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eMath April 2019 Newsletter

Hello Math Teachers and Learners. Spring has sprung! In fact, many schools in New York are on Spring Break this week, including our own of Red Hook. At eMath Instruction we’ve been working away on materials for both our Common Core High School courses and our Next Generation Middle School courses. Of course, we’ve also published some new Add-Ons, so let’s discuss those first.

In Common Core Algebra I Add-Ons this month we have a Form C Assessment and an extra practice lesson. First, we bring you the Unit #9 (Roots and Irrational Numbers) Form C Assessment. We also have posted a Unit #10 Lesson #5.5 Practice Lesson on Two Way Frequency Tables. This short practice sheet gives your students more use in the terminology and reasoning involved in two way frequency charts. This is a great resource for students who just may need a bit more practice on these types of problems.

For Common Core Geometry Add-Ons this month we bring you an enrichment lesson and a Form B Unit Assessment. First we have Unit 9 – Lesson 10.5 on Finding the Equation of a Circumscribed Circle. This is a fantastic lesson that incorporates algebra, the equations of circles, and how we find the circumcenter. This lesson is not for the faint of heart as the algebra involved is tough. Consider using this for strong students who want more of a challenge! We also have the Unit 9 Assessment.Form B for Circle Geometry. It’s always good to have an additional assessment for this unit.

Our Common Core Algebra II Add-Ons this month are a Form C Assessment and an enrichment lesson. First, we bring you the Unit 11 Circular Functions Form C Assessment. Use this as a makeup or to help review for the Regents. Either way, it is a great resource. We also bring you Unit 12.Lesson 5.5.Enrichment Activity on Independent Events. This Lesson/Activity uses infinite geometric series to determine the probability of players winning an unfamiliar game. This lesson is a nice intersection of work students did with geometric series and work they did with probability. Although not material tested on the New York State Regents exam, it is a great lesson to show kids another application of geometric series.

Finally our Algebra 2 with Trigonometry Add-Ons are an additional lesson in Unit 11 as well as the Unit 11 Probability Form B Assessment. The additional lesson is Unit 11.Lesson 8.5 on Pascal’s Triangle and the Binomial Expansion. Our original text does not look at Pascal’s Triangle, so this is a lesson to introduce it to kids as well as show them how to use it to help expand binomials. We also explore some interesting patterns in the triangle including how the rows sum to powers of 2.

In other news, we’ve now posted the first version of our N-Gen Math 6 Curriculum on our site. If you haven’t gotten our email blasts about our Next Generation Standards aligned Middle School curriculum, let me give you the quick summary. We are writing courses for 6th, 7th, and 8th grade Math to align to the “new” New York State Next Generation Math Standards. The Next Gen Standards are to be fully implemented in the 2020-2021 school year. So, that means next year K-8 is still aligned to the CCSS. We will be posting our Next Gen courses for 6th, 7th, and 8th in their Beta (rough draft) forms as we “finish” them and go through a round of edits. We hope N-Gen Math 7 will be posted this June and N-Gen Math 8 by next September. That will give schools an entire year to take a look at them before the standards officially go into place. For now, here are their three awesome covers:

O.k. So that’s it for April! I hope that you all are having great Spring Breaks or will have a great break next week. As always, let us know if you have any thoughts.

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eMath March 2019 Newsletter

Ahh, March! We’re finally at the inflection point (almost) on the sunlight curve, which means we are picking up daylight at a greater rate than at any other time of the year.

Temperature will need to wait for another month before it climbs at its most rapid pace. It’s a somewhat remarkable fact that the daylight and temperature sinusoidal curves have just about a month offset from each other (temperature shifted one month forward from daylight).

I love seeing so much of the world through a mathematical lens. Speaking of which, since we’ve hit the midpoint of March we have a whole bunch of add-ons to tell you about. Let’s get into them.

