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eMath October 2019 Newsletter

October has rolled around with beautiful colors and cold nights everywhere in upstate New York. We’ve been working hard to create add-ons, middle school curricula, and new videos. We’ve also been getting great feedback on both our add-ons this year and the trial version of the middle school curricula. We will have more on that feedback in a later post. For now, let’s get into the latest round of add-ons.

For Common Core Algebra I Add-Ons we have three new resources to share. First, we created a table of contents of QR codes for our videos. This would be a fun insert for kids in their binders so that they can scan a QR code for a given lesson at any point to be taken to that video. We’ve placed this resource at the end of the add-on list. We also bring you the Unit 3 (Functions) Form D Assessment. Finally we’ve also published the Exit Tickets for Unit 4 (Linear Functions and Arithmetic Sequences). I’m hopeful that we are caught up on Exit Tickets enough that we are staying ahead of where teachers are in the curriculum.

In Common Core Geometry Add-Ons this month we have a similar slate of resources. We’ve created the YouTube QR Code list and placed it at the end of the add-on list. As well we have the Unit 3 (Euclidean Proof) Exit Tickets and Form C Assessment. You can never have too many tests with geometry proof to choose from. We hope you like the latest installment.

Common Core Algebra II Add-Ons also include the YouTube Video QR Code List (again located at the end of the add-ons). We then bring you the Unit 3 (Linear Functions) Form D Assessment. Finally, we also have published the Unit 4 (Exponential and Logarithmic Functions) Exit Tickets as well. This was a long unit with lots of lesson, so there are many exit tickets that go along with it.

In Algebra 2 with Trigonometry Add-Ons, we don’t have a QR Code list for you because there are no videos for this course (in case you were wondering). What we do have is a new lesson, a new assessment, and a new round of exit tickets. First, we bring you Unit 3 – Lesson 14.5 – The Vertex Form of a Parabola. This new lesson in Algebra 2 with Trig emphasizes writing the equation of a parabola in vertex form if its vertex and one other point is known. We also offer the Unit 3 (Quadratic Functions) Form C Assessment. Finally, we bring you the Unit 4 (Radicals and the Quadratic Formula) Exit Tickets.

In other news, we’ve just started to record and upload videos for our middle school series. The first unit of N-Gen Math™ 6 is up on our site. We hope to add many more this month. Watch for them to start going up for the first few units of each course. Speaking of videos, it’s time to get back to recording those. Have a great rest of your October!

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eMath September 2019 Newsletter

It’s September and schools are now in full swing here in New York and around the country. Temperatures are starting to get cooler, at least in the great Northeast. We’ve been working hard here at eMathInstruction on add-ons and on our new Middle School curriculum. So much work and so little time. Let’s get right to the new resources.

In our Common Core Algebra I Add-Ons this month we bring you three additional resources. We received a lot of good feedback on our exit tickets from the last month so we decided to create a lot more of them this month in all of our courses. In Algebra I we bring you both the Unit 2 and Unit 3 Exit tickets. We will continue to put out exit tickets each month, with at least one additional unit added. We also have the Unit 2 Form D assessment for Algebra I to give you more options for this course.

Common Core Geometry Add-Ons for September include exit tickets as well as two other resources. First we have the Unit 2 Exit Tickets on Transformations, Rigid Motions, and Congruency. We also bring you a set of problems on Congruency and Rigid Motions. We all known how challenging this connection can be for students, especially when it comes to expressing their thinking in words. This problem set gives students another four lengthy problems to get this practice. We also have the Unit 2 Form C assessment.

The Common Core Algebra II Add-Ons will start to sound a bit repetitive. We wanted to get ahead on exit tickets for certain courses so we also created the Unit 2 and Unit 3 exit tickets for Common Core Algebra II. We also bring you the Form D Assessment for Unit 2.

A similar scenario plays out in our Algebra 2 with Trigonometry Add-Ons. We have the Unit 2 and Unit 3 exit tickets for this course as well as brining you the Unit 2 Form C Assessment. Hopefully we’ve published enough exit tickets now to last all of the courses until the October add-ons are published.

