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eMath August 2018 Newsletter

Wow! Is it already August 15th? For those of us living in New York, that generally means we have just over two weeks of summer break left before school begins. How time flies.

Speaking of the waning summer, if your school is still looking to purchase workbooks for this coming school year, make sure to do so as soon as possible. We’ve still got quite a bit of them in stock now, but by next week, the delivery times will start to push past Labor Day weekend. For New York City teachers, we now have all of our workbooks, including Common Core Algebra I in Spanish, on ShopDOE and the FAMIS ordering systems. Find all of the important information using the document below:

eMath Instruction ShopDOE and FAMIS List 2018

Now that the school year is almost upon us, we have new additions to each course. As always, please feel free to send us suggestions about what you would like to see as monthly add-ons to various courses. Always best to catch us with your suggestions at least a month ahead of time. Assessments are always in demand and we have a bunch for you this month.

In our Common Core Algebra I Add-Ons, we bring you a Unit 3 (Functions) Quiz. This quiz goes through Lesson 3 of the unit and we provide you with both a Form A and a Form B version of the quiz. This is the first year of our Common Core Geometry Add-Ons. For the Geometry Add-Ons this year we want to make sure you all have a Form B test for each unit. So, for this month we give you a Unit 1 and Unit 2 Form B assessment. These mirror assessments can be used as makeup for the typical exams or just as replacements.

For our Common Core Algebra II Add-Ons, this month we bring you a Unit 2 Quiz (Also Functions). This quiz should be given after Lesson 3. We provide both a Form A and Form B version of this quiz. In Algebra 2 and Trigonometry Add-Ons, we provide a Unit 1 and Unit 2 Form B quiz. In Alg2/Trig, the first two units are very short, so we did not write full unit assessments for them. Here we provide a Form B for the “quizzes” for each of these units.

This year we are going to have our eye on the changes coming due to the Next Generation Standards in New York State. For those outside of the state (or those out of the loop), New York decided, like many states, to massage the Common Core Standards and given them a less politically charged name (they’ve even taken it off of the NY standardized tests). These standards do not go into effect at the K-8 level until the 2020-2021 school year. They will first be tested at the 3-8 levels in the spring of 2021. Here is a graphic of the timeline:

Here’s a link to that page:

Next Generation Math Standards Implementation Timeline

Now, I get a lot of questions about when we will be incorporating the Next Gen changes into our Alg I/Geo/Alg II series of curricula/books. Well, New York State has been vague, at best, about when the changes will be implemented at the high school level. BUT, if you look at the fine print of the Timeline graphic above, you see:

Two things to note here: (1) NYSED has not yet decided on when these standards will be implemented, so we must assume the status quo in terms of the assessment content and (2) the implementation of the Next Gen standards on tests will not happen before June of 2021.

We plan to really start modifying our high school texts later this academic year and will continue to create lessons that fit these standards as add-ons. We do not plan on actually changing the workbooks until the 2020-2021 academic year. We also hope to release something for kids younger than 9th graders for the Next Gen standards as well. More on that later this year.

That’s it for now. Continue to enjoy the rest of summer. Get out to your local fairs, waterparks, and festivals. As for me, I’m looking forward to taking a long weekend to camp with the kids.

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New York City ShopDOE and FAMIS Listings

For the past three years, eMathInstruction has been working to get our books available on the New York City ordering portals ShopDOE and FAMIS. Just yesterday, we got the last of our current books, Common Core Algebra I in Spanish, up on the two sites!

In order to find our materials on ShopDOE and FAMIS easier, we have published a ShopDOE and FAMIS item list. The two sites differ in how you find books on them (ShopDOE uses item numbers whereas FAMIS uses ISBNs). The pdf file below gives a complete list of these numbers:

eMath Instruction ShopDOE and FAMIS List 2018

As well, in our Shop, we also have these numbers listed for each individual book. Just go to the workbook’s product page and click on the ShopDOE/FAMIS Information tab:

Once you click on that tab, you will then see an exhaustive listing of both the ShopDOE and FAMIS information:

Visit the site to see all of the listings and get those book orders in. By mid-August books demand will start to outpace supply and we all know what happens then.

 

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TI-Inspire Quick Reference Guide (by Great Neck Middle School Period 8 Algebra I)

Zach Boyt, a teacher at Great Neck Middle School, just sent us a really cool guide for the TI-Inspire that his 8th period Algebra I class created.

