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A new school year has started in the great Northeast. The light is getting dimmer while the trees are getting prettier. We’ve been all sorts of busy this past month at eMathInstruction working on making our site easier to use and coming up with add-ons to the courses. Let’s get right into those.

Let’s begin with the Common Core Algebra I Add-Ons. This month we’ve added two new lessons. One fits into Unit #3 between Lesson 6 and 7 (so I’ve given it Lesson 6.5). The lesson title is Motion and Average Rate of Change. We’ve seen quite a few motion problems on the Common Core Algebra I Regents Exam, so I thought it was time we devoted a lesson just to them. We also added Unit 4 – Lesson 9.5 on Solving Absolute Value Equations. We emphasized simple algebraic equations and more complicated graphical ones. Interestingly enough, there is no mention of solving any absolute value equations algebraically in the Common Core Standards, only graphically. Which is why you’ve only seen them that way on the Regents exams. Here’s a good example from June of 2016.

Moving right along to Common Core Geometry, recall that our add-ons to the Common Core Geometry curriculum this year will be the Unit Reviews and Unit Assessments. This month we’ve added on every student’s favorite, Unit #3 – Triangle Congruence Proof. We’ve given you a long set of additional problems and a nice assessment. We’ve also published the standards alignment documents in our Table of Contents section. If you’ve been itching to do some standards mapping to our Geometry curriculum, check out that link.

For our Common Core Algebra II Add-Ons this month we bring you an additional assessment and lesson. We created a Unit 3 Formative Assessment make up exam. This rounds out the Form B exams for Common Core Algebra II. Now each unit has both an assessment and a mirror make up assessment. We may consider adding additional make up assessments if teachers think it’s a good idea. We also added a lesson to Unit 4. Lesson 7.5 is titled Exponential Modeling Revisited and looks at moving between time units in exponential modeling. For example, if a growth model is given in hours, what would its equivalent look like if modeled in days instead. We’ve seen numerous questions on the New York State CC Alg II Regents exam on these types of questions.

Finally there is the old-faithful Algebra 2 with Trigonometry Add-On for this month. After a great deal of resistance on the part of yours truly, I’ve finally created a lesson on factoring trinomials with a method other than guess and check. I created Unit 3 – Lesson 6.6 – Factoring Trinomials Using the AC Method. Teachers who are familiar with this method of factoring already probably have a sense for how this lesson will work. I still believe guessing and checking is important for students, but this method does work and does produce reliable results, at least it does if a student can find the two integers that satisfy the product and sum conditions.

A final note on add-ons in general. I’ve been struggling with how to arrange them and have decided to keep placing resources into the add-ons so that they are in Unit order. That means add-ons from last year mix with ones from this year. For teachers who want to only see new add-ons, this isn’t the greatest way of organizing them. Still, for the teacher who just wants to see what resources are there for a particular unit, this is a very effective way to  have them arranged. As always, if you have any thoughts either way, feel free to reach out to me.

In other New York Math News, it looks like the Board of Regents finally voted on and adopted the New York State Next Generation Mathematics Learning Standards (or NYSNGMLS). Click on that link to open the full 170 page pdf document on the standards. They were just adopted so there are many news articles on them. Here’s a good one out of Albany itself:

Goodbye Common Core: New York’s New English, Math Standards Are Here – Albany Times Union

One of the most important parts of this piece is the following excerpt:

I’ve been waiting on some official word of the timeline before we started to modify our own text. Looks like I have a few years to make that happen. We may, when the time comes (2020), publish a New York edition to our Common Core texts. I’m hopeful by that time we’ve moved to an electronic only textbook. Thanks to Brian Battistoni, my good friend and colleague from Arlington High School, for the heads-up that the Next Gen standards had been officially adopted.

Well, I think that’s it for now. I’m hopeful that everyone has had a good start to their school year. As always, if you are having any troubles with your subscriptions or any suggestions on the curriculum, don’t hesitate to email me at: Kirk@emathinstruction.com. I’m busy, but never too busy to help.