In other eMathInstruction news, we are busy working on our middle school courses. As a reminder, we have published the rough draft versions of our N-Gen Math™ 6, N-Gen Math™ 7, and N-Gen Math™ 8 courses that are aligned to the Next Generation Mathematics Standards for New York State. This year we will be recording the videos that go along with these lessons as well as creating the answer keys and reviews for the units. We won’t have anything to sell until late Spring of 2020. But, schools are encouraged to use the lessons and homework sets that we’ve published this year on a trial basis. Read all about our plans in the following post:

The N-Gen Math™ Middle School Series (6th through 8th) First Drafts

There is no busier time here at eMathInstruction than the month of Septembers. It’s when we are helping out schools who are having problems with their accounts, filling orders, creating products, and getting everything set for the school year ahead. Of course we welcome your input and questions. Feel free to always let us know what you think by sending us feedback on our Feedback Form. Until next time, keep working hard and enjoy the oncoming Autumn.

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eMath August 2019 Newsletter

It’s mid-August, which means the start of school is just a few weeks away in New York. In many other states, it has already begun. At eMathInstruction, summer is our busiest season as we fill orders and work on our first round of add-ons for the year. Let’s get into the add-ons for August. This year I wanted to play around with exit tickets, so am going to be releasing a new unit of them for each course each month. Let’s get into all the details.

In Algebra I Add-Ons this month we have three resources to add. First, we have the Unit 1 exit tickets. For all the exit tickets, I created them so that there are three identical problems per page that teachers can photocopy and then cut and hand out to their students. I’d love feedback on this format. The answer keys to the exit tickets are very bare boned and intended for teacher and not student use. We have also created an enrichment practice set for Unit 1 on Mindful Manipulation. This is a follow up to our Seeing Structures in Expressions lesson and challenges kids to use real number properties to rewrite expressions in creative ways. Finally, we also are contributing the Form D assessment for Unit 1. This now gives teachers four mirror assessments for this unit to choose from.

For Common Core Geometry Add-Ons this month we also have Unit 1 exit tickets. Exit tickets for Geometry will become very interesting once we venture into the realms of transformations and proofs, but for now they were relatively easy to create and will hopefully give teachers good feedback on how a given lesson went. We also bring you the Form C version of the Unit 1 Assessment, giving teachers three assessments for this unit to choose from. Finally, we created an enrichment lesson in Unit 2 on Kites. This is a fantastic lesson to do with kids after the lessons on isosceles triangles and reflections. We examine how students can use the nature of kites to reflect points across lines. This is an exceptionally nice lesson to reinforce the idea that points that lie equidistant from the endpoints of a segment must lie on that segment’s perpendicular bisector.

Our Common Core Algebra II Add-Ons for August again include Unit 1 exit tickets. We also bring you the Form D assessment for Unit 1. We will continue for all of our courses to bring you new unit assessments each month so that you can give your students a variety of these and feel confident from year to year about the integrity of your testing. Finally, we also have a Unit 2 enrichment lesson on sets with infinite numbers of elements. This is a really cool lesson (according to a very big math geek) that gets into more complex set terminology and also looks at Dedekind’s test for sets with infinite cardinalities. This is a really nice lesson to do with students who need a little more depth in sets, mappings, and functions.

Algebra 2 with Trigonometry Add-Ons this month include the Unit 1 exit tickets (that’s starting to sound a bit repetitive) as well as two additional resources. First, we bring you the Unit 1 Form C assessment. We also have created a great set of problems on linear regression. The problems mainly emphasize looking at equations of best fit lines for large data sets and interpreting them as well as evaluating their use. This is a good set of problems to simply allow kids to work more with this extremely important topic.

Besides our add-ons, we’ve been busy this summer finishing up the first drafts of our three middle school courses, N-Gen Math™ 6, N-Gen Math™ 7, and N-Gen Math™ 8. I’m not going to rehash everything in this post since I wrote one just a few days ago about the courses. If you missed it here’s a convenient link:

The N-Gen Middle School Series

Most importantly remember two things about these courses:

  1. They are aligned to the New York  Next Generation Math Leaning Standards that go into place in the 2020-2021 school year for the K-8 level (the 2021-2022 school year for Algebra I).
  2. We won’t have anything to sell for these courses until the spring of 2020.

We are very excited this coming year to create videos and other materials for these courses. For now, though, I need to get back to the last half of August! Enjoy the beginning of the school year everyone.



