Dividing Fractions; "Reciprocal"

This first video is not very loud, and parents of younger children may want to simply use it as an example of how to teach the concept.

I show first (by drawing it out) that 6/2 = 3, then show how 6 divided by ½ cannot equal 3, but instead equals 12.  Use several examples of this.  12/4 = 3, but 12 divided by ¼ = 48.

(1) Visual aid of how inverting (flipping upside down) the second term, then multiplying the fractions will actually give the correct result.  =)



(2) A reciprocal is an inverted fraction, that when multiplied by the original fraction, gives an answer of 1.
When dividing fractions, you invert (flip upside down) the second term.  This inverted fraction is the reciprocal of the original fraction, and vice versa.
You cannot invert mixed fractions.  You would need to change a mixed fraction into an improper fraction first.



(3) Dividing fractions, part 1



(4) Dividing mixed numbers



(5) Dividing fractions, part 2


Apologies

If you have clicked the facebook link on the right, I had previously copied the wrong code.  I think it was a sample code, lol.  So if you did click it, intending to follow Homeschooler's Resources on facebook, you may have followed "Facebook Platform" instead.  To undo this, click Facebook Platform, and if you had "liked" it, on the bottom left, you can click "unlike."  To see if you are following Homeschooler's Resources on facebook, see if it still says "Like" at the top or not.  "Like" will disappear after someone has liked a page.
I'm sorry if you were confused by any unexpected updates from Facebook Platform in your News Feed.  =D

Issues with videos not playing

A few days ago, I noticed certain videos would not play while I was using my Firefox browser.  Neither here on the blog, nor on YouTube.  It keeps telling me I need to upgrade my Adobe Flash Player, but the videos still wouldn't play.  As of right now, none of them will play in FF.
I've googled this to try to find and fix the problem, and apparently others are having the same issue.
I have not been able to remedy this yet on my end, so if you are using Firefox and are unable to get the videos to play, you might try viewing the blog in another browser for now.  Maybe Firefox will resolve its issue w/ Adobe Flash soon.
Try Internet Explorer, Safari, Google Chrome, or any others you like.  I have all these on my computer, and  use different browsers for various sites.
Hoping to find a solution!

ETA:  I found this link which said I had to uninstall old versions first, then restart my computer, then install the new version.  I then restarted my computer again, just to be sure, lol.
A couple of years ago, I would have looked at those instructions and threw up my hands!  I would have had no clue.  If that is you, don't feel bad.    Just download one of the browsers above, which actually, is pretty easy.
(I remember just a few years ago asking my Mom how to reply to an email!)  =D
Before the fix, Google Chrome seemed to work best for me for watching videos, since I destest the slowness of Internet Explorer, and apparently, there is some download I am missing in Safari.  I think there is a box I unchecked while downloading the browser.  That might be it.
So the videos are working now for me in Firefox, but apparently others have gotten it fixed, and it quit working again.  We'll see.
Keepiomf dimnfgers fvrosdfed.  Um... I meant "keeping fingers crossed!"  That didn't work so well, lol!

Multiplying Fractions, cross cancellation

(1) Multiplying fractions with whole numbers


(2) Multiplying mixed numbers



Apologia Biology, Module 13, Phylum Chordata

M13 Recap blog post at Sahm-I-Am 
Quizlet Vocabulary Game, M13 

Members of Phylum Chordata have a vertebrae.  That is, some kind of vertebrae.  Some have a notochord, which is a tough, flexible material.  In fact, ALL members of this phylum have a notochord at some time in their existence.  Some will harden into a vertebrae, like humans.  =)
This difference is the first level of classification for this phylum.

Note:  Dissections are not only to learn about the parts and organs different animals, but to prepare the student for learning about human anatomy.  Since I know at least some of my students will not take the advanced biology, The Human Body, I have included a few things that pertain more to humans than the organism being discussed.  Also, I could not find a video about the circulatory system of a fish.  =D


Here's a review of a few terms if you are still not quite familiar with them.
  • Dorsal - referring to the back, or it might seem to be the top if the animal is not upright like a human, but it is its back.  Like a dorsal fin on the back of a fish.
  • Ventral - referring to the front, or belly-side of an organism.
  • Anterior - in front of, or the end that contains an organism's head.
  • Posterior - in back of, or the end that contains an organism's tail.
A shark has an anterior dorsal fin and a posterior dorsal fin.  This indicates which is in front of the other; they are both on its back.
Something can also be "anterior to" another body part, meaning it is in front of it, and "posterior to" another body part would mean it is in back of it.


Don't let these big words scare ya!
► Phylum Chordata (core DOT uh)
♦ Subphylum Urochordata (YER uh core DOT uh)  You're a core dotta, haha.  The members of this subphylum only have a notochord for the first part of their lives, during the larval stage.
♦ Subphylum Cephalochordata (SEF uh low core DOT uh).  This subphylum has organisms that will have a notochord all their lives.
♦ Subphylum Vertabrata - The notochords of this subphylum harden into a backbone before they are hatched or born.   

