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Geometry 1Monday November 7, 2011Materials: vocab (concurrent, point of concurrency, circumcenter of a triangle, Circumscribed, Incenter of a triangle, inscribed, median of a triangle, altitude of a triangle, orthocenter), Thm (5-6, 5-7,5-8, 5-9)Objective: The student will understand triangle partsAgenda

1. DN: pg 272 activity2. Collect HW3. How to write a proof4. Online book5. Pg 272 5-3

a. 3 or more lines intersecting at one point are concurrent1. The point of concurrency is where they intersect

b. Thm 5-6i. Perpendicular bisectors of the sides of a triangle are concurrent at a point

equidistant from verticesii.What does this mean?

c. Thm 5-7i. The bisectors of a triangle are concurrent

d. The circumcenter of a triangle is the point of concurrency of the perpendiculat bisectors

i. Circumscribed is set inside a circle1. All vertices are on the circle2. Ex 1 finding the circumcenter

a. QC 1e. The Incenter of a triangle is the point of concurrency pf the angle bisector

i. A circle is inscribed in a triangle1. The circle has a point on all sides of the triangle2. Ex 2

a. QC 2f. The median of a triangle is the line running through the midpoint of a side and

the vertex of the opposite anglei. Thm 5-8

1. The medians of a triangle are concurrent to a point that is 2/3 the distance to the other side

2. The point of concurrency between the medians is the centroid3. QC 3

g. The altitude of a triangle is the perpendicular bisector from the vertex to the opposite side

i. QC 4h. The lines containing the altitudes are concurrent at the orthocenter

i. Thm 5-9

1. The altitudes of a triangle are concurrent6. Group pg 275

7. Clean, make notes8. Draw a triangle, label the parts9. MS: How do the parts of a triangle fit

together?10. HW: pg 279 1-10

Tuesday November 8, 2011Materials: vocab (Negation statement, inverse, contrapositive, Equivalent statement, Indirect reasoning, Indirect proof), Thm ()Objective: The student will understand indirect reasoningAgenda

1. DN: How can I prove something without justifying the steps?2. Collect HW3. Pg 280 5-4 Inverses, Contrapositives, and indirect reasoning

a. The Negation statement has opposite truth valuei. The inverse of a conditional switches the hypothesis and conclusionii.The contrapositive switches and negates both

b. Ex 1c. Ex 2d. An Equivalent statement has similar truth value.e. Look over table on pg 281f. Indirect reasoning is the reasoning in which all possibilities are eliminated except

for one truthfuli. Have students think up an indirect statement

g. Indirect proof is proof involving indirect reasoningi. Ex 5ii.Steps to writing indirect proof

1. State assumption as a negative2. Show assumption leads to contradiction3. Conclude

iii. QC54. Group pg 283

1-9, 24, 2516-21, 24, 2526-33, 37, 39, 40

5. Clean, make notes6. MS: How do I write indirect proof7. HW: Go home and prove 5 thing indirectly

Wednesday November 9, 2011Materials: vocab (), Thm (larger triangle, triangle inequality). Pg 288Objective: The student will understand triangle inequalitiesAgenda

1-9, 19-2211-2210, 19-22, 23, 27, 29, 36

1. DN: How are indirect and direct prood similar/different2. Collect HW3. pg 289 Ch 5-5 Inequalities in Triangles

a. the comparison property of inequalityi. if a= b+c and c>0, then a>0

b. corollary to triangle exterior angle thm i. The measure of the exterior angle is greater than each of the remote

interior anglesc. Larger triangle theorem thm 5-10

i. The larger side of a triangle lie across the larger angleii.QC 2iii. Biconditional of 5-10 and 5-11iv. QC 3

d. Triangle inequality theoremi. The sum of 2 sides of a triangle is bigger than the third

1. QC 4, 2. Ex 5, QC 5

4. Groups pg 2925. MS: Describe the relationship between sides and angles of a

triangle?6. HW: pg 288

Thursday November 10, 2011Materials: vocab (ratio, proportion, extended proportion, scale), Thm (side splitter, Triangle angle bisector), pg 368 and 400, WIR6Objective: The student will understand triangle inequalitiesAgenda