Zach was blown away by the quality and thoroughness of the guide. And, I have to say I was as well after looking at it. This is a really good resource to have if you use the TI-Inspire in your classes. Here’s the guide:

NMS Team Blue Pd 8 NSpire Guide

Thank you to Mr. Boyt’s 8th Period Algebra I class for sharing this excellent resource! Good luck to everyone taking the exam tomorrow.

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Problem Sets for Live Reviews (June 11th, 13th, and 18th)

We have Live Regents Review Sessions coming up.

A few teachers have suggested that we post the problems we are going to work through. These problems sets are rather long (15 to 25 pages each). We are posting them as we get them up.

Algebra I Problems:

CC Alg I Live Review Handout 2018   (pdf)

Common Core Algebra I Live Review Problems

Algebra II Problems:

CC Alg II Live Review Handout 2018  (pdf)

Common Core Algebra II Live Review Problems  (word)

Geometry Problems:

CC Geo Live Review Handout 2018  (pdf)

Common Core Geometry Live Review Problems (word)

We likely will not be able to do all the problems in each of these sets (there are a lot of them). But, I will try to get through as many as possible in the three hours we have on each night.

 

 

 

 

 

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eMath May 2018 Newsletter

Well, Spring has definitely sprung here in the great Northeast. As I sit here massive thundershowers are hitting us. We even have a tornado warning! I grew up in Illinois, where the flat terrain essentially guaranteed that tornadoes were commonplace. But, surrounded by mountains (or large hills as some would insist) here in Red Hook, we don’t tend to see twisters here.

But, enough about the weather (actually I’m going to come back to it eventually). We are heading into the homestretch of the school year. With roughly a month to go before standardized testing sets in, teachers should be heading into full on review mode. To that end, let’s discuss the add-ons for Common Core Algebra I, Common Core Algebra II, and Algebra 2 with Trigonometry. Last year for each of these courses we put out short (10 points each) Unit Review quizzes for each unit. For both CC Algebra II and Alg 2 with Trig we put multiple quizzes out for the longer units as well. We released these quizzes between the April and May add-on rounds from last year.

This year we are releasing the Form B (or makeup) quizzes for all three courses. We organized the quizzes from last year and rereleased them as Form A. We then also released Form B as new content. For each course, both documents, Form A and Form B, contain quizzes for all units. These quizzes will help spot check the students as you conduct unit review. Since Teachers have access to the Word document as well, you have the flexibility to combine quizzes as you like and need to.

We will start up with more add-ons in August! Including add-ons for Geometry.

In other exciting news, eMathInstruction will host Live reviews for the New York State High School Regents exams!!!

Last year we live streamed reviews for CC Algebra I, CC Algebra II, and CC Geometry (in that order). We did this using only Instagram Live, since that was where we thought we could reach the most students. By the time we did our last review, CC Geo, we had over 20k viewers. Granted, some of them probably weren’t students at all and left as soon as they realized it was a big, old geek (me) talking about math, but still! Over 20 thousand unique viewers. Even if 5,000 were students, that would be great.

This year we hope to live stream it on Instagram Live, Facebook Live, and YouTube Live. We still have to work out the details on that. But, the dates and times have been set:

Algebra I Review: Monday, June 11th, 6 until 9 p.m.

Algebra II Review: Wednesday, June 13th, 6 until 9 p.m.

Geometry Review: Monday, June 18th, 6 until 9 p.m.

Kids will be able to tune in via Instagram Live (at least) and have a chance to comment (briefly) at certain times during the video. They will need to follow:

@emathinstruction

 

Last year we streamed to my own personal account (@kirkweiler if you want to see me post pictures of my garden), but this year we are only Instagram Live Feeding to @emathinstruction. Have your students follow that to watch. Once we know how to watch on YouTube Live and Facebook Live we will let people know via Facebook.

Finally, back to the weather! In my experience, many math teachers are weather junkies. We like both the predictable, science side of it as well as its probabilistic nature. A neat website to help you visualize the weather patterns, especially air velocity, is a site called Ventusky.com.

It’s a super cool site where those little streaks you see in the image actually move on the screen relative to the velocity of the wind currents. It is especially impressive when you are looking at a hurricane. Here’s a hurricane like pattern off the coast of Japan (thankfully not an actual hurricane/typhoon).

So, check it out if you have the time. It is a CPU drain, so just keep that in mind and close whatever browser window you use to look at it, either on your computer or phone, once you’re done.

