Ms. Linner's Blog

Welcome!

To reach Mrs. Linner by email, please click here.

Come by before school (8:00) for extra help if you need it, but don't wait until the last minute!

Click here for the AP Statistics blog.

Syllabi for Accelerated Math and for AP Statistics .

Second semester recaps

PLEASE practice on USATestprep.

Here's the review handout from class today:

Download Spring 2009 Final Review

Graphing calculators are allowed on the final exam. Calculators with computer algebra systems (TI-89, TI-92, etc.) are not allowed.

 HW due Tuesday: Purple book p 239 at least 9 of the problems. Don't choose only odd problems!

Thank you for turning in your homework. Good job on the quiz! 

Your practice exam for the EOCT will be on Thursday and Friday. The REAL EOCT will be on May 13th and 14th. The content matches the Math I curriculum.

We will meet in the outside classroom on Tuesday, May 5.

 You should have all the HW problems through the Day 8 homework done for checking on Thursday. Check the calendar for the Circles and Spheres unit for assignments.

Download AM1 Circles and Spheres Unit Outline

 

 

Vocabulary words for this exercise: Arc, bisect, chord, circle, congruent, conjecture, converse, diameter, endpoints, intersection, major arc, minor arc, perpendicular, Pythagorean Theorem, radius, secant, semicircle, tangent

 

Don't wait until the last minute to review for the End of Course Test. Let's start with some statistics: what is the mean absolute deviation of these numbers -    4, 7, 8, and 11?

For the weekend: Work problems 26-29 from page 88 in the purple book PLUS problems 25-30 on page 66 (also in the purple book). We're going to test over all this stuff on Thursday of next week.

Test/quiz retakes will be held from 7:45 to 8:15 every day  3/30-4/3 in room 313. These are optional, and the retest grade will count.

Tuesday night: Go back over the worksheet to fine-tune your skills.

Finish the worksheet from today in order to prepare for a quiz over complex/imaginary number operations.

To clarify what we saw in class today, although sqrt(-4*-25) is positive, sqrt(-4) * sqrt(-25) is negative because it's equal to (2i * 5i ) or -10.  Make sure you know how to add, subtract, multiply, and simplify imaginary and complex numbers.

Wow! What a day. Starting with the problem 4x² + 3 = 0, you found multiple ways to reach the "final" answer. You solved for x, remembering that you needed the +/- sign. You multiplied by a funny form of one to change the preliminary answer to the simplified form. What a super job! You revisited the discriminant. Now you know what each of these means: discriminant < 0, discriminant = 0, and discriinant > 0. 

You guys have been amazing! Your solutions to the quadratics on Tuesday showed insight and creativity. Your perseverance on today's task was fabulous. HW due Thursday: bring questions about quadratics. Knock yourselves out. What concerns do you have? What creative ideas do you have? Keep up the good work. I'm so proud of you.

We removed some applications from calculators today in class to prevent our students from accidentally cheating on the tests. Programs which perform the processes that students are tested on, such as solving for roots of polynomials, factoring, and FOILing, are considered cheating tools equivalent to bringing a cheat sheet to a test. While we know that these programs are freely available on the web and can be reloaded for use during the summer, they are not acceptable in class or on tests. Please take care to keep your calculator free of programs that might interfere with your learning or demonstrating your valuable math skills. Use of a calculator with these types of programs/applications on it during a test will be grounds for disciplinary action.

Let's prepare for a test on rational expressions to be taken on Monday, 3/16. You have practice questions on the two worksheets handed out this week in class. Work! Check with me in the morning if you have any questions you cannot resolve. Solutions to some of the problems are on the walls outside Mr. Slater's and Mrs. Lassiter's rooms. Seriously, if you have problems, Monday morning is your last opportunity for before school assistance before the test.

For Thursday: FINISH the worksheet from class today (last night's homework!). You can check your work outside Mrs. Lassiter's classroom. Come by Mrs. Linner's class before school if you can't resolve any differences.

Link to an online explanation of completing the square.

Today we "completed the square."

For instance, when you have an expression like

x^2 + 10 x + 50, the expression is equivalent to (x+5)^2 with 25 left over. 

 

If you started with
x^2 + 10 x + 10,

 

you would want to make it of the form

 

x^2 + 10x + (10/2)^2 + something, or x^2 + 10x + 25 + ???

 

so you'd have to add 15 to the 10  already have to make the 25, therefore you add 15 and take away 15 like this:

 

x^2 + 10 x + 10 +15 - 15

=(x+5)^2 - 15

 

Why wold we do such strange things??? Because now we know this is a parabola shifted 5 units to the left of the origin and shifted down 15 units.