For Common Core Algebra I Add-Ons we bring you a practice lesson and a Form C assessment, both for Unit #8 – Quadratic Functions and Their Algebra. We created a Lesson #6.5.Finding the Zeros of a Quadratic.Practice which provides students more work with finding and thinking about the zeros of a quadratic. This is a great lesson for students to get a  practical application of the zero product law and connections between factors and zeros. We also bring you the third assessment for this unit in our Unit #8 Formative Assessment.Form C.

The Common Core Geometry Add-Ons for this month contain a Form B assessment and our first progress quiz in a unit. First, we have the Unit 8 – Right Triangle Trigonometry Form B Assessment. It’s always nice to have a makeup for this test given the diagram work inherent in trig problems. Then, we bring you a Unit 9 – Circle Geometry Progress Quiz to be given after Lesson 6. This unit we felt was particularly long with a particularly great amount of very new material for them. So, we felt that a quiz at this point gives the teacher a good sense for where students are at on this challenging material.

Common Core Algebra II Add-Ons also bring two assessments, both for Unit 10 – Polynomial and Rational Functions. First, we have a Progress Quiz that covers only the polynomial material for the unit (the first four lessons). We felt that teachers might want to assess this material in isolation before moving onto the rational expressions work. We also have a Unit 10 Form C Assessment.

Finally, Algebra 2 with Trigonometry Add-Ons contain a practice lesson and a Form B assessment. These are both for Unit 10 – Exponential and Logarithmic Functions. First we bring you Lesson #7.5 – Log Law Practice. We all know how strange the log laws are when first exposed to them. This lesson gives lots of extra practice in manipulating logarithmic expressions using the laws. We also bring you the Unit 10 Form B Assessment.

In other news, I had a fantastic visit with the students and teachers from Edward R. Murrow high school in Brooklyn.

I got to present to about 3,000 of their students (or so I was told) over the span of the day. I did a presentation of some cool math and math history. The reception I and the presentation got from the kids was just amazing. They took part when I asked them to play around with some problems and just overwhelmed me with their positive attitudes and energy. The fact that it was a Friday may have helped, but I have to think it was more about how the culture of their school and especially their math teachers encourages them to explore ideas in their learning that sometimes go outside of the box.

Thank you, thank you, thank you students and teachers at Murrow!!!

Oh, and it was Pi Day yesterday, one of our few mathematical holidays. I love the number Pi and find it fascinating in so many ways. It’s existence as a number is obvious from the simple perspective that all circles are similar and thus the ratio of their circumference to diameter would have to be a constant. The fact that it is a number slightly greater than 3 and that it is irrational is fantastic. I took a moment to visualize its size compared to a circle whose diameter was 1 and produced this graphic on FX Draw:


In other news, we sent out an announcement recently about our new line of middle school curricula. We are producing  Math 6, Math 7, and Math 8 curricula , similar to what we have for high school courses. These courses will align to the Next Generation standards that will start to be implemented at the middle school level in the fall of 2020. We are posting our Beta versions of the texts as we finish them and their first edits. We already have Math 6 posted:

N-Gen Math 6

And here is its super cool cover, by the awesome Michael Frey. (To see more of Michael’s work just click on his name.)

Wait until you see the ones for Math 7 and Math 8. We plan to post the Beta version of Math 7 as early as May, but more likely at the beginning of June. Math 8 will not be available until September or October of next fall. Next year we will be recording videos for the three courses and creating more resources for them, like the answer keys and other items.

For now, I think that just might be enough. Have a great beginning of your Spring everyone.







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eMath January 2019 Newsletter

Hello 2019! As we turn our calendars to a new year, we have a lot going on at eMathInstruction. Let’s begin by discussing the newest Add-Ons for the courses.

Our Common Core Algebra I Add-Ons include a practice packet and a Form C assessment, both for Unit 7 on Polynomials. First, we bring you a Skills Practice set on multiplying polynomials. This skills worksheet emphasizes the ability to multiply binomials, including conjugate pairs. We all know how critical it is to be able to multiply polynomials well before students begin to factor. This worksheet gives them plenty of extra practice. We also bring you the Form C Assessment for Unit 7.