1. DN: 2. Collect HW3. Pg 366 7-1 Ratios and proportions

a. A ratio is comparison of two quantitiesi. Have class create a few ratiosii.Remember slope?iii. QC 1

b. A proportion is 2 ratios that are equali. And extended proportion is 3 or more ratios set equalii.Properties of proportions

1. Cross multiplying2. Ex23. Ex 3 and QC

c. The scale is the ratio of lengths to corresponding sides of a scale drawingi. What does this mean?

1-1510-2728-31, 35-40

4. Pg 398 7-5 Triangle proportionsa. Side splitter theorem

i. The midsegment of a line divides the sides proportionatelyii.Ex1 and QC 1

b. Corollary 7-4 If 3 parallel lines intersect 2 transversals then the segments are proportional

i. QC 2c. Triangle angle bisector theorem

i. If a ray bisects the angle of a triangle, then the opposite side is proportional to the other two sides

ii.Ex 3 and QC 35. Group: pg 368, 400

6. MS: How do triangles relate with proportions?7. HW: WIR6

12-21 1-1021-28 11-2435-44 25-33

Geometry 2AMonday November 7, 2011Materials: vocab (concurrent, point of concurrency, circumcenter of a triangle, Circumscribed, Incenter of a triangle, inscribed, median of a triangle, altitude of a triangle, orthocenter, Negation statement, inverse, contrapositive, Equivalent statement, Indirect reasoning, Indirect proof), Thm (5-6, 5-7,5-8, 5-9), pg 279Objective: The student will understand triangle partsAgenda

1. DN: pg 272 activity2. Collect HW3. Online book4. Pg 272 5-3















i. Thm 5-9

1. The altitudes of a triangle are concurrent5. Pg 280 5-4 Inverses, Contrapositives, and indirect reasoning






iii. QC56. Group pg 275, 283

7. Clean, make notes8. Draw a triangle, label the parts9. MS: How do I write indirect proof10. HW: pg 279 1-10, Go home and prove 5 thing

indirectlyWednesday November 9, 2011Materials: vocab (ratio, proportion, extended proportion, scale), Thm (larger triangle, triangle inequality, side splitter, Triangle angle bisector). Pg 288, pg 368 and 400, WIR6Objective: The student will understand triangle inequalitiesAgenda






1-9, 19-22 1-9, 24, 2511-22 16-21, 24, 2510, 19-22, 23, 27, 29, 36

26-33, 37, 39, 40


1. QC 4, 2. Ex 5, QC 5

4. Pg 366 7-1 Ratios and proportionsa. A ratio is comparison of two quantities

i. Have class create a few ratiosii.Remember slope?iii. QC 1









ii.Ex 3 and QC 36. Groups pg 292, 368, 400

7. MS: Describe the relationship between sides and angles of a triangle?

8. HW: pg 288

Friday November 11, 2011Materials: WIR6Objective: The student will review trianglesAgenda

1. DN: Simplify the ratiosa. 6/8b. 10/4c. 5/10d. 260/50

1-15 12-21 1-1010-27 21-28 11-2428-31, 35-40

35-44 25-33

2. Collect HW3. Centers (10 mins)

a. Review of week 12b. parts of a trianglec. triangle inequalities

4. MS: How do proportions relate to triangles?5. HW: WIR 6

Geometry 3BTuesday November 8, 2011Materials: vocab (concurrent, point of concurrency, circumcenter of a triangle, Circumscribed, Incenter of a triangle, inscribed, median of a triangle, altitude of a triangle, orthocenter, Negation statement, inverse, contrapositive, Equivalent statement, Indirect reasoning, Indirect proof), Thm (5-6, 5-7,5-8, 5-9), pg 279Objective: The student will understand triangle partsAgenda
















i. Thm 5-9









indirectlyThursday November 10, 2011Materials: vocab (ratio, proportion, extended proportion, scale), Thm (larger triangle, triangle inequality, side splitter, Triangle angle bisector). Pg 288, pg 368 and 400, WIR6Objective: The student will understand triangle inequalitiesAgenda