That’s it for me for now. We’ll get back to you all with way more news about the Live events as we get closer. Make sure to announce them to your students so they can have a night before (literally) review. You never know who it might push past the passing line.

 

 

 

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TI-Inspire Directions for CC Algebra I Unit 10 (Statistics) by Jeanne Oliveira

Our good friend Jeanne Oliveira from Germantown Central School District is working out TI-Inspire directions for all of the calculator work we do in CC AlgI. She just created pdf files for the TI-Inspire directions for our Unit 10 on Statistics in Common Core Algebra I. We wanted to post these in case they would help students as we head into the final stretch. Please note that not all lessons in Unit 10 will be listed because not all have intensive calculator work (most, but not all). Here they are:

Algebra I Unit 10 Lesson 1

Algebra I Unit 10 Lesson 2

Algebra I Unit 10 Lesson 3

Algebra I Unit 10 Lesson 4

Algebra I Unit 10 Lesson 7

Algebra I Unit 10 Lesson 8

Algebra I Unit 10 Lesson 9

Algebra I Unit 10 Lesson 10

Thank you to Jeanne for providing this great resource!

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eMath April 2018 Newsletter

Well, it’s April 16th, so the weather in New York is now turning sunny and spring is in full tilt with the flowers blooming, the birds singing and …

Actually, I’m just kidding. I woke up to snow this morning. Still, not all is dreary. We are quickly approaching the final stretch of the academic year (you are likely just starting the fourth quarter). We have been busy at eMathInstruction working on a variety of different resources, updating our website, and creating add-ons for the courses. Let’s get right into those.

For Common Core Algebra I Add-Ons this month we have added a quiz and a new lesson. For Unit 10 (Statistics) we have added a Form B mid-unit quiz. Last year we added the original quiz and this year we have a makeup or Form B of the quiz. These are always handy when it comes to students who are absent or even if you want to give Period 1 the Form A and Period 2 the Form B. We always try to make them as similar as possible, while still making the questions unique. For Unit 11 (the final unit) we added Lesson 6.5 on Additional Piecewise Functions work. In this lesson we have piecewise functions that include linear, quadratic, and root functions. I still believe that the idea of piecewise functions is challenging enough so that it should be as basic as possible, i.e. just piecewise linear, but clearly the makers of standardized tests disagree with me as they often will include pieces that are non-linear.

For Common Core Algebra II Add-Ons we bring you two activities centered on the probability and statistics units (Units 12 and 13). For Unit 12 (Probability) we have created a Die Rolling Probability activity. We have the students use the random number simulator on the calculators to simulate rolling two die and summing their rolls. We then have them investigate the empirical versus theoretical probabilities associated with this experiment as well as answer a variety of conditional probability questions. There is no associated homework with this activity. In Unit 13 (Statistics) we created Lesson 4.5 on Sampling a Population. We created a data set of 200 values that students then randomly sample from. Students calculate sample means and standard deviations from their samples and then compare these to the population statistics. Like the Die Rolling Activity, this lesson has no homework associated with it.

In our Algebra 2 with Trigonometry Add-Ons this month we have a quiz and another lesson. For Unit 10 (Exponential and Logarithmic Functions) we offer up a mid-unit quiz that covers all of the content through Lesson #6 (Graphing Basic Logarithms). In Unit 11 (Probability) we created Lesson 7.5 on More Binomial Probability Practice. In this lesson we use the calculator to find binomial probabilities and cumulative binomial probabilities for a variety of applied problems.

In other exciting news, eMathInstruction will be at the national NCTM conference next week!!!

We will have a booth set up where you can come and chat and we will also be presenting on Friday afternoon. Drop by and say hi if you are at the conference.

In Geometry news, Version 2.0 of our workbook is now for sale. This new book has the Unit Reviews now included at the end of each unit, so its quite a bit longer than the original book. We’ll begin to add-on to this course starting in August. As always, if you have suggestions in terms of what you’d like us to add, please reach out (make up tests, mid-unit quizzes, extra problem sets, extra lessons).