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It’s that time of the year again in New York. The wonderful month of July has past us by and we are now in the thick of getting ready for the coming academic year. Many New York schools start right before or after Labor Day weekend, so the countdown has definitely begun. I know that many of our members outside of New York have already begun their school year. Either way, here at eMathInstruction we hope that everyone has had a wonderful summer vacation and is charged up for the year ahead.

We have been busy this summer as well. For those familiar with the site, you may have noticed the look of it has changed. We’ve kept all the resources in the same places, but hopefully made them even easier to use. Our excellent website designer Stephen Suess (no relation to the good Doctor) will continue to make upgrades as the year progresses. So, watch for more improvement. As always, if you find anything amiss, please email me and we will try to fix it.

One of the very exciting developments we had this year was the addition of our first Spanish language text. We created a Spanish Language edition of Common Core Algebra I, Curso Común de Álgebra I. This translation was edited by my good friend Yamir DeJesus-Decena. She is an excellent math teacher of all levels at Arlington High School who also happens to be fluent in Spanish. Many thanks to Yamir for a great job on the editing of the book. Right now only the workbook is available. We have not yet created an electronic answer key in Spanish nor have we posted the Spanish version of the files. Pricing on the book is the same as for the English version.

We just put out the latest round of add-ons to each course. We are keeping the add-ons in Unit order, so the news ones are mixed in with the older ones. For Common Core Algebra I Add-Ons we’ve rounded out our Form B assessments by creating makeups for Units 1 and 2. All units now have two assessments each (at least). Common Core Algebra II Add-Ons were a bit more complicated. We added a new lesson on Equivalence and the Calculator. We thought students could use even more work with how to use their calculator to check algebraic manipulations. We also added a Form B assessment for Unit 2. We will continue to add Form B assessments to Common Core Algebra II to make sure each unit has at least one. For the Algebra 2 with Trigonometry Add-Ons we also created a lesson on Using Tables on Your Calculator. As well we added a lesson where students use the online graphing calculator Desmos to explore the slope-intercept and point-slope form of a line.

Finally, there is Common Core Geometry. Geometry is brand new this year, so it has far fewer resources than the other courses. In fact the “add-ons” for Common Core Geometry this year will be the Unit Reviews and Unit Assessments for the course. For this month, we’ve added the reviews and assessments for Units 1 and 2. Next month we will add them for at least Unit 3 and possible also Unit 4, depending on timing. We plan to have all of these done by the March 2018 newsletter.

This year will be an interesting one for us at eMathInstruction. We plan to work on some performance task assessments for various courses, work on new lessons based on curriculum changes coming to New York State (does anyone really know when these will be implemented?), and we will start to develop a prototype of an electronic only textbook app. That last piece is very exciting. We believe that within 5 years very few schools will be using paper and will move exclusively to tablet/computer based learning. We want to be able to deliver our materials in that format when the time comes.

For now, I’ll let those who still are on vacation get back to it. Enjoy what time you have left, if you are still off. For those already back in the classroom, have a great start to your year. As always, let me know if you have any comments. I can be reached at: Kirk@emathinstruction.com.

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Well, it’s finally mid-May, which means that nice weather has returned to upstate New York. It also means that we are hitting the homestretch of the school year, with some schools finishing up quite soon. New York schools don’t finish until the third or fourth week of June, but final exams (Regents Exams) in math come in mid-June.

We have lots of exciting news and one last round of add-ons for this school year. First, we’ll start with the news which is mostly about Common Core Geometry. We are now done with the workbook and are printing up a bunch for summer orders. The answer key is being uploaded as I write this newsletter. It will definitely be available by Memorial Day weekend if not by the end of this week. We continue to record the videos and upload them as they are edited. We hope to have all of Unit 2 uploaded this week. That’s the particularly challenging unit on Transformations and Rigid Motions.

Another exciting set of events we have coming up are our Instagram Live Review sessions for the New York State High School Regents Exams. We will hold one review session for each of Common Core Algebra I, Common Core Geometry, and Common Core Algebra II. We are still settling on final times, but right now here is our proposed schedule:

Common Core Algebra I – Sunday, June 11th  from 3 to 5 p.m.

Common Core Algebra II – Wednesday, June 14th from 6 to 8 p.m.

Common Core Geometry – Thursday, June 15th from 6 to 8 p.m.

