HolcombMath

Friday, March 30, 2007

Geometry (Class 64)

Announcements
Quiz Friday, March 30 focusing on Chapter 9 Lessons 1, 2, and 3 (Classes 57 to 63).

Overview
Today’s class focuses on circles and on taking Quiz 10 covering right triangle trigonometry and applications of the Pythagorean Theorem.
Textbook Sections
§10.3 (Txt. p.613) Inscribed Angles
§10.1 (Txt. p.595) Tangents to Circles

Key Attitudes
Mathematics is about looking for patterns.

Key Ideas
The measure of an inscribed angle is 1/2 the measure of its central angle.
The measure of a minor arc is equal to the measure of the central angle.
The measure of a major arc is equal to 360-the measure of the minor arc.
A tangent to a circle is perpendicular to the radius at the point of tangency.

Key Skills
Simplifying square roots.
Using properties of special right triangles to solve problems.

Vocabulary
circle
center
chord
diameter
radius
central angle
inscribed angle
minor arc
major arc
tangent
point of tangency

Handouts
Chapter 10-Lesson 1: The Measure of an Inscribed Angle
Chapter 10-Lesson 2- Tangent to a Circle

Assignment
Chapter 10- Lesson 1- All practice problems and finish packet.
Txt. p.608 #32-41
Disclaimer- The assignment as stated in class is the official assignment. Every effort is made to keep this posting accurate, but you should refer to what was stated in class as the final word.

Thursday, March 29, 2007

Algebra (Class 65)

Overview
In the last class students worked to develop their ability to write an equation for a line when given the y-values for x = 0 and 1. Today we extend this skill so that students can write the equation for a line given any two x-values.
Textbook Sections
§8.5 (Txt. p.371) Determining an Equation of a Line

Key Attitudes
Mathematics is about generalizing and applying patterns.

Key Ideas
Any two points can be used to find the slope of a line.
The slope of a line can be used for the coefficient of the x variable in an equation of a line.
The y-value when x = 0, the y-intercept, can be used for the constant in an equation of a line.
Equations for all lines can be written in the form y = mx+b where m represents the slope and b represents the y-intercept

Key Skills
Drawing and labeling a coordinate graph.
Plotting points on a coordinate graph.
Determining the coordinates of points on a coordinate graph.
Finding the slope of a line given two points.
Finding the y-intercept using equations.
Operations with integers and positive or negative rational numbers.

Vocabulary
coefficient
constant
variable
slope-intercept form

Handouts
No Handouts Posted

Assignment
Practice Worksheet 6.2 (Why did the Skeleton Visit the Butcher Shop) and Worksheet 7.5 (How does the toggle toxx feel today?)
Disclaimer- The assignment as stated in class is the official assignment. Every effort is made to keep this posting accurate, but you should refer to what was stated in class as the final word.

Wednesday, March 28, 2007

Geometry (Class 63)

Announcements
Quiz Friday, March 30 focusing on Chapter 9 Lessons 1, 2, and 3 (Classes 57 to 63).

Overview
Today we finish our work with special right triangles and turn our focus towards circles. In particular we study the relationship between the central angle and an inscribed angles.
Textbook Sections
§9.4 (Txt. p.551) Special Right Triangles
§10.3 (Txt. p.613) Inscribed Angles

Key Attitudes
Mathematics is about looking for patterns.

Key Ideas
Half of a square and half of a equilateral triangle create special right triangles whose side lengths can be determined without the use of trigonometric tables.
An inscribed angle is 1/2 the central angle for the same arc.

Key Skills
Simplifying square roots.
Using properties of special right triangles to solve problems.

Vocabulary
inscribed angle
central angle
tangent line
point of tangencey

Handouts
No Handouts Posted

Assignment
Chapter 9-Lesson 3 Practice Problems (end of the packet) #9-12, 17, 27, 28, 37, 39
Finish Chapter 9-Lesson 3. (Not all the practice problems!) You will be handing in this work with the practice problems you have finished next class.
B4 also needs to complete Chapter 10-Lesson 1 Practice Problems a, b, c (Go ahead and do more of them if you want to get ahead-- all will be assigned next time.)
Disclaimer- The assignment as stated in class is the official assignment. Every effort is made to keep this posting accurate, but you should refer to what was stated in class as the final word.

