Estimated Value and What It Means In Real Life

Estimated value is working out and anticipating the outcome of a scenario. I believe when estimated value starts being valued and used in your everyday life, that is when you have true maturity and common sense. I have a cousin who, ever since we were little, could never think forward and estimate the consequences of his actions. I remember when we were about seven and nine, we were at my grandma's house playing with some of my other cousins. All the sudden, he decided that it would be an awesome idea to slide down the laundry shoot. He could not visualize the possible outcomes of doing this. He didn't see that he could get stuck in the shoot, fall through and hurt himself, break the shoot, or break something else with his fall. All he could get through his head was that it seemed like a good idea, even though there was absolutely no positive outcome. Even at seven, I used some estimated value and tried to tell him not to. But of course he didn't listen and got stuck in the laundry shoot and it took six people to get him out. Estimated value is important not only because it is a right of passage into the adult world, it can also keep you from making stupid mistakes like trying to slide down a laundry shoot.

Comparing Pythagorean Theorem and the Equation of a Circle

The Pythagorean theorem is a^2+b^2=c^2 and the equation of a circle is (x-h)^2 + -k)^2 = r^2
These two equations are similar because since both equations use the same specific values plugged in. They also are similar because they are both true with any right triangle and any circle and both use the shapes' grid points to calculate the distance.

Internally Tangent Circle in Real Life

This astronomical clock in Prague is an example of internally tangent circles in real life because the small circle with astrological signs has a common external point with the circle with numerical signs.

Polyhedrons in Real Life

These plant terrariums are examples of polyhedrons in real life because they are 3D shapes made of polygons.

conditional statements

original:
"If I stay up on Netflix all night then I won't be able to stay awake at school the next day"

inverse:
"If I don't stay up on Netflix all night then I will be able to stay awake at school the next day"
This isn't true because I could be staying up all night not on Netflix, maybe studying or reading, and still not be able to stay awake the next day.

converse:
"If I am not able to stay awake at school the next day then I stayed up on Netflix all night"
This isn't true for the same reason inverse isn't true, I could've stayed up doing other things or I could've just not had a good night of sleep.

contrapositive:
"If I am able to stay awake at school then I didn't stay up on Netflix all night"
This statement is true because I was able to stay awake at school so that means I didn't stay up on Netflix all night.

Why I Like Math..

Most people don't enjoy doing math, and admittingly I am one of those people. But one of the reasons I do like math, is that it applies to things that I do enjoy doing. If I didn't know math, things that I do enjoy to do would be a lot harder. I couldn't cook because I wouldn't be able to get correct measurements in recipes. I wouldn't be able to play field hockey and lacrosse if I couldn't estimate shooter's angles when they take shots on me.  So I don't really dislike math. I dislike the idea of sitting down at a desk and mindlessly doing problems that don't mean anything to me. But when I use math in real life, it is helpful and I couldn't get along as well if I didn't.