In our Common Core Geometry Add-Ons we bring you the Form B Assessment for Unit 6 on Quadrilaterals. This is a nice assessment to pair with the original assessment as a makeup or use it as your original assessment for this year. We also bring you a worksheet for Unit 7 (Similarity) with more practice on similarity. This three page worksheet has extra similarity proofs as well as algebraic problems involving similarity.

Common Core Algebra II Add-Ons this month include two resources for Unit 7 (Function Transformations). First, we have a skill sheet that can be used at the end of the unit simply to give students more practice on various topics within function transformations. We also bring you the Form C Assessment for Unit 7.

Finally, our Algebra 2 with Trigonometry Add-Ons include a Form B Assessment for Unit 7 (Trigonometric Functions) and a quadratic trigonometric equation practice worksheet for Unit 8. The worksheet for Unit 8 concentrates on solving trigonometric equations that you must first factor to find solutions. There are no trigonometric identities involved in these equations, so the worksheet can be used immediately after finishing the first day of these types of equations or saved for later practice.

Well, that’s it for now. I hope you all stay warm throughout this part of the winter. We still have many weeks to go before Spring comes along!

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eMath November 2018 Newsletter

I can’t figure out if it is mid-November or mid-January. It’s 30 degrees outside and we are expecting to receive 3 to 8 inches of snow and ice tonight. Too cold, by far, for this year. But, here’s a little Koch Snowflake to celebrate the impending storm:

Things are warming up at eMathInstruction as we post a new round of add-ons and work on a whole new trilogy of books (more on that in December). With that teaser out of the way, let’s talk about the add-ons for the month.

For Common Core Algebra I Add-Ons this month we bring you two of our Form C assessments. We now have Unit 3 (Functions) and Unit 4 (Linear Functions) Form C Assessments available. As we mention most months, these assessments mirror the first two (Forms A and B) and so can be used for various periods, makeups, etcetera. We likely will keep adding these year after year in order for teachers to have a great back supply of tests and questions to pull from.

In our Common Core Geometry Add-Ons we have more Geometry proofs and a Form B assessment. In Unit 3 we bring you some extra practice on  Additional Triangle Proof Day 2. This worksheet has practice writing longer proofs that involve both CPCTC (how could they not?) and partitioning. Not our students’ favorite proofs, but good to practice just in case. We also bring you the Form B of the Unit 5 Assessment (The Tools of Coordinate Geometry).

Common Core Algebra II Add-Ons bring you two additional assessments for Unit 4. First, we have a Form B of the Unit 4 Mid-Unit Quiz. Unit 4 is our lengthy unit on Exponential and Logarithmic Functions. The quiz should be given after Lesson 7. We also bring you the Form C of the Formative Assessment for Unit 4.

Finally our Algebra 2 with Trigonometry Add-Ons include an enrichment lesson and a full unit quiz, both for Unit 5. First we bring you Lesson 5.5 on the Discriminant of a Quadratic. This is a great enrichment activity that is particularly good for advanced/honors students who are comfortable with their algebra. It looks at the connections between the solutions to linear-quadratic systems and the values of the discriminant of the systems. We also bring you a Form B for the full unit quiz for Unit 5.

In other eMath news, we attended the AMTNYS (Association of Teachers of New York State) Annual Conference in Saratoga Springs, New York, recently. We got to speak to so many great teachers there. A shout-out to all of you that stopped by our booth, chatted with us, and shared some of your stories. Thank you also to all of the exceptionally hard working teachers at this conference that give talks that share your classroom work and great ideas. Finally, the largest recognition should go out to those who organize the conference, i.e. the officers and other members of AMTNYS. All of these folks are full time teachers and volunteers who spend countless hours of work to put on a this conference. They don’t get recognized for this work and know they won’t, but do it anyway because it helps improve math education for all New York students. If that doesn’t epitomize what it means to be a teacher, I don’t know what does. I tip my hat to you all!

