SY2022-23 Keys IMP 2 (013) Period 7AC-Keys Period 7AC (Section 013) Assignments

Please complete the attached worksheets. There is no need to concentrate on problems that do not deal with the application of trig to solving missing angles and sides in triangles. SOOOOOO...concentrate on any problem that deals with a picture of a triangle displaying some sides and some angles.

I STRONGLY advise you to attempt at least 8-10 of the problems on the attached worksheets.

Please walk through this PowerPoint and take notes on it.

Please complete the attached worksheets.

Please complete the attached worksheets.

Please complete the attached worksheet, skipping #11 on Page 134.

We did NOT start this in class. But you may like some additional practice. Remember that you cannot prove that triangles are congruent until you first identify, notate and write down THREE congruency statements with reasons!

We started this in class. Perhaps you'd like to finish it. Remember that we are using multiple postulates and theorems here: Definition of a Straight Angle, Triangle Sum Theorem, Exterior Angle (Sum) Theorem, Vertical Angles Theorem, etc.

We started this in class. Perhaps you'd like to finish it. Remember that you cannot use (or end) a proof with CPCTC UNTIL you prove that your triangles are congruent first.

We did NOT start this in class. But you may like some additional practice. Remember that you cannot prove that triangles are congruent until you first identify, notate and write down THREE congruency statements with reasons!

We have now done and corrected (in class) all the proofs that have valid triangle congruencies and do NOT employ theorems related to parallel lines. It's now time to take care of the rest of the proofs: the ones that use the Alternate Interior Angles Theorem and the ones that do not end with a triangle congruency. Look at the following problems on the Crime Solver and 'solve' them according to the instructions below:

1.Page 1, #3: Write the proof till you reach non-congruency then answer why
you can’t prove!





2.Page 2, #2: Write the proof till you reach non-congruency then
answer why you can’t prove!





3.Page 2, #4: Write the proof
till you reach non-congruency then answer why you can’t prove!





4.Page 3, #1: Write the
proof.





5.Page 3, #2: Write the proof till you reach non-congruency then
answer why you can’t prove!





6.Page 4, #4: Write the
proof.
Take a look at the following video for another explanation of writing triangle congruency and parts congruency proofs. HOWEVER, there are a few things I would like you to do differently from the video:
In example 1, you do not have to have the first line of the proof. But it doesn't hurt if you do.
In example 1, the second line of the proof should be broken down into 2 distinct steps.
In example 1, the third line should read Vertical Angles THEOREM.
In example 2, you do not have to have the first line of the proof. But it doesn't hurt if you do.
In example 2, the ticks in the shared side should be parallel and not crossed.
In example 3, the third line should read ISOSCELES TRIANGLE THEOREM and not base angles theorem.
In example 3, the fifth line should read Vertical Angles THEOREM.

https://www.youtube.com/watch?v=6saYBeHzArE

Complete the attached worksheet but don't follow the instructions at the top of the first page. INSTEAD, write a 2 column proof of triangle congruency (USUALLY just 4 lines) for each problem according to the model I presented in class. If you think the triangles canNOT be proved congruent, then list as many congruency statements of segments and angles as you can but conclude with a triangle NON-congruency statement and no reason.

Take a look at the following video for another explanation of writing triangle congruency and parts congruency proofs. HOWEVER, there are a few things I would like you to do differently from the video:
In example 1, you do not have to have the first line of the proof. But it doesn't hurt if you do.
In example 1, the second line of the proof should be broken down into 2 distinct steps.
In example 1, the third line should read Vertical Angles THEOREM.
In example 2, you do not have to have the first line of the proof. But it doesn't hurt if you do.
In example 2, the ticks in the shared side should be parallel and not crossed.
In example 3, the third line should read ISOSCELES TRIANGLE THEOREM and not base angles theorem.
In example 3, the fifth line should read Vertical Angles THEOREM.

https://www.youtube.com/watch?v=6saYBeHzArE

We began this in class on a piece of loose-leaf folded horizontal, horizontal, vertical and titled "Triangle Postulates & Theorems". So far, we have completed 1-13 ODDS. In the next class, we will complete 2-14 EVENS. If you were absent, please come by Room 113 during AcLab or after school and transcribe my work onto your own paper. These postulates (ESPECIALLY #5, #9 and #13) are crucial to your understanding and successful creation of geometric proofs.

Complete the following worksheet according to the instructions at the top of the table.

Complete the following worksheet according to the instructions at the top of the table. You may skip page 5 as we did that one together in class.

Take some time between now and Friday to 'hop around' these 9 slides and do a variety of practice problems in preparation for your quiz. Personally, I would concentrate on the problems that require drawing pictures, solving for missing angle measures using algebra AND making assumptions (true or false) based on figure/picture analysis.

Please complete the following 4 worksheets after you have filled in your Angles Graphic Organizer.

Please complete the following 4 worksheets after you have filled in your Angles Graphic Organizer.

You completed part of this in class. Please use the attached Glencoe Geometry Textbook pages (as well as your own Google searches and prior knowledge) to complete the remainder of the attached angles graphic organizer that you did not complete in class.

Please complete the following 4 worksheets after you have filled in your Points, Lines and Planes Graphic Organizer.

We completed this and reviewed it in class. If you were not present, please use the attached Glencoe Geometry Textbook pages (as well as your own Google searches and prior knowledge) to complete the attached points, lines and planes graphic organizer.

