Bring CALCULATOR and PROTRACTOR to final exam on Wednesday 6/2!!!!!!
4/9/2010 Review Chapter 10
Lecture/Overview
Check on/complete formula index cards
Read pg. 421
Do page 422 #1 - 22
HW pg. 423 #1 - 24
Chapter 10: Areas and Volumes of Solids
3/22/2010 10.4 Pyramids
1) Warm-Up: Draw a pyramid or cube.
Collect Pg. 401 #1 - 8 Plus Vocab -> Self-Test to check for understanding of right prisms and cylinders.
2) Activity 1: Find the volume and surface area of a cylinder in a small group
V = ?????
SA = ?????
3) Pyramids Introduction - read page 402/discuss
4) Activity 2: Pyramids: Find the surface area of the 'net'
Cut out and then fold the net into a pyramid
Find the area of the Base.
Find the Lateral Area (area of the sided)
Find the Total Area = Base + Lateral Area
Find the volume of the pyramid.
Volume = Area of the Base * Vertical Height / 3 = Bh/3 = 1/3 Bh
5) HW: Class Practice: Pg 403 #1 - 15
3/23/2010 10.5 Right Circular Cones
1) Warm-Up: Sketch a net that would make a cube, cylinder or pyramid.
Collect and review HW.
2) Activity 1: Experiment pg. 405
Each group makes 2 figures from nets and counts the vertices, edges, and faces
V = F + E - 2
3) Activity 2: Read page 406/Discuss Cones
What do they have in common with pyramids?
Write the formulas on pg. 406 on your formula index card.
4) Activity 3: Cut out/ build a cone from a 'net.'
Find the Area of the Base.
Find the Slant Height to measure the lateral area.
Find the Total Area
Find the volume.
5) Pgs. 407 - 408 #1 - 15 HW
3/24/2010 10.6 Spheres
1) Warm-Up: Find the volume, lateral area, and total area of a given cone.
Collect and review HW.
2) Full Class Activity: Read page 410 / Discuss
3) Group Activity 1: Rotate the stations!
Find the Surface Area and Volume of:
A basketball
A tennis ball
A mid-sized ball
A baseball/softball
etc.
4) CW: Page 411 CP #1 - 6
5) HW: Page 411 WE #1 - 15
#16 = Extra Credit
6) Is it possible to make a triangle that adds up to moer than 180 degrees on a sphere?
Are all Geometries the same?
How is this possible?
3/26/2010
Quiz on Chapter 10
3/15/2010 10.1 Lines and Planes in Space
Parallel/Skew/Intersecting Lines
parallel/intersecting planes
Discuss vocab (see above)
Read 389-390 out loud
Class Practice - verbally - p. 389 #1 - 11
Written: pp. 390 - 391 #1 - 24
3/16/2010 10.2 Make a cube from a "net"
Count vertices, edges, and faces.
Find area and volume.
3/17 10.2 Right Prisms: Classroom Exercises #1 - 11
3/18 CW: Cylinder Activity with net
Formula Index Card
CW Pg. 399 #1-6
HW pg 399-400 #1-20
CHAPTER 9 - CIRCLES
2/23/2010
Vocabulary of Circles - create a circle and label: center, radius/radii, diameter, chord, tangent line, secant line, diameter, circumference, point of tangency
CW pg. 347 #1 - 14 all
HW pg. 347 - 8 #1 - 26 all
HW BRING COMPASS AND PROTRACTOR to class Tuesday and Thursday
2/24/2010 Tangents -
1) Do the Exploration on page 350 (participation grade).
Check/correct/discuss/collect HW From Friday pages 185 - 186
Review Triangle Inequality x + y > z , where x, y, z are the lengths of the sides of a triangle.
triangles: The Koch Snowflake
p.176 #1 - 5 Experiment
Tuesday 11/3/09 Test Chapter 4: Using Congruent Triangles
Wednesday 11/4/09 Begin Chapter 5: Polygons
Convex vs Concave polygons
Regular polygons - equilateral triangles, squares, pentagons, hexagons - we will construct them all (the pentagon is the most challenging and I will look it up).
