# Category Archives: Sharing Resources (Everything but assessments)

Teachers who use the curriculum share resources here. They range from reviews to projects to Smart Notebook Files for smart board use.

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!!!

# 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.

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.

# 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.

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.

# 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

# Efofex

So, we just relaunched our website and our homepage now has some new additions, specifically three offerings from a company named Efofex.

I would imagine the name of this company would be a mystery to just about anyone who isn’t a math teacher/geek. But, just in case:

Efofex = f(x)

Anyhow, their software is out of this world. My only complaint is that I didn’t know about it until about a year ago. In a nutshell, it allows you to create basically any math graphic that you need for worksheets, assessments, or demonstrations. For example, let’s say I needed a graph showing two exponential curves, one which has been vertically shifted with respect to the other:

Now, I’ve never been able to draw good exponential curves on MS Word and a graph even close to this would have taken me at least 15 minutes to make. On this program, it took only one.

I think the thing I first fell in love with, sad to say, is its ability to graph simple number lines. I used to loathe creating lessons or answer keys that needed graphs on one-dimensional number lines. But now, to graph something like:

is extremely easy and we get this beautiful graphic:

Most of the time, I create the diagrams in black and white because I’m putting them in workbooks. But, color can be added to any drawing in any way. Some of my very favorite graphics to now create are from statistics. From box plots, to histograms, to normal distribution curves, this software can make them all. I find dot plots especially helpful given how hard they are to make on Excel. Here’s a simple one I created in the past on the Efofex software:

The images have a bit of blur right now when imported in the website, but are crystal clear when in Word.

Efofex makes drawing geometric diagrams a snap. I’m so thankful for this right now as I write Common Core Geometry. I couldn’t even image doing so without having Efofex to make the diagram work so much faster. Here’s a good example. Say you are creating one of those problems with the altitude drawn from the vertex of a right triangle to its hypotenuse. Always fun, right?!? Well, this little diagram took me 45 seconds (yes I timed myself) to create:

The software for Efofex works seamlessly with MS Word and other programs. In fact, once downloaded, it creates a tab in MS Word that allows easy access.

You can see how all of this works by taking a look at a recent video I did on FX Draw and FX Stat (where I sound kind of like a robot – sorry!!!).

I would encourage teachers to try the 30 day free trial of the software. There is no catch. After 30 days, it just becomes inactive. But, it is such a great set of programs, I bet most teachers would continue to want to use them. They are offered on an exceptionally affordable subscription basis, which I love because you then get great updates all the time. For example, they just added three-dimensional graphing functionality. So cool!!!

Feel free to email to ask questions if you have them: Kirk@emathinstruction.com

Hello my math teacher friends. To those on vacation still, I hope your August is relaxing and Labor Day weekend doesn’t arrive too soon. For those of you back in classes, I hope the beginning of the school year is going well and you are starting to get to know all of your little angels (or angles :-).

We are doing a ton over at eMathInstruction. Within days (or even hours), we will be relaunching our website and coming out with some very exciting new software by an awesome company called Efofex. But, more on that in another post coming soon. I’ll also be posting preliminary Common Core Geometry materials. But, that is also deserving of its own post.

The relaunch will allow users more control over their Membership pages. You will be able to add additional subscription codes as well as other features. The launch will occur at night, so hopefully none of you will be stuck without our site in the middle of your class day.

We just published our first round of Course Add-Ons. These are the additional curricular items that come with the Teacher Plus subscription to our courses. Many of these curricular resources were created based on excellent feedback that I received in a Facebook post. I’ll keep doing these posts to get more ideas. Feel free to add your voice to the conversation. You can check out what I’ve created under the Course pages, but I’ll give you a little description here.

In Common Core Algebra I, I decided to make up a mid-unit quiz and created two forms of it so that you have a back-up for that student who is already absent after only 6 days of school. The quiz covers through Lesson 6 (Seeing Structure in Expressions). I also created a Unit 1 Skill Building set. This set of problems covers through Lesson 5 and is good for the student who needs more practice identifying properties and simplifying simple linear expressions. Finally, I created a Warm-Up lesson on solving one and two-step equations. This is particularly good to assign to students or use in class before beginning Unit 2. Students are expected to be fluent in linear equation solving after 8th grade Common Core, but we know that many of them will need this basic brush-up before moving on to solve more challenging equations.

Now, for Common Core Algebra II, I’ve created three new resources to start off the year. I thought it would be good to have a Form B of the Unit #1 Formative Assessment. This test exactly mirrors the one that is under Common Core Algebra II Unit Assessments. It could be used as a make-up, a re-take, or even if you wanted to pass out two forms of the test at the same time (wandering eyes…). Besides the test, I also created two additional curriculum resources. One of these is an additional set of problems to help students work with interpreting graphs of functions. We all know how students can struggle with reading graphs, especially when it comes to functions. This worksheet could be used toward the end of Unit 2 in order to reinforce graphical ideas. I also created an additional set of problems on Inverse Functions. Although it is early in the course, students can easily become confused about inverses and this set of problems hits all the main ideas.

Finally, for Algebra 2 and Trigonometry, I modified the two resources on Graphs of Functions and Inverses of Functions to fit the emphases and timeline of Algebra 2 with Trigonometry (see above paragraph). As well, I created a Unit quiz for Unit #1 that can be used as a take-home or a short in-class quiz.

Every month, around the middle of the month, until June, I will be putting out the eMath Newsletter where I’ll release the add-ons and discuss the issues of the day. I’ll always make sure to announce the Newsletter on our  and encourage our Members to give us comments there in terms of what resources they’d like to see us create next month.

# Common Core Algebra I – Regression and Residuals Reviews – by Brett Widman

Brett Widman, who contributes a lot of material here on the Forum, has given us another great resource. He created a Common Core Algebra I Review on Regression and Residuals. We don’t have much time left with the kids, but if they are confused about this fairly complex topic (especially for Algebra I students), check out Brett’s review.

As always, thanks Brett!

Algebra 1 WU Regression and Residuals

# Common Core Algebra I Regents Exam M.C. Review Videos – by Kevin Dorey

A new contributor to the site, Kevin Dorey of Pittsford Central Schools, just sent us a great email. He has been making videos that go through ALL of the multiple choice problems from previous Common Core Algebra I exams.

This is a truly great resource to share with those students who are willing to go the extra mile to try to master the material on this upcoming exam. I want to really thank Kevin for making these and choosing to share them on the eMath Forum. Here are the links: