Transformations

This unit adds to what you know algebraically about transformations.

12/13 Review of Transformations, partially with software explorations. Here are the links:
                 Review Exploration
                 Point Exploration
           HW p.298-304 read Lesson 1, read and reflect on Set 1, do all of Set 2
12/14 Reflections and the other transformations they can make
           HW p.298-304 read Lesson 2, read and reflect on Set 1, do all of Set 2
12/15 Constructing reflections and composition of transformations
           HW p.312-316 read Lesson 3, do 21-25 and all of Sets 2 and 3
12/16 More on Transformations and Isometries
           HW finish handout

12/20 Transformations and Symmetry
           HW p.319-324 read Lesson 4, do all of Sets 1 and 2
12/21 Review/Summary
           HW p.325 read Summary, do p.326-329/11-50
12/22 Test on Ch 8: Transformations
12/23 A Cappella Concert
           HW Have a fun and relaxing break!

This link is just a fun way to review the basics.

Christmas Break: 12/24 - 1/3
Parent Conferences: 1/3

Ch 7: Quadrilaterals

This chapter really explores the properties of the "special" quadrilaterals: trapezoids, parallelograms, rectangles, rhombuses, and squares. You will need to be able to prove all the properties as well as having them mentally available to use.

11/23  Quadrilateral Properties Packet
          HW finish packet for class on 11/29
11/24  Thanskgiving

11/29  Going over the Packet
          HW read p.258-259, do p.260-264/5-21, 56-59 and read p.265-266, do p.267-269/4-9, 18-23, 31-50
11/30  Converse/Equivalence of Parallelogram Properties
          HW read p.270-271, do p.272-273/5-21 (if not done in class), 44-55, Set 3
12/01  Rectangles, Rhombuses, Squares and Trapezoids (Lessons 4 and 5)
          HW read and do p.276-280/19-22, Sets 2 and 3 and read and do p.281-285/16-28, 46-52, Set 3
12/02  What can you know about diagonals to determine a quadrilateral?
          HW finish handout

12/06  Midsegment Theorem and Midpoint Quads
          HW finish handout (look through Lesson 6 sets for hints)
12/07  Summary and Extra Problems
          HW read p.292, do p.293-295/17-55
12/08  More Extra Problems
          HW finish handout
12/09  Ch 7 Test of Quadrilaterals

Parallel Lines (Flat and Curved Surfaces)

Chapter 6 is about Parallel Lines. Chapter 16 is about non-Euclidean surfaces (ie curved surfaces) and what what happens to parallel lines if the surface isn't flat (Euclidean). We will be putting them together to compare and contrast the uber-important, as yet unproven, Parallel Lines Postulate.

10/28   Ch 6 Lesson 1: The perpendicular bisector
                        HW p.215-216/18-29, 33-37, 42-45
11/02   Ch 6 Lesson 2: Proving Lines Parallel and Lesson 3: Constructing Parallel Lines
                        HW p.222-224/7-40
11/03   Ch 16 Lessons 1 and 2: Saccheri Quadrilaterals Day 1
                        HW p.227-229/19-28, 42-47 and p.694/31-40, 44-46 and p.698-700/7-13, 42-48
11/04   Ch 6 Lesson 4: Parallel Lines and Angles
                        HW read p.230-231, do p.232-235/5-7, Set 2

11/08   Ch 16 Lesson 2: Saccheri Quadrilaterals Day 2
                        HW p.699-701/14-35, Set 3
11/09   Ch 6 Lesson 5: Triangle Angle Sum and Lesson 6: AAS and HL
                        HW p.240-241/31-46, Set 3 and p.247/31-50
11/10   Ch 16 Lesson 3: Lobachebsky and Riemann
                        HW p.704-706/Sets 1, 2, and 3
11/11   Veterans' Day - no school

11/15   Ch 16 Lesson 4: Revisiting the Triangle Angle Sum
                        HW p.709-712/Set 1 (must do!), Set 2 problems 21-32
11/16   Summary of Euclidean and Non-Euclidean Geometry
                        HW finish "neutral geometry" proofs in handout
11/17   Euclidean Problems from other textbooks
                        HW finish handout
11/18   Review Ch 6 and Ch 16: Extra Proofs
                        HW read p.249 and p.713, do p.252-254/25-55 and p.714-715/1-35

11/22   Test of Parallel Lines and non-Euclidean geometry

Inequalities (Ch 5)

This is a very short chapter. Keep up.

10/25   Lesson 1 (Inequality Properties) & Lesson 2 (Exterior Angle of a Triangle)
            HW p.188-189/45-48, Set 3 and read p.190-191, do p.192-194/1-15, Set 2
10/26   Lesson 3 (Triangle Inequality A) & Lesson 4 (Triangle Inequality B)
            HW p.197-199/read and consider Set 1, do Set 2 and do p.202-203/10 - 48
10/27   Summary and extension
            HW p.206-209/15-25, Set 2
            After we've had a chance to go over the homework), we'll have a quiz on Chapter 5. There will
            be just 2 or 3 questions, one of which will ask you to prove a major theorem from the chapter
            (Theorem 12, 13, 14, or 15).
10/28   Quick Quiz; Perpendicular Bisector (Ch 6, Lesson 1)
            HW p.215-216/18-29, 33-37, 42-45

Quadrilateral Congruence

We will spend some time in class - and you will spend some time outside of class - learning about quadrilateral congruence. We studied triangle congruence. How much did you need to know about two triangles to know that they were the same size and shape. Only three pieces of information were necessary if they were the right three pieces: ASA, SAS, SSS. There are more trios but we do not have enough theorems to prove them yet. We do have enough skill to determine which things we need to know about two quadrilateral to prove they have the same size and shape.

