September 29, 2008
Lesson Plans — Week 8 — September 29 – October 3, 2008
Lesson Plans — Week 8 — September 29 – October 3, 2008
Pre-Calculus
Standards: Models for Real World Phenomena; Algebraic Functions; Trigonometric Functions; Sequences and Series
Monday, September 29: 2.1 Determine whether a relation represents a function; Find the value of a function; Find the domain of a function; Identify the graph of a function; Obtain information from or about the graph of a function
Tuesday, September 30: 2.1 Determine whether a relation represents a function; Find the value of a function; Find the domain of a function; Identify the graph of a function; Obtain information from or about the graph of a function
Wednesday, October 1: 2.3 Find the average rate of change of a function; Use a graph to determine where a function is increasing, is decreasing, or is constant; Use a graph to locate local maxima and minima; Determine even and odd functions from a graph; Identify even and odd functions from the equation
Thursday, October 2: 2.4 Graph the functions listed in the library of functions; Graph piecewise-defined functions
Friday, October 3: 2.2 Graph linear functions; Draw and interpret scatter diagrams; Distinguish between linear and nonlinear relations; Use a graphing utility to find the line of best fit; Construct a linear model using direct variation
Geometry
Standards: Number and Operations; Algebra; Geometry; Measurement; Data Analysis and Probability
Monday, September 29: Classify triangles and find the measures of their angles; Use exterior angles of triangles
Tuesday, September 30: Classify triangles and find the measures of their angles; Use exterior angles of triangles
Wednesday, October 1: Classify triangles and find the measures of their angles; Use exterior angles of triangles
Thursday, October 2: 3.4 Classify polygons; Find the sum of the measures of the interior and exterior angles of polygons
Friday, October 3: 3.4 Classify polygons; Find the sum of the measures of the interior and exterior angles of polygons
Statistics
Standards: Experimental Design; Data Analysis
Monday, September 29: Review Descriptive Statistics – Frequency distributions and their graphs; Measures of central tendency; Measures of variation, Measures of position
Tuesday, September 30: Review Descriptive Statistics – Frequency distributions and their graphs; Measures of central tendency; Measures of variation, Measures of position
Wednesday, October 1: Review Descriptive Statistics – Frequency distributions and their graphs; Measures of central tendency; Measures of variation, Measures of position
Thursday, October 2: TEST
Friday, October 3: TEST
For all classes.
Activities: Lecture, Board work, Classroom participation
Material: Book problems and Teacher made handouts
Assessment: Daily assignments graded for accuracy. Unit test planned.
In order to address the Physical Activity requirement… My classes and I will enjoy a 15 minute walk once a week.
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September 25, 2008
Pre-Calculus — Chapter 2
Pre-Calculus
Chapter 2 (9 Days)
7 Days, TEST Day 8 and 9
1. Book 2.1 page 95: C: 4; E: 5 – 12, 13adefh, 15, 17cdefgh, 19bce. 20adf, 21, 22, 23, 25, 26, 27, 29, 30, 31, 33,
35, 37, 38, 39, 40, 41, 43, 47
2. Book 2.1 page 95: E: 48, 50, 53, 55, 56, 57, 58, 59, 60, 61, 63, 64, 67, 69, 73, 76, 79, 80, 81, 82, 85, 91abcde,
93acd, 94a
3. Book 2.2 page 108 C: 1, 9; E: 9ac, 10ac, 19, 20, 26, 27, 34
4. Book 2.3 page 122: E: 1 – 14, 17, 18, 19, 20, 21, 22, 37, 38, 39, 45, 46, 51, 52, 53
5. Book 2.4 page 132: C: 1, 3; E: 9 – 15, 19 – 28, 31, 32, 33, 34, 35bc, 37
6. Handout 2510
7. Review page 167: 1, 3, 6, 7, 9, 10, 13, 15, 17, 19, 23, 25, 26, 29, 32, 45, 49, 50, 53, 54
TEST (2 Days)
2.1 Determine whether a relation represents a function; Find the value of a function; Find the domain of a function; Identify the graph of a function; Obtain information from or about the graph of a function
2.2 Graph linear functions; Draw and interpret scatter diagrams; Distinguish between linear and nonlinear relations; Use a graphing utility to find the line of best fit; Construct a linear model using direct variation
2.3 Find the average rate of change of a function; Use a graph to determine where a function is increasing, is decreasing, or is constant; Use a graph to locate local maxima and minima; Determine even and odd functions from a graph; Identify even and odd functions from the equation
2.4 Graph the functions listed in the library of functions; Graph piecewise-defined functions
2.5 Graph functions using horizontal and vertical shifts; Graph functions using reflections about the x -axis or y -axis; Graph functions using compressions and stretches
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September 23, 2008
September 22, 2008
Lesson Plans — Week 7 — September 22 – 29, 2008
