Answer Key for Quad Word Problems

You can download the answer key for the quadratic word problems here.

Quadratics

For the quadratic functions we will be using books with a more investigative focus.  After each investigation we will summarize the results and I will collect the "Check Your Understanding" to check your understanding.

Day 1  Investigation 2/all pp.332-334
              HW pp.346-357/A 7-10; C 17; R 28,29; Rv 43-45, 4
Day 2  Investigation 3/1-7 pp.336-337  HW see day 3
Day 3  Investigation 3/8-12 pp.337-339
               HW pp.348-358/A 11,12; C 18-23; R 30; E 37,38; Rv 48-50
Day 4  Investigation 4/1-5 pp.340-342  HW see day 5
Day 5  Completing the square and Investigation 4/6-9 pp.342-343
               HW pp.348-358/A 13-15; R 31, 33; E 39, 40; Rv 51, 52

On the 6th day we will add a few things that are not in the book (vertex form and quad regression).
On the 7th day we will review techniques for factoring and solving.
On the 8th day, there will be a quiz.  This will probably be the last day before vacation. The quiz should only take half the block, then we can play a game.

Since I am not issuing textbooks for this unit, I have uploaded the pdf of the unit into the conference.  You don't have to go online, you can just use that. Or download it from here. (Note: If there are contents links on the side, you may not be able to click on them - use actual page numbers at the top).

The reflection

Our analysis of 3D systems using rref led to several different results - more than we saw when using rref on 2D systems.  Of course, in 3D, more things can happen - as you saw from your brainstorming with your three "planes".  I would like you to write a reflection of the similarities and differences between systems of equations and their rref matrices in 2D and 3D.  This should come after your final analysis of the systems on the worksheet.  With 2D we knew which systems were consistent, inconsistent, and dependent from their rref matrices and what the system looked like when the lines were drawn.  Were you able to do the same with your 3D systems?

Matrices

Now we learn how to deal with lots of information at once. There are many applications of matrices that are not covered in our text so we will be exploring some of them via worksheet. Make sure you bring your calculator every day!

11/14  Intro to Matrices (dimensions, transpose, scalar mult., add/subtract...)
          HW p.222/24-28 even, 38-46 even
11/15  Matrix Multiplication
          HW p.230/18-24
11/16  Networks
          HW finish handout
11/17  Transformations using matrices
          HW finish handout
(Note: I will be out on 11/18 but the handout that day is self-explanatory.)

11/21  Intro to RREF
          HW p.257/19-37 odd
11/22  Practice by using the RREF tool on the computer
          HW finish handout
11/23-11/27 no class due to Thanksgiving break

11/28  Review of Matrices so far
11/29  Intro to Inverse Matrices
          HW finish handout
11/30  Solving Systems using matrices
          HW p.249/23-31 odd, 32, 33
12/01  3D Systems (and higher!) and their solution options (now with matrices)
          HW Reflection and p.257-258/34-36, 38-40

12/05  Review of Matrices
          HW finish handout
12/06  Extra Challenge Problems on Matrices

12/08  Ch 4 Matrix Test

The last day this week you will work through a packet reviewing exponential properties.

An introduction to the mathematics of 3D

We will be moving into chapter 4 which studies matrices - a technique that allows us to handle huge amounts of data. 3D makes a great bridge topic between systems of equations and matrices. Remember, this is only an introduction. You do not have to be an expert! That comes in two years. ;-)

Day 1: Representing 3D with points, equations of planes, graphs.
Day 2: Solving systems of equations in 3D - there are many possible outcomes. (Answer Key)

The homework both days is to finish the handouts.

Systems of Equations and Linear Programming

Note date changes due to storm/power outage!

Chapter 3 explores applications of systems of equations and systems of inequalities. You will do a lot of graphing. Get some graph paper and a ruler!

Day 1:  3.1  Solving Systems by Graphing
                  HW (due after Transformation Quiz) p.161-163/13-23 odd, 47-52, 79, 80
Day 2:  3.2  Solving Systems by Substitution and Elimination
                  HW p.161-162/137-42, 53 and p.169-171/21-35 odd,36-39,43-45,63,64

Day 3:  3.3  Linear Inequalities (and going over TI drawings!)
                  HW p.176-178/26-31, 41-51, 54, 73, 74
Day 4:  3.4  Systems of Linear Inequalities
                  HW p.183-186/9-45 by 3's, 46-48, 51, 68-70
Day 5:         Systems of Linear Word Problems
                  HW Finish Handout of problems
Day 6:  3.5  Linear Programming (Day 1)
                  HW Finish Handout of problems

***** 2 days without power *****
Day 7:  3.5  Linear Programming (Day 2)     (Answer Key)
                  HW Finish Handout of harder problems
Day 8:  3.5  Review
                  HW Finish Review Handout

Day X:  A-Block only - an activity
                  HW review for test
11/08  Ch 3 Test

We will spend time (before or after the test depending on the block) looking at 3D Systems of equations before moving on to Matrices, the topic of Chapter 4.