Tuesday, March 27, 2007

Algebra (Class 64)

Overview
Today we work towards developing the ability to write an equation, and graph, a linear relationship based on patterns observed while playing the “Guess the Rule” game.

Also, here is a link for checking polynomial long division answers. The format is a bit different than we use, but the answers are the same. Interactive Polynomial Long Division

Textbook Sections
§8-3(Txt. p.360) Slope of a Line
§8-4 (Txt. p.366) The Slope-Intercept Form of a line.

Key Attitudes
Mathematics is about generalizing and applying patterns.

Key Ideas
The slope of a line can be found from values in a table.
The slope and y-intercept of a line are a key pieces of information for writing an equation of a line.
The y-intercept can be found once the slope is known by writing and solving an equation, or by asking “What do I have to add to this value after I multiply by the slope?”

Key Skills
Drawing and labeling a coordinate graph.
Plotting points on a coordinate graph.
Determining the coordinates of points on a coordinate graph.
Finding the slope of a line given two points.
Finding the y-intercept using equations.
Operations with integers and positive or negative rational numbers.

Handouts
No Handouts Posted

Assignment
Worksheet 17.14 #1-12
Disclaimer- The assignment as stated in class is the official assignment. Every effort is made to keep this posting accurate, but you should refer to what was stated in class as the final word.

Monday, March 26, 2007

Geometry (Class 62)

Announcements
Quiz Friday, March 30 focusing on Chapter 9 Lessons 1, 2, and 3 (Classes 57 to 63).

Overview
Some right triangles are special. Today we see which triangles these are, and why they are considered special. We then use their “specialness” to solve problems. As time permits, we begin our study of Chapter 10- Circles.
Textbook Sections
§9.4 (Txt. p.551) Special Right Triangles
§10.3 (Txt. p.613) Inscribed Angles
§10.1 (Txt. p.595) Tangents to Circles

Key Attitudes
Mathematics is about looking for patterns.

Key Ideas
Half of a square and half of a equilateral triangle create special right triangles whose side lengths can be determined without the use of trigonometric tables.

Key Skills
Simplifying square roots.

Vocabulary
special right triangle
30-60-90 triangle
isosceles right triangle

Handouts
Chapter 9-Lesson 3: Special Right Triangles
Chapter 10- Lesson 1: The Measure of an Inscribed Angle

Assignment
Chapter 9-Lesson 3 Practice Problems (end of the packet) #1-8, 18-26
Disclaimer- The assignment as stated in class is the official assignment. Every effort is made to keep this posting accurate, but you should refer to what was stated in class as the final word.

Friday, March 23, 2007

Algebra (Class 63)

Overview
In the last class we developed our ability to use slope triangles and proportions to find the y-intercept of a line when given the coordinates of two points on the line. In today’s class we see how equations can be written and used to find the y-intercept.
Textbook Sections
§8-3(Txt. p.360) Slope of a Line
§8-4 (Txt. p.366) The Slope-Intercept Form of a line.

Key Attitudes
Mathematics is about generalizing and applying patterns.

Key Ideas
The slope of a line is ∆y/∆x.
The y-intercept always has a 0 for the x-value.
The x-intercept always has a 0 for the y-value.
The y-intercept or x-intercept can be found using an equation once the slope is known.
All equations for lines can be written in the form y = mx + b where m represents the slope, b represents the y-intercept, x and y represent variables for the horizontal and vertical position on a coordinate graph.

Key Skills
Drawing and labeling a coordinate graph.
Plotting points on a coordinate graph.
Determining the coordinates of points on a coordinate graph.
Finding the slope of a line given two points.
Finding the x-intercept or y-intercept using equations.
Operations with integers and positive or negative rational numbers.