We’ve been doing some major behind the scenes work on our website recently. We added a second server which does two things for us. First, if the primary server were ever to “crash” then the second server would keep the site up and running. But, even better, the second server allows us to “load balance” the traffic to the site. Hopefully this means shorter page and download times. Now, with all major website work, there are always hiccups in the system. Most of you probably have not had any trouble, but some of you, when trying to go to our main site, have experienced errors such as a “failure to redirect” or “emathinstruction.com” sent an invalid response or even scary messages like “corrupted content error.” I’ll be honest, I don’t really understand what’s happening. But, apparently a one-time fix of clearing the computer’s cache gets the job done. How to clear cache is very browser dependent (Chrome, Firefox, Edge, Internet Explorer, Safari …). The University of Wisconsin (go Badgers) has an awesome site with links to every major browser and operating system:

How to Clear Web Browser Cache (University of Wisconsin)

You know cache is the issue if you can get to our site through one browser but not through another one.

Have a great rest of your April. I hope that spring has arrive for you soon, if it hasn’t already shown up (no sign yet here).

Kirk

 

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eMath March 2018 Newsletter

Good morning everyone. I’m writing today from my house in Red Hook, New York, just a hundred miles or so north of New York City. We’ve had three nor’easters in the last week with another possible one next week. You might call this serious winter. We just call it March. And since it is mid-March, it’s time to put out the eMath March Newsletter. We’ve got plenty to report and add-ons to discuss, so let’s get to it.

This month for our Algebra I Add-Ons we bring you a new lesson in statistics. Unit 10.Lesson 4.5 is on the subject of outliers, how to identify them and what the effect of removing them is on the statistics for a data set. We stick to the standard definition of an outlier being any data value  ± 1.5IQR below or above the first or third quartiles, respectively. On the New York State Regents Exam in Algebra I, we’ve repeatedly seen multiple choice exam questions that require knowing this definition, for example #16 on the January 2018 exam:

To rule out (2) as the correct choice, think about how much work must be done. They must calculate Q1 and Q3, 41 and 68, then the IQR (27), and then 1.5*IQR (40.5). Subtracted and added to Q1 and Q3 gives you a “non-outlier” range of 0.5 to 108.5. Notice how this makes the 120 clearly an outlier but the data point of 0 is barely an outlier. So, it’s pretty important to know this technical definition of an outlier (which is not universally accepted) in order to not choose (2). Given the rather subjective nature of the correct answer, i.e. (1) that the mode is the “best” measure of central tendency, it is important to know why each of the other statements is true. Don’t get me wrong, I don’t think it is unreasonable for kids to know this, but I think that this is the type of curricular detail that needs to be explicitly spelled out as a piece of knowledge kids must learn.

We created two new videos for Common Core Algebra I. One of them goes with our add-on lesson Unit 8.Lesson 7.5.Linear-Quadratic systems. We also did a short video on a graphical reason for why the method of completing the square works. Both of these videos will be posted soon with a QR code added to the lesson when finished (likely today or Monday).

For Common Core Geometry, we have finally finished our Unit Reviews and Unit Assessments with Unit 10 – Measurement and Modeling. We have a fantastic Review with lots and lots of modeling problems, including additional density problems. These Reviews and Assessments finish Version 1 of our Common Core Geometry curriculum. We will begin releasing add-ons (additional lessons, activities, and assessments) beginning in August of 2018.

For our Common Core Algebra II Add-Ons, we’ve created a lesson, a mid-unit quiz (form B), and a video. Let’s start off with Unit 11.Lesson 8.5.More Work Graphing Sine and Cosine. This is a huge set of problems that give kids basic work graphing the sine and cosine function including amplitude, midline, and frequency (no horizontal shifting). We also give them a variety of curves and have them come up with the equations. This is an excellent problem set to give to kids over spring break (coming soon hopefully to a school near you). We also created a Form B of our Unit 11 (Trig) mid-unit quiz. We reposted the Form A quiz and you now have two similar quizzes to test their knowledge half-way through the Trigonometry (Circular functions) unit. Finally, we created a video to go with our Unit 10 lesson on the Sum and Difference of Perfect Cubes. I must say I’m disappointed that this topic got approved for the Next Generation Learning Standards at the Algebra II level:

I find almost no utility in having kids memorize:

x^3+y^3=(x+y)(x^2-xy+y^2) and x^3-y^3=(x-y)(x^2+xy+y^2)

I do think they are interesting patterns to study. I think the connections that can be made between these problems and the imaginary roots of quadratics are quite interesting. But, I see no utility in any type of realistic math problems where memorization of these patterns is helpful. I think it just takes up time and mental space that could be spent better elsewhere. What are your thoughts?