Platonic Solids - made from regular convex polygons - tetrahedron, cube, octohedron, dodecahedron, icosahedron
(4, 6, 8, 12, and 20-sided). Faces = sides, edges = line segments made where faces meet, vertices = corner points.
Build Platonic Solids from Nets = Possible Project
CW p. 191 #1 - 15
HW - p. 192 #1 - 21
Thursday - Project Day!
ake a Mobius Strip
Construct equilateral triangle, square, hexagon, octagon; perhaps a pentagon
Review and collect p. 104 – 106 #1 – 16, especially #9 – 16.
SSS = Side-Side-Side congruence.
Do CW p. 108 #1 – 8.
HW p. 109 #1 – 11, p. 111 #15 – 16. Skip any 2, #1 – 3 are challenging.
Tuesday 10/06/09
Warm-Up: define vocabulary p. 112.
Do p. 112 #1 – 3, try #4.
Read page 113 – 114. Do p. 114 #1 – 6.
SAS Postulate: Side-Angle-Side
Read pages 115 – 116.
CW: Do p. 116 – 117 #1 – 18 all.
HW: Finish CW, do pages 117 – 118 #1 – 11 all, 2 of #12 – 15.
Wednesday 10/07/09
Review and collect HW, do #12 – 16 all, p. 118 – 119.
Experiment page 120.
Read p. 120 Consumer applications.
Read p. 121 ASA = Angle-Side-Angle Postulate.
HW p. 122 #1 - 9
Thursday 10/08/09
CW p. 122 – 123 #1 – 11.
Read p. 125 – 127.
AAS = Angle-Angle-Side and Hypotenuse-Leg = HL.
HW p. 125 #1 – 2.
HW pages 127 – 128 #1 – 17 all.
HW: Bring a compass and protractor Monday.
Monday 10/12/09 BRING A COMPASS and Protractor.
Experiment p. 132 Hypotenuse-Leg Verification.
CW Written Exercises #1 – 15 pages 128 – 129.
HW #16 – 19, p. 130; p. 136 #1 – 24 all.
Tuesday 10/13/09
CW p. 137 – 138 #1 – 20,
HW p. 139 #1 – 20
Chapter 3 Test Wednesday 10/14/09
HW Mixed Review pages 140 – 141.
Thursday 10/15/09 Review for Unit test Friday
Friday 10/16/09 Midterm Test Chapters 1 – 3!!!
________________________________________________
Geometry: Tuesday 09/29/09
Warm-Up:
1)Draw a line segment. Measure how long it is ______.
2)Draw a ray.
3)Draw a line.
4)Draw a circle. Find its radius ____ and diameter _____.
5)Draw an acute angle. Measure it. _____
6)Draw a right angle. Measure it. _____
7)Draw an obtuse angle. Measure it. _____
8)Draw an angle bisector for the obtuse angle. (Cut the angle in half).
9)Measure each angle you made in number eight. ____ and _____
Are they equal?
10) Draw two parallel lines. Draw a transversal that cuts across the two parallel lines.
11) Measure the eight angles formed by the transversal, both interior and exterior.
12)Do the same-side interior angles add up to 180 degrees? Are the alternate interior and exterior angles equal? Are corresponding angles equal? How “parallel” are your lines?
13)Draw a triangle.
a.Measure the three angles that form the triangle.
b.Add them up.
c.Do they sum (add) to 180 degrees?
Cumulative review:
Read page 39 out loud – chapter one review.
Read page 85 out loud – chapter two review.
HW p. 88 #1 – 16
Wednesday 09/30/09 3.1 Intro to Triangles: They add up to 180
Proof that the angle sum measures 180 degrees, using parallel lines.
HW p. 93 #1 – 10, p. 94 #11 - 16
Thursday 10/01/09
Warm-Up p. 96 #26 – 27
Angle sum formula for a polygon = (n - 2)180, where n = the number of sides.
Classifying triangles: p. 97 scalene, isosceles, equilateral
Classifying by angles: p. 97acute, right, obtuse, equilateral
Legs and base – all triangles but the right triangle
Legs and hypotenuse – right triangles
CW p. 98 #1 – 19
HW p. 99 #1 – 17 skip any 2.
Friday: 10/02/09: Triangles review
CW Define vocabulary p. 101
Warm up p. 101 #1 – 8
Congruent Triangles: corresponding angles
Corresponding sides
Write triangles in the same order as their vertices (corner-points).