We will simply be taking questions from students who are watching the Live Session. We will have all of the previous Regents exams open and can work out questions on any of those or anything else the students throw our way. For those of you not familiar with Instagram, students will have to follow me (@kirkweiler). As well, they will only be able to watch via their phones as Instagram is not a computer or tablet based app (how weird is that?). There may be work arounds for this limitation. We went with Instagram instead of Facebook because we found that most teenagers have Instagram accounts, but not Facebook accounts.

Please do let us know if you have thoughts about the timing of the sessions. We tried to pick what we thought made the most sense after speaking with both students and teachers about it.

Our final round of add-ons for this school year are all about review materials. For each course, we added review quizzes for each unit. These are short, “keep them honest” quizzes that hit on major topics of each unit. They are only 10 points each and are designed to help a teacher get some feedback on where students are at on each unit, without taking up too much time for assessment during this last month of intense review. In Common Core Algebra I, we have a packet of quizzes for Units 4 through 10. For Common Core Algebra II we have these quizzes for all 13 units. For Algebra 2 and Trig, we supply the quizzes for Units 7 through 13.

We will keep posting eMath Newsletters in June and July, but won’t be posting additional add-ons during this time. We will begin to add new ones in the August newsletter, starting with our first round ever of Common Core Geometry add-ons. We plan making the Unit Reviews and Assessments the add-ons for Common Core Geometry next year, which is why the price of those subscriptions are slightly less than others. We don’t know yet what the add-ons will be for the other courses, but plan on exploring Performance Tasks for these courses as well as creating some lessons that address the modifications we are seeing in the Common Core curriculum in New York state.

For now, have a great May! Enjoy Memorial Day weekend and the final sprint. I’ll see you back here in mid-June!!!

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Spring has sprung here in upstate New York. We’ve had a beautiful April so far. Many school districts in New York are just coming off of spring break, although lucky ones might still be on it. We waited a bit longer than usual to post our newsletter because of both Passover and Easter, but the add-ons are up on the site for the three courses and we have much news to tell.

I’m going to start with Common Core Geometry. We’ve been busy on all fronts with that course. My producer, Joey Shavelle of JoLo Studios, and I have been working on the videos for the course. We have about 70% of them recorded and about 25% of them edited and posted at this point. We plan on having them all done and linked to on our site by the beginning of August. Most will be up by the end of this school year. We decided to edit and post all of them for our Unit #4 on Constructions because I know how easily students forget these techniques.

