Ch 12: Circles

Circles will be the unit that puts more ideas together than we have seen before.  It actually can serve as a review of the year to date.  There are many relationships to learn but if you understand where they come from, you will have a better chance of remembering or rederiving them on the fly.

3/22  Lesson 1:  Circles, Radii, and Chords
         HW p.488-490/Set 2
3/23  Unit Vocab plus Lesson 2:  Tangents
         HW p.494-496/24 - 34, 39 - 53

3/27  Lessons 3 and 4:  Central Angles and Arcs, Inscribed Angles
         HW p.500-503/1 - 18, 23 - 29, 43 - 47, Set 3
3/28  Prove three cases for Inscribed Angles
         HW p.507-509/26 - 58, Set 3
3/29  Lesson 5:  Secant Angles
         HW p.513-515/17 - 57
3/30  Extra Angle Problems (End of Term 3)
         HW finish worksheet

4/03  Lesson 6:  Tangent Segments and Intersecting Chords
         HW p.517-521/Sets 1 and 2
4/04  Extra Intersection Problems and Mixed Problems
         HW finish worksheet of proof problems
4/04  Review
         HW p.523-526/9 - 54
4/06  Good Friday, no school

4/10  Test of Ch 12

MCAS Week

The week of the English MCAS is a little crazy.

3/19  Regular schedule (no class for us)
3/20  Blocks: Hmrm G H A   We will go over the 2011 Math MCAS
3/21  Blocks: E F C D (no class for us)
3/22  Blocks: B A G H F  We will do the Clinometer Lab
         Ch 12, Lesson 1: HW p.488 - 490/Set 2
3/23  Start the Circle Chapter in earnest

Mid-Year Exam results

You can download the answer key for the mid year exam.
The average for all 8 sections was 20.425. The average for my class was 18.48.
For each problem, here are the overall vs my section averages:

1. 4.09  vs  4.54
2. 2.90  vs  2.52
3. 2.34  vs  2.1
4. 3.19  vs  2.96
5. 4.29  vs  4.16
6. 3.63  vs  2.2  (clearly due to the fact that 12 out of 25 didn't do the problem!)

My conclusion, pacing was an issue.  Let's work on it so the final is more enjoyable.

Ch 11 The Right Triangle

The next chapter provides a connection between similarity and right triangles. It then gives us our introduction to trigonometry. I have lots of supplementary materials so the seven lessons of the chapter will take three weeks.

2/28  Similarity and Right Triangles (lessons 1 and 2)
          HW p.431-432/Set 2 and p.438-440/42-50, 53-57
2/29  Special Right Triangles (lesson 3)
          HW p.445-447/Set 2
3/01  Extra Practice with Right Triangles
          HW finish worksheet of problems
3/02  The Tangent Ratio (lesson 4)
          HW p.450-453/17-34, Sets 2 and 3

3/06  Sine and Cosine Ratios (lesson 5)
          HW p.458-460/Sets 2 and 3
3/07  Mixed Practice
          HW Worksheet of Word Problems (plus...)
3/08  Slope (lesson 6)
          HW Coordinate Geometry and trigonometry worksheet
3/09  An Area Formula, the Law of Sines and the Law of Cosines (lesson 7)
          HW p.472-474/Sets 2 and 3
       
3/13  Extending the Law of Sines and the Law of Cosines
          HW Worksheet of extension problems
3/14  Mixed Problems, "Solving" Triangles
          HW Worksheet of extra problems
3/15  Review (summary p.475)
          HW p.478-480/35-64
3/16  Ch 11 Test of Trig and Right Triangles

Remember that the English MCAS is 3/20 - 3/22 so we will go over last year's MCAS test on 3/20.

Hints for the Similarity Review problems

First, in problem 5, the median should be AD (not AB). Secondly, also in problem 5, it may be helpful to draw a line that through D that is parallel to BQ.

Remember that you do not always need to prove some triangles are similar to get the ratios you need. Parallel lines and angle bisectors also give you useful ratios.

Topic List for the MidYear Exam

You can download the topic list here. Remember that the table of contents in the book also serves as a topic list.

The schedule up to February Break

We will have time to finish the Similarity Chapter before break but after the Mid-Year exam. Below is the schedule of how we will do it. All sections of Honors Geometry are getting two days of review before the exam.

2/07 AA Similarity and all that implies
          HW p.403-405/Set 2 and p.412/40-61
2/08 Review Day 1
          HW Work on proof problems
2/09 Review Day 2
          HW More problems to work on
2/10 Mid-Year Exam
          HW finish problems from Tuesday

2/14 Similarity Practice Problems (from another book)
          HW Finish worksheet of problems
2/15 Perimeters and Areas
          HW p.417-419/Sets 2 and 3
2/16 Review Problems
          HW finish worksheet, there are also review problems in the text
2/17 Ch 10 Similarity Test

2/18 - 2/26 February Break

Starting Similarity (Ch 10)

We will begin Chapter 10, the study of similarity. Our study will be interupted by the Mid-Year Exam on Friday, February 10th. It may be interupted again by February break. We shall see how we go on.

2/01 Sketchpad Exploration of Area (of similar squares)
        HW finish handout
2/02 Ratio and Proportion, Similar Figures
        HW p.389-391/Sets 2 and 3
2/03 Side-Splitter Theorem
        HW p.396-398/Sets 2 and 3

Area (Chapter 9)

We are beginning Area but this is a topic you know a lot about already and the chapter is short. It won't take long.

1/19 List what you already know about area
        HW p.341-342/Set 2 and p.346-347/Set 1
1/20 Work through some more of these problems
        HW p.347-350/Sets 2 & 3, p.353-357/Sets 1-3

1/24 Polyhedra and Tessellation Test
1/25 Work through even more of these problems
        HW p.360-364/Sets 1, 2 & 3
1/26 Prove the Pythagorean Theorem
        HW p.367-368/Set 1 and 2 (Set 3 is a bonus)
1/27 Worksheet of extra, harder problems from another book
        HW finish worksheet (check your answers here)

1/31 Test of Ch 9: Area!

Polyhedra

Polyhedra are 3D solids made of polygons. We are focussing particularly on polyhedra made of regular polygons. You should be able to determine information about them without actually building and counting. Every day there is a handout so the homework is to work your way through the packet.

1/10 Nets and Regular Polyhedra
1/11 Semi-Regular Prisms and Anti-Prisms
1/12 Half Day B A G F (no class)
1/13 Archimedean Solids (the rest of the semi-regular polyhedra)

1/16 Martin Luther King Day
1/17 Summary and Duals
1/18 Review of Polyhedra
1/19 Start Area

1/24 Test of Polyhedra