CW p. 103 – 104 #1 – 11
HW p. 104 – 106 #1 – 16
EC p. 106 #17 – 22
Monday: Unit Test Chapter
Geometry Tuesday 9/8/09:
Warm-Up: What is aproof? A theorem? A conjecture?
Proof of the existence ofinfinitely-many primes. Proof bycontradiction.
Hypothesis: The “If” part
Conclusion: The “Then” part
All seniors are students(true).
All students are seniors(false).
Draw a Venn diagram for theabove.
Class Practice
p.51 #1 – 16, p. 52 #17 – 22
Review complementary andsupplementary angles p. 53 #1 – 6.
HW Written Exercises p. 52 #1– 20
Wednesday 9/9/09:
Applications of Geometry toArt
pp. 54 - 55
1 and 2 Point Perspective
Enlarging/Reducing an image
Tuesday part 2: Read pages 56– 57.
HW pp. 57 – 58 #1 – 6
Extra Credit pp. 58 – 59 #1 –11
skip any 2,.
Thursday 9/10/09:
Writing proofs instatement-reason form
Read pages 60 – 61
Pages 61 – 62 ClassroomPractice #1, 2
HW: pp.62 – 64 #1 – 8
Monday 9/14/09
Warm-Up: Get out and turn inHW
No HW = Detention
Review HW: Mathematicalproofs in statement-reason form.
Do 5 problems chosen from
Page 63 #9 – 16.
Students write the proofsdown.
HW: DO three proofs frompages 62-63 #1 – 16 that we did not do in class together.
Tuesday 9/15/09 2.5 Parallel Lines
Warm-Up: Copy the list ofdefinitions:
Parallel lines –go the same direction and never cross. In the language of Algebra I, they havethe same slopes and are co-planar (on the same plane).
Skew Lines –never cross but are non-coplanar (on different planes going differentdirections).
Arrowheads showtwo lines are parallel, as in the sides of a parallelogram (4-sided figure withtwo sets of parallel sides).
Transversal – aline that cuts across a pair of parallel lines.
Interior Angles –the angles formed inside of two parallel lines cut by a transversal.
Exterior Angles –the angles formed on the outside of two parallel lines cut by a transversal.
C.A.: Corresponding Angles are congruent.
A.I.A.: AlternateInterior Angles are congruent.
A.E.A.: AlternateExterior Angles are congruent.
Same side interior angles are supplementary.
Postulate: Corresponding Angles are Equal.
CW:p. 68 #1 – 14 all
HW:p. 69 W.E. #1 – 20.
Wednesday 09/16/09
Moreon Parallel Lines: Cutting beneath the surface.
Warm-Up:Get out your HW for Q&A and collection.
CW:P. 70 – 71 #23 – 32
CW:p. 71 #1 – 35 odds
HW:p. 71 #2 – 36 evens
2.6:Proving Lines Parallel
Converse:When you switch the “if” and “then” parts in a conditional statement.
Theconverses of the AIA, AEA, and CA Theorems and Postulates are all true. That is to say, if any of the following aretrue, then the two lines cut by a transversal are parallel:
CA are congruent
AIA are equal
AEA are equal
Both lines areperpendicular to a third line.
CW: pp. 73-4 #1 – 8 CE
HW:pp. 74 – 75 #2–22
Thursday: 09/17/09
Warm-Up: pp. 74 – 75 #1 – 23odds
CW: Together: p. 75 #24 – 25,26, 28, 29 – 30 (?).
HW: Draw two parallel lines and a transversal. Measureall of the angles formed. How parallel are your lines?
Bring a compass and protractor bothon Friday!!!
Friday 09/18/09
Constructions Day
Copy a linesegment
Copy an acuteangle
Copy an obtuseangle
Create aperpendicular line from a point:
On the line
Off the line
Bisect a linesegment
Bisect an angle
Constructparallel lines using a point not on the line.
HW:Repeat all class constructions. Numberand label each.
Geometry 08/31/09 Chapter 1 Review
Warm-Up: p. 39 Do #1 – 5.u
Check Warm-up
Collect HW p.38 #1 – 54.