You were given this worksheet by the substitute during my absences on 3/20 and 3/21.

Please complete both sides of this worksheet. Make sure you read the rounding instructions at the top of the first page. For all of these problems, you will be using the log function on your calculator.

PERIOD 5: If you would like a paper copy of this, just stop by my room and I can give you one.

Please complete both of these worksheets. Make sure you read the sample problems at the top of each page. You do NOT have to follow those examples if you can think of another way to solve the problems that's easier for you. For all of these problems, you will be using the log function on your calculator.

Using your Small World Summary Sheet and your knowledge of logs, you should be able to answer the 3 questions on page 449 as well as the additional 7 questions I'm adding. Please use a piece of folded loose leaf that's properly headed and has room for notes.

Here are the additional questions. They are also on slides 27 and 28 of today's PowerPoint.

4.What about compounded every month?




5.What about compounded daily?




6.What about compounded continuously?


7.Why did Adam approach the banker and
speak to him with “practiced uncertainty”? What does that say about his
character and/or personality?




8.Look at
all
your
data
for
#1
through #6. What observations can you make or what conclusions can you draw based on the data?
Make at least two observations
or draw at least two conclusions…and not anything
so
simplistic as the amounts are changing or the amounts are growing. Think deeper.




9.How would Adam’s profits change…daily and
continuously…if he deposited $100,000 instead of $1000?




10.Looking at
ALL
your
data…for $1000 and $100,000…what
strikes you as oddly interesting about the values, especially those for daily
and continuous compounding?

See what you can do with this mixture of growth and decay/interest problems. Feel free to print the worksheet out if you do not want to write your answers on folded, headed loose-leaf

NOTE: When you reach #26-29, you will encounter a new phrase that I completely forgot about: compounding interest CONTINUOUSLY. Our current interest formula can't handle compounding continuously (compounding every single second every single day every single week every single month every single year). So we need a new one. PLEASE look at the amended Small World (Exponential) Summary Sheet for our new formula:
PN = PO * e^(t*.##)
where
PN is the new principal
PO is the old principal
e = 2.7183
t = time, usually years
.## = interest rate as a decimal

Here's some practice for your Quiz 3!

Using your Small World Summary Sheet and your knowledge of logs, you should be able to answer the 5 questions on page 434. Please use a piece of folded loose leaf that's properly headed and has room for notes. If you are still not confident enough to use logarithms, use the table function on your calculator.

Please complete both of these worksheets. Make sure you keep in mind the sample problems we did in class as well as the examples at the top of each page. For some but not all of these problems, you will be using the log function on your calculator.

Based on our discussion and modeling of page 1 and #5 on page 2 AND our doing the opener with the coin problem (#12 if you received a paper copy in class or #9 if you are printing out the pdf file posted here) on page 4, I think you can now complete the remainder of this 4-page packet.

Please complete both of these worksheets. You will NOT be using the log function on your calculator for this worksheet. In fact, you will not be using your calculator at all. These are just translation problems: translating from exponential form to logarithmic form AND translating from logarithmic form to exponential form.
Base^Exponent = Power
or 
log(subscript Base)Power = Exponent

NOTE: Your are NOT solving for any variables! As stated above, you are just translating from one form to another.

Based on our discussion of page 430 from the text, you should now be able to do all problems on this worksheet. For any question that mentions logarithms, since we do not know how to work with them yet, use the table function on your calculator. As proof of your answer, copy the table of values so that there are 1 or 2 entries below the one you found your answer at and 1 or 2 entries above. Circle the entry that contains your answer.
NOTE: Skip creating a table for 2a and simply use the table on your calculator to determine the answer to 2a.

You have now had time to read and take notes on this activity. We have also done page 429 and I modeled how to look for a pattern in order to create an exponential formula in the form of y = a^x, where y is your output, x is your input and an exponent and usually time. 'a' is any number or a combination of numbers. With page 429, it was a combination of numbers (bc^t) and 'b' was .89 and 'c' was (1 + .05) or 1.05. So, you should now be able to answer the 3 questions on page 430.

Here is a little exponent simplification practice. Try it out.

Complete the attached worksheet using information from our Properties of Exponents information sheet. DO NOT USE LOOSE LEAF! If you do not have a copy of the worksheet, come by my room and get one.

On a sheet of loose leaf folded and headed like the one we created in class for our first homework of the new year (See PowerPoint for example), answer questions 1-4 on page 429 of your text. We did 1a and 1b in class. 2a and 2b are similar. #3 and #4 can only be answered accurately if you do what is asked in the "Gather" paragraph between #2 and #3. YOU MUST GATHER MORE DATA BY TESTING OUT AT LEAST 4 OR 5 MORE YEARS!!! Then you can begin to develop an exponential formula of the form y = #^x which can be used to answer #3 and #4.

On a sheet of loose leaf folded and headed like the one we created in class for our first homework of the new year (See PowerPoint for example), answer questions 1-3 on page 421-2 of your text. Each question makes some mention of our new vocabulary: tangent, secant and derivative.

For all calculations, PLEASE do not use the PI key on your calculator as I do not think all calculators are calibrated the same in terms of how many decimal places are used for PI. Let's all use 3.14 so we will all get the same answers.

On a sheet of loose leaf folded and headed like the one we created in class for our first homework of the new year (See PowerPoint for example), answer questions 1-3 on page 420 of your text. Each question is very straightforward in terms of what you did on pages 413, 415, 416 and 417. The questions are asking you to do the same things but in a different context. In addition, it is an extension of an opener we did that came from page 394.