 

HW is to make up 20 problems like this and figure out how to rewrite them in vertex form.

 

Convert from the form x^2 + bx + c into the vertex form: (x+h)^2 + k.

Download Rational Functions Assignments

Finish up the resistance worksheet this weekend. You guys were great this week.

Testing on Thursday: operations on polynomials (addition, subtraction, multiplication, division, simplification, combining like terms, factoring). You should be able to factor out a GCF, factor trinomials, factor perfect squares and cubes, factor by grouping, factor differences of squares and cubes as well as sums of cubes. You cannot factor sums of squares using these methods.

Monday: FInish up the factoring by grouping worksheet we flewthrough in class today AND do the review on page 123, problems 1-19. By now you should be able to add, subtract, mutiply, and divide polynomials. You should also be able to factor out a GCF, factor special products (including differences of cubes and sums of cubes--remember SOAP), and factor trinomials completely.

If any of this seems confusing, you might want to search on the topic. There are lots of good explanations and demonstrations on the 'net.

Let's quiz on Wednesday and test on Monday.

Thursday: HW problems from page 83 (1-18) and page 87 (1-12). Can you factor trinomials?

Wednesday: Become an expert in the areas you know you are weak (long division of polynomials, synthetic division, dividing polynomials by a greatest common factor). We will finish the quiz on Thursday-after you are more knowledgable.

Tuesday: Make up 10 problems to work that use greatest common factor. Work them.

Here's a website that addresses factoring:

http://www.wtamu.edu/academic/anns/mps/math/mathlab/int_algebra/int_alg_tut27_gcf.htm

Here's an interactive website to practice factoring greatest common factors out of polynomials:

http://www.algebrahelp.com/worksheets/view/factoring/gcf.quiz

Monday: You guys were amazing! You practiced synthetic division today. Work enough problems tonight to verify for yourself that you can perform these calculations. You will probably have a quiz on Wednesday. Quizzes were given back today. Tests should be returned tomorrow.

You made sure you all knew how to add and subtract polynomials, then you invented a method for dividing polynomials. Incredible.

Finish problems 62 and 63, at least 6 from 53-61, and enough of the other problems from the worksheet to be experts.

Tuesday: Students taught each other how to simplify expressions like (a+b)(a-b), (a+b)^2, and (a-b)^2. They learned that there are patterns which can make the simplification process muchfaster than FOILing. Students cooperated very well in helping correct misunderstandings. HW for tonight is problems 1-18 and 22-24 from page 70. Bring both of these HW assignments (Mon & Tues) for a grade on Wednesday.

Monday: Today we did some more manipulating of polynomials-regrouping, simplifying, and a little multiplying. For tonight's HW, practice multiplying polynomials. If you need a refresher, the section immediately preceding the HW assignment explains the procedure very well. In a nutshell, you are performing manipulations using the distributive property very carefully. The assignment? Problems 1-11 from page 66.

Great class today! You taught each other a lot of the content for this unit.

Key words: monomial, polynomial, term, factor, simplify, coefficient.

After today's class you should be able to identify monomials and binomials, and convert the product of a binomial and a monomial into a simplified polynomial. You can convert some polynomials into factored form (by grouping). When the polynomial is graphed as Y1 in your calculator, you can predict where the graph will cross the x-axis AND YOU CAN EXPLAIN WHY. You can tell when the graph of a factored polynomial will "bounce" off the x-axis.

And you know what a negative exponent does to a number.

Let's test on Thursday.

Complete the cumulative task for HW in preparation for the test. Answers are outside Mr. Slater's door. Go over the quiz and previous homeworks to make sure you know how to work all these types of problems.

Thanks for all the good answers in class today. Your discussion was very productive.

HW due Tuesday, January 27th: Complete the odd problems on the multi-page review worksheet distributed in class today. 

___________________________

Binomial formula: P(x = k) = (n C k) p^k * q^(n-k)

p = probability of a success

q = probability of a failure = 1 - p

n = number of trials (like the number of coins flipped or questions asked)

k = the number of successes you're interested in

n C k = "n choose k" or n! / (k! (n-k)!)

Conditions for a binomial setting:

(1) n is fixed at _____

(2) p is fixed at _____

(3) trials could result in only successes or failures. Success = _______________ and failure = __________________

(4) Trials are independent because ___________________

HW due Monday, January 26th: Print out one page of a website for binomial formula.