Finally, we have our Algebra 2 and Trigonometry add-on of the month. This month we’ve added an additional lesson in Unit 10 (Exponential and Logarithmic Functions). We’ve put in Lesson 4.5 on Additional Exponential Modeling. In this lesson we look at how to transition between different time units when modeling something using exponential growth and decay. This is a particularly nice lesson from an applied perspective.

That’s it for add-ons, but I’d like to keep discussing a bit more. Let’s begin with a cool 3D visualizing program for Geometry teachers that many of you likely have if you bought a PC within the last 3 years. All Windows 10 computers (and I believe some Windows 8) come with a program called 3D Builder:

Just type its name into your Search bar on a PC to see if you have it. Now, this program wasn’t installed because Microsoft thinks we are all Geometry teachers. Nope! This is a program designed to allow you to create 3D printer files. But, that doesn’t mean it isn’t great for 3D modeling. For example, remember the water-tower problem on the first CC Geometry Regents exam:

Now, imagine making the problem come alive by showing the students not just a model of it on 3D Builder but also that model taken apart into the three component pieces:

One of my favorite parts of this program is its Split command under the Edit Menu:

This function’s purpose is to slice a 3D object using a plane so that you only keep part of it to print. BUT, Geometry teachers can use it to show kids cross-sections of any orientation. With our cone example, here is an example of it showing a horizontal cross-section:

Notice those rotation arrows? They allow you to rotate the slicing plane into any orientation. So, if you wanted to see a classic vertical cross-section you could just rotate the plane 90 degrees to get:

Or, my favorite, the elliptical cross-section formed when slicing with an inclined plane:

Once you’ve rotated the plane, you can then move it left, right, up and down, allowing you to show kids how cross sections can change as you move the slicing plane in various directions. The Next Gen standards for Geometry state that kids will need to be able to visualize cross-sections of common solids, even with planes that are not horizontal or vertical:

Will they have to recognize that certain cross-sections of cubes are hexagons? Inquiring minds want to know.

Well, I think that’s about it for 3D Builder. I’ll be discussing this program and Tinkercad, one of my favorite online 3D modeling programs in additional posts. Only a few years ago, visualizing 3D geometric concepts would have been very difficult. Now, programs to do so are not just easy to find, but completely free.

We have some exciting changes coming to the website in the coming months, including a new way of organizing the Add-Ons and the Assessment Items. But, more on that in the April newsletter. For now, happy Pi-Day, happy March, and enjoy your spring break if you still haven’t been on it yet.

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eMath February 2018 Newsletter

It’s mid-month, which means it’s time for our newsletter. Valentine’s Day is now passed but we still have plenty of treats for you this month. So, let’s get right into it.

We’re going to start the discussion with Geometry, which is quickly starting to get filled out and ready for Version 2. We finished editing all of the videos and posting them to YouTube. That also means we were able to add the QR codes to the worksheets.

In addition to finishing the videos and adding the QR codes we have also increased the graphics quality considerably on the diagrams in the book. Every diagram that shows up in Geometry has been made by the FX MathPack, which was created by the Efofex software company, and which we sell in our Shop. The resulting PDF files are larger in size, but the sharpness of the images is now excellent.

We have, of course, posted the latest Common Core Geometry Unit Review and Unit Assessment. For this month, we released the Unit #9 (Circle Geometry) Review and Assessment. This is a monster review packet of problems along with a great assessment. That means that next month we will be releasing the final Common Core Geometry Review and Assessment (Unit #10 on Measurement and Modeling). Next year, of course, we will begin to release add-ons for Common Core Geometry, likely including new lessons (Intro to Parallel Lines, the General Area Formula for a Triangle, …) and make up assessments.

Alright, enough Geometry. Now for the Common Core Algebra I Add-Ons. This month we bring you a mid-unit quiz and a new lesson. Both are designed for Unit #9 (Roots and Irrational Numbers). We have a Form A and Form B mid-unit quiz that covers all of the material through Lesson #4 (Solving Quadratics Using Inverse Operations). We also bring you a lesson that connects the process of Completing the Square with area models. We think this lesson could be taught in either Unit #8 (after completing the square) or in Lesson #9 right before (or I suppose after) Finding Zeroes by Completing the Square. In the lesson, we look at why the algorithm of dividing the linear coefficient by 2 and then squaring the result makes sense from an area perspective. It’s super cool! I hope to have a video version of it next month.