NOTE: PLEASE make a graph of the area equation. (Sorry I didn't request this of you when you were in class or in my initial posting of this assignment.) You will probably have to use a squiggle on the A axis. Have your time range from 0 to at least 40 hours.
REMEMBER: The equation we are using is a combination of our oil spill radius formula (r(t) = 70 + 6t) and the area formula (A(r) = PI*r^2). The combined formula gives us the area of the oil slick.

For all calculations, PLEASE do not use the PI key on your calculator as I do not think all calculators are calibrated the same in terms of how many decimal places are used for PI. Let's all use 3.14 so we will all get the same answers.

We have now finished Questions 1, 2 and 3a of Photo Finish on page 417 of your text. I would like you to do one more thing in preparation for our next class. (If you were in period 1, you have already started this. Please finish it if you need to. Make sure everything in the list below is on your graph.)

Please make a full page graph of Speedy's segment of her 1600-meter relay race. Based on our in-class work, you should have at least 5 points to graph...her starting point, her ending point and 3 points in between. If you did not take a picture of your opener (since 3 of those points were found in class when we did the openers of the last two days), you can always plug the formula for the distance Speedy ran at a given time in the race into your calculator or desmos.com and refind those points or select new ones. You can use the table on your calculator to see a whole list of points.

NOTE: Speedy's segment of the race starts at 0 seconds and goes to 50 seconds...starts at 0 meters and goes to 400 meters.

Remember to:
Calculate a good scale for your t (or x) axis, remembering that you want to make your graph as large and visible as possible.
Title your t axis.
Calculate a good scale for your m (or y) axis, remembering that you want to make your graph as large and visible as possible.
Title your m axis.
Label both axes.
Plot at least 10 but ideally more points on your graph and, ideally, label them.
Connect the points, keeping in mind that this is a quadratic equation and your graph should look like a piece of a parabola.
Label your connected line with Speedy's equation.
If you do not have a piece of graph paper, come by and pick one up in Room 113. LOOSE-LEAF IS NOT ACCEPTABLE for a graph that is not a sketch. And this graph is not a sketch. Thanks ahead of time for getting this done before class so we do not have to use time in class.

On a sheet of loose leaf folded and headed like the one we created in class for our first homework of the new year (See PowerPoint for example), answer questions 1-5 on page 416 of your text. Each question is very straightforward in terms of what you did on pages 413 and 415. The questions are asking you to do the same things but in a different context.

REMEMBER: When a question asks you how high ABOVE the ocean Clayton is, it is asking for the answer to the quadratic equation. When a question asks you how far Clayton has FALLEN, it is asking you to subtract the answer to the quadratic FROM the initial height...in this case 64.

For #5, you are being asked for the rate of change (speed) at a point very, very, very, very, very close to the point Clayton hits the water (h = 0). For your very, very, very, very close point, I would use a time 1 less than your answer to #2 plus .999. In other words:
t = (#2 - 1) + .999. Like #5 on page 415, that means you're looking at an interval of .001 seconds.

IF YOU WERE NOT IN CLASS TODAY (January 30), THEN BEGIN WITH THIS before you start on the second assignment (Page 415):

On a sheet of loose leaf folded and headed like the one we created in class for our first homework of the new year (See PowerPoint for example), answer questions 1-4 on page 413 of your text. Each question is very straightforward BUT you must read the introduction in order to understand the meaning of each variable of the formula you're being asked to use. 

Also, for question #3, finding the average speed involves two steps. First, add the distance fallen at 0 seconds to the distance fallen at 3 seconds followed by dividing that sum by the total number of seconds traveled...in this case 3.

IF YOU WERE IN CLASS TODAY (January 30), THEN BEGIN WITH THIS and ignore the above instructions for Page 413 because we did it and corrected it in class:

On a second sheet of loose leaf folded and headed like the one we created in class for our first homework of the new year, answer questions 1-5 on page 415 of your text. You are doing the same thing for each question but using different start and stop times. In class, we will not only check our answers but also discuss what comparison conclusions you can draw after each step of the exercise.

NOTE: On page 415, #1b, #2b, #3, #4 and #5 are asking you to do the same thing: calculate average speed for an interval of time: 
(starting distance left to travel - final distance left to travel) / (starting time - final time).
For 5 seconds, you know your h or distance left to travel is always zero because the bundle is on the ground.
In each question, you are basically using the slope formula at smaller and smaller and smaller intervals.
In #1, your interval is 2...2 seconds until the bundle hits ground.
In #2, your interval is 1...1 second until the bundle hits ground.
In #3, your interval is .5... .5 seconds until the bundle hits ground.
In #4, your interval is .1... .1 seconds until the bundle hits ground.
In #5, your interval is .001... .001 seconds until the bundle hits ground. (Your starting time is 4.999 seconds.)

On a sheet of loose leaf folded and headed like the one we created in class for our first homework of the new year (See PowerPoint for example), answer questions 1-5 on page 405 of your text. For questions 1 and 5c, use a separate sheet of graph paper. GRAPHS ON LOOSE LEAF ARE NOT ACCEPTABLE. Remember to scale them, title them, squiggle them if necessary, plot your points and connect them. Labeling points is always a good idea. Divide the front page of your graph paper in two and dot Graph #1 in the top half and Graph #5c in the bottom half.

