Review and the Final

We will spend five regular class periods reviewing for the final (3 days of skills, 2 days of concepts) and then one extra long class period doing a variety of review activities.  Here is the answer key for the large packet of review problems.

List of concepts.  List of skills.

A:  6/06     F:  6/06    Day 1 Review of Function and Statistics Skills
A:  6/10     F:  6/07    Day 2 Review of Coordinate & Deductive Geometry, Transformation Skills
A:  6/11     F:  6/10    Day 3 Review of Exponent Skills, Polynomials and Probability
A:  6/12     F:  6/12    Day 4 Review of Deductive Proof Writing (proof answer key)
A:  6/13     F:  6/13    Day 5 Review of Quadratics and Modeling (modeling answer key)

A:  6/17     F:  6/14    Day 6 Review Activities
6/19  Drop in for questions to room 816 between 12:00pm and 2:00pm.

6/20  Math Final 8:30am to 10:30am
Room numbers for   A-Block:  169       F-Block:  166

Make sure you bring pencils, an eraser, a calculator (with spare batteries?), a stomach full of a healthy breakfast and a brain refreshed by a good night's sleep.

You can get your score on the final from me on Monday, 6/24 between x and x in room y.

Right Triangle Trigonometry

Our last unit of the year is about using the similarity of right triangles to find information.  It is the beginning of all you can do with the topic of Trigonometry (you would be amazed at how useful this topic is in all branches of math and science).  We don't have a lot of time for this unit so we are only covering selected sections of chapter 9.

5/27  Memorial Day

A:  5/28    F:  5/24    9.06  Getting Started
                                 CW p.737-738/1-4   HW p.739-740/5, 7-11, 13
                                 (note: on problems 9 & 10, use the fact that you could do it if it was
                                           30 degrees but 27 degrees is less steep)
A:  5/29    F:  5/29    9.07  Special Right Triangles
                                 CW p.742-743/1-5   HW p.744-745/2-14
A:  5/30    F:  5/30    9.08  Sine, Cosine, Tangent (and their inverses)
                                 CW/HW p.749-751/2-18
A:  6/03    F:  5/31    9.09  Area of non-right triangles
                                 CW p.756/1-5   HW p.757-759/6-9, 12-19
A:  6/04    F:  6/03    Review (download worksheet with answers)
                                 CW p.759/21 and p.760/1-6

6/05  Trig Quiz

Similarity

We will study Similarity - a branch of mathematics dealing with scaling.  (If I get a photograph enlarged, it will be similar, just bigger.  A scale model of a building is similar, just smaller.)  Most of the material will come from chapter 7 with a few pieces from chapter 8.  Due to MCAS, the schedule is laid out explicitly for both sections

A: 5/09    F: 5/10    7.08  Ratio and Parallel
                               HW p.568-570/4, 6, 8-13
A: 5/14    F: 5/13    7.08 & 7.14  Ratio and Similarity
                               HW p.598-599/2-10
A: 5/15    F: 5/15    8.05, 8.07, 8.09, 8.10  Circle and Sector Area, Arc Length, Inscribed Angles
                               HW p.646-648/1-4, 6, 10  and  p.658-660/1, 2, 8-10, 12, 13  and
                                      p.669-672/1-5, 7, 8, 12, 14  and  p.677/1, 3-5
A: 5/16    F: 5/16    7.15  Similarity Shortcuts (AA, SSS, SAS)
                               HW p.606-607/7-13
A: 5/20    F: 5/17    7.15  More Practice using Proofs
                               HW p.605,607/1-3, 5, 6, 15
A: 5/21    F: 5/20    7.16  Similar Area and Volume
                               CW/HW p.611-612/1-12
A: 5/22    F: 5/22    Review (answer key)
A: 5/23    F: 5/23    Similarity Quiz

5/13  Math MCAS Day 1  (C E F D B)  <-- Lost an A-Block!
5/14  Math MCAS Day 2  (A G H B)

Probability

We will be doing a quick unit on probability - chapter 5 in the textbook.

