Week of 10/31/2016

Geometry

Circles and Chords

A chord is a segment that joins two points of the circle. A diameter is a chord that contains the center of the circle.

Theorems:

1.2. 3.

In a circle, a radius perpendicular to a chord bisects the chord.In a circle, a radius that bisects a chord is perpendicular to the chord. In a circle, the perpendicular bisector of a chord passes through the center of the circle.

Proof of Theorem 1:

Statements		Reasons
1.		1.	Given
2.		2.	Two points determine exactly one line.
3.		3.	Perpendicular lines meet to form right angles.
4.		4.	A right triangle contains one right angle.
5.		5.	Radii in a circle are congruent.
6.		6.	Reflexive Property - A segment is congruent to itself.
7.		7.	HL - If the hypotenuse and leg of one right triangle are congruent to the corresponding parts of another triangle, the triangles are congruent.
8.		8.	CPCTC - Corresponding parts of congruent triangles are congruent.
9.	E is the midpoint of	9.	Midpoint of a line segment is the point on that line segment that divides the segment two congruent segments.
10.		10.	Bisector of a line segment is any line (or subset of a line) that intersects the segment at its midpoint.

 

Theorem:

In a circle, or congruent circles, congruent chords are equidistant from the center. (converse) In a circle, or congruent circles, chords equidistant from the center are congruent.

Theorem:

In a circle, or congruent circles, congruent chords have congruent arcs.(converse) In a circle, or congruent circles, congruent arcs have congruent chords.

;

Theorem:

In a circle, parallel chords intercept congruent arcs.

http://www.regentsprep.org/regents/math/geometry/gp14/circlechords.htm

Week of 10.31.2016-11.4.2016 College Readiness Math

Tutoring: Wednesday morning and Friday afternoon
Assessment: Quiz late in the week

No homework all week!

Monday
Happy Halloween1
Today, we finish up the questions with the scale drawing and look at other conversion problems.
Help:https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-geometry/cc-7th-scale-drawings/v/constructing-scale-drawings

Tuesday
It is the day to look at the conversion with height and weight of the students
Help:http://www.metric-conversions.org/length/feet-to-inches.htm


Wednesday
The day to look  at area, surface area and volume of figures and a review for the unit.
Help:http://www.math.com/tables/geometry/surfareas.htm


Thursday
 A prefinal exam assessment, you do not study for this assessment. We continue with volume today
Help:http://www.math.com/tables/geometry/volumes.htm


Friday
A little quiz to wrap up the measurement unit is today, I will run a quiz preview before the quiz.
Help: ( check any previous websites for the unit)

Have a great weekend!

Week of 10/24/2016

Geometry

Formulas for Angles in CirclesFormed by Radii, Chords, Tangents, Secants

Formulas for Working with Angles in Circles(Intercepted arcs are arcs "cut off" or "lying between" the sides of the specified angles.)

There are basically five circle formulas that you need to remember:

1.  Central Angle:  A central angle is an angle formed by two intersecting radii such that its vertex is at the center of the circle. Central Angle = Intercepted Arc <AOB is a central angle.  Its intercepted arc is the minor arc from A to B. m<AOB = 80° Theorem involving central angles: In a circle, or congruent circles, congruent central angles have congruent arcs.

2.  Inscribed Angle:An inscribed angle is an angle with its vertex "on" the circle, formed by two intersecting chords. Inscribed Angle = Intercepted Arc <ABC is an inscribed angle.  Its intercepted arc is the minor arc from A to C. m<ABC = 50°           Special situations involving inscribed angles: An angle inscribed in a semi-circle is a right angle. In a circle, inscribed circles that intercept the same arc are congruent. A quadrilateral inscribed in a circle is called a cyclic quadrilateral. The opposite angles in a cyclic quadrilateral are supplementary.