Which one are we?  Hint:  We don't have a larval stage.  =)



(1) p. 393-394, Subphylum Urochordata
Sea Squirt






(2) p. 395, Subphylum Cephalochordata
Lancelet





(3) p. 396-398, Subphylum Vertebrata; The Endoskeleton
Spongy bone, as it is called in your text, is also called cancellous bone.

Osteoblasts, osteoclasts, osteocytes, periosteum
Osteo/osteum refers to bone.   
Cytes refers to cells.   
Peri refers to surrounding something, like the word "perimeter."
  • Osteoblasts are the bone cells that help build new bone matrix.
  • Osteoclasts are the bone cells that break down old bone so that new bone can be formed, often for growth or remodeling.
  • Osteocytes are mature bone cells that are surrounded by the bone matrix.
  • Periosteum is a tough thin membrane that makes up the outer layer of bone.  It is filled with nerves and blood cells that supply oxygen and nutrients to the cells in the bone, and when you break a bone, the periosteum feels pain. 



Put this skeleton back together


(4) p. 399, The Circulatory System
A closed circulatory system is one where the blood is enclosed in blood vessels.
Arteries, Veins, Capillaries of humans




(5) p. 400-401, The Nervous System
The lobes of a human brain.
The cerebrum consists of the majority of the brain, made of different lobes.
The other part is the cerebellum.
►Scroll down to see an image of brain lobes.  Read about their functions.

Brain and spinal cord.
The spinal cord is the bundle of nerves that extend from the brain and make up the central nervous system.  The spinal cord is protected since it runs down the center of the vertebral column.

Spinal cord and nerves.
The spinal cord is enclosed by the vertebrae.  Arteries, veins, and nerves branch out from the spinal cord.
The cartilage between each vertebra is for cushioning and also allows you to tie your shoes!  =)
See how the nerves come from your spinal cord to your whole body.


(6) p. 401-402, Reproduction
Oviparous (development in an egg, hatched outside the female's body)
Ovoviviparous (development in an egg, hatched inside the female's body)
Viviparous (development inside the female, gains nutrients, etc. though the placenta)



(7) p. 403-404, Class Agnatha (jawless fish)  Lol, Agnatha talked so much, her jaw deteriorated.
Lamprey




(8) p. 409-413, Class Osteichthyes (bony fish)
Remember, osteo refers to bone.  Ichthyes means fish.
Circulatory system of humans


Bronchial tubes end in bronchioles, which end in alveoli, which are air sacs where the oxygen exchange takes place.  (It kind of looks like broccoli trees.)
If someone has asthma, because of the swelling of the bronchial tubes he is only able to take shallow breaths.  He will not be able to "exchange oxygen" sufficiently because the oxygen he is trying to breathe in would not get all the way to the aveoli where the exchange between oxygen and carbon dioxide takes place.
It feels like closing your nose and breathing with your mouth through a thin straw while something is constricting your chest and lungs. 


How your lungs put oxygen back into oxygen-depleted blood.




(9) p. 416-419a, Perch Dissection
►Awesome labeled perch dissection.
(You can also view the unlabeled perch to see if you can name everything.)
rice crispy, fondant-covered, dissected perch at Applie's Place.  She did an awesome job!




(10) p. 419-422, Class Amphibia
Amphi means both sides; bio means life.  Anphibia means dual life.




(11), p. 422, Frog Dissection
►Awesome virtual frog dissection.  Wish I could find something this good for all the dissections.  =)
At the top right, click on Demo.
You will be told different buttons to click on.  As you hover over the buttons, the name of that button appears at the bottom of the screen.  Body parts will do the same thing, so you'll know if you are on the right part.

►See the Applie's yummy frog!  I'm not that creative.  =D



Anatomy & Physiology, L2 - The Skeletal System


Put this skeleton back together Now this link is something about the weather! =\

The Human Skeleton


Skeleton up close



Spongy bone - bones get stronger w/ exercise



More about the Human Skull



Dancing Skeleton =)



Parallelograms in depth

At 22:35 "All triangles add up to 100," but he meant 180.
All the measurements of the angles in a triangle add up to 180°.

Geometry - Parallelograms from Yay Math on Vimeo.

Factoring Polynomials - Solving for x

(1) Solving Polynomial Equations for x
She gets two answers.  In this case, if you plug either of those back into the original equation, they both work.  Sometimes, one will not work, and you throw it out as a possibility.


(2) More on Trinomials - solving for x  (Trinomials are a type of polynomial.)
►Accompanying worksheet for this video.



Introduction to Factoring Trinomials - reverse of FOIL

YayMath.org  "Factoring means turn it into pieces you can multiply." 
►Accompanying worksheet for this video.



A trinomial has 3 terms.   x² + 2x - 63
A binomial has 2 terms.   x - 7
The 2 factors of a trinomial are binomials, and each can be written in parentheses.
(x + 9)(x - 7)  They are called binomial factors.
When these binomial factors are multiplied, they will equal the trinomial.

After checking for a greatest common factor and factoring it out, then you can factor the trinomial.

