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

Problem: 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.
 Phrase Expression the sum of nine and eight 9 + 8 the sum of nine and a number x 9 + 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.
 Phrase Expression nine increased by a number x 9 + x fourteen decreased by a number p 14 - p seven less than a number t t - 7 the product of 9 and a number n 9 · n   or   9n thirty-two divided by a number y 32 ÷ 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.
 Phrase Expression five more than twice a number 2n + 5 the product of a number and 6 6n seven divided by twice a number 7 ÷ 2n   or three times a number decreased by 11 3n - 11
Anatomy

Anatomical motions

What motions involve increasing or decreasing the angle of the foot at the ankle?

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 Triangles Corresponding Congruent Angles Corresponding Proportional Sides a/f = b/d = c/e = factor ΔABC ~ ΔFDE
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".

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.

If 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.