3.  Tangent Chord Angle:An angle formed by an intersecting tangent and chord has its vertex "on" the circle. Tangent Chord Angle =  Intercepted Arc <ABC is an angle formed by a tangent and chord. Its intercepted arc is the minor arc from A to B. m<ABC = 60°

4.  Angle Formed Inside of a Circle by Two Intersecting Chords:When two chords intersect "inside" a circle, four angles are formed.  At the point of intersection, two sets of vertical angles can be seen in the corners of the X that is formed on the picture.  Remember:  vertical angles are equal. Angle Formed Inside by Two Chords =  Sum of Intercepted Arcs Once you have found ONE of these angles, you automatically know the sizes of the other three by using your knowledge of vertical angles (being congruent) and adjacent angles forming a straight line (measures adding to 180). <BED is formed by two intersecting chords.  Its intercepted arcs are .   [Note:  the intercepted arcs belong to the set of vertical angles.]   also, m<CEA = 120° (vetical angle) m<BEC and m<DEA = 60° by straight line.

5.  Angle Formed Outside of a Circle by the Intersection of:"Two Tangents" or "Two Secants" or "a Tangent and a Secant". The formulas for all THREE of these situations are the same: Angle Formed Outside = Difference of Intercepted Arcs  (When subtracting, start with the larger arc.)

Two Tangents:<ABC is formed by two tangents intersecting outside of circle O. The intercepted arcs are minor arc  and major arc .  These two arcs together comprise the entire circle. Special situation for this set up:  It can be proven that <ABC and central <AOC are supplementary.  Thus the angle formed by the two tangents and its first intercepted arc also add to 180º.

Two Secants:<ACE is formed by two secants intersecting outside of circle O. The intercepted arcs are minor arcs  and .

a Tangent and a Secant:<ABD is formed by a tangent and a secant intersecting outside of circle O. The intercepted arcs are minor arcs  and .

Source: http://www.regentsprep.org/regents/math/geometry/gp15/circleangles.htm

Week of 10.24.2016 College Readiness Math

Tutoring Wednesday morning and Friday afternoon


Assessment : TBA

Monday
It is time to review the conversions via the cards and to create a real-world word problem

HW; None

Tuesday
We look at scale drawings
HW; None

Wednesday
You create a scale drawing of a marked off picture
HW; None


Thursday
It is measurement day, be ready to use a ruler
HW: Assessment in class on Friday


Friday
It is a mini test today on the conversion units and the scale drawing.
HW: None

Have a great weekend!

Week of 10/17/16

Geoemtry

We will be working on circles and volume.

Find Out Things About Circles

This page will show you how to calculate various things that pertain to a circle.Notes about circles: The radius R, or the distance from the center of a circle to its edge, is usually the defining property of a circle. The diameter, or the distance across a circle that passes through the center of the circle is 2R (twice the radius). The circumference, or distance around a circle is 2R. The area enclosed by a circle is R2 Note that =3.1415926535...

http://www.webmath.com/geo_circle.html

College Readiness Math

Tutoring: Thursday morning and Friday afternoon

Assessments: Quiz on Friday ( likely)

Monday
Today, you finish the unit two test and explore units with heart rates.
HW; None


Tuesday ( picture day)
We look at miles per gallon versus gas consumption and the creation of a mathematical model.
HW: None

Wednesday ( PSAT)
We only have 2nd today, so the class will be a continuation of the gas consumption and modeling
HW: None

Thursday
A look at ratios and proportions to solve problems
HW: None

Friday
A quick quiz is possible today and a look at the Golden Ratio and measurements of objects in terms of varying units
Help:http://www.mathsisfun.com/numbers/golden-ratio.html
HW; None

Have a great weekend!

Week of 10/10/2016

Geometry

We are testing on Friday. Find attached a copy of the test review.

College Readiness week of 10.10.2016

Tutoring: Friday afternoon and Wednesday morning

Assessments: Quiz on Monday and test on Thursday  and  Friday

Homecoming Week, hope to see you dressed up with the Spirit Days.