I will NOT be available at the Open House on Thursday night. Please visit any other Accelerated Math 1 teacher (Ms. Stoll, Ms. Lassiter, or Mr. Slater) for general questions or email me for more specific concerns.

Topic for Wednesday, January 21: Means and dispersion in a binomial distribution. Assignment: Probems 9-14 on page 365. Instructions are found at the top of page 364.

Please report to the media center on Thursday.

I'm glad that you all found the HW on mean, median, and mode so easy. Bring it to class tomorrow, along with your completed HW from tonight.

And for that, complete at least every other problem from the two-sided worksheet handed out today.

HW due Wednesday: Analyzing games learning task. Recall that the expected value is found by taking the total of all the (outcomes multiplied by their probabilities). Also, revisit the circluar permutations problems from the previous night's HW. 

HW due Tuesday, January 13: The Acc Math 1 -Counting and probability review worksheet.  THE ANSWERS TO THE PUZZLE HAVE BEEN COMPLETED BELOW. THIS IS CALED PASCAL'S TRIANGLE.

                  1

                1   1

            1    2   1

         1   3    3    1

      1    4    6    4    1

   1     5   10  10    5     1

NOW, CAN YOU COMPLETE THE NEXT ROW?

HW due last week: Go back and rework the problems from last night, using the information we discussed at the end of the class on Friday. Expected value = the sum of the products of each x and its probability. For instance, if the probabilities of x = 1, 2, and 3 are .1, .2, and .7 respectively, the expected value is (1*.1) + (2*.2) + (3*.7).

Also, work through all problems through problem 12 on the sheets from class today.

To "roll" 100 dice into lists in your calculator instead of actually rolling real ones, use the following steps.

From the home screen use MATH-PROB-RANDINT(1,6,100) STO L1.

Repeat using L2 for a second die.

Your screen will look like this: RandInt(1,6,100)->L1    and there will be a row of random numbers below the command with an ellipses afterward.

To see your results, hit STAT EDIT. If you want to add the two values together, go to the very top of L3, where the title L3 is highlighted, and type L1+L2 and hit ENTER.

If you want to use logic to see how many times the two numbers are the same, you can use the command L1=L2 in L4. Every 0 represents the numbers NOT matching, while every 1 represents a match.

p. 358 1-7 due Fri.

Welcome to the second semester. I look forward to many celebrations of excellent problem-solving! Remember to take pleasure in finding patterns, solutions, and solutions, and keep working on problems even when they seem difficult. You have what you need to be a mathematical success.

Today we looked at probability, combinations, and permutations again. Your HW is to complete the second sheet of the packet handed out in class today. That's pages 3 and 4. We already considered problems 1-6 and 8. I'm very interested in hearing your solutions to problem 7 tomorrow.

Accelerated Math News

Click here for the AP Statistics blog and assignments.

HW due 12/10/08: Finish the worksheet handed out in class today. You can use combination notation for some of the problems. You can also leave the results in fraction form.

We'll have a little test on Thursday on probability.  You're doing very well!

Begin to study for the final. The topics you've learned this semester include functions, transformations, logic, triangles, polygons, the distance formula, the midpoint formula, and probability. Start looking up these topics in your textbook and practicing some problems each night.

We're starting the probability unit.

*** The Gator cheerleaders showed up to practice with the band tonight and, when they were done, they went into the gym and cheered for the freshman basketball team. Go Trojans! Go Gators!***

Work the problems from p.341 so we can figure out what we already know. Bring this Monday, December 8.

Cool website alert!!!   

http://www.slu.edu/classes/maymk/AppletsSLUBelowCalc.html#TrianglesGeometry

Please bring the Surveillance task and the Quadrilaterals Revisited worksheet to class on Wednesday. We will test on the remaining portions of this unit on Thursday.

HW due on Monday after the break: The Surveillance of the Village task.

Please note that the Cobb County email system and Pinnacle will be out of service throughout the break.

HW due 11/19/08: The handout from class. There are three sides to this handout. Remember, you will have a test on Thursday.

HW due 11/18/08: Problems 15-17 on page 254. The greatest attention will be paid to problem 16.

HW due 11/17/08: Problems 14 - 18 on page 245 of the text. You can check your answers to problems 15 and 17 in the back of the book.

HW due 11/14/08: Problems 1-4 from page 219. You have to write out the entire proof on paper.

Don't forget to study for your quiz over distance and midpoint on Wednesday, 11/12/08!