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The N-Gen Math™ Middle School Series (6th through 8th) First Drafts

I am extremely happy to announce that the first drafts of our middle school courses for 6th, 7th, and 8th grade math are now posted on our site.

N-Gen Math™ 6        N-Gen Math™ 7        N-Gen Math™ 8

These three courses are aligned to the New York State Next Generation Math Standards. For those not in New York, these standards closely correlate to the Common Core State Standards. To compare the two sets of standards, read the Crosswalk created by the New York State Education Department. We will eventually give a standards map for both sets of standards.

The Timeline for the Next Generation standards has them going into effect at the K-8 level in the 2020-2021 school year. We are providing the lesson plans and homework sets for all three courses for the 2019-2020 school year in their first draft (or Beta) form for schools to pilot in their classrooms. Schools have our permission for the 2019-2020 school year to photocopy the lessons and homework sets and use them with their students.

During the 2019-2020 school year we will be busy at eMathInstruction creating videos to go with each lesson. Just like with our high school courses, these videos will be of the entire lesson, from the first problem to the last. We will begin to post them during the 2019-2020 school year for schools to begin to use, where possible. We will also be creating unit reviews and assessment items, which will be released in the 2020-2021 school year. Workbooks and teacher subscriptions will be available for order during the spring of 2020 for the 2020-2021 school year. We anticipate pricing will be similar to the pricing on our high school courses.

If you use these lessons, keep in mind they are in their first draft form. There will be typos, grammar and spelling errors, and maybe even a mistake or two in math. We will likely catch most of these errors in our proofreading process, but if you want to let us know about mistakes you find or comments you have, feel free to either use our Feedback Form or email us at


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TI-Nspire Directions for Algebra I and Geometry by Jeanne Oliveira

Our good friend and longtime contributor, Jeanne Oliveira, from Germantown CSD has created an amazing collection of TI-Nsprire directions that go with the eMath Curriculum for both Algebra I and Geometry. Some of these we’ve posted in the past. But now we have the full collection. These include both PDF versions of the instructions and TNSP versions. I’m going to post them by unit in zip folders for easier download.

Algebra I:

eMathInstruction Alg I Unit 01 Nspire Instructions

eMathInstruction Alg I Unit 02 Nspire Instructions

eMathInstruction Alg I Unit 03 Nspire Instructions

eMathInstruction Alg I Unit 05 Nspire Instructions

eMathInstruction Alg I Unit 06 Nspire Instructions

eMathInstruction Alg I Unit 07 Nspire Instructions

eMathInstruction Alg I Unit 08 Nspire Instructions

eMathInstruction Alg I Unit 09 Nspire Instructions

eMathInstruction Alg I Unit 10 Nspire Instructions

eMathInstruction Alg I Unit 11 Nspire Instructions



eMathInstruction Geometry Unit 05

eMathInstruction Geometry Unit 06

eMathInstruction Geometry Unit 07

eMathInstruction Geometry Unit 08

eMathInstruction Geometry Unit 09

eMathInstruction Geometry Unit 10


Jeanne spent a lot of time on these and plans to do a set for Algebra II as well. We’d like to thank her for sharing these materials with the wider math education community. Thanks Jeanne!

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Regents Live Review 2019

In just two weeks students all around New York State will sit down to take their (Common Core) Algebra I Regents exam. As we’ve done in the past two years, I will be doing a Live Review session for each of the three major high school math Regents exams (Algebra I, Geometry, and Algebra II).

I will be going over questions from past Regents exams. The question packets for each Regents are given below. Fair warning: they are extremely long (around 20 pages each)!!!

Common Core Algebra I Live Review Problems 2019 (pdf)

Common Core Algebra I Live Review Problems 2019 (MS Word)

Common Core Geometry Live Review Problems 2019 (pdf)

Common Core Geometry Live Review Problems 2019 (MS Word)

Common Core Algebra II Live Review Problems 2019 (pdf)

Common Core Algebra II Live Review Problems 2019 (MS Word)

We likely will not make it through the entire packet on any one of the nights. I think it really would take about 5 hours to do a complete review.

The reviews will be shown on YouTube Live (Kirk Weiler Channel) and Instagram Live (follow @emathinstruction). The video will be much better on the YouTube Live platform. We mainly will have Instagram Live going for students to comment (whatever it takes to get them to the review ;-).

Can’t wait to “see” you all there.