We are also working hard to do final edits on both the workbook (must remove typos!!!) and the answer key. Our plans are to have both workbooks and the answer key subscriptions available by Memorial Day weekend of this May. We have priced the Teacher Plus subscriptions at $125 per subscription, which is less expensive that those for our other courses. We did this because the first version of the answer key will not have Unit Reviews and Assessments. BUT, we will be adding those on as we move through the year next year. We plan to publish the Unit 1 Review and Assessment as our August add-on for the course. In other exciting, and nerve-racking news, eMathInstruction will do its first live video event this June and hold a review for each of the major New York State Regents high school math exams (i.e. CC Algebra I, CC Geo, and CC Alg II). We considered a number of platforms and talked to the demographic we want to reach (i.e. the students) and decided to try it on Instragram Live. We believe this will allow us to field questions and answer whatever comes in. In order to ask questions and watch students will need to follow me. My Instagram username is @kirkweiler. I’m planning on holding them on Monday, June 12th (Common Core Algebra I), Wednesday, June 14th (Common Core Algebra II) and Thursday, June 15th (Common Core Geometry). I’m going to try to make these marathon sessions and probably try to go from 5 to 7 or 5 to 8. Please give me feedback on both dates and times. It’s a bit tricky given that Geo and Alg II are on the same day. We will do a practice run in early June. More details in our May newsletter. O.k. Let’s discuss the Common Core Algebra I Add-Ons. As always, we want to give teachers tools that can use and modify. So, we rounded out our Form B assessments with a Unit #11 Formative Assessment Form B. This is the final unit in the course and we now have Form B assessments for each unit except Units #1 and #2 (perhaps add-ons for next year?). We also posted short, 10 point, review quizzes for Units #1 through 3 in a bundle (so a single file has them all). These are good quizzes to simply do a quick check of understanding for students. They are certainly not comprehensive assessment of all topics in the units (see Formative assessments for that). For the Common Core Algebra II add-ons we bring you two resources for Unit #13 on statistics. First, we round out our formative assessments with a Form B assessment for Unit #13. As well, we created a packet with four extended statistical simulation problems similar to the ones that we’ve seen tested so far on standardized tests. We tried to make these problem accessible and hope that they give you some extra problems to help students grapple with this type of thinking. I have to say that I spoke with a relative of mine who is a math professor at Penn State and even he is a bit confused by the statistical simulation questions. Finally, we have our Algebra 2 with Trigonometry add-ons. For this course we created review quizzes for the first six units that are also just 10 points each. These small quizzes allow a teacher to review a unit and hold students accountable for the material, but not take an entire period for the assessments. Most of them consist of two to three multiple choice questions along with a few free response questions. We actually have 8 quizzes in this packet because we broke up the long units #3 and #6 in half to provide more feedback. O.k. So, that’s about it. I need to get back to editing Common Core Geometry. I hope that everyone is enjoying the nicer weather and all that comes with it. The school year is now more than three-quarters over and we are just about in the homestretch. See you all in May. Posted on ## eMath December Newsletter Well, it definitely feels and looks a lot like winter here in Red Hook, New York. It’s cold and snowy outside, but things are continuing to heat up at eMathInstruction. We’ve got a lot of news, including a new round of add-ons and updates on Common Core Geometry. Let me get right to it. In our latest Common Core Algebra I Add-Ons, we continue to crank out the Form B assessments based on the positive feedback we’ve been getting. We’ve heard teachers will give both tests during a class period or even slice and dice them up together. So, we do plan to continue to come out with these each month. For this month, we have both a Unit #6 and Unit #7 Form B assessment. As well, we also published a very basic lesson and homework set on percents (creatively entitled Percent Warm-Up). I’ve found over the years that many students are not ready for high school lessons on percents without a basic reminder of what they mean and how they related to ratios and proportions. For Common Core Algebra II Add-Ons, its much of the same. We have new Form B assessments for both Units #8 and #9. We have been trying to make these as close to possible to the original tests so that teachers can truly use them as either makeups or for the full class in a mix-it up scenario. We also thought, since we were at Unit #8, to put together a nice set of review problems for the course as a whole. So, we came up with a six page Mid-Course Review problem set. This set certainly doesn’t cover every important problem or topic, because then it would be 20 