Thanksgiving Break is soon upon us (and early this year). Enjoy the long weekend. May it be filled with family, food, and relaxation!!! -Kirk



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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.




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eMath December 2017 Newsletter

Well, its cold and dark outside, so it must be December. The waning days of 2017 are upon us. Since it is mid-month, it’s time to release our latest round of add-ons and give you the latest eMathInstruction news. But, first, let’s do the add-ons.

For Common Core Algebra I Add-Ons this month we bring you two new lessons, both in Unit #7 on polynomials. We added lessons 7 and 8 which look at both multiplying and factoring polynomials with the help of area models. The second lesson specifically looks at how to factor trinomials by essentially using the AC Method of factoring, but in an area array so that students can more easily see how this factoring relates to the previous lesson where we multiply binomials using area. We do plan to eventually make videos for these two lessons as we feel they are a great addition to the curriculum.

As usual, our Common Core Geometry additions this month are in the form of a Unit Review and a Unit Assessment. This month it is Unit #7 – Dilations and Similarity. We’ve put together a huge packet of problems on this unit that should give your students lot of extra practice on these tricky concepts and how they link together. It does look like, at this rate, that we should have the last Unit Review and Assessment for Geometry in the March add-ons.

Our Common Core Algebra II Add-Ons this month include one video and one new lesson. We made a video for a lesson we released last year in Unit #6 – Using Structure to Factor Expressions. This is a great lesson where students need to recognize the structure of complex algebraic patterns in order to efficiently factor them. We’ve updated the lesson to add the QR code for easier access to the video. Our new lesson comes from Unit 8 (Radicals and the Quadratic Formula). The lesson is on A Closer Look at Extraneous Roots and should be taught after Lesson 2 on Solving Square Root Equations. This lessons takes an in-depth look at why certain square root equation have extraneous roots introduced and why squaring an expression is an irreversible algebraic manipulation.

Finally, for our Algebra 2 and Trigonometry Add-Ons we have two nice new resources. First, we have a Unit #7 (Trigonometric Functions) mid-unit quiz, Form B. Last year we put out a Form A for this quiz and we decided it made sense to create a make-up for this quiz as well. We also created a large set of practice problems on graphing sine and cosine functions. This is a nice resource that gives students lots of extra practice in terms of graphing sine and cosine functions (without a horizontal shift) and also coming up with the equations based on the graphs.

That’s it for add-ons. Besides those, we’ve been hard at work on other projects. Just this week I went down to Long Island and visited Ward Melville High School in the Three Village School District. They had won our contest earlier this year with the dubious prize being my teaching at their school for the day. It was a blast!!! Hopefully we will eventually have video and pictures to share. I got to teach in a black box theater (definitely a first and maybe a last time for me). I mainly taught a Geometry lesson on using linear functions to model the following (mathematical) doodle:

It was a nice activity because it necessitated the use of both the slope-intercept (red portion) form of the line and the point-slope form of a line (blue portion). We also used the online graphing program, Desmos, to create the doodle. Of course, my tendency to take it way too far lead me to create a Desmos graph that would allow the user to vary the number of lines plotted so that graphs like this could be created:

Here’s that Desmos sheet if you want to play around with the doodle yourself:

Mathematical Doodle with Adjustable Line Count

And just because we are on the topic of Desmos, here are some other Desmos graphs I created that are particularly fun to play around with. Feel free to open these and play them as eye-candy for your students as they walk into the door.

Archimeade’s Rotating Spiral

Logarithmic Spiral with Rolling Ball

Complex Ferris Wheel

Lissouj Figures

Dynamic Polar Roses

Rotating Spiral

Well, I think that is longer than what anyone wanted to read. It’s time for me to get back to creating curriculum and stocking up the wood stove (did I mention it’s cold in upstate New York today?). Have a wonderful holiday season everyone. Enjoy the long break coming up!

