Thursday, May 28, 2009

Generation H

High school students love to greet each other with hugs. Some schools ban it. Some schools, a very few, encourage it. These are not PDA (Public Display Of Affection) type hugs, not romantic type hugs, just hello hugs and goodbye hugs. As teachers we are told the upper shoulder is the only appropriate touch place and even that can be only a few seconds. Too risky to break that rule. However it seemed okay to hug students at Honors Day when handing out awards. Really, what's wrong with a hug in front of 1000 people? What can happen? I hug students when they move away....or if they do something drastic like dropout of school. I want them to know they will be missed and that it matters that they will no longer be with us. The hugging thing is a little overdone but I think I would welcome it more likely than ban it. What about you? Are you a hugger or a handshake? Does hugging have any place at school?

Wednesday, May 20, 2009

No More Grocery Checkers?

New grocery store technology coming soon! How does it work? Here's how:
You know how it goes. You select an item....put it in buggy.....go to check out lines. Then you take everything back out of your buggy, get it scanned, put it back in bags and then out to the car.

A lot of those steps are going away. Soon your buggy will have a scanner on it. When you put an item in your buggy it will automatically scan the price and keep a running total for you. If you go over your limit, you can "unscan" it and put the item back. It will come off your bill. When finished the total is automatically put on your debit card or credit card and out you go. Bring those cloth bags and you are in business. No more checkout lines. No more checkers. Just you, your cart, and your scanner.

What do you think?

Friday, May 15, 2009

Done!!! Go Play!!!

Yea!!!!!! Geometry End Of Course Tests are done in my area! If you haven't had yours yet, you will have it in the next few days. All of my students are finished and out celebrating! This blog is taking a break from math and will talk about other things for awhile. Whew!

Tuesday, May 12, 2009

How Many Lines of Symmetry? (LOS)

1. Circle has infinite # LOS.
2. Parallelogram has NO LOS.
3. Rhombus has 2 LOS.
4. Reg Hexagon has 6 LOS.
5. Square has 4 LOS.
6. Rectangle has 2 LOS.
7. Reg Pentagon has 5 LOS.
8. Equilateral Triangle has 3 LOS.
9. Kite has 1 LOS.
10. Isosceles Trapezoid has 1 LOS. Non-Isosceles Trap has NO LOS.

Every regular polygon has the same number of LOS as it does sides!

Tips For Taking Your EOCTs

General Test Taking Strategies:
1. Don't leave anything blank. Eliminate any answers you can and make an educated guess between remaining answers.
2. There is usually a "sucker" answer for those who don't read carefully. Don't let that be you.
3. Remember there is a formula sheet. Use it.
4. Use your calculator! Eliminate careless errors.
5. Always ask yourself, "Is my answer reasonable?"
6. If you don't know where to start, skip it and come back to it.
7. Eat something before the test. Don't be hungry! Feed and water your brain.
8. Look for shortcuts, "catches" on all graphing problems. Count vertically/horizontally on the graph whenever you can.
9. Be prepared and approach the test with confidence! Know you can do well!
10. Ask for scratch paper. Use it. Draw.

Specifically for Geometry:
a. Notice whether two triangles are congruent or similar.
b. Notice if you have a right triangle. Look for right angles.
c. Notice 9-12-15 is same as 3-4-5 triangle.
d. Vertical angles are ALWAYS congruent. Nothing to do with parallel lines.
e. Know Slope Formula. Parallel lines have same slope.
f. If one slope =2/3 and another slope = -3/2, the lines are perpendicular.
g. On scale factor, notice if you are going small to large, or large to small.
h. Switch the "if" and "then" statements to get converse. The converse may or may not be true.
i. Regular hexagons have 6 lines of symmetry.
j. Pentagons contain 540 degrees.
k. Be able to identify a transversal.
l. Know concentric circles when you see them.

Monday, May 11, 2009

Exterior Angles Of A Triangle

What do you know about the exterior angles of a triangle?

1. Each exterior angle forms a linear pair with its adjacent interior angle.
2. In other words, each exterior angle + adjacent interior angle = 180 degrees
3. Exterior angle = Sum of the two remote interior angles.
4. In other words, an exterior angle = sum of the non-adjacent interior angles.
5. In any regular convex polygon, exterior angles always add to 360 degrees.
6. In any regular convex polygon, each exterior angle = 360/number of sides.
7. You can extend a side of a polygon to form an exterior angle.
8. What else?

Saturday, May 9, 2009

30-60-90/45-45-90 Triangle Relationships

30-60-90 Triangles

The side opposite the 30 degree angle is the short side. Let's start there. This side is half of the hypotenuse...or you could say the hypotenuse is two times the short side. The hypoenuse is the longest side. That leaves the side opposite the 60 degree angle....the middle side. It is always √3 times the short side. In other words:

Short Side = x
Medium Side = √3 x
Long Side = 2x
45-45-90 Triangles

The two sides opposite the 45 degree angles are congruent. The third side is √2 times the shorter sides.

Both Congruent Sides = x
Hypotenuse = x √2

Remember Your Right Triangle Trig Ratios?


Sin A = Opposite/Hypotenuse

Cos A = Adjacent /Hypotenuse

Tan A = Opposite/Adjacent

Remember you can use these ratios is you have a right triangle. Angle A refers to either of the two acute angles in the triangle but not the right angle. If you do not have enough info to use the Pythagorean Theorem, you can usually use these trig ratios.

Friday, May 8, 2009

What Are Skew Lines? Aren't You Dying To Know?

Everybody needs to understand skew lines :) .....before they take any end of course test.

Skew lines are lines that do not lie in the same plane. That is, they are noncoplanar. Think of two lines that are not parallel, yet they do not intersect. Those lines are skew lines.

The lines in this drawing are skew lines. They are not in the same plane. The do not intersect. They are not parallel.

Tuesday, May 5, 2009

Deductive or Inductive? For My Students

Way back in the beginning of the year you learned about 2 kinds of reasoning. Later you learned to write proofs. Remember how much fun that was!!!!

Inductive Reasoning: This kind of reasoning is based on patterns that you observe. Here's an ex.
Based on this pattern, what is the sum of the first 9 consecutive positive odd numbers?
a. 49
b. 64
c. 81
d. 100

Answer: c Do you see the pattern?.

Deductive Reasoning: This kind of reasoning is based on facts...theorems, postulates, properties. When you write a proof using theorems, you are using deductive reasoning.

Friday, May 1, 2009

Random Facts On The Geometry EOCT

1. Concentric circles look like a bulls eye. They have the same center.
2. If a figure is enlarged it is called a dilation. The scale factor is greater than 1.
3. If the scale factor is less than 1, the figure gets smaller.
4. Volume is easy. Just find the area of the base, then multiply that by the height. If it is a pyramid or cone, do the same thing, then divide it by 3. Use cubic units.
5. The sum of the exterior angles of a convex polygon is always 360.
6. Geometry uses DEDUCTIVE reasoning and INDUCTIVE reasoning. Deductive reasoning is based on facts, like in proofs. Inductive reasoning is based on patterns.
7. If you have 3 skirts, 4 shirts, and 5 hats, you can make 3x4x5 or 60 different outfits!
8. Lines that are not parallel and are not in the same plane are called SKEW lines.
9. The scale factor is the "ratio of the sides" in the order stated.
10. Parallel lines have the same slope.
11. Any two sides of a triangle must add up to be greater than the third side.
12. A hexagon contains 6 equilateral triangles.
13. The MEAN is the average. The MEDIAN # is the middle number. The MODE is the one that occurs the most frequently. The RANGE is the highest # - the lowest #.