Monday, August 28, 2017

Weak of August 28, 2017

Open House:
Our open house is this Thursday, August 31, 2017

Foundation Of Algebra

Evaluate expressions
A variable is a letter, for example x, y or z, that represents an unspecified number.
To evaluate an algebraic expression, you have to substitute a number for each variable and perform the arithmetic operations. In the example above, the variable x is equal to 6 since 6 + 6 = 12.
If we know the value of our variables, we can replace the variables with their values and then evaluate the expression.

Calculate the following expression for x=3 and z=2
$$6z+4x=\: ?$$
Solution: Replace x with 3 and z with 2 to evaluate the expression.
$$6z+4x=\: ?$$
$$6\cdot {\color{blue} 2}+ 4\cdot {\color{blue} 3}=?$$
$$\: \, 12+12=24$$




Similar Triangles Review

Similar triangles have the same shape, but the size may be different.
Remember "≅" means "is congruent to" and "~" is "similar to". Examples
Corresponding TrianglesCorresponding Congruent AnglesCorresponding Proportional Sides
a/f = b/d = c/e = factor
<B = <D
<C = <E
a/f = 6/3 = 2
b/d = 8/4 = 2
c/e = 10/5 = 2
<B = <D
<C = <E
a/f = 3/3 = 1
b/d = 4/4 = 1
c/e = 5/5 = 1
Two triangles are similar if:
  • two pairs of corresponding angles are congruent (therefore the third pair of corresponding angles are also congruent).
  • the three pairs of corresponding sides are proportional.
Notice the corresponding angles for the two triangles in the applet are the same. The corresponding sides lengths are the same only when the scale factor slider is set at 1.0. Study the side lengths closely and you will find that the corresponding sides are proportional.

Monday, August 21, 2017

Week of August 21, 2017

Tutoring is every morning from 7.45- 8.10 a.m. every day.

Foundations of Algebra :


  • Simplify \mathbf{\color{green}{ \sqrt{24\,}\,\sqrt{6\,} }}

Neither of 24 and 6 is a square, but what happens if I multiply them inside one radical?
\sqrt{24\,}\,\sqrt{6\,} = \sqrt{24\times 6\,} = \sqrt{144\,}
Now I do have something with squares in it, so I can simplify as before:
\sqrt{144\,} = \sqrt{12 \times 12\,} = \mathbf{\color{purple}{ 12 }}

  • Simplify \mathbf{\color{green}{ \sqrt{75\,} }}

The argument of this radical, 75, factors as:
75 = 3 × 5 × 5
This factorization gives me two copies of the factor 5, but only one copy of the factor 3. Since I have two copies of 5, I can take 5 out front. Since I have only the one copy of 3, it'll have to stay behind in the radical. Then my answer is:
\sqrt{75\,} = \sqrt{3\times 25}
= \sqrt{3\,}\,(5) = \mathbf{\color{purple}{ 5\sqrt{3\,} }}
This answer is pronounced as "five, times root three", "five, times the square root of three", or, most commonly, just "five, root three".

§Connective tissues have diverse structures and functions (continued)
Specialized connective tissuesThis diverse group includes cartilage, bone, fat, blood, and lymphCartilage consists of widely spaced cells surrounded by a thick, nonliving matrix composed of collagen secreted by the cartilage cellsBone resembles cartilage, but its matrix is hardened by deposits of calcium phosphateAdipose tissue is made up of fat cells that are modified for long-term energy storage
Adipose tissue can also serve as insulation for animals living in a cold environment

How to tell if triangles are congruent

Any triangle is defined by six measures (three sides, three angles). But you don't need to know all of them to show that two triangles are congruent. Various groups of three will do. Triangles are congruent if:
  1. SSS (side side side)
    All three corresponding sides are equal in length.
    See Triangle Congruence (side side side).
  2. SAS (side angle side)
    A pair of corresponding sides and the included angle are equal.
    See Triangle Congruence (side angle side).
  3. ASA (angle side angle)
    A pair of corresponding angles and the included side are equal.
    See Triangle Congruence (angle side angle).
  4. AAS (angle angle side)
    A pair of corresponding angles and a non-included side are equal.
    See Triangle Congruence (angle angle side).
  5. HL (hypotenuse leg of a right triangle)
    Two right triangles are congruent if the hypotenuse and one leg are equal.
    See Triangle Congruence (hypotenuse leg).