Handouts
No Handouts Posted

Assignment
Graph, find the slope, the coordinates of three points on the line, and the y-intercept for the lines passing through the following points:
1) (-5, 3) and (3, 2)
2) (-5, 3) and (3, 4)

Finish practice worksheets 17.6 and 17.7
Disclaimer- The assignment as stated in class is the official assignment. Every effort is made to keep this posting accurate, but you should refer to what was stated in class as the final word.

Thursday, March 22, 2007

Geometry (Class 61)

Overview
Today we put our trigonometric ratios to work to solve for missing sides and missing angles of right triangles using graphs of the trigonometric functions and trigonometric tables. In addition, we learn the names of the three basic trigonometric functions we have been working with. As time permits we will start to examine some special right triangles and the relationships between the lengths of their sides.
Textbook Sections
§9.5 (Txt. p.558) Trigonometric Ratios
§9.4 (Txt. p.551) Special Right Triangles

Key Attitudes
Mathematics is about justification.

Key Ideas
The three basic trigonometric functions are sine=opp/hyp, cosine=adj/hyp, and tangent=opp/adj
Trigonometric ratios can be used to find missing lengths of sides in right triangles and the measure of missing angles.
Trigonometric ratios are different for different angles and can be found by i)measurement, ii)referring to a table or graph, iii) using a calculator

Key Skills
Using trigonometric ratios to solve right triangles.
Writing and solving proportions.
Graphing data.
Using a graph to make predictions.

Vocabulary
sine
cosine
tangent

Handouts
No handouts posted.

Assignment
§9.4 (Txt. p.562) #10-12, 28-30, 34
§9.5 (Txt. p.570) #11, 12, 22-24, 28-30
Use values for Trigonometric Ratios from a calculator or from page 845 of your text.
Disclaimer- The assignment as stated in class is the official assignment. Every effort is made to keep this posting accurate, but you should refer to what was stated in class as the final word.

Wednesday, March 21, 2007

Algebra (Class 62)

Overview
Today we continue to work with graphs of lines. In particular we focus on finding the slope, y-intercept, and x-intercept when given two points on a graph by using triangles and our skills for working with ratios.
Textbook Sections
§8-3(Txt. p.360) Slope of a Line
§8-4 (Txt. p.366) The Slope-Intercept Form of a line.

Key Attitudes
Mathematics is about generalizing and applying patterns.

Key Ideas
The slope of a line can be found by finding the ratio of the change in y to the change in x.
The change in y and change in x can be found by subtracting the corresponding y-values or corresponding x-values.
For lines the slope is the same no matter what two points on the line you pick.
The y-intercept can be found by using the slope to “move to” the y-axis.

Key Skills
Finding the slope of a line given two points.
Finding the x-intercept or y-intercept using triangles.
Finding missing values in a ratio.
Adding and subtracting fractions.

Handouts
No Handouts Posted

Assignment
Practice Worksheet
Disclaimer- The assignment as stated in class is the official assignment. Every effort is made to keep this posting accurate, but you should refer to what was stated in class as the final word.

Tuesday, March 20, 2007

Geometry (Class 60)

Overview
We have seen that two right triangles are similar if one pair of angles, other than the right angles, are congruent. This means that all 40˚ right triangles, for instance, have the same ratios of sides-- Opposite/Hypotenuse, Adjacent/Hypotenuse, and Opposite/Adjacent being three key ratios. Today we extend the ratios we have calculated for 40˚ right triangles to all right triangles by compiling the data that the class created. We will then graph this data and put it to work solving right triangles.
Textbook Sections
§9.5 (Txt. p.558) Trigonometric Ratios

Key Attitudes
Mathematics is about justification.

Key Ideas
If two right triangles have one additional congruent pair of angles, then the triangles are similar.
If two right triangles are similar, then the ratios of their sides are equal.
If you know the measure of one non-right angle in a right triangle and the length of one side, then you can find the lengths of the other sides and the measures of the other angles.
If you know the length of two sides of a right triangle, then you can find the lengths of all of the sides of the right triangle.
A graph can be used to approximate values for trigonometric ratios.