Lesson Plans September 22 – 26, 2008
Pre-Calculus
Standards: Models for Real World Phenomena; Algebraic Functions; Trigonometric Functions; Sequences and Series
Monday, September 22: 1.5 Use interval notation; Use properties of inequalities; Solve linear inequalities algebraically and graphically; Solve combined inequalities algebraically and graphically; Solve absolute value inequalities algebraically and graphically
Tuesday, September 23: Review Unit on solving equations and inequalities
Wednesday, September 24: TEST
Thursday, September 25: TEST
Friday, September 26: Homecoming activities
Geometry
Standards: Number and Operations; Algebra; Geometry; Measurement; Data Analysis and Probability
Monday, September 22: 3.1 and 3.2 Identify angles formed by two lines and a transversal; Prove and use properties of parallel lines; Use a transversal in proving lines parallel; Relate parallel and perpendicular lines
Tuesday, September 23: 3.1 and 3.2 Identify angles formed by two lines and a transversal; Prove and use properties of parallel lines; Use a transversal in proving lines parallel; Relate parallel and perpendicular lines
Wednesday, September 24: 3.1 and 3.2 Identify angles formed by two lines and a transversal; Prove and use properties of parallel lines; Use a transversal in proving lines parallel; Relate parallel and perpendicular lines
Thursday, September 25: 3.1 and 3.2 Identify angles formed by two lines and a transversal; Prove and use properties of parallel lines; Use a transversal in proving lines parallel; Relate parallel and perpendicular lines
Friday, September 26: 3.3 Classify triangles and find the measures of their angles; Use exterior angles of triangles
Statistics
Standards: Experimental Design; Data Analysis
Monday, September 22: 2.5 Find the first, second, and third quartiles of a data set; Find the interquartile range of a data set; Represent a data set graphically using a box-and-whisker plot; Interpret other fractiles such as percentiles; Find and interpret the standard score (z-score)
Tuesday, September 23: 2.5 Find the first, second, and third quartiles of a data set; Find the interquartile range of a data set; Represent a data set graphically using a box-and-whisker plot; Interpret other fractiles such as percentiles; Find and interpret the standard score (z-score)
Wednesday, September 24: 2.5 Find the first, second, and third quartiles of a data set; Find the interquartile range of a data set; Represent a data set graphically using a box-and-whisker plot; Interpret other fractiles such as percentiles; Find and interpret the standard score (z-score)
Thursday, September 25: Book Review Chapter 2
Friday, September 26: Homecoming activities
For all classes.
Activities: Lecture, Board work, Classroom participation
Material: Book problems and Teacher made handouts
Assessment: Daily assignments graded for accuracy. Unit test planned.
In order to address the Physical Activity requirement… My classes and I will enjoy a 15 minute walk once a week.
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September 21, 2008
Geometry — Chapter 3
Geometry
Chapter 3+ Test
5 days
1. Handout 3110
2. Handout 3120
3. Handout 3130
4. Handout 3210
5. Book 3.1 Study Example 5 on page 118. Answer the Check Understanding 5. page 118: 1, 3, 4, 5, 11 – 17, 23 – 25, 37 – 40, 42 – 44
6. Book 3.2 Study Example 4 on page 124. Answer the Check Understanding 4. page 125: 4, 5, 6, 8, 9, 10, 14, 18 – 23, 27 – 30, 32 – 35, 37, 38, 51 – 53, 56 – 58
3 days
7. Handout 3310
8. Handout 3320
9. Book 3.3 page 134: 1 – 11, 24 – 28, 31 – 37, 42 – 47, 50, 64 – 67, 72
10. Handout 3330
2 days
11. Handout 4510
12. Handout 4520
13. Book 4.5 page 213: 7 – 10, 21 – 26, 28, 34 – 36, 47, 48
14. Review
TEST (2 Days)
15. Handout 3410
16. Handout 3420
17. Book 3.4 Write this section’s Key Concepts. page 147: 1 – 25, 32 – 35, 40 – 43, 47 – 48, 55, 56, 64 – 73
18. Book 3.5 page 155: 5, 7, 8, 11, 14, 15, 17 – 30, 33 – 37, 77 – 80
19. Book 3.6 page 161: 1, 5, 6, 7, 12 – 17, 20 – 23, 25, 27, 28, 43, 44, 51 – 54, 63
Quiz
3.1 and 3.2 Identify angles formed by two lines and a transversal; Prove and use properties of parallel lines; Use a transversal in proving lines parallel; Relate parallel and perpendicular lines
3.3 Classify triangles and find the measures of their angles; Use exterior angles of triangles
4.5 Use and apply properties of isosceles triangles
3.4 Classify polygons; Find the sum of the measures of the interior and exterior angles of polygons
3.5 Graph lines given their equations; Write equations of lines
3.6 Relate slope to parallel and perpendicular lines
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Statistics Notes — How to Use that Calculator to Find Measures of Position, Box-and-Whisker Plot
You got it, you might as well learn to do something on it than play games.