Read p. 39 #1 – 6 Chapter Summary.
Do p. 40 #6 – 27 Guided Practice
Do p. 41 #1 – 22 Practice Test
HW: Do p. 43 #1 – 18
Tuesday: p. 42 #1- 6 Warm-Up
Review HW p. 43 #1 – 18 due today.
Continue p. 42 #7 – 29 odds Guided Practice – take notes.
HW: Do p. 42 #8 – 30 evens
Finish/Review Constructions: Bisectors, etc.
Wednesday
WARM-UP: Clear your desk of everything but a pencil, eraser, compass, and protractor.
Warm-Up: Create and measure the angles formed by two intersecting lines. Make a conclusion about “vertical angles.”
Proofs:
Read pages 46 – 49 out loud.
Discuss the proofs.
What is a proof? A mathematical argument that shows a theorem is true.
What is a theorem? A theorem is a mathematical statement which is always true, provided the conditions of the theorem are met.
Additional Proofs:
There are infinitely many primes (by Euclid, the father of Geometry).
CW p. 48 #1 – 11
HW pp. 48 – 49 #1 – 18.
Geometry with Mr. Kalafus Week of 08/17/2009
Monday: Bisecting Angles
1)Angle bisectors
a.Read p. 20
b.P. 20 #1 – 5
2)Quiz 1.1 – 1.4
3)Experiment 1 #1 - 3
4)Experiment 2 #1 – 4
5)HW 8: p. 21 #1 - 10
YOU WILL NEED A COMPASS TO MAKE CIRCLES AND DO CONSTRUCTIONS ON MONDAY.
Tuesday 8/18/09 Concepts: Constructions
Focus Questions: How do you use a compass and striaghtedge to construct various figures?
1)Warm-Up: Construct an equilateral triangle.
2)Collect and discuss HW 8.
3) Construction #1: Bisect a line segment
Construction #2: Bisect an angle
Construction #3: Equilateral Triangle
Construction #4: Square
Construction #5: Hexagon
Construction #6: Copy a line segment
Construction #7: Copy an angle
4) HW: p. 22 #1-6, p. 27-8 #1 - 15
Wednesday: Postulates of Equality: Algebra Tie-In to Geometry
1)Warm-Up:
a.Copy the Addition, Subtraction, Multiplication, Division and Substitution Postulates on pages 29 – 30.
b.Collect and discuss HW
2)DO p. 30 #1 – 9 Guided
3)READ pages 33 – 35
4)DO p. 35 #1 – 18 Guided
HW: p. 31 #1 – 12 all.
p. 36 #1 – 17
You may skip 4 problems
Thursday: Vertical Angles
Focus Question: What are vertical angles? How can you find their measures?
1)Warm-Up: Open to p. 38. Do #1 – 10
2)CW: p. 38 #11 – 54
3)HW: Finish p. 38 #1 – 54 all.
Geometry with Mr. Kalafus
Week of 08/17/2009
Monday:
Focus Question: What is the nature and use of mathematics? How should you comport yourself in class? What are the procedures?
1)Warm-Up: Index cards with parental contact info, last math class/teacher, math strangths and weaknesses
2)Introductions and ice-breaker: 2 truths and a lie
3)Procedures:
a.Entering and starting class – sharpen pencil, straight to seat, check agenda for do-now (warm-up)
b.Bathroom – extreme emergency only as per school rules,
go during passing periods
c.HW – expect HW nightly Monday through Thursday with some weekend readings or short assignments
d.HW is an essential component of practice. Don’t fall behind.
e.Bring your book and supplies every day
f.Keep an ORGANIZED notebook with notes, HW, tests, quizzes, and handouts.
g.SHOW WORK ALWAYS – USE A PENCIL – USE A CALCULATOR AS LITTLE AS POSSIBLE
h.Class rules
i.Hansdbook
4)Pre-Test – Algebra Skills Check-Up
5)Geometry: study of shape and space
a.Architecture
b.Engineering/Design
c.Perspective drawing in art
d.Scale models
6)Read page 4. Do experiment #1.
7)Do thought experiment #2.
8)Read page 5. Do exercises #1 – 2; do #3 if we can find string.