For Common Core Algebra II Add-Ons this month we have two new resources for Unit #10 on Polynomial and Rational functions. First, we added Lesson #1.5 on the End Behavior of Polynomials. We felt like our current lessons on Polynomial Graphs and their Equations just didn’t do this topic justice. So, we added one that looks more closely at how the end behavior (a.k.a. long-run behavior) of polynomials is dependent on its leading coefficient and degree. We also added an activity on Rational algebra (called Rational Puzzles Activity). This activity has students investigate interesting patterns that emerge when you manipulate an integer and then explain these patterns using rational algebra. We think this is a really great activity for kids once they have learned how to simplify rational expressions as well as add, subtract, multiply and divide them.

Finally, for Algebra 2 and Trigonometry add-ons this month we have a huge new set of Trigonometry Application problems. Students can always use more practice with the Law of Sines and Law of Cosines and this problem set gives them plenty!

On a final note, recently my kids and I have really gotten into the 3D printing craze. The great thing about 3D printing, besides that it is now relatively affordable, is it has given rise to tons of free websites and other programs that allow for unparalleled 3D modeling. My favorite, right now, is a site called Tinkercad. This is a completely free online program from the makers of AutoCAD:

The platform is easy to signup for and quite easy to use. The great thing is that it allows kids (and adult kids) to play around with 3D geometry, including the movement (translations, rotations, and reflections) and scaling (dilation) of figures to achieve whatever you are trying to make. My kids and I had a challenge to model Luke’s original lightsaber (geek alert). Here’s a picture of it from online:

And here is my version of it on TinkerCAD:

Not perfect, but pretty good. The 3D print of it was small, but also awesome! This won’t be my last discussion of these types of programs. We live in an age when experiencing 3D Geometry is easier than it ever has been before. If we want kids to be able to visualize the cross-sections of solids, then why not allow them to cut them open? The programs that allow them to do this are everywhere and I would encourage math teachers to play around with them. In fact, if you have a new PC (even relatively new with Windows 10) you already have one of these programs pre-installed on your computer called 3D Builder. Here is a screenshot of a recent “Ball in Box” design I finished:

Alright, well, only one month (more or less) until Pi Day. Hopefully the snows will soon melt and give way to spring. But, I’m not holding my breath.

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eMath January 2018 Newsletter

Hello all! We are just about at the mid-point of the academic year, which means it is very, very cold in upstate New York. We are working hard at eMath this January to bring you new materials and to continue to update older ones. Let’s get right into the add-ons for this month.

For Common Core Algebra I Add-Ons this month we bring you a new lesson and an additional problem set, both from Unit #8 on Quadratic Functions and Their Algebra. First, we have added a lesson on solving Linear-Quadratic Systems Algebraically and Graphically. This is a topic that some already do in Algebra I and others will do once the New York State Next Generation Standards kick in a few years from now. We thought we’d get a jump on those and add this lesson now. We’ve also added a problem sheet with extra Quadratic Word problems (technically Lesson 9 in this unit). I think you can never go wrong with more quadratic word problems as kids need as much practice with these as possible.

In Common Core Geometry, we continue with the Unit Reviews and Unit Assessments. This month it is Unit #8 on Right Triangle Trigonometry. We’ve put together a great packet of Review problems and a good assessment that should help you assess your students’ knowledge of this important subject. It looks like at this pace we will be publishing the last Unit Review and Assessment in March (Unit #10 on Measurement and Modeling). That will round out Common Core Geometry for this academic year.

For Common Core Algebra II Add-Ons we have two new lessons in Unit #9 on Complex Numbers. We’ve always felt that this unit was a bit brief so we added lessons that we think would be great for enriching the unit. The first lesson (#2.5) is on the Division of Complex numbers. This is a challenging topic both conceptually and mechanically. The second lesson (#5) is on the Complex Plane. Graphing complex numbers and finding their modulus (absolute value) are emphasized in this lesson.

Finally, for Algebra 2 with Trigonometry we bring you a nice add-on for Unit #8 (Trigonometric Algebra). We created a nice review set of Trig Equations that emphasize all of the equation solving techniques in this unit, including basic equations, quadratic trig equations, equations involving trig identities, and equations that need to be solved graphically. This is a great problem set to use as additional review at the end of this unit.

That’s it for now. Here at eMathInstruction we’d like to wish everyone a happy and thoughtful Dr. Martin Luther King Jr. Day. As we go through some rough times in our country and we question our basic identity on a daily basis, we hope that this day above all others makes us reflect on the commonalities that bring us together rather than the differences that seem to be tearing us apart.