Monday
It is the day for you to shine, quiz day, You shall look over tasks 1 to 4 for unit two.
Help;http://tutorial.math.lamar.edu/Classes/Alg/SolveLinearEqns.aspx
HW: None

Tuesday
We move along to linear inequalities today, you can use your linear equation solving skills.
Help:https://www.mathsisfun.com/algebra/linear-equations.html
HW; none

Wednesday
We are working on linear inequalities again today and I hope you have great success. Also, you will isolate variables in an equation. Finally, you will review for the unit test.
Help:http://www.purplemath.com/modules/ineqlin.htm
HW; Study for test

Thursday
It is part one of the test today after review time
Help:http://www.virtualnerd.com/middle-math/equations-functions/expressions/equation-solution-definition
HW; Study for part two of the test

Friday *( Pep Rally today)
It is part two of the test today with review ahead of the assessment.
Help:http://www.icoachmath.com/math_dictionary/equivalent_equations.html
HW; none

Have a great weekend, hope to see many of you at the homecoming dance.

Week of 10/03/2016

Geometry:

This week we will be working on:

•  Angles of Sine, Cosine, and Tangent
•  Solving Trigonometric Ratios

College Readiness Math week of 10.3.2016

Tutoring: Thursday morning and Friday afternoon

Assessment: Quiz  on Friday

Monday
It is review day of all concepts learned before the break. Also, we look at the interpretation of equations.
HW; None
Help: ( minimal on the web)


Tuesday
It is the interpretation of equations today with minimal teacher assistance.
HW: None


Wednesday
Today, we move on to the quadratic equations
Help: https://www.mathsisfun.com/algebra/quadratic-equation.html
Hw; None



Thursday
Equation day again as we study equations in unit two. The focus will be quadratic equations again today.
Help: https://www.khanacademy.org/math/algebra/quadratics
HW ; Study for the unit test by completing review sheet


Friday
It is quiz day, so I hope you are ready for the assessment. I will give a detailed quiz preview in class.

HW; None


Have a great weekend!

Week of 9/19/16

Geometry

• MONDAY: Triangles and Parallel Lines
• TUESDAY: Review Similarity (Module 3 Review)
• WEDNESDAY: Unit Assessment  
• THURSDAY: Complementary Angles of Sine and Cosine
• FRIDAY: Complementary Angles of Sine and Cosine

College Readiness Math 

Tutoring: Wednesday morning and Friday afternoon

Assessments: A quiz is on Tuesday and unit test is TBA

Monday

today, we look the most in-depth linear equations with some practice for you! Also, we look at the second dice trick. 

Help:https://www.khanacademy.org/math/algebra-home/alg-basic-eq-ineq/alg-old-school-equations/v/algebra-linear-equations-1

HW; Study for quiz 

Tuesday

You shall shine on the unit two quiz and we explore the equations and the story behind the equation.

Help:https://www.khanacademy.org/math/algebra/one-variable-linear-equations/alg1-linear-eq-word-probs/v/basic-linear-equation-word-problem ( there is minimal information available in relation the writing of a story for the linear equation) 

HW; None

Wednesday

Today, you look writing stories for equations and solving word problems related to linear equations. 

Help:http://www.mathgoodies.com/lessons/vol7/equations.html

HW; None

Thursday
We look at linear inequalities today and the relation to the linear equation.  Also, we look at rearranging equations for a specified variable.
Help:https://www.khanacademy.org/math/algebra/one-variable-linear-inequalities/alg1-two-step-inequalities/v/solving-inequalities

HW: Study for unit mid assessment 

Friday

It is time for a mid unit assessment with a reflection of the unit thus far.

Help:https://www.khanacademy.org/test-prep/sat/sat-math-practice/new-sat-heart-of-algebra/v/sat-math-h6-easier

HW: None 

Enjoy the week off !