9)HW 0: MATERIALS REQUIRED ASAP: COMPASS AND PROTRACTOR
10)HW 1: MATH PHILOSOPHY: Imagine a world without numbers. What would be different? Be general in the introduction then provide specific examples. Conclude with a statement regarding whether you would want to live in a world without numbers.
11)HW 2: Get syllabus signed.
Tuesday 8/18/09 Concepts: Point, Line, Ray, Segment, Midpoint
Focus Questions: What is a point, line, ray, segment, midpoint? How do we identify/name them? How does the number line work?
1)Warm-Up: Draw a picture of a cat or dog using only straight lines and dots.
2)Collect and discuss HW – a world without math, remind students to purchase a compass and protractor, signed syllabus.
3)Vocabulary:
a.Point – a location in space usually represented by a dot. Points have no dimension, they are very small.
b.Infinite – something which goes forever.
c.Line – A line is made up of many points. Two points define a line, so we name the line by any two points on it. Lines extend both directions forever and are straight.
d.Collinear points – We call points on the same line collinear.
e.Line segment or segment – a piece of a line that starts and stops. Named by the endpoints (starting and stopping points).
f.Ray – A “line” which goes one direction only. Start at the endpoint of the ray, the first letter in the name. Start drawing a line towards and then through the second point with an arrow at the “end” of the ray showing it continues forever in one direction.
g.Number line – all points can be paired with a real number and all real numbers can be paired up with a point.
h.Midpoint – a point in the middle of a line segment.
i.Length (no marks above the letter) – the distance between two points in a straight line.
4)P. 8 #1 – 15 Guided Practice or with partners.
5)Read pages 6 – 7.
6)HW 3: pp. 8-9 #1 – 25.You may skip any 3 problems but should ask about them in class on Wednesday. Extra credit #29 or #30.
7)GET YOUR PROTRACTOR AND COMPASS. YOU WILL NEED THEM ON WEDNESDAY.
Wednesday: Angles
How are angles formed? How do you classify angles? How do you measure angles? What are some common angles? How do you name angles?
1)Warm-Up:
a.Draw a number line. Label points A = -3, M = 0, and B = 3. Find the midpoint of AM and the midpoint of BM.
b.Draw Ray CD.
c.Draw Line XY.
2)Collect and discuss HW – segments, rays, lines.
a.Go over 11 – 16 especially.
3)Vocabulary
a.Protractor
b.Angle
c.Vertex
d.Sides
e.Measure of an angle
f.Acute
g.Right
h.Obtuse
i.Straight
j.Perpendicular lines
4)DO p. 12 #1 – 12 Guided
5)DO p. 16 #1 – 13 guided
6)Read pages 10-11, 15 – 16.
7)HW 4: p. 13 #1 – 18 all
8)HW 5: p. 16 – 17 #1 – 16 all.
Thursday: Vertical Angles
Focus Question: What are vertical angles? How can you find their measures?
1)Warm-Up: Define and give an example of each of the vocabulary words on p. 14.
2)Collect and discuss HW 4 & 5.
3)Review: Do p. 14 #1 – 8 T/F. If false make true.
4)Consumer applications: p. 14.
5)Puzzle problem p. 17.
6)Vocab
a.Vertical Angles – vertical angles are formed by intersecting lines
b.Congruent – two angles are congruent if they have EXACTLY the same measure, same size/shape
c.Theorem: Vertical Angles are Congruent
7)Guided practice p. 19 #1 – 5.
8)Read p. 18.
9)Guided practice p. 19 #15, 16 (with partners).
10)HW 6: Quiz Friday on 1.1 – 1.5, study p. 22 #1 – 6 and vocabulary.
11)HW 7: p. 19 #1 – 14 Written Exercises
Friday: Angle Bisectors
1)Warm-up: Draw two intersecting lines. Measure each of the the four angles formed. What do you notice?
2)Collect and discuss HW 6.
3)Angle bisectors
a.Read p. 20
b.P. 20 #1 – 5
4)Quiz
5)Experiment 1 #1 - 3
6)Experiment 2 #1 – 4
7)HW 8: p. 21 #1 - 10
YOU WILL NEED A COMPASS TO MAKE CIRCLES AND DO CONSTRUCTIONS ON MONDAY.