Week of 4/22 - 4/26
Day 4  5.00  Introduction (and Pascal' Triangle)
                     CW p.372-374/1-12    HW p.376-377/1, 2, 4-6, 8, 9, 11, 12, 14

Week of 4/29 - 5/03
Day 1  5.01  Getting Started (and the Binomial Theorem)
                     CW p.376/3, 10   HW p.377/16 and p.379-380/1-9
Day 2  5.02  Probability (and some important vocabulary)
                     HW read p.385, do p.386-388/1-4, 8-10
Day 3  5.03  Conditional Probability
                     CW p.392/1, 2, 4, 5    HW p.393-394/6, 7, 8, 10
Day 4  5.04  Probability of Compound Events
                     CW p.398/1, 2    HW p.398-400/5-10

Week of 5/06 - 5/10
Day 1  5.06  Expected Value (handout of extra problems)
                     CW p.412/1-4     HW p.413-414/8-10, 12-16
Day 2  Review (download book version of Review Problems (with answers) and another review)
Day 3  Probability Test

Ch 3: More Quadratics

We finish up the Quadratic Unit with Chapter 3.  The test will be during the week after April Vacation.

3/25  3.01  do Getting Started p. 153-154/1-14
3/27  3.02  Deriving the Quadratic Formula HW p.160-161/1-5, 12-16, 18, 19, 21, 24, 25, 27
3/28  3.03  Building Quadratic Functions from Roots HW p.165-166/1, 3, 5-7
3/29  Good Friday - no school

4/01  Extra Practice  (the link contains the selected problems and the answers)
4/02  3.04  Factoring non-monics  HW p.170-171/1, 2, 4-6, 9, 11
4/03  3.05  HW Check Quiz  Getting Started with Graphing CW p.175-176/1-4 
                    HW p.176/6-12  and p.182/8, 10-13
4/04  Extra practice with factoring, completing the square and quadratic formula
          Note: There is a typo on the worksheet: #6 should have -20x, not +20x
          Answer Key

4/08  3.07  Graphing Quadratic Equations  HW p.189-191/1, 2, 4-6, 8-16
4/09  3.08  Jiffy Graphs of Parabolas 
          HW read Minds in Action on p.192 and p.194 plus p.197-200/1,3,8-14
4/10  Extra Graphing Practice
4/11  HW Check Quiz More Solving Practice (turned in)

4/22  Review (view Skills Notes)
4/23  Extra Topics and connections
4/24  Ch 3 Test of Quadratics

Chapter 2 is the beginning....

Quadratics is a big topic and we will need two chapters to cover it (just this year).  We start with the utility of factoring.  To make sure that you are keeping up with the ideas covered in the homework, there will be a homework quiz every week of this unit.  Keep up!

3/04  2.02  Showing expressions are equivalent
                  HW p.72-74/1-3, 6, 7, 9-13, 15, 16
3/05  2.03  Zero Product Property
                  CW p.79/1-4, 6   HW p.79-80/7-15
3/06  2.04  Transforming Expressions
                  CW/HW p.83-85/1-9
3/07  Half-Day C B H F
3/08  Extra practice (download it here)

3/11  2.06  Polynomial Vocabulary (Quick HW Quiz of 2A)
                  HW p.97-98/3-9, 11, 12 and p.102-104/1, 2, 4, 18, 19
3/12  2.07 & 2.08 Normal Form (also called Standard Form)
                  CW/HW p.103/5-11, 13  and  p.106-108/1, 2, 4-6, 11, 13, 18
3/13  2.10  Factoring Difference of Squares
                  CW/HW p.121-123/1,4,5,13,14,16,17,19,20,21,24,25  and  p.116/11
3/14  2.11  Factoring Sums and Products (Quick HW Quiz of 2B)
                  CW/HW p.130-132/1, 3, 4, 6, 7, 8, 13

3/18  2.12  Factoring by Completing the Square (monic, even "b")
                  CW/HW p.138-142/1-3, 7, 8, 11, 12, 17, 20, 22 (I will collect 11 and 12)
3/19  SNOW DAY
3/20  2.12  More Practice with completing the square (non-monic, odd or irrational "b")
                  CW/HW p.139-142/5, 6, 9, 10, 13, 14, 18, 19, 21
3/21  MCAS (Homeroom G H A)  Review of Chapter (download here) (Quick HW Quiz of 2C)
3/22  MCAS (D E F B C)  Review of Chapter (download here) (Quick HW Quiz of 2C)

3/25  Test of Chapter 2

Important Dates
3/25  MCAS and the First night of Passover
3/26  second night of Passover
3/28  end of term 3
3/29  Good Friday - no school

Quadratics Begin!