pages, but it is a nice sampling of problems. We thought it would be ideal for either a Winter Break assignment or perhaps even during January Regents week, depending on where you are in the course. Finally, there are the Algebra 2 with Trigonometry Add-Ons. It’s all about Unit #7 this month. This is a long unit that begins a three unit swing through trigonometry. Because of the length of the unit, we’ve included a mid-unit quiz and a Formative assessment for it. But, the fun add-on for this month is a graphing activity on Desmos where students model the length of daylight as a function of the day of the year in Poughkeepsie, New York and Brisbane, Australia. I love Desmos for data modeling because I enter the data once and only once and then simply give students a link to the Desmos page so they can try to fit the data. Don’t worry, though. If you want to use this activity, and it is a really fun one, you don’t even need to enter the data. I’ve already done it for you. The big news for this month is that Common Core Geometry is done and now in its Beta testing version. That’s just my way of saying that the entire rough draft is done and posted online. Here’s how the table of contents is looking: I’ve written about the first draft of it here so I don’t bore you more with details. I’m now hard at work on the answer key for Geometry. We are working on a new recording space for the Geometry videos and will likely begin in early February. I’m very much looking forward to getting back to that side of things, although both the text and even the answer key have been a lot of fun. O.k. That’s it for now. I need to add more logs to the fire and get back to working on that Geo answer key. Thank you to everyone for feedback. And I’d like to thank everyone who has given our curriculum a chance and has supported us. As always, let me know if you have any thoughts: Kirk@emathinstruction.com. Have a safe and happy holiday season!!! Posted on ## Common Core Geometry Beta Version Finished – by Kirk The first version of Common Core Geometry is now done and completely posted. It consists of 10 total units: The total text is now at 95 lessons with homework sets. I’m always happy if a curriculum is somewhere between 100 and 110 lessons. I’ve found over the span of my career that in a 185 day school year, the 100 lesson count is a good benchmark given all sorts of extra days needed for reinforcement, review, assessment, assemblies, fire drills, snow days/delays, Regents exams, and so many other things that stop us from teaching content. I would assume as I now head into the Answer Key part of the process that I will likely add some additional lessons. There is no mention of surface area in the Common Core Standards or on the New York State Formula sheet, but I still think it is a topic worthy of inclusion in that last unit on Measurement. I’ve only included one lesson on radian measurement, but I believe that could probably use another day. I’m sure extra days on practice of proofs would also be helpful as well as reinforcement days here and there. Of course, all of that may also come in our second version of the text. After the answer key is done, or partly done, we will begin work on the videos. We are planning on making these much better quality than those for Common Core Algebra I and Algebra II, so they may take some additional time to create. We anticipate beginning the videos in early February, but don’t have a completion date yet for those. We will have all materials ready for the 2017-2018 school year. We invite teachers to use any of the Geometry lessons and homework sets we’ve posted. Because we have not begun the Answer Key, they are in their Beta version and teachers should work through them before giving them to students. We appreciate feedback both in terms of typos and in terms of mathematical content. I can promise we will correct the typos and will consider suggestions on mathematical content as long as they don’t radically alter the order or structure of the course. Although Phase 1 of Common Core Geometry is now done, we have two phases yet to go (Answer Key and Videos). It’s about time I got started on Phase 2. I hope everyone had a great Thanksgiving and are ready to get the next month over with before the big break. As always, you can email me with feedback at: Kirk@emathinstruction.com. Posted on ## eMath October Newsletter Here in the great Northeast, the leaves have changed and the days are getting colder. Since I last wrote, I’ve been hard at work on Common Core Geometry and the latest round of add-ons. Speaking of which, we just put them up on the site. Remember, links to them are at the bottom of each course page. You can also click on any of the blue links below to be taken directly to the add-on pages. As always, we base what we create on feedback we get, especially on Facebook and other social media. So, let us know where you want the emphasis to be placed. For Common Core Algebra I Add-Ons this month, we have a Form B for the Unit #3 Assessment, a Unit #4 Progress Quiz, and a worksheet on turning visual patterns into arithmetic sequences. We’ve heard from a lot of you that you want more assessment, especially make-ups/Form B’s. With all of our Form B assessments, we attempt to make them mirror the original so