To easily determine signs when factoring trinomials:

1.  If the sign of the last term in a trinomial is negative, such as x² + 2x - 63
the signs between the terms in the binomial factors will be one positive and one negative.
Example 1:  
x² + 2x - 63
(x + 9)(x - 7)

Example 2:
x² - 2x - 63
(x - 9)(x + 7)

Do you see the difference?
• In the first example, only the last term in the trinomial was negative.
• In the second example, both the last term and the middle term were negative.
• So no matter what the middle term is, if the last term in a trinomial is negative, the signs between the terms in the binomial factors will be one positive and one negative.

So what does the sign of the middle term in the trinomial tell us?
It is what you use to determine which of the binomial factors will be positive, and which will be negative.
• In the first example, the middle term of the trinomial is positive (+2x), showing that the 9 in the binomial factors should be positive since it is greater than 7, because if you combine +9 and -7, you will get +2.
• In the second example, the middle term of the trinomial is negative (-2x), showing that the 9 in the binomial factors should be negative, because if you combine -9 and +7, you will get -2.


2.  If the sign of the last term of a trinomial is positive, the signs between the terms of the binomial factors will either be BOTH positive or BOTH negative.
• If the last term in the trinomial is + 63, the terms in the binomial factors will either be 
( __ - 7) and ( __ - 9), or they will be ( __ + 7 and ( __ + 9).
• Then the sign of the middle term of the trinomial will determine what they both will be.

Example 3:
x² + 2xy + y²
(x + y)(x + y)

Example 4:
x² - 2xy + y²
(x - y)(x - y)

If you use the FOIL method and multiply the Inner and Outer terms (from the binomial factors), you will get either both positive terms or both negative terms to add together, equaling the middle term of the trinomial.
In example 3, +xy and +xy will give you +2xy.
In example 4, -xy and -xy will give you -2xy.


►Found this video at Virtual Nerd: Determining Signs when Factoring a Trinomial


Multiplying Polynomials - FOIL and more

• Monomial - 1 term
• Binomial - 2 terms
• Trinomial - 3 terms
• Polynomial - more than 1 term

(1) YayMath.org - Foil method
►Accompanying worksheet for this video.
►Online quiz.


(2) Multiplying a binomial by a polynomial


(3) Multiplying vertically - I like this method!



Rules for Exponents

There are a lot of videos here!  About 35 minutes total, so I suggest taking more than one day to watch these, and taking notes as you do. The first several videos are shorter.


Interactive lessons -- may be best to do after viewing the videos here.
Click Unit 5Lesson 20Play Lesson.  Click on the lesson titles on the left.
You may read along with the lesson in the left sidebar.
Note:  Lesson does not seem to work in Safari browser.


(1) Product Rule


(2) Quotient Rule


(3) Power Rule


(4) Using the rules


(5) Simplifying fractions with exponents


(6) Exponents, powers of base 10


(7) Level 1 Exponents, part 1 - the "why" of some of the above, and a few new concepts.


(8) Level 1 Exponents, part 2

In the last example, he leaves "3 to the negative 36th power." 3^-36, (since I can't write exponents on here except for °²³).  I have been taught and have seen taught in various videos online that you should try to not have a negative exponent in your answer.
In the 5th video, she showed how to get rid of negatives by moving the negative exponent to either the top or bottom of a fraction.  So the last answer could be written as a fraction: 1/3^36.  "1 over 3 to the 36th power."


Dividing Polynomials

YayMath.org
►Accompanying worksheet for this video.

Algebra 2 - Dividing Polynomials from Yay Math on Vimeo.


Systems of Equations: Inconsistent/Consistent; Independent/Dependent

When graphing systems of equations, you can figure out whether they are consistent or inconsistent.
If they are consistent, you then see whether they are independent or dependent.

(1) The differences


►If the lines are parallel to each other:
•there is no solution (There is no place of intersection - which would have been the solution, therefore no solution.)
•and they are inconsistent (have no points in common)
►If lines intersect:
•they have a solution such as (2, -4) or where ever they intersect, and that is what you write. "(2, -4)"
•they are consistent (have at least one point in common)
•and they are independent (of each other -- they go their own direction)
►If lines land in the same place, on top of one another:
•the solution is along the entire line - any and all points on the line will work as the solution, so you would say "entire line" or "infinite."  There is an infinite number of possible points along the entire line.
•they are consistent (have at least one point in common)
•they are dependent (do not go their own direction)

(2) Using substitution to tell the difference


Natural #'s, Whole #'s, Integers, Rational, & Irrational #'s

Natural Numbers vs. Whole Numbers at Virtual Nerd
►If that video helped you, here are more videos from Virtual Nerd about kinds of numbers.

YayMath.org

Algebra - Properties of Real Numbers from Yay Math on Vimeo.

Other examples:
►6/3 = 2, so this fraction is a natural number.  It is also a whole number, an integer, and a rational number.
►√4 = 2, so this is a natural number, a whole number, an integer, and a rational number.
Any number that can be written as a fraction is a rational number.  2 can be written as 2/1.
►√-1 is irrational, because the number inside the square root has been squared; multiplied by itself.
Such as √16 = 4.  16 is a square of 4.  So 4 is the square root.
BUT what would be the square root of √-16?  There is no answer, so this is irrational.