Saturday, August 3, 2024

# Common Core Algebra 2 Unit 13 Lesson 9 Answers

## Common Core Algebra Ii

Common Core Algebra II.Unit 9.Lesson 2.Complex Numbers

In this course students will learn about a variety of advanced topics in algebra. Students will expand their understanding about functions by learning about polynomial, logarithmic, and trigonometric functions. These new functions along with linear, quadratic, and exponential, will be used to model a variety of problems, including compound interest, complex numbers, growth and decay, projectile motion, and periodic phenomena.

Polynomial and rational algebra is extensively covered including advanced factoring and polynomial long division. Advanced work in probability is included that focusses on the use of conditional probability. Extensive statistics work is done to help students understand how population parameters can help to infer properties about populations. This course is aligned to the Common Core State Standards for Algebra II.

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O.k. So, after a bit of legwork, it turns out that it is not hard to post TI-83/84 programs to this site and its not even hard to have you download them.

A few days ago, I posted a document detailing three Statistics programs I wrote for the TI-83/84 to do the statistical simulations that are required in the new Common Core Algebra II. I created the simulation programs based on the simulations recommended in the G.A.I.S.E. Report . The New York State Department of Education has been referencing that report highly whenever they speak of the statistics in Common Core Algebra II. Heres another posting of the article I wrote explaining the three programs:

But, now, you dont need to type them in. I want to sincerely thank Jenn Sauer, a great educator from my neck of the woods over in the beautiful town of Saugerties. Jenn was kind enough to brainstorm the statistics a bit with me and give me super helpful suggestions on the programs themselves. Here they are for download.

Save them in a safe spot where you will know where they are.

O.k. Now, how do you get them onto your calculator especially if you are not used to doing this? First things first, you need to download TI Connect. Its free and easy. Heres the link:

Alright, once you have TI Connect youll see this main screen:

You will then navigate to whatever folder you stored the programs in. Select them all at once and then send them to your calculator.

## New Cc Algebra Ii Statistics Videos By Kirk

A few weeks back, I published three new lessons to go with our final unit in Common Core Algebra II Statistics. These lessons extended the work that we began in inferential statistics by introducing more formal ways of finding variation within sample statistics, such as sample means and proportions. By continuing to use simulation, we introduce students to the Central Limit Theorem for both sample means and sample proportions and extend this to a final lesson on margin of error. All of the lessons and their answer keys can be found at this post:

Simulation and Inferential Statistics by Kirk

It took awhile, but I finally found time this weekend to record the videos for these lessons. I hope the videos are in time to help both students and teachers with this challenging material. I believe that these lessons will help students understand inferential statistics and how the results of the simulations can be extended to standard methods within statistics. Here are the YouTube links to the three new videos:

YouTube Statistical Simulation Programs from eMathInstruction

One of the things I mention in the video is using Google Sheets to analyze the results of the simulations. Google Sheets is super convenient to use given that everyone has access to it. I also find it is much, much easier to use than Excel in terms of creating distribution histograms of the simulation results. Heres a distribution of 1000 sample means that I created just now:

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## Interactive Video Lesson Plan For: Common Core Algebra Iiunit 13lesson 9distribution Of Sample Proportions

#### Activity overview:

In this lesson we look at the distribution of sample proportions taken from a population with a given proportion. We then use the standard deviation of the proportions to predict how likely a sample proportion would be.

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## Statistical Simulation The Effect Of The Treatment On Sample Means

More than any other topic, I was most worried about writing lessons for the statistics standards in Common Core Algebra II. Ive been a high school math teacher in New York now for 16 years. The extent Ive taught stat has been the normal distribution in half-standard deviation increments . I taught college statistics over a decade ago at Syracuse University, but its been awhile.

So the prospect of somehow trying to tackle a standard like:

S-IC.5: Use data from a randomized experiment to compare two treatments use simulations to decide if differences between parameters are significant.

Whew! Right?

Well, these have been some of my very favorite lessons to write. Thats mostly because Ive gotten to do math and understand math better than before. And thats been thrilling.

Heres the lesson and homework set that I just created to address this standard. In order to run do the lesson, you MUST download and install the TI83/84 program MEANCOMP. Place data in L1 and L2 and the program will do amazing simulations!

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## Simulation And Inferential Statistics By Kirk

So, Ive made quite a few posts lately because we are near the time when teachers will be working through the very confusing topic of inferential statistics in Common Core Algebra II. With so little guidance from NYSED on the matter, we are left to sift through sample problems, standards, and the Modules. Ultimately, inferential statistics is a topic that is much, much too large to simply squish into Algebra II.

If anything, the state should almost consider renaming the course Algebra 2 with Statistics if they are honest about the content.

Whats ultimately very difficult is that the CC Standards and the GAISE report for inferential statistics emphasize on using statistical simulation instead of formulas to develop things such as confidence intervals and margins of error. The theory, at least, is that the formulas are much more understandable if students develop a more intuitive grasp of inferential statistics by using probabilistic thinking generated through simulation.

Im not sure I even understood what I just typed.

Notice, there are no sample means under this simulation that fall outside of the range 17.0 to 19.2. This, in fact, would be a rough approximation for our confidence interval and half the width between these, i.e. /2=1.1, would be a rough width for our margin of error. By the way, the actual margin of error is a theoretical 0.99 ). Heres a link to that simulator and our other two as well:

Difference of Sample Means Web Based App

## Statistical Simulators And Additional Lessons Common Core Algebra Ii

Well, its getting to be crunch time in Common Core Algebra II now that April looms before us. As at Arlington, Im sure that many districts are beginning Probability soon and will then turn to statistics in Common Core Algebra II.

I still am a little in the dark about the expectations that the state has in terms of what it wants students to know and be able to do when it comes to inferential statistics. Some of what we know comes from the CC Standards themselves, some comes from the Modules, and some comes from the sample questions. But, these three things are often contradictory.

At the end of the day, I feel like the original curriculum that I created does a good job at using Statistical Simulation to give students a good feel for how probability ties into inferential statistics. Ive written statistical simulators for the TI-83/84 calculators and much, much faster simulators that are web-based. I describe all of these simulators in detail and supply links to the calculator code and web based apps in this earlier post of mine:

NORMSAMP is a very simple program. The user specifies a mean and standard deviation for an infinite population that is normally distributed. The program will then simulate a sample from this population of any size and perform multiple simulations. This output is a list of sample means and a list of sample standard deviations.

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## Statistical Simulation In Common Core Algebra Ii

So, the statistics standards in Common Core Algebra II specify a lot of use of simulation to establish confidence intervals and other statistical measures of variability. I like these standards, but was having a hard time thinking about how to really fulfill them in a meaningful way.

So, I attacked them head on. Based on work from the G.A.I.S.E. Report , I created three programs for the TI-84+ operating system that perform these simulations.

The first program allows you to pick a random sample from a population to calculate sample means and see their distributions. The second allows you to pull a sample from a population with a known proportion, and then see a distribution of sample proportions. Finally, the last program scrambles up treatment data to test the difference in treatment means.

I have not gotten them up on TIs site, yet, but plan to later on in the spring. Im offering them now, in case people want to type one or all of them into their calculators and start to really play with these simulation standards.

The document includes an explanation of the three programs and their code.