that you have as much equity and cross comparison as possible. Unit #4 on Linear Functions and Arithmetic Sequences is a long unit. So, we created a mid-unit quiz that assesses through Lesson #7. We even included a Form A and Form B of the quiz. Finally, we’ve all seen kids struggle on standardized exams turning visual patterns into arithmetic sequence rules. So, I created a short worksheet with a bunch of these patterns for you to use for practice with your kids. This is especially good for a sub day or other time you need a quick resource. For Common Core Algebra II Add-Ons this month, it is much the same as with CC Alg I. We created a Form B make-up assessment for both Unit #4 and Unit# 5. Unit #4, of course, is that beastly long Exponential and Log unit, so it may help a lot to have a make-up for that one. Of course it also doesn’t hurt to have a make-up for Unit #5 (Sequences and Series) either. We also added a new lesson! No video yet, but we now introduce Unit #6.Lesson #5.5.Using Structure to Factor. This was a lesson we felt we had to create based on some of the very complex factoring we’ve seen on the first two Common Core Algebra II Regents exams in New York State. I must say, I love this lesson and this factoring. It’s all mixed up and forces kids to think about larger patters with gcf’s, difference of perfect squares, and trinomials. Check it out if you have this subscription. Finally, for Algebra 2 with Trigonometry Add-Ons, we offer two new Formative Assessments for Units 3 and 4. We never did write unit assessments for Algebra 2 and Trigonometry (our first course). So, that’s going to be a focus of the Algebra 2 with Trigonometry Add-Ons this year. We want to make sure that teachers who are using that course have access to quality assessments. So, besides the add-ons, I’ve obviously been busy, busy, busy with writing Common Core Geometry and working on technical issues with our website. Since the last eMath Newsletter, we’ve put up three more units. Check out all of the materials we have up now under the courses tab: Only three more units to go!!! We are trying to get the rough draft of the entire curriculum done by the beginning of winter break. That’s when we will start production on the answer key and on the videos. They will go hand in hand and I will likely post videos to YouTube by the unit. I suspect we will have Unit 8, on Right Triangle Trigonometry, posted some time next week. The last two units, on Circle Geometry and Three Dimensional Geometry, will take a bit longer to get done and up because it’s… Conference Season!!! I will be in Rye on November 10th through the 12th for the AMTNYS Fall conference. I’ll be showing teachers how to create interactive lessons on Desmos to address Common Core Algebra standards. I’ll also be showing teachers how to use our new Efofex software line to create graphics for all sorts of fields (geometry, algebra, statistics, etcetera). Don’t miss out. On November 19th, I’ll be at the ATMNYC conference at Hunter College. I’m going to be talking about the thinking that goes into the new emphasis on transformations in Common Core Geometry. I’m really excited about the talk as I’ve never had a chance to speak to teachers about H. Wu’s work on rigid motions and how it leads to congruence in geometry. O.k. Enough for now. As always, email me with questions, suggestions, or any issues you are having, Kirk@emathinstruction.com. Have a great rest of your October and a safe and happy Halloween. Posted on ## TeacherTube – by Kirk Since the beginning, I’ve been recording videos and posting them for Common Core math lessons on YouTube. I think I posted them on YouTube because it was easy, given that I had a gmail account, and because it is the most popular video sharing platform of all time. I didn’t give much thought to whether schools blocked or didn’t block it because my own school allowed students to access it and trained teachers how to create links to videos so that objectionable content wasn’t accessed. Still, over the years, I’ve heard from a variety of teachers that their schools block YouTube and, hence, their students couldn’t access it during the school day. I kept looking around for different sites to host the videos as well as YouTube and settled on TeacherTube since it seems like schools generally do not block this site. Over the coming month or so, I will be uploading all of the Common Core Algebra I and Algebra II videos to my channel on TeacherTube. eMathInstruction TeacherTube Channel This is a long process. The videos themselves are each about one quarter gig, which means pretty darn large. They each take only about five minutes to upload, but then you need to title them, tag them, and (optional) index them to a Common Core Standard. That last one is a bit irritating because I can only add one standard, even if there are four or five tied to a given lesson. Oh well, everything has its shortcomings. All told, I’m hopeful to be done uploading CC Alg I videos by around September 21st and CC Alg II videos by October 1st. I don’t know TeacherTube well enough yet to organize them in any great way. I hope to create a hyperlinked Table of Contents eventually that I will share on our site. The videos will remain on YouTube and the QR codes on the worksheets will remain