On a sheet of loose leaf folded and headed like the one we created in class for our first homework of the new year (See PowerPoint for example), answer questions 1-4 on page 402 of your text. For question 1, use a separate sheet of graph paper. GRAPHS ON LOOSE LEAF ARE NOT ACCEPTABLE. Remember to scale it, title it, squiggle it if necessary, plot your points and connect them. Labeling points is always a good idea.

NOTE: This assignment is related to several previous text activities that we did not do. You may want to do them as linear equation review as well as prep work for this assignment. HOWEVER, they are optional and will not be entered into Gradebook. The previous activities are:
1. Story Sketches, Page 392-3, Problem #s 2-4
2. If Looks Don't Matter, What Does?, Pages 398-399, Problem #3

On a sheet of loose leaf folded and headed like the one we created in class for our first homework of the new year (See PowerPoint for example), answer questions 1-4 on page 390 of your text.

NOTE: This assignment consolidates some of the topics addressed in our activities from pages 388 and 389. In addition, it begins to introduce more pointed attention to slope and linear equations.

Previously, I gave you more detailed instructions for problems 3a and 4a. After working with my 5th period class this morning, Gabe Gomez alerted me to the fact that the very first line of the introduction states that the graph's y-axis is not height but AVERAGE height. So I misinterpreted 3a and 4a as asking YOU to calculate the average height. Sorry about that and thank you, Gabe...a future math teacher if I've ever seen one!!!

Therefore, do NOT follow my previously posted instructions. Interpret 3a and 4a as simply asking for a straightforward subtraction calculation of the younger age's height from the older age's height in order to get the increase.

3b and 4b are asking you to use our percentage increase/decrease formula.

On a sheet of loose leaf folded and headed like the one we created in class for our first homework of the new year (See PowerPoint for example), answer questions 1-4 on page 402 of your text. For questions 1a, 2a and 3a, use a separate sheet of graph paper. Fold your paper once horizontally and draw each graph in one half of one side of the graph paper. Remember to scale it, title it, squiggle it if necessary, plot your points and connect them. Labeling points is always a good idea

NOTE: Most of this assignment is linear equation/slope review. I honestly think it is within your capability based on the slope lists you created today for the opener. BUT if a question does perplex you, be ready to ask a question about it in class before we check the exercise and I give you time to wrap things up.

On a sheet of loose leaf folded and headed like the one we created in class for our first homework of the new year (See PowerPoint for example), answer questions 1-4 on page 389 of your text. Question 1 should be done on a full piece of graph paper!

NOTE: For this assignment...even though it is very similar to our last homework assignment...it is NOT using our US population data. It is using the text's WORLD population data, which is given to you on page 386!!!!!!!

On a sheet of loose leaf folded and headed like the one we created in class for our first homework of the new year (See PowerPoint for example), answer questions 1-4 on page 388 of your text. 

NOTE: For this assignment...even though it is very similar to our last homework assignment...it is NOT using our US population data. It is using the text's WORLD population data, which is given to you on page 386!!!!!!! The percentage of land surface area for earth is also given to you on that page.

Though your first homework of the new year is BASED ON "A Crowded Place", p. 386 of your text, IT IS NOT AN EXERCISE FROM THE BOOK! NOR IS IT PAGE 386 of your text! It is simply based on that page.

All instructions are given in the 4 PowerPoint slides attached here as a Word doc called "A Crowded Place - The US, Page 386". Please read them and follow them as closely as possible. There is no need to refer to your text at this time.

If you have a hard time accessing the website that gives you the population numbers we will use in our table, I am also attaching a PDF file of those numbers.

Answer Questions 1-12 (or as many as you can) on the attached worksheet. Do this on a new piece of folded and typically headed piece of loose leaf OR do it on the worksheet itself if you've printed it out or received a copy. PLEASE SHOW ALL WORK.

Minimally, showing all work with the quadratic formula involves these steps:
Showing me your a, b and c substitutions into the quadratic formula BEFORE any simplification...with parentheses around negative numbers.
At least ONE simplification step combining as many steps of product multiplication and sum addition/subtraction as possible.
A final answer using +/- BEFORE you put your solutions into curly braces with x =.
Your final answers in curly braces with x = OR your final answers in coordinate point form.

Read page 70. Try to absorb the formula given at the top of the page. It's the quadratic formula...our all-purpose quadratic solving formula based on the quadratic standard form.

On a folded, properly headed piece of loose leaf, please do Questions #1, #2 and #3. For #2, we went over the first 7 steps of deriving the quadratic formula. It is now up to you to complete the additional 4 steps. If you were not present for what we did today, the PowerPoint is attached and it contains the first 7 steps. It ALSO contains the instructions only for steps 8-12. But YOU will have to do the algebra! NOTE: Step 8 is asking you to COMPLETE THE SQUARE on the left side of the equation we ended up with in Step 7.

Make sure you attach/staple your #2 answer to your work for #1 and #3.

First, read page 70 of your text. Notice the new, all-purpose quadratic solving formula at the top of the page. This will be so useful as we move into next week and our final Unit 1 quiz.

When you have read page 70 and attempted Questions #1 and #3 on a folded and typically headed piece of loose leaf, answer Questions 1-18 on the attached worksheet. Do this on a new piece of folded and typically headed piece of loose leaf OR do it on the worksheet itself if you've printed it out or received a copy. PLEASE SHOW ALL WORK.