Key Skills
Using trigonometric ratios to solve right triangles.
Writing and solving proportions.
Graphing data.
Using a graph to make predictions.

Vocabulary
trigonometric ratio

Handouts
No Handouts Posted

Assignment
§9.2 (Txt. p.538) #10-12, 18-21, 28, 31
§9.3 (Txt. p.546) #8-10, 16-19, 34
Finish graphs of trigonometric ratios from class
Quiz Corrections
Disclaimer- The assignment as stated in class is the official assignment. Every effort is made to keep this posting accurate, but you should refer to what was stated in class as the final word.

Monday, March 19, 2007

Algebra (Class 61)

Overview
Today we work towards developing a process for finding the y-intercept of a line when we know the coordinates of two points on the line.
Textbook Sections
§8-3(Txt. p.360) Slope of a Line
§8-4 (Txt. p.366) The Slope-Intercept Form of a line.

Key Attitudes
Mathematics is about generalizing and applying patterns.

Key Ideas
The slope of a line can be found by finding the ratio of the change in y to the change in x.
The change in y and change in x can be found by subtracting the corresponding y-values or corresponding x-values.
The y-intercept can be found by using the slope to “move to” the y-axis.

Key Skills
Polynomial division
Finding the slope of a line given two points
Finding other points on a line when given two points
Finding the y-intercept of a line given two points
Finding the x-intercept of a line given two points

Vocabulary
y-intercept
x-intercept
slope
change in y (∆y)
change in x (∆x)

Handouts
No Handouts Posted

Assignment
5 Problems from Class-- Finding slope and y-intercept
Practice Polynomial Division Worksheet
Disclaimer- The assignment as stated in class is the official assignment. Every effort is made to keep this posting accurate, but you should refer to what was stated in class as the final word.

Friday, March 16, 2007

Geometry (Class 59)

Overview
Today we continue to develop understanding of how the ratios of the sides of right triangles can be used to find missing sides and angles. We develop a table of ratios based on triangles that the class constructs. In our warm-up we discuss the concept of Pythagorean Triples (http://en.wikipedia.org/wiki/Pythagorean_triple). We also take Quiz 9.
Textbook Sections
§9.5 (Txt. p.558) Trigonometric Ratios
§9.2 (Txt. p.535) The Pythagorean Theorem
§9.3 (Txt. p.543) The Converse of the Pythagorean Theorem

Key Attitudes
Mathematics is about justification.

Key Ideas
If two right triangles have one additional congruent pair of angles, then the triangles are similar.
If two right triangles are similar, then the ratios of their sides are equal.
If you know the measure of one non-right angle in a right triangle and the length of one side, then you can find the lengths of the other sides and the measures of the other angles.
If you know the length of two sides of a right triangle, then you can find the lengths of all of the sides of the right triangle.
If the square of the longest side of a triangle is equal to the sums of the squares of the lengths of the two short sides of the triangle, then the triangle is a right triangle.
If the square of the longest side of a triangle is greater than the sums of the squares of the lengths of the two short sides of the triangle, then the triangle is an obtuse triangle.
If the square of the longest side of a triangle is less than the sums of the squares of the lengths of the two short sides of the triangle, then the triangle is an acute triangle.
To simplify a square root, you factor out the largest perfect square and take its square root, then write the result as a product.

Key Skills
Using trigonometric ratios to solve right triangles.
Writing and solving proportions.
Determine if a triangle is right, acute, or obtuse when given the lengths of the sides.
Simplifying square roots

Vocabulary
Pythagorean Triple
Converse of the Pythagorean Theorem
Trigonometric Ratios
Reference Angle

Handouts
No Handouts Posted

Assignment
§9.1 (Txt. p.531)#21, 22, 25, 26, 28, 35
§9.2 (Txt. p.538) #7-9, 16, 17, 25
Finish drawing, measuring, and calculating the trigonometric ratios for the triangle you were assigned.
Disclaimer- The assignment as stated in class is the official assignment. Every effort is made to keep this posting accurate, but you should refer to what was stated in class as the final word.

