as simple as adding the three sides, which in this case means combining the like terms, which would be the integers 6 and 7. The perimeter is 13 + root 13.
In the square root 12 problem, the numbers had to be carefully selected. In this case, there will be two irrational numbers. If anything is to be combined, then the radicals have to simplify to the same radicand. Otherwise, the exercise is pointless.
If we square 6, we get 36 again. If we take the square of the square root of 12, we get 12, of course. 36 + 12 = 48, which is the square of the hypotenuse. Therefore, the hypotenuse is root 48.
We can't add any of the numbers as they are written, but we can simplify both of the radicals, as shown:
Both of the radicals have the square root of 3 in simplest form, and their coefficients can be added. The perimeter is 6 + 6 square root 3.
Interestingly, in both examples I wrote for lessons today, a double number appeared in the answer. This is actually something else to be careful about. Some students might see that as a co-incidence. Others might see it as a pattern and come to expect it.
There is an easy solution to that: give them some more problems to work on!
The Formula being Marriage = Brains X Muscle X Height. Or something like that.
And packing a garage for the winter isn't just a 3-D jigsaw puzzle. You still need to access to the winter things.
Or you could toss some stuff to the curb on bulk pick-up day, but that never happens.
One day, maybe we'll have a garage big enough so that there's also room for the car.
If everyone waits until the end of the season to watch, will the show make it to the end of a season?
They're decomposing numbers ... there's less of them every year ...
Happy Halloween!
Secant you will find what Man was Not Meant to Know.
SPOILER ALERT: Hypotenuse comes out on Top!
You don't meet nice shapes on Skid Row.
Don't feed the plant! Plus a Constant.
Coming to a Theta near you! It's got a Killer soundtrack and high Rotten Tomatoes score!
Happy 7th Birthday, (x, why?)! Back? After seven years and 921 comics (more or less), I'm not going anywhere!
Funny thing about using song lyrics. Thanks to the Internet I can check on the lyrics I'm not sure about, and discover that the ones I've "known" since I was a kid aren't actually the words, but they've been stored that way. As for "Signs", I discovered that every site had one of two distinct sets of lyrics. My "understanding" was somewhere in between, but still incorrect. Glad I checked. I learned that lesson all the way back in Comic #99 -- before I uploaded it, thankfully!
Starting Year 8 ... now.