Monday, September 18, 2017

Week of September 18, 2017

Foundations:
Complete unit homework packet.

Anatomy:
Muscle packet is due tomorrow.

Geometry:
3.1 and 3.2 quiz is tomorrow. Unit test is on Friday 9/22.

http://www.mathwarehouse.com/trigonometry/sine-cosine-tangent-practice3.php

Wednesday, September 13, 2017

Week of September 13,2017

Welcome back from a 4 day weekend. I hope everybody is safe from Hurricane Irma.

This is a very short week. Kindly complete your study guides for Foundations, Anatomy, and Geometry and complete all missing work.


1st Six Week Progress Report Distribution is on Friday, September 15, 2017

Tuesday, September 5, 2017

Week of September 5, 2017

Foundations of Algebra

Writing Algebraic Expressions

Writing Algebraic Expressions
Group workProblem: Ms. Jensen likes to divide her class into groups of 2. Use mathematical symbols to represent all the students in her class.
Solution: Let g represent the number of groups in Ms. Jensen's class.
Then 2 · g, or 2g can represent "g groups of 2 students".
In the problem above, the variable g represents the number of groups in Ms. Jensen's class. A variable is a symbol used to represent a number in an expression or an equation. The value of this number can vary (change). Let's look at an example in which we use a variable.
Example 1: Write each phrase as a mathematical expression.
PhraseExpression
the sum of nine and eight9 + 8
the sum of nine and a number x9 + x
The expression 9 + 8 represents a single number (17). This expression is a numerical expression, (also called an arithmetic expression). The expression 9 + x represents a value that can change. If x is 2, then the expression 9 + x has a value of 11. If x is 6, then the expression has a value of 15. So 9 + x is an algebraic expression. In the next few examples, we will be working solely with algebraic expressions.
Example 2: Write each phrase as an algebraic expression.
PhraseExpression
nine increased by a number x9 + x
fourteen decreased by a number p14 - p
seven less than a number tt - 7
the product of 9 and a number n· n   or   9n
thirty-two divided by a number y32 ÷ y   or   
In Example 2, each algebraic expression consisted of one number, one operation and one variable. Let's look at an example in which the expression consists of more than one number and/or operation.
Example 3: Write each phrase as an algebraic expression using the variable n.
PhraseExpression
five more than twice a number2n + 5
the product of a number and 66n
seven divided by twice a number÷ 2n   or   
three times a number decreased by 113n - 11
Anatomy

Anatomical motions

 What motions involve increasing or decreasing the angle of the foot at the ankle?
This multi-part image shows different types of movements that are possible by different joints in the body.
Figure 1. Movements of the Body, Part 1. Synovial joints give the body many ways in which to move. (a)–(b) Flexion and extension motions are in the sagittal (anterior–posterior) plane of motion. These movements take place at the shoulder, hip, elbow, knee, wrist, metacarpophalangeal, metatarsophalangeal, and interphalangeal joints. (c)–(d) Anterior bending of the head or vertebral column is flexion, while any posterior-going movement is extension. (e) Abduction and adduction are motions of the limbs, hand, fingers, or toes in the coronal (medial–lateral) plane of movement. Moving the limb or hand laterally away from the body, or spreading the fingers or toes, is abduction. Adduction brings the limb or hand toward or across the midline of the body, or brings the fingers or toes together. Circumduction is the movement of the limb, hand, or fingers in a circular pattern, using the sequential combination of flexion, adduction, extension, and abduction motions. Adduction/abduction and circumduction take place at the shoulder, hip, wrist, metacarpophalangeal, and metatarsophalangeal joints. (f) Turning of the head side to side or twisting of the body is rotation. Medial and lateral rotation of the upper limb at the shoulder or lower limb at the hip involves turning the anterior surface of the limb toward the midline of the body (medial or internal rotation) or away from the midline (lateral or external rotation).
This multi-part image shows different types of movements that are possible by different joints in the body.
Figure 2. Movements of the Body, Part 2. (g) Supination of the forearm turns the hand to the palm forward position in which the radius and ulna are parallel, while forearm pronation turns the hand to the palm backward position in which the radius crosses over the ulna to form an “X.” (h) Dorsiflexion of the foot at the ankle joint moves the top of the foot toward the leg, while plantar flexion lifts the heel and points the toes. (i) Eversion of the foot moves the bottom (sole) of the foot away from the midline of the body, while foot inversion faces the sole toward the midline. (j) Protraction of the mandible pushes the chin forward, and retraction pulls the chin back. (k) Depression of the mandible opens the mouth, while elevation closes it. (l) Opposition of the thumb brings the tip of the thumb into contact with the tip of the fingers of the same hand and reposition brings the thumb back next to the index finger.
Geometry
Properties of Equality (for proving algebraic expressions)

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.
$$6+x=12$$
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.

Example
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.
$$6z+4x=\: ?$$
$$6\cdot {\color{blue} 2}+ 4\cdot {\color{blue} 3}=?$$
$$\: \, 12+12=24$$

Anatomy

Skeleton: https://www.brainpop.com/health/bodysystems/skeleton/


Geometry

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
ΔABC ~ ΔFDE<A = <F
<B = <D
<C = <E
a/f = 6/3 = 2
b/d = 8/4 = 2
c/e = 10/5 = 2
ΔABC ≅ ΔFDE<A = <F
<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 :

SIMPLIFYING RADICALS

  • 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".

Anatomy
CONNECTIVE TISSSUES
§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
Geometry

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.

Constructions

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.