Thursday, March 15, 2007

Algebra (Class 60)

Overview
Today we practice using polynomial long division and we return to take another look at equations of lines-- in particular we find how to determine the slope when given the coordinates of two points.
Textbook Sections
§6-7 (Txt. p274) Polynomial Long Division
§8-3(Txt. p.360) Slope of a Line

Key Attitudes
Mathematics is about generalizing and applying patterns.

Key Ideas
Polynomial division works like long division with numbers
Place holders need to be used when the dividend is missing terms.
The slope of a line can be found by calculating the ∆y/∆x
The slope of a line can be used to find other points on a line.

Key Skills
Polynomial division
Finding the slope of a line given two points
Finding other points on a line when given two points

Vocabulary
Slope
∆y
∆x
y-intercept
slope-intercept form of an equation
dividend
divisor
quotient

Handouts
No Handouts Posted

Assignment
§8-3 (Txt. p.363) #1-5
§6-7 (Txt. p.276) #7, 8
§6-6 (Txt. p.271) #17-19

Wednesday, March 14, 2007

Geometry (Class 58)

Announcement
Quiz Friday focusing on Chapter 8 Lessons 3 to 5 and Chapter 9 Lesson 1

Overview
Today we start the development of the three key trigonometric ratios, what they mean, where they come from, why they work, and how to put them to work.
Textbook Sections
§9.5 (Txt. p.558) Trigonometric Ratios

Key Attitudes
Mathematics is about justification.

Key Ideas
If two right triangles have one additional congruent pair of angles, then the triangles are similar.
If two right triangles are similar, then the ratios of their sides are equal.
If you know the measure of one non-right angle in a right triangle and the length of one side, then you can find the lengths of the other sides and the measures of the other angles.
If you know the length of two sides of a right triangle, then you can find the lengths of all of the sides of the right triangle

Key Skills
Using trigonometric ratios to solve right triangles.

Handouts
Chapter 9-Lesson 2: An Introduction to Right Triangle Trigonometry
Chapter 9-Lesson 2: Trigonometric Ratios Record Sheet

Assignment
§9.1 (Txt. p.531)#13, 14, 17, 18, 19, 20, 33
§8.6 (Txt. p.503)#23, 24

Tuesday, March 13, 2007

Algebra (Class 59)

Overview
In today’s call we work extend our skills involving algebraic fractions to include working with mixed numbers. In addition, we also learn how to generalize our method of doing long division involving whole numbers to doing long division involving algebraic expressions.
Textbook Sections
§6.6 (Txt. p.270) Mixed Expressions
§6.7 (Txt. p274) Polynomial Long Division

Key Attitudes
Mathematics is about generalizing and applying patterns.

Key Ideas
In order to add fractions, you have to have the same size pieces; you have to have common denominators.
Finding a common denominator requires that you adjust the numerator.
Long division of polynomials works just like long division of whole numbers.

Key Skills
Finding the LCD
Adding expressions
Multiplying expressions

Handouts
No Handouts Posted

Assignment
§6-6 (Txt. p.271) 5-16
§6-7 (Txt. p.276) #1-6

Monday, March 12, 2007

Geometry (Class 57)

Overview
Today we begin our work with trigonometry. We start by investigating relationships in right triangles.
Textbook Sections
§9.1 (Txt. p.527) Similar Right Triangles
§9.5 (Txt. p.558) Trigonometric Ratios

Key Attitudes
Mathematics is about justification.

Key Ideas
Right triangles contain other right triangles which are similar.

Key Skills
Proving triangles similar
Writing and using proportions based on similarity statements

Handouts
Chapter 9- Lesson 1: Seeing Similarities

Assignment
Txt. p.519 #1, 4-13
Chapter 9- Lesson 1