Your job is to work through the list of possible combinations of sides and angles for quadrilateral congruence. Prove the ones that can be proved. Provide counterexamples for the ones that cannot be proved. Write it all up neatly. Number the pages. I will grade it.

10/19   Discuss the problem and begin exploring
10/20   Discuss strategies for proving and disproving
10/21   Practice finding counterexamples

10/26   Write-up is due

Finishing Ch 4

10/12  Isosceles and Equilateral Triangles (Ch 4, Lesson 5)
           HW read p.157-159, do p.159-162/12 - 48
10/13  SSS (Ch 4, Lessons 6)
           HW read p.163-164, do p.165-167/9 - 43
10/14  Extra Proof Practice
           HW make plans for worksheet proofs, do p.176-180/7-36,48,51,52

10/18  Test of Ch 4
           HW read Constructions (Ch 4, Lesson 7) p.169-171 and do p.172-174/1 - 38

The beginning of Chapter 4: Congruence

10/04  Quiz of Ch 3, and an angular activity
           HW finish write-up of activity
10/05  Polygons and Congruence (Ch 4, Lessons 1 & 2)
           HW do p.137-138/40-49, read p.139-141, do p.142-145/12-19, 34-55 and (optional) Set 3
10/06  ASA and SAS (Ch 4, Lesson 3)
           HW read p.146-147, do p.148-150/10-18, Sets 2 & 3
10/07  Professional Developement Day (no school)

10/10  Columbus Day (no school)
10/11  Congruence Proofs (Ch 4, Lesson 4)
           HW read p.151-152, look over p.153/Set 1, do p.154-155/Set 2 and p.179/48

The rest of Chapter 3 is easy!

[There is also a bit of a preview for the schedule of some of chapter 4.]

9/27  Bisection (Lesson 4) and Complimentary & Supplementary Angles (Lesson 5)
         HW read pp.98-100 and do pp.100-104/7-9,15-25,34-36,41-47,Set 3
         HW read pp.105-106 and do pp.108-109/23-25,32-46,Set 3
9/28  Linear Pairs & Vertical Angles (Lesson 6)
         HW read pp.9110-112 and do pp.112-115 Sets 1 and 2
9/29  Rosh Hashanah (no school)
9/30  Perpendicular and Parallel Lines (Lesson 7)
         HW read pp.117-118,123 and do pp.119-121/1-8,13-16,Set 2

10/4  Quiz of Ch 3, and an angular activity
         HW finish write-up of activity
10/5  Polygons and Congruence (Ch 4, Lesson 2)
10/6  ASA and SAS (Ch 4, Lesson 3)
10/7  Professional Developement Day (no school)

10/10  Columbus Day (no school)
10/11  Congruence Proofs (Ch 4, Lesson 4)

Finishing the introduction

This week we will finish Chapter 2 (The Nature of Deductive Reasoning) and move into Chapter 3 (Lines and Angles).

9/20 Lesson 5: A Deductive System
        HW read p.60-61, do p.61-64/1-3, 6-25, 32-41, Set 3
9/21 Review Ch 1 and Ch 2
        HW do p.37-38/Sets 2 & 3 and p.71-74/1-16, 31-33, 42-49
9/22 Quiz of Ch 1 and Ch 2
        HW read Lesson 2 p.84-86, do p.86-90/6-19, 23-28, 37-46, Set 3
9/23 Lesson 3: The Protractor and Angle Measure
        HW read p.91-93, do p.94-96/8-43, 48-53

Recap and moving on

The syllabus so far has been:
9/06 Go over Spotter problem, discuss Surfer problem.
        read Lesson 1 p.8-10, do p.11-12 Sets 2 and 3
9/07 Discuss vocabulary of lessons 1, 2, and 3 of chapter 1
        read Lesson 2 p.13-16, do p.16-17 Sets 2 & 3
        read Lesson 3 p.18-20, do p.21 Set 1/16-18, p.22 Set 2
9/08 Constructions and Sundials
        read Lesson 4 p.24-25, do p.26-27 Set 1/1-6, 10-16 and p.29 Set 3
9/09 DIscuss constructed concurrency points. Start p.34 Set 3
        read Lesson 5 p.30-31, do p.31-34 Sets1 and 2 (and finish Set 3)

Impromptu homework checks can happen at any time - usually once a week. Keep up!

For the upcoming week:
9/13 Conditional Statements (the beginning of deductive reasoning) CW worksheet
        read Lesson 1 p.42-43 and do p.43-45 Sets 1, 2, & 3
9/14 More discussion of conditional statements
        read Lesson 2 p.46-47, do p.47-49 Sets 1, 2, & 3
9/15 Half Day (C B A G - no class for us)
9/16 Direct vs Indirect Proofs
        read Lesson 3 p.50-51 do p.52-54/1-7 and 15-8
        read Lesson 4 p.55-57 do p.57-59/3-21

There will be a quiz the week after which covers all of the material in Chapters1 and 2.

We begin...

So far we have looked at some mind-awakening problems, discussed the focus on logical thinking that we will be working on this year and explored intuition and proof using the spotter/surfer problem. Now we begin in earnest.

Start by reading pp. 8-10, then do the Set II and Set III problems on pp 11-12.

Throughout the book, you will be asked to read the lessons and to think about the Set I problems. The Set I problems tend to be worth thinking about but you should not spend a lot of time on them. They are more of a check on the reading. If you have questions, please make sure you bring them up in class!

We will be using a compass and protractor this year. We have them for classwork but you probably want to purchase both for use outside of class. Also, colored pencils tend to be helpful (you don't need a lot of colors but make sure they look different or you have defeated the purpose of using them). ;-)