linked to those videos. The same goes for the links on our site. At least for now. Time spent doing all of this is time not spent writing Geometry or Algebra add-ons, etcetera. But, I am glad that the videos will now be accessible to schools that block YouTube. Thanks to everyone who gave me the suggestion to do this. Posted on ## eMath September Newsletter As Labor Day Weekend starts to fade in our rear view mirror and mid-September approaches, it’s time for the monthly eMath Newsletter. I’ve been really busy since mid-August, mostly filling orders, answering lots of questions, and helping folks troubleshoot our new online Answer Key Subscription Service. My apologies for those who had trouble setting up their accounts. As always, email me if you have any issues. I’ve also been working hard in the last few weeks on the latest round of add-ons that come with our Teacher Plus Subscriptions. I just posted them on the site, so those that have that access (and those that don’t) should go over and check them out. As usual, I wanted to tell you a little about them in the newsletter. For Common Core Algebra I (our most popular course), we have three/four new selections. We came out with a mid-unit progress quiz for Unit #2. We put up a Form A and Form B for your convenience. We created a worksheet that gives students more practice with linear word problems. This one should definitely be done after you have done Lesson #7 in Unit #2. It’s a really good sheet that can be used as extra credit or just more practice for struggling learners. Finally, we created a small worksheet to prepare kids for inequality work later in Unit #2. This sheet is great for a two year CC Algebra I course where kids have a really hard time comparing two numbers using the greater than and less than operators. For Common Core Algebra II, I started off with one of my favorites, a Desmos Classroom Activity on Forms of a Line. Students are supposed to come out of Common Core Geometry with some exposure to both the slope-intercept and point-slope form of a line. This Desmos Activity allows students to practice in an interactive way with equations of lines in both forms. It could be used as extra credit, extra practice, or even to replace Unit #3.Lesson #3. Don’t worry if you’ve never done a Classroom Activity on Desmos. I’ve also created a detailed Teacher Direction sheet. Email me if you still have questions. I’ve also created a mid-unit quiz for Unit #4 of Common Core Algebra II. This is a mammoth unit, so I thought having a quiz that covered the topics from the first seven lessons would be helpful. It’s not a long quiz, but it assesses all of the fundamentals of exponential functions. Finally, I added a brand new lesson to Common Core Algebra II on the asymptotes of exponential and logarithmic functions. The term asymptote does not arise in the Common Core Algebra II PARCC standards, but New York State put it on their June Regents examination in CC Alg II, so I thought it might make sense to have a lesson on these important graphical features. No video, yet! Finally, Algebra 2 with Trigonometry. I feel like this is sometimes the forgotten child of the three courses. It has been all but phased out in New York State, and, yet, plenty of schools still use our text. We love the course and recognize the important differences and similarities between it and Common Core Algebra II. For this month, I’ve added three new resources for the course. First, I have a full (but somewhat short) Unit #2 Quiz (on linear functions). I also included a Unit #3 Mid-Unit progress quiz. Unit #3 is a long unit on quadratic functions and their algebra, so I thought it appropriate to see what kids know after the first eight lessons. Finally, I included a brand-new lesson in Algebra 2 with Trig on Factoring by Grouping. This lesson was long overdue. Now that I’ve gotten the add-ons out of the way, let’s talk about Common Core Geometry. I’ve really taken a pause on that since late August. I’ve simply been too busy with running the business and writing the add-ons, but now I should be able to get back to writing it. I’m in the middle of Unit 5 right now (the first four units have been posted) and hope to have it finished by the end of next week. I’ll post all of the first draft pdf files at that point. I’m going to continue to write units and maybe record some videos (just to try out some new tech that I have). My goal is to be done with all lessons and homework sets in first draft form by December winter break. The answer key and videos will take some time as well, but, with some hard work, I will hopefully be done with it all by late winter/early spring. Only then will we have Common Core Geometry subscriptions and workbooks to sell at eMathInstruction. For those of you already working with the curriculum, I image some will be almost done with Unit #1 soon. Unit #2 in CC Geo is on transformations and many of the lessons involve the use of tracing paper. We create our own because we couldn’t find anything on the market we liked. I’m hoping that by Monday of next week (9/19/16) we will have it on our site for sale. It will come in 50 sheet spiral packs that students can rip sheets from (for$5 each) or in stacks of 500 (for \$20 each). Here are a few pictures of the tracing paper:

