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Abby's Astounding Geometry Blog!-


This blog is for Miss Jovanovich's algebra and geometry classes to share ideas, ask questions, and reflect on what skills and topics we are studying. If we are lucky, we might even get a chance to connect with other students studying the same stuff.

by teacher: Tina Jovanovich
Blog Entries

Article posted June 14, 2012 at 05:41 PM GMT • comment • Reads 49

I can’t believe this is my last blog!!! Freshman year went by way too fast.  I’m gonna miss all my pals at York next year soooo much!  Looking back on the year, there are a few things I wish I would’ve know a little earlier.  I decided I would share them for the incoming freshmen, and maybe make life a little easier for them:)



 





  1. Keep you binders organized.  It’s a pain when you get to finals, and can’t find any of your notes.


  2. Keep an open mind about people.  Everyone changes so much in high school, don’t hang on to your opinions of them from middle school.


  3. Respect the upper class men.  You don’t need to be afraid of them, but keep in mind that you’re a lot younger.


  4. Find the bathrooms with mirrors.


  5. Enjoy high school.  It’s so much better than middle school.


  6. Do your homework! You’re going to have to actually study for tests now.


  7. Challenge yourself.  If you’re acing a CP class, then you need to be in honors.  Don’t breeze through high school.


  8. Don’t mess with Mrs. Adams the librarian.  She’s a lot scary than she looks on the first day.


  9. Use your planner often.  There won’t be any homework websites to go to this year.


  10. Go to athletic events, especially soccer, football, and basketball.  It’s a great way to get involved and meet new people.


Article posted June 14, 2012 at 05:41 PM GMT • comment • Reads 49



Article posted June 14, 2012 at 05:40 PM GMT • comment • Reads 44

We finally made it!  Finals are around the corner, and so is summer!  I can’t wait to ditch my backpack and head to the beach.  But first, I have to survive finals.  To review for Geometry, I’ve posted one of my favorite homework problems from a past unit below.



 



 



KL⎮⎮JM in isosceles trapezoid JKLM.  Find the values of x and y if m⦟J=(23x-8)º, m⦟K=(12y-13)º, and m⦟M=(17x+10)º.



 



m⦟J=m⦟M



23x-8=17x+10



6x-8=10



6x=18



x=3



 



m⦟J+m⦟K=180



23x-8+12y-13=180



61+12y-13=180



12y=132



y=11



 



I chose this problem because I was from one of the first units of the semester, and I didn’t remember that unit at all.  I thought that it would be nice to review since I had forgotten about it.

Article posted June 14, 2012 at 05:40 PM GMT • comment • Reads 44



Article posted June 14, 2012 at 05:40 PM GMT • comment • Reads 102

We finally made it!  Finals are around the corner, and so is summer!  I can’t wait to ditch my backpack and head to the beach.  But first, I have to survive finals.  To review for Geometry, I’ve posted one of my favorite homework problems from a past unit below.



 



 



KL⎮⎮JM in isosceles trapezoid JKLM.  Find the values of x and y if m⦟J=(23x-8)º, m⦟K=(12y-13)º, and m⦟M=(17x+10)º.



 



m⦟J=m⦟M



23x-8=17x+10



6x-8=10



6x=18



x=3



 



m⦟J+m⦟K=180



23x-8+12y-13=180



61+12y-13=180



12y=132



y=11



 



I chose this problem because I was from one of the first units of the semester, and I didn’t remember that unit at all.  I thought that it would be nice to review since I had forgotten about it.

Article posted June 14, 2012 at 05:40 PM GMT • comment • Reads 102



Article posted June 13, 2012 at 03:35 PM GMT • comment • Reads 37

This week in Geometry, we started a new unit on trigonometry.  Using this trigonometry, we can find missing side lengths and angle measures in right triangles.  The trig functions that we use to do this are sine(sin), cosine(cos), and tangent(tan).  These functions are used in the following formulas: sinβ=opposite/hypotenuse, cosβ=adjacent/hypotenuse, and tanβ=opposite/adjacent.  Depending on what variables you have, you can rearrange these formulas to find any value in a right triangle.  There’s an easy way to remember these formulas, and that’s with the acronym: SOH CAH TOA!  Not only is it fun to say, but it can help you remember which function goes with which sides of the right triangle.  SOH stands for sine-opposite-hypotenuse, CAH stands for cosine-adjacent-hypotenuse, and TOA stands for tangent-opposite-adjacent.

Article posted June 13, 2012 at 03:35 PM GMT • comment • Reads 37



Article posted May 23, 2012 at 05:08 AM GMT • comment • Reads 39

In Geometry, we used many different formulas to find the area of different figures in this unit.  We found the area of circles, circle sectors, circle segments, triangles, regular polygons, rectangles, rhombi, kites, and parallelograms.  Some of these formulas were review, such as the circle area (A=r𝜋²), triangle area (A=½bh), rectangle area (A=bh), and parallelogram area (A=bh).  While I enjoyed learning the new formulas, and they were verrrrry helpful, the basic formula for finding the area of a rectangle or parallelogram is still my favorite.  I love this one because it’s so simple, yet one area problem can often take you up to 10 minutes!  Finding those 2 simple variables can be so complicated and can involve so many steps, but once you have them it’s smooth sailing.