Minimally, showing all work with the quadratic formula involves these steps:
Showing me your a, b and c substitutions into the quadratic formula BEFORE any simplification...with parentheses around negative numbers.
At least ONE simplification step combining as many steps of product multiplication and sum addition/subtraction as possible.
A final answer using +/- BEFORE you put your solutions into curly braces with x =.
Your final answers in curly braces with x = OR your final answers in coordinate point form.

We started this page in class. I know it seems like we answered #1-3 in class. But I'd like you to rethink the 'explain why you chose that method' part of those questions. Sure. We talked about using the 'taking the square root' method for #1. And the Zero Product Property for #2. But WHY are they the best methods for dealing with vertex form and factored form? That is what I'd like you to think about and formulate a response to.

For #4, you're kind of on your own. In one of my classes, in response to #3 (the standard form quadratic), someone mentioned using the 'X' method for standard form equations. Someone else mentioned the calculator and graphing. Whether you agree with them or have an entirely different approach, #4 is asking you to consider how you might use the a, b and c coefficients/terms to solve a standard form quadratic. So you may need to throw out the 'X' method and calculator graphing altogether if they don't involve the use of a, b and c. You may have to think totally outside the 'box'.

Do the best you can and we will review your work in our next class.

Please read Pages 54-56 and take summarizing, exemplifying or defining notes on what you read. These three pages pretty effectively summarize what we have done with quadratics for the past 10 weeks. They should help you prepare for your quadratic 'final' next week.

After you have watched the 4 videos I assigned as viewing homework, attempt AT LEAST the 1st page of this worksheet. Follow the instructions at the top of the page. Use the just-learned X Method for factoring quadratics when 'a' does not equal 1. You may write your solutions in coordinate point form or in curly braces with 'x ='.

I think you can do all work directly on the worksheet. However, if you choose to do it on loose-leaf, please follow our standard headings and fold your paper horizontal, horizontal, vertical so you have 8 rectangles on each side to work within. You will need a 2nd sheet of loose leaf if you attempt to do both sides of the worksheet.

NOTE: Always check to see if you can 'divide out' the 'a' term before attempting the X Method. Remember: if you can, don't forget to  'reinsert' your 'a' in front of your first parenthetical linear expression for your final factored form.

We corrected the first page of this worksheet in class today. Please make sure you have completed ALL of the second page of this worksheet (Practice 1) for our next class...according to the instructions at the top of page 1. REMEMBER: When factoring and finding solutions, set your equation to 0.
I think you can do all work directly on the worksheet. However, if you choose to do it on loose-leaf, please follow our standard headings and fold your paper horizontal, horizontal, vertical so you have 8 rectangles on each side to work within. You will need a 2nd sheet of loose leaf since there are 26 problems.

On page 2, you will notice that some of the problems have an 'a' not equal to 1. For those, make sure you divide each term by the 'a' value before you begin your factoring. Then 'reinsert' your 'a' in front of your first parenthetical linear expression for your final factored form.

First of all, I'm sorry I did not post this earlier. Hopefully, you absorbed my in-class instruction to tackle these two pages and have already started. If not, try to get this done for Wednesday.

We did page 47 in class. That page gave you your 3rd introduction to factored form and another way to find solutions to a quadratic. Your first way of finding solutions to a quadratic was completing the square and PAUSING!!!

I think you are now adequately prepared to answer the questions on pages 48 and 49 of your textbook. You can either use the area model method we worked with in solving the questions on page 47 OR you can use our completing the square method coupled with PAUSING.

Do the best you can and we will review your work in class on Wednesday.

Please complete ALL of this worksheet (Practice 3) according to the instructions at the top of the page. That means you are completing the square for all twelve standard form equations AND finding their solutions by taking the square root. If you get stumped on any of these, please be ready to ask questions in class on Wednesday. Write on the back of the worksheet or use a piece of folded, properly headed loose-leaf paper.

The steps for completing the square and finding solutions by taking the square root are on your Worksheet 2. However, if you would like a larger print edition of those steps, they are attached below. The 'finding solutions' larger print steps are slightly different than the ones on the worksheet. I added an additional step for situations in which the right side of your equation is NOT a perfect square.

Please complete ALL of this worksheet (Practice 1) according to the instructions at the top of the page. If you get stumped on any of these, please be ready to ask questions in class on Thursday. Write right on the worksheet.

NOTE: I am NOW asking you to do all 12 problems instead of just 6!!!!!!!!!!!!!!!!!!!!!! I have just finished doing the worksheet myself...all the steps for each problem. And as long as I'm following the steps, it only took me about 20 minutes.

Now that I have introduced the steps to Completing the Square to ALL my classes, I am attaching a summary of the steps we created here.

Please complete ALL of this worksheet (Practice 2) according to the instructions at the top of the page. That means you are completing the square for all ten standard form equations AND finding their solutions by taking the square root. If you get stumped on any of these, please be ready to ask questions in class on Monday. Write on the back of the worksheet or use a piece of folded, properly headed loose-leaf paper.

The steps for completing the square and finding solutions by taking the square root are on the worksheet. However, if you would like a larger print edition of those steps, they are attached below. The 'finding solutions' larger print steps are slightly different than the ones on the worksheet. I added an additional step for situations in which the right side of your equation is NOT a perfect square.