1-9, 19-22 1-9, 24, 2511-22 16-21, 24, 2510, 19-22, 23, 27, 29, 36

26-33, 37, 39, 40


1. QC 4, 2. Ex 5, QC 5













13. HW: pg 288



1-15 12-21 1-1010-27 21-28 11-2428-31, 35-40

35-44 25-33

Geometry 4BTuesday November 8, 2011Materials: vocab (concurrent, point of concurrency, circumcenter of a triangle, Circumscribed, Incenter of a triangle, inscribed, median of a triangle, altitude of a triangle, orthocenter, Negation statement, inverse, contrapositive, Equivalent statement, Indirect reasoning, Indirect proof), Thm (5-6, 5-7,5-8, 5-9), pg 279Objective: The student will understand triangle partsAgenda
















i. Thm 5-9









indirectlyThursday November 10, 2011Materials: vocab (ratio, proportion, extended proportion, scale), Thm (larger triangle, triangle inequality, side splitter, Triangle angle bisector). Pg 288, pg 368 and 400, WIR6Objective: The student will understand triangle inequalitiesAgenda






1-9, 19-22 1-9, 24, 2511-22 16-21, 24, 2510, 19-22, 23, 27, 29, 36

26-33, 37, 39, 40


1. QC 4, 2. Ex 5, QC 5













13. HW: pg 288



1-15 12-21 1-1010-27 21-28 11-2428-31, 35-40

35-44 25-33

Math Models 5Monday November 7, 2010Materials: Objective: The student will understand linear equationsAgenda

1. DN: Simplify 10x+6-3+4x-4-11x2. Collect projects3. An equation is two valid mathematical expressions that are joined with the equal sign

a. linear equationsi. a linear equation looks like y=mx+b

b. quadratic equationi. y=ax2+bx+c

c. what's the difference?4. solving a linear equation

a. isolate the variable b. one step

i. x-5=10ii. 3x=-6

c. two stepi. 2x+1=7ii. 5x + 6 = -4

5. graphing linear equationsa. start with the y intercept

i. move with the slope, draw pointii. connect dotsiii. ex y=x+1

b. pick two points that satisfy the equationi. plot and connectii. ex y= x+1

6. Groups:a.

The graph of y = 2x + 1 crosses the y axis at (0,2). (True or false). The graphs of y = -x – 1 and y= -x+1 are parallel. (True or false). The graph of y =3x -1 is rising from left to right. (True or false). The graph of y = -3x + 1 is falling from left to right. (True or false). What has to be true of y = mx + b so that its graph will fall from left to right? Write the equation for a line that is horizontal. Where does y = -x -3 cross the y axis?

Teacher note: the closest you can get on m is .37.

Write a function that has a graph that is steeper than the graph of y = x + 1. Write a function that has a graph that is falling from left to right and crosses the y axis at (0, -4). Write a function that has a graph that is parallel to y = x - 4. Write a function that has a graph that is perpendicular to y = -2x + 1.

b. Word problems▪ Kim and Cyndi are starting a business tutoring students in math. They rent an office for $400 per month

and charge $40 per hour per student. If they have 15 students each for one hour per week how much profit do they make together in a month? (assume 4 weeks per month)

▪ Glenna wants to rent a car for a trip to Key West for one week. She calls two car rental companies to get

prices. Mr. Kotter’s Rentals rents a Cadillac Escalade for $99 for one week plus $0.11 per mile over 100 miles. Barbarino’s Rentals has the same vehicle for $75 per week and $0.15 per mile over 150 miles. If it is 432 miles to Key West, which company has the better deal? How many miles would Glenna drive before she would be spending the same amount at either company?

▪ Many counties in Florida missed many school days in the fall of 2004 due to hurricanes that year. A solution for how to make up those days was to add time to each school day for a portion of the year. It was decided that in order to make up a 6 hour school day, 10 minutes would be added to each day. How many extended days would be needed to make up 3 school days?

