HolcombMath

Wednesday, February 04, 2009

Intro to Calculus (Class 49)

Announcements
Very possibly there will be a quiz on Friday focusing on radians and coterminal angles.

Lesson Title
Circular Functions (3)

Overview
Our opener for the day will be focused on comparing answers and approaches for solving Sangaku 9. The remaining time will be spent working on Workshop 14.
Textbook Sections
N/A

Vocabulary
radian
central angle
terminal side
circumference
rotation

Key Attitudes
Math is about using what you know to create something new.

Key Ideas
Given two points on the circumference of a circle, one of the points can be rotated around the center to match up with the other point in an infinite number of ways.
Key Skills
I can explain what a radian is.
I can give a mathematical reason for why radians are “better” than degrees.
I can find the location of a point on the circumference of a circle resulting from a rotation about the center of the circle using radians.
I can determine the quadrant that a point on the circumference of a circle will end up in as the result of a rotation about the center given in radian.
I can determine the measure of coterminal angles.
Turn-In (#48)
Workshop 13

Handouts
Workshop 14

Assignment
Workshop 14
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, February 03, 2009

Geometry (Class 47)

Lesson Title
Proving Triangles Congruent (3)

Overview
The opener today gives students a chance to review factoring algebraic expressions. The lesson for the day continues our work on proving triangles congruent.
Textbook Sections
§4.3 (Txt. p.212) Proving Triangles Congruent

Vocabulary
construction
straight edge
arc
radius
center
diameter
adjacent
opposite
included
non-included

Key Attitudes
Math is about being convinced a statement is always true.

Key Ideas
A factor answers the question “How many of these are in this”?
Triangles can be constructed out of various combinations of angles and sides.
Only some combinations of angles and sides guarantee that all triangle created with this combination will be congruent-- the same size and the same shape. Other combinations only guarantee triangles which are the same shape, and some combinations guarantee nothing at all!
When multiplying two expressions, if the bases are the same the exponents need to be added.
Key Skills
I can identify the factors of a number or an algebraic expression.
I can identify key angle and side combinations which force triangles to be congruent.
I can identify and sequence the reasons which establish triangle congruence.
I can construct a triangle given given two sides and a non-included angle (SSA).
I can construct parallel lines.
I can construct the midpoint of a segment.
I can construct a triangle given the lengths of its three sides (SSS).
I can construct a triangle given its three angles (AAA).
I can construct a triangle given two adjacent sides and an included angle (SAS).
I can construct a triangle given two angles and the included side (ASA)
I can construct a triangle given two angles and the non-included side (AAS).
Turn-In (#46)
Final Exam Free Response Corrections
Txt. p.298 #21-25, 42-46

Handouts
Practice Proving Triangles Congruent

Assignment
Practice Proving Triangle Congruent #TBA
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, February 02, 2009

Intro to Calculus (Class 48)

Lesson Title
Circular Functions (2)

Overview
We will use the opener to compare solutions to Sangaku 9. Then students will take part in two activities concerning triangles. Finally students will have time to work on Workshop 13. A quiz is very possible on Friday focusing on the work we have been doing with radians and coterminal angles.
Textbook Sections
N/A

Vocabulary
radian
central angle
terminal side
circumference
rotation

Key Attitudes
Math is about using what you know to create something new.

Key Ideas
Given two points on the circumference of a circle, one of the points can be rotated around the center to match up with the other point in an infinite number of ways.
Key Skills
I can explain what a radian is.
I can give a mathematical reason for why radians are “better” than degrees.
I can find the location of a point on the circumference of a circle resulting from a rotation about the center of the circle using radians.
I can determine the quadrant that a point on the circumference of a circle will end up in as the result of a rotation about the center given in radian.
I can determine the measure of coterminal angles.
Turn-In (#47)
Homework 16: Finish it.
Sangaku 9

Handouts
Workshop 13

Assignment
Workshop 13 TBA
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.