You have already done this worksheet once. The first time, you simply completed the square for each standard form quadratic. NOW you will be doing the worksheet again. However, this time, you will be finding the solutions to each of the given standard form equations. The 'solutions' or zeroes/roots to any quadratic are its x-intercepts...the one or two points where the parabola crosses the x-axis.

We went over the steps to finding the solutions to a quadratic in class today. Ideally, you would have written them down. However, if you did not, I have written the steps in a word document that is attached here...along with the steps for completing the square. Make note of both sets of steps in your opener document sometime before our quiz next week.

Some things to remember:
1. When you take the square root of the right side of your equation, if it's a perfect square, remove the square root sign and write the principal square root with a +/- sign. (4 is a perfect square. When you take the square root of 4, you get 2. BUT, it is not just +2. It is also -2.)
2. When you take the square root of the right side of your equation, if it's NOT a perfect square, do NOT remove the square root sign. But make sure it is preceded by a +/- sign. (37 is NOT a perfect square. When you take the square root of 37, you get sq.rt.(37). But it is not just +sq.rt.(37). It is also -sq.rt.(37).)
3. Whenever a square root is part of your solutions, it should always come last. For example, 2 +/- sq.rt.(37).

I had asked you to read pages 26 and 27 for our last class. We did page 26 in class today. I would like you to attempt page 27.

Page 27 might be a bit challenging because it's introducing two phrases you may not have encountered before: "completing the square" and "perfect square". See if you can understand their meanings by doing a little internet search. If your search proves fruitful, then do #1-3. If your search doesn't fully enlighten you, just attempt the questions with the understanding you have. Leave blank rectangles if you need to and we will address confusions related to them in our next class.

Please follow our standard, folded loose-leaf format, with space for notes and work on the front and back. Maybe fold your paper horizontal, horizontal, vertical so you have 8 rectangles on the front and 8 on the back. That will give you more than enough space for all 10 questions. (Leave 4 rectangles on the front for notes!!!)

Please complete both sides of this worksheet (Practice 3) according to the instructions at the top of each section of the worksheet or the instructions given in each individual question. If you get stumped on any of these, please be ready to ask questions in class on Tuesday. Write right on the worksheet.

REMEMBER: When talking about the 'h' or 'k' values in your vertex-form equation...i.e., translations, always refer to the amount the parabola has slid. Usually that will be a number of units. For example, 'the parabola translated left 7 units' or 'the parabola slid up 3 units'.

REMEMBER: When talking about the 'a' value in your vertex-form equation...i.e., widenings or narrowings, always refer to the FACTOR by which it has widened or narrowed. Usually that will be a number greater than 1 if narrowed; a number less than 1 if widened. For example, 'the parabola widened by a factor of 8' (where 8 is your 'a' value) or 'the parabola compressed by a factor of 1/2' (where 1/2 is your 'a' value).

You have already read this page and, hopefully, thought about it. Now that we have done almost two weeks of work on using the vertex form, I think you are now capable of answering the 1 question on page 18 ("Is it a homer?")...AND writing a justification/explanation for why your answer is right using WORDS and MATHEMATICS!

Please follow our standard, folded loose-leaf format, with space for notes/DIAGRAM (!!!!!)  and 2 rectangles on the front page: one rectangle for your mathematics to answer the question; one rectangle for your justification/explanation for the correctness of your mathematics.

If you were not in class when we diagrammed the scenario OR if we did not get around to diagramming the scenario in class, I am attaching a rough sketch of what we came up with in my 7th period class. You may refine the attached diagram with new information or information we forgot. THIS DIAGRAM SHOULD APPEAR IN THE NOTES SECTION OF YOUR LOOSE-LEAF.

Please complete both sides of each worksheet (Practices 1 and 2) according to the instructions at the top of each side of the worksheet or the instructions given in each individual question. If you get stumped on any of these, please be ready to ask questions in class on Tuesday. Write or graph right on the worksheet.

NOTE: I have introduced two new ways to talk about translations and widenings/narrowings (stretches/squeezes or expansions/contractions-compressions).

When talking about the 'h' or 'k' values in your vertex-form equation...i.e., translations, always refer to the amount the parabola has slid. Usually that will be a number of units. For example, 'the parabola translated left 7 units' or 'the parabola slid up 3 units'.

When talking about the 'a' value in your vertex-form equation...i.e., widenings or narrowings, always refer to the FACTOR by which it has widened or narrowed. Usually that will be a number greater than 1 if narrowed; a number less than 1 if widened. For example, 'the parabola widened by a factor of 8' (where 8 is your 'a' value) or 'the parabola compressed by a factor of 1/2' (where 1/2 is your 'a' value).

Answer the 6 questions on page 17. We will be checking them as a class group work exercise on Thursday. If you get stumped on any question, make sure you have left space for it on your loose-leaf...to fill in during or after our group work. In other words, please follow our standard, folded loose-leaf format, with space for notes and 2 rectangles on the front and 4 rectangles on the back. Or, if you'd like, fold your paper horizontal twice and vertical once so you have 8 rectangles on the front: 2 rectangles for notes and 6 additional rectangles for your question answers.

This is all based on our recent study of quadratic transformations and vertex form.

Please complete both sides of this worksheet according to the instructions at the top of each side of the page. If you get stumped on any of these, please be ready to ask questions in class on Tuesday.

Based on what we did in class today, finish the three or four transformation graphs that we didn't get to in class today. Use pages 11-12 and 14-15 of our text to guide you. If you do not have a graphing calculator at home, use Desmos.com's graphing calculator. The link is in the Useful Links section of Classwork in Classroom.