AAA does not work.

Two triangles that have the same shape, but one is larger than the otherIf all the corresponding angles of a triangle are the same, the triangles will be the same shape, but not necessarily the same size. For more on this see Why AAA doesn't work.
They are called similar triangles (See Similar Triangles).

SSA does not work.

Given two sides and a non-included angle, it is possible to draw two different triangles that satisfy the the values. It is therefore not sufficient to prove congruence. See Why SSA doesn't work.


Another way to think about the above is to ask if it is possible to construct a unique triangle given what you know. For example, If you were given the lengths of two sides and the included angle (SAS), there is only one possible triangle you could draw. If you drew two of them, they would be the same shape and size - the definition of congruent. For more on constructions, see Introduction to Constructions

Properties of Congruent Triangles

If two triangles are congruent, then each part of the triangle (side or angle) is congruent to the corresponding part in the other triangle. This is the true value of the concept; once you have proved two triangles are congruent, you can find the angles or sides of one of them from the other.
To remember this important idea, some find it helpful to use the acronym CPCTC, which stands for "Corresponding Parts of Congruent Triangles are Congruent".
In addition to sides and angles, all other properties of the triangle are the same also, such as area, perimeter, location of centers, circles etc.

Monday, August 14, 2017

Week of August 14, 2017

Foundations of Algebra:

Integer Rules for Addition, Subtraction, Multiplication, and Division

Anatomy and Physiology:

Connective Tissues:


As the name implies, connective tissue serves a "connecting" function. It supports and binds other tissues in the body. Unlike epithelial tissue which has cells that are closely packed together, connective tissue typically has cells scattered throughout an extracellular matrix of fibrous proteins and glycoproteins attached to a basement membrane.


In vertebrates, the most common type of connective tissue is loose connective tissue.
It holds organs in place and attaches epithelial tissue to other underlying tissues.

Loose connective tissue is named based on the "weave" and type of its constituent fibers. There are three main types:
  • Collagenous fibers are made of collagen and consist of bundles of fibrils that are coils of collagen molecules.
  • Elastic Fibers are made of the protein elastin and are stretchable.
  • Reticular Fibers join connective tissues to other tissues.


Another type of connective tissue is dense or fibrous connective tissue, which is found in tendons and ligaments. These structures help attach muscles to bones and link bones together at joints. Dense connective tissue is composed of large amounts of closely packed collagenous fibers. Much of the dermis layer of the skin is composed of dense irregular connective tissue.



Adipose tissue is a form of loose connective tissue that stores fat.
Adipose lines organs and body cavities to protect organs and insulate the body against heat loss. Adipose tissue also produces endocrine hormones.
Cartilage is a form of fibrous connective tissue that is composed of closely packed collagenous fibers in a rubbery gelatinous substance called chondrin.
The skeletons of sharks and human embryos are composed of cartilage. Cartilage also provides flexible support for certain structures in adult humans including the nose, trachea, and ears.
Bone is a type of mineralized connective tissue that contains collagen and calcium phosphate, a mineral crystal. Calcium phosphate gives bone its firmness.
Interestingly enough, blood is considered to be a type of connective tissue. Even though it has a different function in comparison to other connective tissues it does have an extracellular matrix. The matrix consists of the plasma, while red blood cellswhite blood cells, and platelets are suspended in the plasma.
Lymph is another type of fluid connective tissue. This clear fluid originates from blood plasma that exits blood vessels at capillary beds. A component of the lymphatic system, lymph contains immune system cells that protect the body against pathogens.


Sequences of Transformations - Module 18.1 - YouTube

Monday, August 7, 2017

Week of August 7, 2017

Foundations of Algebra:

Integer Rules for Addition, Subtraction, Multiplication, and Division

Anatomy and Physiology:

Important links:
  1. youtube channel....  Taylor-Sensei Youtube
  2. Online Anatomy Book Openstax College - Anatomy and Physiology
  3. Another Online Anatomy Book: WikiBooks Human Physiology
Practise help sites
  1. Wiley Interactive Page - extremely useful!
  2. McGraw-Hill Essential Study Partner - must be in internet explorer
  3. Holes Student Online Learning
Game sites:
  1. The Anatomy Arcade
  2. BBC Body interactive


What in the world are geometric transformations? And how do they relate to real life?