For Friday, November 7: Work problems on midpoint, distance, incenter, and circumcenter from the text. Can you find the equation of the perpendicular bisector of a segment if you know the endpoints of the segment?  That would be a good goal for tonight!  Start with odd problems until you know you're doing them correctly, then try some even ones!  We're going to take on the last standard from the unit--finding the distance from a point to a line on Friday. Yippee!

Friday, October 31: Work problems related to distance and midpoint for your quiz on Monday.

Thursday, October 30.  Your questions today were wonderful! You investigated your conjectures with such enthusiasm. Specifically, you looked at the special segments in triangles: medians, angle bisectors, perpendicular bisectors, and altitudes. Can you define each one? Can you name the point of concurrency for each one?  What is special about each?

RE: the incenter     Which segments help us to find the incenter? Where will it always be found?  What is special about this point?

HW Complete the front and back of the first page in the packet handed out in class today. If you are up to the challenge, take on the last side of the last page, too. Bring this and the HW due Thursday to class for a grade on Friday.

Use this website above to investigate the concepts we studied in class. Tell your friends, too.

HW due Thursday, 10/30: Do at least 15 problems from pages 282 AND 283.

HW due Wednesday, October 29: Work problems 1-13 from page 274 in the text. If you have questions, read the few pages that precede this page.  ALSO, reconsider all the lines of the handout that we did not finish in class today down to the lines related to Cyclic and Circumscribed polygons.

HW due Tuesday, Oct 28: Prove the conjecture that we faced in class about a kite and do problems 1-10 from page 331.

Click here for the kite conjecture.   

Quadrilaterals are everywhere! What makes a parallelogram a rhombus? What makes a rhombus a square? How many pairs of parallel sides does a trapezoid have? How little information would you need to determine that a quadrilateral was one of the special types we lookd at in class today? What statements can you develop to describe and differentiate among types of quadrilaterals?

For example, if a parallelogram has perpendicular diagonals, then ________.

If a rectangle has perpendicular diagonals, then ____________________.

If a quadrilateral has perpendicular diagonals, then __________________.

How many can you think of?

Wednesday (10-22) you looked at the relationships between sides of triangles and the angles opposite them and quickly reviewed the congruence rules for triangles: SSS, SAS, ASA, AAS for congruence--AAA for similarity--but angle-side-side does not work for either, even backwards!  We're about halfway through the concepts in Unit 2. Have you checked off the topics we've finished?

HW due Thursday: p. 285 8-13, p. 294 1-6

Your investigations on Tuesday (10/21) were marvelous. You found the sum of the angle measures of polygons and the sum of the exterior angle measures. You broke polygons into triangular pieces to evaluate the angle measures and used deductive reasoning and proof to support your conjectures. Well done!  Your HW is to work through both sides of the sheet handed out in class today, looking through your book to find the names of the properties demonstrated. This will become a valuable resource for you as we learn how to prove our theories.

Students in Accelerated Math I will participate in Achievement Series testing online at various times during the school year. Students may be assessed in October, November, December, February, March, April, and/or May depending on their grade levels an academic needs.

The Achievement Series is a locally developed assessment that measures student achievement on Georgia Performance Standards in subjects such as Math I (and Accelerated Math I).

These tests are multiple-choice and will be taken on the computer during regular class time. Each test will take about one class period and will have between 20 and 50 questions, depending on the test.  Results from the tests will provide the school with important information about the specific strengths and weakesses of students in regard to the GPS tested. As always, test scores are only one measure of what and how well students are learning.

This is not a high-stakes test. It is a tool used by teachers to help identify the instructional needs for their classrooms in order to meet the needs of all students.

Students: bring your calculators and we'll see you in the Media Center!

Due Tuesday: Check your answers for the worksheet we looked at in class today. We'll review those and any other topics we can on Tuesday. The Benchmark test is on Wednesday. It is not a big grade. We just need to know if you have learned anything.

If you did not hand in your project today, hand it in on Tuesday for a single-letter-grade penalty. Any later will cost you a letter grade per day.

Due Monday: The big brochure project is due on Monday. You must have a cover and one page for each of the transformed graphs. A link to the rubric is found below. ALSO, we converted equations of lines from slope intercept form into standard form, Ax + By + C = 0. We observed that the ratio of A to B was the same for parallel lines. Now, write the equations of two perpendicular lines in slope-intercept form. Convert these equations into standard form and look for a pattern. Make a conjecture. Check your conjecture by looking at another pair of perpendicular lines.