We completed this worksheet in class and checked it after we finished completing our Quadratic Graphic Organizer and taking notes on vertex form. If you were not in class, please follow the instructions on the worksheet and complete it.

We completed #3 and #4 in class. Please complete the back page on your own, showing all work or specifying how the answer was found on the calculator if you are not showing work. 

In addition, please attempt #1 and #2, keeping in mind that when determining intervals of increase and decrease, always place your finger on the far left of the graph and move it to the far right. Each time your finger is falling (moving down) is an interval of decrease and each time your finger is rising (moving up) is an interval of increase. Use set or interval notation to specify the intervals of decrease or increase. Use both if you want more practice writing each type. In total, I think there are 3 intervals of decrease and 2 intervals of increase.

If you were in my Periods 1 and 2 today, I think I may have written a wrong numerical limit when I was showing my work. Just looking at the visible portion of the graph and NOT any extensions towards infinity...
The most left limit or least x value is -3.25; the most right limit or greatest x value is 4.
The most bottom limit or least y value is -1; the most top limit or greatest y value is 1.

NOTE (and this is VERY important for your quiz on Wednesday): When a domain or range is asked for IN CONTEXT, that means you are talking about reality. Infinity does not figure into reality. It only figures into talking theoretically about mathematics. So in #8 and #9, ONLY consider the real life limits of the ball. That means where it starts and stops in reality...not theoretically as seen in the total pictured graph (that DOES, mathematically, move towards infinity). In other words, the domain IN CONTEXT cannot start at -infinity and end at +infinity because, IN REALITY, it never reaches infinity. Where does it start IN REALITY and where does it stop IN REALITY? Consider the REAL start and stop values of your h (y values) and t (x values).

NOTE: The copy of the worksheet that was previously attached had no formula or numbers on it!!!! I am attaching another copy now that has the formula and numbers.

Complete #1-4 on the attached worksheet (handed out in class on paper on 9/16). You may do your work on the worksheet or, alternatively, use a piece of loose-leaf in our standard folded and headed format. THIS IS GOOD PRACTICE FOR YOUR QUIZ!

Answer the 5 questions on page 10. We will be checking them as a class group work exercise Monday of next week. If you get stumped on any question, make sure you have left space for it on your loose-leaf...to fill in during or after our classwork next week.

This is all based on your reading of "A Corral Variation" on page 10 of your text and the corral opener we had in the first week of school. Be prepared to summarize and/or ask about any confusions related to the story and the questions. Create a folded loose-leaf document with room for notes and rectangles for questions #1-5...like we did for "Victory Celebration" last week.

This worksheet introduces you to quadratic vocabulary and the basics of quadratic graphing. We did and corrected #1-11 in class. Your homework is to complete the worksheet. That's #13-17. 

In class, I may have said do #13-16. But I think if you read carefully and think critically, you can handle #17 as well. 

REMEMBER: Submit your work BEFORE we correct it in class on Monday. During our review in class, you may amend or edit your work IN A DIFFERENT COLORED INK then resubmit the corrected/edited version on Classroom.

Here are the answers to #1-12. Soooooooo, try to do #12 FIRST then check your answers with these afterwards. 
1. ax^2 + bx + c
2. parabola
3. axis of symmetry (In this case, it's x = -2)
4. vertex (The plural is vertices. And in this case, it's (-2, -2)
5. maximum
6. minimum
7. x-intercepts (In this case, (-.5, 0) and (-3.5, 0))
8. zeros/roots (In this case, {-.5, -3.5}
9. 1; {3}
10. 0; the null set
11. 2; {0, -2}
12a. x = 3
12b. (3, -2)
12c. 2; {2, 4}
12d. -infinity < x < +infinity OR
All Real Numbers OR
{x |  -infinity < x < +infinity} OR
{x | x belongs to All Real Numbers} OR
(-infinity, +Infinity)
12e. -2 <= x < +infinity OR
{x |  -2 <= x < +infinity} OR
[-2, +Infinity)

This assignment asks you to broadly think about quadratics and their application to a real life situation. We read page 4 of the text and took notes on important points, vocabulary, equations, numbers and questions. You should do the same if you were absent from class.

Once you have read and taken notes on page 4, answer questions #1-4 on page 5. #1 should be a diagram with as many labeled parts as possible. #2 is a series of 3 well-worded questions. #3 is 3 well-worded explanations of HOW you would use the equation given on page 4 to answer the questions in #2. HINT: For each question, you have to think about whether or not you would substitute a known number into the h variable OR the t variable. Finally, #4 is one, two or three calculations to numerically answer one, two or all three of the questions in #2 using the equation used in #3. HINT: For each question, try subbing in a number for h or t and see what you get. Alternatively, you can look at the graph on your calculator. If you don't have a graphing calculator, then use the link I posted in the Useful Links section of Classwork in your Google Classroom.

Please follow the format for homework that I demonstrated in class. Consult the attached document for that format if you were absent from class.

REMEMBER: Submit your work BEFORE we correct it in class on Monday. During our review in class, you may amend or edit your work IN A DIFFERENT COLORED INK then resubmit the corrected/edited version on Classroom.