After the quiz, please read and work through p.65-67 problems 1, 2, 3, 5, 8, 13, 14, 15.

Exponents and Radicals

This is a quick review unit before we move into quadrilaterals.  Looking over the pre-tests leads me to believe that all of retained some portion of what you know about dealing with exponents and radicals - and all of you lost much of what you knew.  The review packet you started before vacation should be finished by the second class after vacation.  We will spend the week reviewing and finish with a quiz.

Day 1:  Review the exponent rules
                 when do you add, subtract, multiply?
                 what do you do with negative exponents?
             Extra Practice: p.39-41/1-24 and p.44-47/1-19, 22
Day 2:  Go over review packet
             Discuss radicals and fractional exponents
             Scientific Notation
             HW p.10/4-7,20  &  p.14/1,2,6,7,8-12  &  p.18/2,5-9  &  p.32/9,10  &  p.57/9-11,13,15
Day 3:  Practice, practice, practice (worksheets with answer keys)
             HW p.33/1-8  and  p.59/1-3,5,8  and  p.60/1-4,6
Day 4:  Quiz

Reviewing for the Ch 6 Test

We will be reviewing the entire chapter for a test before vacation (and the start of our next topic: Exponentials and Radicals).

2/07  Midpoint Quadrilateral Proofs for A-Block
2/08  Snow Day

2/11  Review with Extra Practice Sheets
2/12  A-Block Review Activity
2/13  A-Block Test of Ch 6, F-Block Review Activity
2/14  A-Block Exponential Activity, F-Block Test of Ch 6
2/15  F-Block Exponential Activity

2/16 - 2/24  February Break

Quadrilateral Properties

This unit kicks off with you turning in your project of quadrilateral conjectures.  Since you have already been thinking about quadrilaterals for a week - thinking about their properties - proving properties is only a step away. (Again, all dates are for A-Block. F-Block dates are a day later after Tuesday.)

Note that we will be using the books in class but most of the homework in this unit is worksheets of problems.  Please make sure to bring them with you since they contain notes on the material.

1/29  Definitions in general, quadrilateral definitions in particular (turn in Quad Conjecture Project)
         HW prove the properties of isosceles trapezoids and kites
1/30  CW p.512-513/1-8;  Prove the properties of parallelograms
         HW prove the properties of rectangles, rhombuses and squares
1/31  CW p.522/2-13;  Converses - how can I prove I have a special quadrilateral?
         HW finish handout

2/04  Extra Practice using Quad Properties
         HW finish handout
2/05  Review for quiz
         CW/HW p.518-520/1-7, 9-28 and p.524/1-8
2/06  Quick Quiz on Quadrilaterals (section 6D)
         HW p.520/32
2/07  Start reviewing for Ch 6 Test with Midpoint Quadrilateral Proofs

Invariance Project

To help you with your project:

The instructions (note F-Block does not have class on January 29 so their project is due on January 30)

The rubric (you may still email me or ask questions in class if you are not sure what I am looking for)

Writing Proofs

We will be working through 6C - writing proofs.  Make sure you keep up with the homework because the practice is very important.  Please remember that F-Block doesn't meet on Tuesdays so all assignments are one day later.