Due Friday: Work odd problems from pages 32-35 in the textbook until you are an expert.

NEW UNIT!!!!  Our new unit (#2) covers some aspects of geometry. Today we used Geometers' Sketchpad to investigate the distance between two points and the found the midpoint formula of a segment. You correctly observed that the method for finding distance was just an application of the Pythagorean Theorem.  There is no assignment for tonight, but you should be making progress on your projects that are due on Monday!

How did you like the software???

9/26 Solve at least 6 of the problems on the back sheet of the packet handed out in class today.

9/25 Complete problems 1-3 from the Walking, Falling, Making Money handout today. The logic problems are for fun.

9/24 You should have finished the review worksheet by now. We went over some of the problems in class today. Please be sure to pick up or print up a copy of the rubric for the project due Oct 6th. As you requested, there will be logic problems and rates of change problems for pickup tomorrow.

9/23 Please prepare for the test by working through the Math 1 review worksheet handed out in class today. NP-please pick up a copy before school.

9/22 Complete the portion of the Functionland packet related to CONTRAPOSITIVES (Problems 14 and 15). What makes contrapositives different from inverses and converses?  The test has been postponed until Thursday.

Here is the draft of the rubric for the project due 10/6.

9/19 Read number 8 in the Functionland packet and compelte numbers 9 and 10. The reference to the Dormouse played on the apparent narcolepsy of the Dormouse. What was the Dormouse likely to do any minute? (You can read this book online!)

We will have our test on Thursday.

9/18 Complete the first 7 problems on the Functionland packet handed out in class today. I'll have your rubric for the project posted and handed out on Friday.

9/17 We  figured out the formulas today that helped us fill in the table on page 1 of the Painted Cubes packet. You have what it takes to finish the entire packet now.  We'll check it for a homework grade on Thursday.  Your test on this material will be on Tuesday.

9/16 We worked on sequences today--writing equations for sequences in explicit form and in recursive form. Use this knowledge as you complete 1-5 in the Painted cubes packet.

9/15  We finished the sequences packet today and began to look at the sequences found in the Painted Cubes packet. Please read the directions. The questions that you're asking have been answered there.  Bring problems 1-5 completed to class on Tuesday.

We reviewed the transformations of the parent graphs on Friday and touched on sequences again. We will revisit the sequences as functions packet on Monday. Bring your thinking caps!

Bring your re-worked quiz to class with you, along with your calculator if you have one, for the test on Thursday.

Complete the review worksheet handed out in class in preparation for Thursday's test. Each problem should take you no more than 1.5 minutes. Review the quiz results you got back today and complete the other quiz completely and correctly now that you know so much (Smarty-pants!).

Here are a few problems from the books which address the topics we're covering:

p. 53  #4-8, 10, 13, 14

p. 100 #7-12

p. 128 # 4, 5, 8<<<<<<<< HOMEWORK DUE FRIDAY, SEPT 5th

P. 129 #5, 6, 7  <<<<<<<<<<<<<<< HOMEWORK DUE MONDAY, SEPT 8th

p. 138 # 4-7, 10-15 <<<<<< Not assigned, but you can do them!

p. 139 # 17-22 DUE TUESDAY, SEPT. 9th

9/2/08 Because of an attack of the math-eating bacteria over the long weekend, we reviewed Tuesday and will quiz on Wednesday.

Lesson 2.12 in the text reviews some of the concepts we worked with last week, but we have also investigated many other topics from units 1 and 2.

Section 3.2 in the text has some nice problems related to factoring-a useful tool in finding roots and graphing.

Accelerated Math assignment for the Labor Day weekend:  Work problems in the book related to domain, range, zeros, intercepts, etc. You should be an expert on all quadratics by Tuesday.  There is a quiz on Tuesday.

Accelerated Math assignment for August 27th: Two things--FIRST write up the newspaper article covering the interview you had with the quadratic function expert. It would be great if you typed this, but we can live with hand-written essays. Please note that the article is more than just the Q&A page that you filled in during the interview. SECOND-use what you know and what you figured out during the interview and even your textbook if necessary to complete the worksheet handed out in class today. Bring both of these assignments to class on Thursday.

Accelerated Math assignment for August 26th: Complete problems 1-4 and 9 and 10 from the worksheet handed out in class on Monday. Add the position of the vertex, the x and y-intercepts, the axis of symmetry, and whether the graph opens up or down.  Be prepared to discuss the same elements for problems 5-8.

Older Accelerated Math assignments are written in red on the AP Stat blog.