Transformations

We have been talking about what functions are and how we can combine them. Transformations are about manipulating functions - moving them around, changing their size, flipping them over. We are studying the topic in general but every time we study a particular kind of function in the future, we will again discuss how the transformations affect that function. This is section 2.7 in the text.

Because of the Friday Professional Developement Day, A-Block will have one more day on the topic (a moving-around activity!!). Thus, I have used a table.

Date	A-Block	B-Block
10/05	Transformation Exploration	no class
10/06	Summary of Transformation Exploration, Graphical Transformations	Transformation Exploration
10/11	Transformation Word Problems	Summary of Transformation Exploration, Graphical Transformations
10/12	Double Horizontal Transformations	no class
10/13	Kinesthetic Transformations HW in the book p.139-140/15-45 by 5's, 47-57 odd, 58, 60-65	Transformation Word Problems
10/14	no class	Double Horizontal Transformations
10/17	Drawing on the TI and Transformation Review	Drawing on the TI and Transformation Review HW in the book p.139-140/15-45 by 5's, 47-57 odd, 58, 60-65
10/18	Solving Systems by Graphing HW in the book p.161-163/13-23 odd, 47-52, 79, 80	Solving Systems by Graphing HW in the book p.161-163/13-23 odd, 47-52, 79, 80
10/19	Transformation Quiz	no class
10/20	Solving Systems by Substitution and Elimination	Transformation Quiz
10/21	no class	Solving Systems by Substitution and Elimination

More thinking about functions

For this week (9/26 to 9/30) we look more deeply into the functions we have been studying.

Day 1:  Go over the more abstract homework of last week
       HW Extra Practice with Function Operations
Day 2:  Discuss strategies for solving problems
       HW Extra Special Function Practice
Day 3:  "How Do You Know?" Worksheet

Thursday, September 29th is Rosh Hashanah so there is no school. I will also be out on Friday, September 30th.

On Monday, October 3rd we will review and on Tuesday, October 4th we will have a test of the material in Ch 2.

A web site for reviewing...

I would like to recommend a web site were you can watch video lessons whenever your miss class or just want to see the presentation again. It is called brightstorm.com. Here are some for the material we have been covering recently:

• Piecewise Functions
• Composition of functions
• Definition of an Inverse

A week spent looking at functions a different way

This week (9/19 - 9/23) we will be looking at special functions and inverse relations.

Day 1 Special Functions (2.6)
       HW p.129-131/17-25 odd, 26,27,53,55,65,66,73
Day 2 Inverses (2.5)
       HW Finish worksheet of inverses three ways
Day 3 More with Inverses (2.5)
       HW p.122-123/12-48 by 3's,50-52,62 and p.132/90
Day 4 Putting together all the function ideas so far
       HW Finish worksheet of more challenging/conceptual problems

A reminder: short quizzes can happen any time. They are an excellent way for me to check if you are doing and understanding your homework. They also help you know if you can do the problems and do them under pressure. If you do not do well on a quiz, you can get help and then retake the quiz. My goal is for you to understand all of the material, not to have you memorize procedures. Please ask whenever you need help.

We start using the book...

This week (9/12 - 9/16) we will be moving into the book. We will be covering the topics of the book and using it for homework but the questions posed in class will usually be more thought provoking than the presentation given in the book.

Day 1 Absolute Value by hand and with the calculator (1.7, 1.8)
       HW p.58-59/36-72 by 3's
Day 2 Intro to Functions (2.3)
       HW p.108-110/29-38, 47-67 odd, 82, 83
Day 3 Function Operations (2.4)
       HW p.115-116/11-56 by 3's, 59-62
Day 4 More practice with function descriptions and operations
       HW Finish handout of problems

You will also need to explore your calculator using this link. I will be collecting the final certificate of completion on Tuesday, September 20th.

Let's Get Started!

We started the year with two days of Math Challenge problems to get the math part of your brain moving again. This week we will do an Algebra 1 review sheet, a worksheet of literal equation solving (meaning the answers have letters in them) and the Pre-Test to see what you remember from Algebra 1. Remember that you can go to the math caching website for more Algebra 1 practice. (You don't need an answer sheet but here is the link if you want it.) Next week we will start using the book and you will need to have your calculator.