1/16  Formal introduction to Proof (6.08/6.09)
         CW p.479/1,3,5,6;  HW p.484/1-5, 8-11
1/17  Analysis and Proof (6.10/6.11)
         CW p.488/6-9 and p.490/1;  HW p.492-494/1, 4-7
1/18  End of Term 2

1/21  Martin Luther King Day - no school
1/22  More Practice (6.11)
         CW/HW p.492-494/2, 3, 8-11
1/23  More Practice (6.12)
         HW finish handout
1/24  And more practice (6.13)
         CW p.500-501/1, 2, 6;  HW p.502-503/8-15

1/28  Quick Quiz on Writing Proofs
1/29  Quadrilateral Exploration due

Continuing with Deductive Geometry

We will be working our way through Chapter 6, Congruence and Proof.  Please keep in mind that this list of assignments may change as we go through the unit so check back to get the most up-to-date info on assignments.

1/03  Recap of Computer Labs (if you did not finish them before vacation, finish them now)
         HW p.436/3, 5, 7  and (for A-Block) p.447-449/1-7
1/04  Finish discussing p.435/1, 2  (6.02, 6.03)
         HW (for F-Block) p.447-449/1-7

1/07  Investigating Triangle Congruence (6.0)
         CW/HW p.430-433/3-17
1/08  Investigating Lines and Transversals (6.04)
         CW/HW p.453-454/1, 2, 3, 5-8
1/09  Introduction to Proofs: Vertical Angles (6.05)
         CW p.454/4 and p.457 Experiment;  HW p.459-461/1-7
1/10  Parallel Lines (6.06)  [Half-Day B A G F]
         CW p.465/1,2;  HW 465-468/3-12

1/14  The Parallel Postulate (6.07)
         CW p.471/3-5;  HW p.472-476/1-9, 11-13, 15 (due the day after the quiz)
1/15  Quiz (A-Block)
1/16  Quiz (F-Block) 
1/17  Writing Proofs (6.08 and 6.09)
1/18  End of Term 2

Computer Labs

We will start our deductive geometry unit with an exploration using GeoGebra (a free geometry/algebra program that you can download for use at home).  Here is the schedule:

Wednesday, 12/19  A-Block in room 700,  F-Block has their test
Thursday, 12/20  both classes meet in room 816, we use the laptop cart
Friday, 12/21  F-Block in room 700

This should be a fun way to head into vacation but don't forget that you are supposed to learn something!

Answer Key for the Review

Here is the answer key for the Transformation and Coordinate Geometry Review.

Studying for the big Unit Test

The test on Tuesday puts together the function transformation material with the coordinate geometry material.  It is a lot to put together and I have trying to help you see that it is all interconnected so that you do not have to memorize lots and lots of things.  Below are some hints about studying:


I have given you a Review sheet which lists the concepts and skills that you need to be able to do.  Make sure you find the test and quiz questions that relate to every concept and skill so that you can self assess which skills you understand well and which you could use more help with.

I have given you a packet of review problems.  Use them to test how well you feel able to do problems without looking at notes or getting help.

Here is the answer key to the Pairs Coordinate Geometry assessment.  Use it to help you understand any problems that you may have gotten wrong, or what you could have done better if you did not get full credit.

Don't just read over notes and problems - Do Them!  Practice is the best way to study for a math test!

Putting together Coordinates and Transformations

The last part of this unit (before the big test) is dealing with transformations of figures through their coordinates. This is not a long unit because we have dealt with many of these ideas separately already but we will be adding rotations. We will be using a packet though it is from the same book series. As always, any classwork not finished in class becomes part of the homework.

Note that the dates are for A-Block. F-Block is one day later after Mondays.

12/06 8.05 Getting Started CW In-Class Experiment and p.621-622/1,2,3,5
          HW p.622-623/6-8, 10-12

12/10 8.06 Reflections CW all p.624-625 and p.626/1,2
          HW p.627-629/7-9, 11-15
12/11 8.07 Translations CW p.631-634/1-6, Minds in Action, 7-9
          HW p.635-637/1-7
12/12 8.08 Rotations CW p.643 In-Class Experiment, p.644-645/1-4
          HW p.645-646/7-10
12/13 8.09 Isometry and 8B Review CW p.653-654/5-7, 8a
          HW p.656/1-7 (this will be collected, do it neatly)

12/17 Entire Unit Review
12/18 Test of Transformation and Coordinate Unit

12/19 Computer Lab about Triangle Congruence (Day 1)
12/20 Computer Lab about Triangle Congruence (Day 2)

12/22-01/01 Christmas Break
01/02 Parent Conferences, no school

Finishing up the Coordinate Geometry Unit

The rest of the unit will be done with worksheets so the homework every night is to finish the worksheet started in class.