Finally, a note on  our new software products from Efofex. There’s been a lot of interest in the programs given their ease of use. I was talking to a teacher on the phone about Geometry just a couple of days ago and he was bemoaning how difficult making diagrams for geo can be. Efofex MathPack, one of the packages we sell, makes creating these things so easy that I’m chomping at the bit to get back to writing it all. I just wish the software would have been around back in 2005 when I first started work with the Arlington Algebra Project. Imagine how long this would take using the standards graphics on MS Word?

And my own least favorite graphs to draw, exponentials:

If you are interested in seeing what the Efofex software can do, try downloading a free 30 day trial of it. No muss, no fuss, and no spam if you decide you don’t like it. It just stops working. If you have any questions about it, don’t hesitate to contact me.

O.k. So, that’s about it for September. I hope that everyone’s school year is starting off well and the temperatures are cooling everywhere (I’m sure Phoenix is still quite hot my Arizona friends). I’ll be working hard on Common Core Geometry and more add-ons in the next month. Tune in for all the updates in the October newsletter. As always, contact me via email if you have questions or suggestions: Kirk@emathinstruction.com.

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## Common Core Geometry – by Kirk

So, the summer has been a great mix of working on Add-Ons for the three courses we currently offer and thinking a lot about Common Core Geometry. I’ve now completed the first four units and a rough course outline that’s been indexed to the CCSS Standards for CC Geometry (as defined by PARCC and refined by NYSED).

I’ve got all of the lessons for those four units posted at this point under our Courses section:

You can find the course outline if you click on the Table of Contents and Standards Documents link. All of the lessons and homework sets posted for the first four units are in rough draft form only. All diagrams that occur in those files were created on our new Efofex software.

The units of the course (at least at this point) are:

Unit 1 – Essential Geometric Tools and Concepts

Unit 2 – Transformations, Rigid Motions, and Congruence

Unit 3 – Euclidean Triangle Proofu

Unit 4 – Constructions

Unit 5 – The Tools of Coordinate Geometry

Unit 7 – Dilations and Similarity

Unit 8 – Right Triangle Trigonometry

Unit 9 – Circles with and without Coordinates

Unit 10 – The Geometry of Three Dimensions

I don’t think the order of the units is anything too radical, but I wanted to discuss why I have them in this order and my overall thinking at this point. I do want to be clear up front that I believe geometry is the most tactile of all mathematical fields. It is about space and that deserves not just proof and algebraic problems, but also the tools of geometry, which include compass, ruler, straightedge, protractor, and, yes, tracing paper. We currently developing a really good tracing paper that we will begin to sell on our site right after school begins.

Geometry is really all about exploring physical space using tools we develop in mathematics, whether that be transformations, Euclidean logic, or Cartesian coordinates. I began the course in Unit 1 by making sure that students have some of the very basics down, including a really good sense for circles and arcs of circles.

In Unit 2, I wanted to establish certain properties about space by using H. Wu’s rigid motion work with congruence. This is an awesome unit, but probably one of the newer ones in the Common Core. Within this unit, though, we use rigid motions to establish a number of important facts, such as SAS, ASA, and SSS criteria for triangle congruence, facts about the perpendicular bisector of a segment, and parallel line properties.

Unit 3 puts us back on more solid ground with Euclidean triangle geometry proof. I did bring parallel lines back into the mix so that students could also be exposed to AAS and HL methods of proving triangles congruent. We look at many of the classic problems of geometry in this unit, including why the angle bisector represents all points equidistant from the sides of an angle.

In Unit 4 we explore the beautiful world of constructions. I know constructions can be a mystery to students, a set of directions that they need to memorize to carry out the construction. I make sure within every lesson that the constructions have both purpose and are proven by using Euclidean triangle proof.

I haven’t created the remaining units, but want to explain how they will unfold (hopefully). In Unit 5, I am going to introduce coordinate geometry. I wanted to do this relatively early in the course for two primary reasons: (1) so students could have a break from the world of Euclidean reasoning and (2) so that we could use coordinate geometry as well as Euclidean geometry and Wu’s transformation work to explore quadrilaterals (Unit 6) and similarity (Unit 7).

Of course, once we’ve established the concept of similarity in Unit 7, we will naturally move to right triangle trigonometry in Unit 8. Right triangle trig is one of the most applied fields within geometry and we will make sure students understand its basis in similarity and then its application in the real world.

Unit 9, which will come towards the end of the third marking period, will challenge students will the geometry of the circle. But, at this point, we will have a good background in congruence, similarity, the distance formula, and other tools that will allows students to explore the geometry of circles in the Euclidean and Cartesian planes.

Finally, Unit 10 will concentrate on three dimensional geometry as well as measurement and geometric modeling.

I will continue to work on lessons (Unit 5 here I come) for the remainder of the summer and will then begin video work for the first few units once Labor Day is behind us and my own kids have gone back to school (Max and Evie). Hopefully by late September all videos will be done for Units 1 through 4.

Work will continue on the units with pauses in October and November for all sorts of conferences (AMTNYS, AMTNYC, etc). I think, given my current pace, that the first draft of all units should be done by Winter break. I would then expect videos and answer keys to be done with books ready to order by late winter or early spring.

Feel free to give me feedback if you try the materials. If you have questions about the order or any given lesson, just shoot me an email: Kirk@emathinstruction.com