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eMath May 2019 Newsletter

Wow! Is it May already? Right about now teachers in New York are finishing curriculum and heading for the big push to the New York State Regents exams in mid June. We are here to help with more add-ons and Live reviews in June. Before we get to those, let’s discuss the latest and last round of add-ons for this academic year.

In Common Core Algebra I Add-Ons we bring you the Form C Assessment for Unit 10 (Statistics) and Unit 11 (A Final Look at Functions and Modeling). These two assessments mean that we now have three unit tests per unit in Algebra I. We’ll try to add a fourth next year.

For Common Core Geometry Add-Ons we have an introductory lesson for Unit 10 (Measurement and Modeling) along with Unit 10’s Form B Assessment. To begin, we have created a Lesson 0 for the unit on Rates, Densities, and Conversion Factors. We felt that there was quite a bit of work in this unit on applying concepts like density. This lesson reviews these various ideas early in the unit. Use this for kids who struggle with ratio and rate concepts. Our Form B for Unit 10 now means we have two unit tests per unit in Geometry. More to come.

Common Core Algebra II Add-Ons this month also bring two Form C Assessments. We now have a Unit 12 (Probability) and Unit 13 (Statistics) Form C. It’s especially nice to have more statistics questions for this very challenging unit.

Finally our Algebra 2 with Trigonometry Add-Ons also feature two additional assessments, both Form B. First we have the Unit 12 (Statistics) Form B and then we have our Unit 13 (Sequences and Series) Form B.

Lots of assessments this month!

Now for the fun part. We are yet again holding our YouTube Live and Instagram Live Review sessions this year for the New York State Regents Exams. For each exam we will be going over old Regents test questions for 3 hours. Here’s our schedule for this year:

Algebra I (Algebra 1):  Tuesday, June 18, from 6:00 to 9:00 p.m.

Geometry: Wednesday, June 19, from 6:00 to 9:00 p.m.

Algebra II (or Algebra 2): Thursday, June 20, from 6:00 to 9:00 p.m.

We will be broadcasting on our YouTube Channel (click link) and on our eMathInstruction Instagram Live account. YouTube will be much better quality, although commenting will be allowed on Instagram (only go there if you can stand constant comments from teenagers).

We’ll put out more information in the coming two weeks, including the problem sets we will work through at each of the sessions. For now, have a great Memorial Day weekend!

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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 February 2019 Newsletter

Happy mid-winter everyone! As I sit here in Red Hook, New York the days are getting longer as we head up the daylight curve. We aren’t at the inflection point yet (the Spring Equinox) but we’re getting there:

This month we bring you lots of good resources in our monthly add-ons. Let’s get right into those.

For Common Core Algebra I Add-Ons this month we bring you a mid-unit quiz and a new lesson. To begin, we created a progress quiz for Unit #6 (Exponents). The quiz covers all material from the first five lessons. We also have a new lesson for Unit #8 (Quadratic Functions and Their Algebra). We have created a lesson on the axis of symmetry formula for a parabola. The Standards are pretty specific about wanting kids to find turning points on parabolas by using completing the square. Still, what we all know is that -b/(2a) is a fast, reliable way of finding it that is likely easier for many students.

In Common Core Geometry Add-Ons this month we  have a new unit assessment and a new lesson. We bring you the Form B version of the Unit 7 Assessment (Similarity and Dilations). For our new lesson we created what we call a warm-up for Unit 8 (Right Triangle Trigonometry). We provide a lesson to help kids understand the various right triangle side length terms: opposite, adjacent, and hypotenuse. Use this lesson if your kids struggle identifying those sides when setting up trig ratios.

Our Common Core Algebra II Add-Ons and Algebra 2 with Trigonometry Add-Ons are very similar, so I’ll just summarize them here. For both courses we bring you two additional unit assessments. For Common Core Algebra II we have the Form C (third version) Unit Assessments for Unit 8 (Radicals and the Quadratic Formula) and Unit 9 (Complex Numbers). For Algebra 2 with Trigonometry we have the Form B Unit Assessments for Unit 8 (Trigonometry Algebra) and Unit 9 (Trigonometric Applications).

I’m going to keep it relatively short this month. Presidents’ Day Weekend is upon us and I’m looking forward to a (very) short vacation before getting right back to writing. Have a great rest of your February! Spring is coming.