Article posted May 23, 2012 at 05:08 AM GMT • comment • Reads 39



Article posted May 15, 2012 at 03:42 AM GMT • comment • Reads 35

This week in Geometry, we continued learning about the Pythagorean Theorem, however, we were also introduced to some cool new shortcuts.  These shortcuts can only be used with either a 45º-45º-90º right triangle, or a 30º-60º-90º right triangles.



In a 45º-45º-90º triangle, both legs will always be congruent because it’s always an isosceles triangle.  Therefore, by simplifying the Pythagorean Theorem, we can conclude that the hypotenuse is equal to a leg times square root 2, or (y = x√2).  A trick to remembering these numbers is the are 2 equals sides in this special right triangle, so you multiply by √2.



In a 30º-60º-90º triangle, the length of the hypotenuse is always twice the length of the shorter leg, therefore, (hypotenuse = 2 x shorter leg).  However, we still need to find the length of the longer side, and there is another shortcut for that.  Since the length of the longer leg is √3 times the length of the shorter leg, you have the theorem (long leg = √3 x short leg).  A trick to remembering the √3 is this special right triangle has an angle of 30º, so 30º→√3.

Article posted May 15, 2012 at 03:42 AM GMT • comment • Reads 35



Article posted May 7, 2012 at 05:11 AM GMT • comment • Reads 47

Wow!  That weekend went by fast! Between homework, projects, soccer, track, and the dance, it feels like I should have one more day of controlled chaos before the school week begins.



It’s even harder to believe that we are already one week into the month of May.  All the college students are coming home, and my brother’s gearing up for his AP exams.  April flew by in the blink of an eye!  It’s especially hard to stay motivated for school when the weather so nice as well.



This week in Geometry, we learned more about the Pythagorean Theorem.  With the Pythagorean Theorem, there are patterns that come up in special right triangles that we studied all week.  These right triangles are a 30º-60º-90º triangle, and a 45º-45º-90º triangle.  With these patterns, you can use shortcuts to find the side lengths of the special triangles.  An example of one such shortcut in a 30º-60º-90º triangle is hypotenuse=2(shorter leg).  While you can still find these values using a²+b²=c², it’s much easier and quicker to use these shortcuts.

Article posted May 7, 2012 at 05:11 AM GMT • comment • Reads 47



Article posted April 27, 2012 at 12:44 PM GMT • comment • Reads 34

This week in Geometry, we finished up our unit on transformations with a “quest” Wednesday.  A quest counts as a test but is the length of a quiz.  But we’re not moving away form transformations yet!  The class is making tessellations on Scratch using what we know about rotations, transformations, dilations, and reflections.



We spent some time reviewing algebraic ideas for homework this week.  One of the topics we went over was radicals.  Radicals deal with square roots, but unlike exponents, they can’t always be simplified down to a rational number.  To simplify a radical, you have to factor out any perfect squares from the square root.  Anything that you can’t factor out, stays under the square root sign.



We also brushed up on the Pythagorean Theorem.  If you know the length of 2 sides of a triangle, then this theorem can be used to find the third.  It also can be used to determine whether a triangle is obtuse, acute, or right.  These concepts were not that hard, and I found the switch to Algebra to be a relief.  I think I’ll enjoy the next unit if it involves this much algebra!

Article posted April 27, 2012 at 12:44 PM GMT • comment • Reads 34



Article posted April 23, 2012 at 06:06 AM GMT • comment • Reads 33

This week we had our Spring Break!  Even though I had already taken my mini vacation the previous week, I was ready for break time.  I had so much make-up work to do from the school that I missed!  I really was looking forward to this vacation to catch up on all my work.  While my schoolwork kept me busy, I was also zipping around playing soccer and running track, so this week wasn’t very relaxing for me.  Oh well!



Last week in Geometry, we learned about reflections, which are also known as flips.  In a reflection, there is always a line of reflection.  This is the line that your pre-image is flipped over.  To do a reflection, you first draw lines through all the vertices of your pre-image that are perpendicular to the line of reflection.  You then measure the distance between those vertices and the line of reflection, so you can make a point the same distance away from the line of reflection on the other side.  These new points will make up your image.  I think that reflections are the hardest transformations, especially when the pre-image and image overlap.

Article posted April 23, 2012 at 06:06 AM GMT • comment • Reads 33



Article posted April 12, 2012 at 12:43 PM GMT • comment • Reads 35

For Easter, my family flew down to Miami, Florida.  It was such a nice break from school after the craziness of ending a quarter!  I didn’t do anything but lay by the pool and soak up the sun.  My biggest worry was how my tan was progressing :)  On Saturday, my father, brother, and I went jet skiing.  It was quite the adventure.  We went on a tour of Key Biscayne, but I felt more like I was racing to catch our guide.  He didn’t understand the word “slow,” so the four of us were whizzing around the ocean at 60 mph the whole time.  To make matters worse, it was windy so the ocean was choppy.  I didn’t realize that those little jet skis could get so much air!  Navigating the waves was tricky because if you let your body move when you hit them then you’d end up jerking your jet ski to the side.  I was hanging on to that jet ski so tight may hands were shaking when I got off!!!  Nevertheless, it was still a fun day.



Last week in Geometry, we looked at some examples of Scratch programs, and had a quick tutorial on how to make one.  We also have started learning about tessellations, and last week we went over translations.

Article posted April 12, 2012 at 12:43 PM GMT • comment • Reads 35



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