Example. 14 weights:
185, 160, 235, 165, 125, 175, 185, 132, 168, 112, 170, 155, 105, 158
>Say hi
>Edit List
Enter data
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>SortA(…… you don’t have to do this, but it makes the list pretty.
See the pretty list. Pretty.
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>STAT
>CALC
>1: 1-Var Stats
>ENTER
Look at all that info. Mean, Sx (sample standard deviation), σx (population standard deviation)
Scroll down
Here is your five number summary
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To Draw a Box-and-Whisker Plot
First make sure there is no other graph equation entered
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>2ND STAT PLOT
>ENTER
Turn Plot 1 ON, Press ENTER
Change Type to Box-and-Whisker, Press ENTER
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>ZOOM
>9:ZoomStat, Press ENTER
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When you want to return your calculator to its normal graphing abilities
>2ND STAT PLOT, Turn Plot 1 Off
>ZOOM, 6:ZStandard
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Geometry Notes — Parallel Lines and The Angles
Parallel lines are coplanar lines that do not intersect.
Lines are parallel if they lie in the same plane, and are the same distance apart over their entire length. Parallel lines remain the same distance apart over their entire length. No matter how far you extend them, they will never meet.
To show that lines are parallel, we draw small arrow marks on them. In the figure above, note the arrows on the lines PQ and RS. This shows that these lines are parallel. If there was another line parallel to these lines, it would have the same small arrow mark. If the diagram has another set of parallel lines they would have two arrows each, and so on.
When we write about parallel lines there is a shorthand we can use. We can write PQ || RS. which is read as “the line PQ is parallel to the line RS“.
The line AB is a transversal. It cuts across the parallel lines PQ and RS. Notice the angle clusters. Notice the repetition of angle measures and their locations.
………
If the transversal crosses the other parallel lines at right angles it is called a perpendicular transversal.
If the transversal cuts across lines that are not parallel, it has no particular properties of note. These lines are no longer parallel. Notice that the angles around E have no real relationship to those around F.
………
You still have your vertical angles and your linear pairs. And those are nice. But there are no relationships of value from one cluster to the next..
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If the transversal cuts across parallel lines (the usual case) there is one key property to note: The corresponding angles around each intersection are equal in measure. In this figure, you can see that the four angles around the point E look just the same as the four angles around the point F.
Corresponding angles are created where a transversal crosses other (usually parallel) lines. The corresponding angles are the ones at the same location at each intersection. If the transversal cuts across parallel lines, then corresponding angles are congruent.
If the transversal cuts across lines that are not parallel, the corresponding angles have no particular relationship to each other. All we can say is that each angle is simply the corresponding angle to the other.
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Alternate Interior Angles are created where a transversal crosses two (usually parallel) lines. Each pair of these angles are inside the parallel lines, and on opposite sides of the transversal.
If the transversal cuts across parallel lines (the usual case) then alternate interior angles are congruent. If the transversal cuts across parallel lines (the usual case) then alternate interior angles have the same measure.
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Alternate Exterior Angles are created where a transversal crosses two (usually parallel) lines. Each pair of these angles are outside the parallel lines, and on opposite sides of the transversal.
If the transversal cuts across parallel lines (the usual case) then alternate exterior angles are congruent. If the transversal cuts across lines that are not parallel, the alternate exterior angles have no particular relationship to each other. All we can say is that each angle is simply the alternate angle to the other.
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Same-side interior angles are created where a transversal crosses two (usually parallel) lines. Each pair of these angles are inside the parallel lines, and on the same side of the transversal.
If the transversal cuts across parallel lines (the usual case) then same-side interior angles are supplementary (add to 180°). If the transversal cuts across lines that are not parallel, the same-side interior angles have no particular relationship to each other.
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Same-side exterior angles are created where a transversal crosses two (usually parallel) lines. Each pair of these angles are outside the parallel lines, and on the same side of the transversal.
If the transversal cuts across parallel lines (the usual case) then same-side exterior angles are supplementary (add to 180°). If the transversal cuts across lines that are not parallel, the same-side exterior angles have no particular relationship to each other.
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You have now learn many special types of angle combinations.
You’ve learned that vertical angles are always congruent.
You’ve learned that angles that form a linear pair are always supplementary.
You’ve now learned that if lines are parallel, that corresponding angles are congruent.
You’ve now learned that if lines are parallel, that both alternate interior and alternate exterior angles are congruent.
You’ve now learned that if lines are parallel, that both same-side interior and same-side exterior angles are supplementary.
One large drawback in geometry is that we don’t always know what things are individually. What we do know is special combinations of things and with a little knowledge and given information, boy howdy, just look at what else we can do. Outstanding.
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