Fill in pages 1 and 2 of the Student Information Form. Please do not leave any question blank. You are more than welcome to submit your form on Google Classroom. BUT, you will not receive credit for this assignment unless you PRINT OUT THE FORM and hand it to me (or put in your period's homework folder near the tardy log) in class. If you print out two pages instead of one double-sided page, then PLEASE do not forget to staple your two pages together. There are staplers by the tardy log near the door as well as on my desk. NOTE: If I did not give you a paper copy in class, I am more than happy to give you one during your passing periods, AcLab or in our next class.

Look at the instructions and examples in Slides 20-24 of the attached Lesson Plan PowerPoint. Your Big Number Board may be a Jamboard slide, a PowerPoint slide, a Google Slides slide, a landscape Word doc or a single-sided piece of unlined paper. Remember: there are 6 elements to your board (see Slide 23); make sure your final submission has all of them. 

NOTE: Slide 24 is a student sample of the assignment and there are a few missing elements; Slide 22 is my model of the assignment and (I don't think!) there are any missing elements. 

On the assigned due date, make sure your board is submitted in Google Classroom AND oriented so that, when I open it up, it is RIGHT-SIDE-UP!

We have not yet gone over my policies and procedures for the smooth operation of our class. We will do that in our next class. However, in preparation for that discussion, could you please read the attached list in case you can't find the one I gave you in class? It contains ALL the different policies and procedures that YOU suggested in your opener from the first day of school. After reading the list, circle up to 5 policies or procedures from any section of the list that you feel would be a good addition to our current policies and procedures. (I'll attach that document as well in case you think it might help you in your decision-making process.) Then, in our next class, you and your podmates will whittle down your 10 or 15 choices to three. After that, I'll collect those final choices and whittle them down to 3-5 NEW policies and procedures to add to the existing ones. Thanks.

Fill in pages 1 and 2 of the Culture Form. You may leave up to 2 questions blank if their wording confuses you. But please answer AT LEAST 10 questions if 12 are too overwhelming. You MUST submit your form on Google Classroom. You will not receive credit for this assignment unless it's submitted on Classroom. NOTE: IF YOU WANT SOME EXTRA CREDIT for this assignment, then have your parents or guardians fill out pages 3 and 4 of the Culture Form. Ask your parents or guardians to answer as many questions as possible. Again, submit THEIR form on Google Classroom at the same time as you submit your own form.

I did not hand out these forms in class. But, I have paper copies. If you would like a paper copy of the student Culture Form as well as the parent Culture Form, I can give it or them to you in the next class OR during a passing period, AcLab or after school.

Look at the instructions and examples in Slides 16-21 of the attached Lesson Plan PowerPoint. Your 'Who Am I?' Board may be a Jamboard slide, a PowerPoint slide, a Google Slides slide, a landscape Word doc or a single-sided piece of unlined paper. Remember: there are 5 elements to your board; make sure your final submission has all of them. On the assigned due date, make sure your board is submitted in Google Classroom AND oriented so that, when I open it up, it is RIGHT-SIDE-UP! For class, you should either have a printed-out copy OR your chromebook/laptop/tablet/etc. to display your work. YOU CANNOT DISPLAY YOUR WORK ON YOUR PHONE!

Some of you seem to be having a hard time trying to come up with three mathematical discourse questions or problems or tasks. I think you may be overthinking the homework.

First of all, look at those 5 elements of a high-cognitive task...which means a task or problem or question that is complex AND gives the opportunity for math discourse. Go down that list once you write a question or problem or task and ask yourself: 
1. Is my question/problem/task open-ended? Yes? Then it's a candidate for math discourse.
2. Does my question/problem/task utilize prior experience or knowledge? Yes? Then it's a candidate for math discourse.

3. Is my question/problem/task related to a mathemetical BIG idea/concept? Yes? Then it's a candidate for math discourse.

4. Can I learn something new by answering or doing my question/problem/task? Yes? Then it's a candidate for math discourse.

5. Does listening to the conversation connected to students answering or doing my question/problem/task help me understand how they are thinking? Yes? Then it IS math discourse!!!!


Your question/problem/task must contain ALL 5 elements of math discourse!!!

BUT, here's something that might give you some more ideas. It's a list of 100 sentence stems that can be used to promote mathematical discourse. However, don't just copy three of theses 100 sentence stems and think you have finished this HW assignment. If you like one of the stems and want to use it, YOU MUST CONNECT IT TO A MATHEMATICAL IDEA OR CONCEPT!!!

For homework, write three questions or tasks (on a piece of loose-leaf) that inspire MATHEMATICAL DISCOURSE, each one slightly more complex
than the preceding one. Remember: 'Complex' means the question or task is more than something you memorize or a series of steps you follow; it gives you something to talk about. Again, a few general characteristics of
these types of questions/tasks are that:



●They are open ended because they don’t
outline an explicit solution pathway.


●They require students to make connections to prior knowledge and
experiences.


●They allow students to explore big mathematical ideas.


●Students can learn from engaging with the task/question.


●Teachers can gain insight into student thinking by observing how
students engage with the task/question.



Be prepared to get into a small group and
present your questions/tasks.
Once you are in that small group, all members will share their questions/tasks and,
after some debate, choose the one that, as a group, you feel best
represents the qualities of GOOD mathematical discourse.

NOTE: You MAY want to refer to slides 7-12 in the attached PowerPoint to refresh your memory of mathematical discourse. Slides 7-12 contain our mathematical discourse opener...2 slides of mathematical discourse definitions and characteristics...the link to the mathematical thinking video we watched in class...AND a slightly different version of the assignment than what is presented here.