7. MS: Explain how to graph a linear equation?8. HW: Real world linear relationships

Tuesday November 8, 2011Materials: Objective: The student will understand quadratic equationsAgenda

1. DN: Graph y-5+6x=10x-4 2. Collect HW 3. solving quadratics

(a) quadratic equation

i. plug in for a, b, and c ii. ex y = x2-8x+16

(b) completing the square i. get equation into ax2+bx=c ii. add (b/2)2 to both sides to complete the square iii. factor and simplify iv. ex y=x2-8x+12

A. -12= x2-8x B. add 16 to each side

(-8/2)2 = 16 C. 4= x2-8x+16 D. 4= (x-4)2

square root both sides E. plus or minus 2=(x-4) F. x= 6 and -2 G. check your work

(c) solve by factoring A. what adds together to give you b but multiplies to give you c B. ex y=x2+5x+6

factors of 6 that add to 5 1+6 no 2+3 yes so it is 2 and 6

(x+2)(x+3) check your work by FOIL

4. graphing quadratic equations(a) plot the y intercept (c)

i. set x= to 0 and solve(b) plot the x intercept(s) aka zeros

i. set y=0

(c) is graph opening up or down i. look at a, is it + or -

(d) find vertex i. plug in to formula ii. -b/2a, Use that to work out x, and then substitute it back into the quadratic to find the y value iii. plot the point

(e) if you like you can plug in other numbers to get more points(f) connect all the points

(g) ex y = 3x2 + x – 2 5. Group work

(a) graph each equation i. y=2x+3 ii. 2x+y=6 iii. Y+7=x iv. 2x+3+y=4x-3 v. y=x

(b) graph each quadratic equation

i. y = x2 + x – 2

ii. y = x2

iii. y = 5x2 + 3x – 2 6. MS: Explain how do graph a quadratic 7. HW: Real world quadratic equations

Wednesday November 9, 2011Materials: Objective: The student will understand systems of equationsAgenda

1. DN: At what point does the line x=3 and y=5 intersect? 2. Collect HW 3. A system of equations is a set of equations with similar variables

(a) What does that mean?(b) The solution of a system of equations is the point at which they intersect(c) solve by graphing

i. Any ideas on how to solve? ii. Graph each equation iii. find the point in which the lines intersect

A. is this a reliable answer? No necessarily, how can you check

B. If you think you have the correct location, plug in to both equations, if it is correct then it works

iv. ex y=-2x+1, y=-3x+4(d) solve by calculator

i. plug into y= on your calculator ii. Graph iii. go to 2nd CALC intersect

A. The calculator will ask line 1, then line 2, then it will say guess press enter 3 times the calculator will tell you that X equals a number and equals a number

REMEMBER the answer is the ordered pair that the two numbers create B. To check your work, plug numbers into original equations

iv. ex y=1/2x+3, 2y= x-2 4. you can also use the calculator method to check your answers

(a) remember you MUST show your work 5. Solve using calc 6. Group:

(a) 4x+2y=8, 3y=-6x+12(b) y=2x, y-x=x(c) y=x, y=x2

7. MS: What did you notice about b and c in group work? What does that mean? 8. HW: How do systems relate into the real world? Solve the system y=-2x2+4x-1 and y=-2x-4

Thursday November 10, 2011Materials: Objective: The student will understand systems of equationsAgenda

1. DN: If a system does not intersect, what does that mean? 2. Collect HW 3. Remember a matrix?

(a) You can solve a system using a matrix and a calculator 4. matrix 5. Group:

(a) Solve for x, check your work

(b) Solve the system and check your work

(c) Graph each Quadratic

6. MS: What does a system of equations 7. HW: Study notes

http://www.youtube.com/watch?v=45jx68vFPjY

http://www.youtube.com/watch?feature=iv&src_vid=nmVe_OZcesA&annotation_id=annotation_952130&v=-FnwxNFN8g0

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