11/26  Recap of coordinate work so far
11/27  Coordinate Proofs - Day 1 (numerical proofs)
11/28  Coordinate Proofs - Day 2 (general proofs)
11/29  Coordinate Proofs - Day 3 (mix of numerical and general proofs)

12/03  Review of Unit (answer key)
12/04  Individual Assessment (A-Block)
12/05  Group Assessment (A-Block)  Individual Assessment (F-Block)
12/06  Group Assessment (F-Block)  start the next section (A-Block)

After this we will be going on to transformations from a geometric perspective (putting together the transformations of functions with the coordinate work that we have been doing).

Excellent description from quiz

I am going to post excellent responses to the question of the relationship between the Distance Formula, the Pythagorean Theorem and the Equation of a Circle:

"The Distance Formula is actually the Pythagorean Theorem unsquared.  Instead of d^2 (c^2) it's just d and (x1-x2)^2 and (y1-y2)^2 are a^2 and b^2.  The equation of a circle is the Pythagorean Theorem.  (x - h)^2 is a^2 and (y - k)^2 is b^2, while the radius  squared is c^2."

"They are all in some way forms of the Pythagorean Theorem, and they can all be used to find the distance between two points on a graph."

"They all tell the distance of something.  The Distance formula tells the distance of point A to point B.  The Pythagorean theorem tells the length or distance of side C. And the equation of a circle calculates the distance of points from the center of the circle."

Good one for the the Pythagorean Theorem - Distance formula link:
"The distance formula is related to the Pythagorean Theorem because they both find distance.  The distance formula uses coordinates and the Pythagorean Theorem uses already known lengths, which can all be found by using coordinates."

Good one for the Distance Formula - Circle Equation link:
The equation of a circle is the distance formula, just after squaring both sides to make it d^2 = (x1-x2)^2 + (y1-y2)^2.  This is because when you are graphing a circle, the point it is centered around, or (h, k), is the same as (x2, y2).  Also, the radius (r^2) is just the distance from the center of the circle to any point on the circle.

And best of all...

"The distance formula is like the pythagorean theorem because finding the distance between two points is the same as finding the hypotenuse of a triangle if the two points were the legs of the triangle.  It is related to the equation of a circle because in a circle you are finding points at a certain distance away from the middle."

Think about your answer.  How does it compare for completeness and clarity?

Beginning Coordinate Geometry

Our next section of this unit is on coordinate geometry.  Much of this material would have been covered last year if you had take Math 1 so we are using copies of some sections from the Math 1 book.

11/08  Post-Quiz do "Getting Started" in 8C, p.659-661/1-11
11/09  Midpoint (and Distance) Formula (F-Block)
           CW p.662-663 In-Class Experiment, p.666/1,2,5,6,  HW p.667-668/7-14, 16-22

11/12  Veterans' Day - no school
11/13  Midpoint (and Distance) Formula (A-Block)

           CW p.662-663 In-Class Experiment, p.666/1,2,5,6,  HW p.667-668/7-14, 16-22

11/14  Parallel Lines and Collinear Points

           CW p.669 In-Class Experiment, p.671 For You to Do;  HW p.672-673/1-7, 9

11/15  Perpendicular Lines

           CW Handout of Exploration  HW p.677-678/1-3, 5-8, 10-12

11/16  Circles, Secants and Tangents  (F-Block)

           CW/HW handout

11/19  Circles, Secants and Tangents (A-Block),  Locus Problems (F-Block)

           CW/HW handout

11/20  Locus Problems (A-Block)

           CW/HW handout

11/21  Follow-up locus problem  (Half Day A C F H)
11/22  Thanksgiving!