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eMath October 2017 Newsletter

Happy October to all!!! The weather in upstate New York is starting to get colder and the trees are finally changing color. As the holiday season approaches (my son considers Halloween to be the first legitimate holiday), we have been busy working on a variety of different things at eMathInstruction.

Without further ado, let’s get right into the add-ons for this month. Our Common Core Algebra I Add-Ons consist of a performance task and a mid-unit quiz. We’ve created a Unit #4 Performance Task on Linear Modeling. This isn’t a lengthy assessment but it will give teachers a good sense for how well students understand linear modeling and how they react in a situation that is somewhat non-routine. We’ve included a sample rubric for the teacher, but teachers may want to create their own. We’ve also created a mid-unit quiz for Unit #5 – Systems of Linear Equations. This quiz (with two forms of it) covers through Lesson #4 (up to and including the Elimination Method).

The Common Core Geometry add-ons for this month can be found under the Unit Reviews and Unit Assessments. This month we published both the Unit #4 (Constructions) and Unit #5 (Coordinate Geometry) Reviews and Assessments. The Construction Unit Review is long and contains all of the classic constructions (up to this point) as well as applications of these constructions (such as reflecting a point across a line). The assessment for this unit is understandably a bit different. We plan to publish one or two unit reviews and assessments per month until all have been completed. We plan to have them all finished by the March add-on round at the latest.

We did something a bit different for Common Core Algebra II Add-Ons this month. We went back and recorded videos for two Unit #4 add-ons lessons we had already created, specifically Lesson 7.5 on Exponential Modeling Revisited and Lesson 15 on Asymptotes of Exponential and Logarithmic functions. We’ve modified the worksheets so that they now contain the QR Codes for the videos. Did you know that the newest OS on the iPhone has an automatic QR reader built into the Camera app? It’s true. All a student, with the latest OS on an iPhone, has to do is point their camera at a QR code as if they were taking a picture of it and the link will open to our video. As well, we also created a lesson on factoring trinomials using the “AC” method, i.e. the product and sum considerations of a trinomial. We are considering recording a video for that an another Algebra II lesson for next month’s add-ons.

Finally, for Algebra 2 and Trigonometry Add-Ons this month we created two forms of a Unit #4 quiz. This unit is on Radicals and the Quadratic Formula. The two forms of the quiz cover all topics through work with the quadratic formula (through Lesson #7).

In other eMathInstruction news, we ran a contest this month to gauge the interest level in having me come and teach for a day at a school. Over 100 schools gave us feedback on Facebook. We had a drawing about a week ago and Ward Melville High School in the Three Village District on Long Island won the drawing. So, I’ll be headed there in mid-December to teach some classes and talk with students. I’m really looking forward to the visit! We are hoping to do another one of these drawings in the spring. Maybe I’ll be coming to your district to do some Regents Review. Who knows?

We have just begun very preliminary work on our Common Core Algebra I App (or eBook). We are working on all sorts of functionality for our new electronic only textbook. Included will be a button to allow problems to be read to the student (or sub parts of problems), the ability to play a video showing the solution to a lesson problem (instead of having to watch the whole video), and the ability for teachers to be able to turn the answer key on and off for given lessons, avoiding the need to separately purchase the answer key subscription. We hope to have an initial prototype of the book done by the end of the academic year and to have it fully functioning by the time the Next Generation Math Standards go into effect in New York State (2020-2021?).

That’s it for now. I hope that the school year is progressing well for everyone, students and teacher alike. New school years always bring surprises, both positive and negative. As always, if you have any questions, concerns, or other feedback don’t hesitate to contact me at





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eMath September 2017 Newsletter

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: I’m busy, but never too busy to help.


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eMath April Newsletter

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.

Construction Unit

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.