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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.

Kirk

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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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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.

Kirk

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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.

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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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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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October in upstate New York is underway with its beautiful colors, chilly air, shorter days, and lots and lots of apples.

Here at eMathInstruction we are gearing up to attend the AMTNYS (Association of Math Teachers of New York State) Annual Fall conference in Saratoga Springs, New York. If you are attending the conference, please drop by and say hello. We love to chat with teachers who are using our curriculum to get vital feedback.

We’ve been busy in the last month creating new resources for you to use this year. We just posted the October Add-Ons for each of the courses. Let’s get into what those add-ons are for the month.

In our Common Core Algebra I Add-Ons we bring you some extra practice and another Form C exam. In Unit 2 we have a nice set of exercises to allow students to practice more on solving and graphing the solution sets to equations and inequalities. Some of the exercises are error analysis where students need to find the mistake and correct it. We also bring you the Form C Assessment for Unit 2. You now have three forms of the Assessments for Units 1 and 2. We’ll keep adding these on because teachers tell us that these extra assessments save a lot of time. Always feel free to let us know what add-ons you think would be helpful.

In the Common Core Geometry Add-Ons we also bring you extra practice and another assessment. We created a nice set of exercises that can be done towards the end of Unit 3 (Euclidean Triangle Proof). This set of exercises has kids justify why triangles must be congruent based on both rigid body motion reasoning and more classic Euclidean reasoning with congruence theorems. This is a great way to revisit two different types of thinking about congruence. We also bring you the Form B Assessment for Unit 4 (Constructions). Always good to have more than one assessment, especially when it contains lots and lots of geometric diagrams, as the Construction Assessment obviously has.

For our Common Core Algebra II Add-Ons its all Form C Assessments. We bring you both the Unit 2 (Functions) and Unit 3 (Linear Functions) Form C Assessments. Who couldn’t use an extra test with a system of three equations and three unknowns? Yes, that topic may be going away with the Next Gen changes, but it’s still in the curriculum now.

Finally, our Algebra 2 with Trigonometry Add-Ons also contain two assessments. We have now created Unit 3 (Quadratic Functions) Mid-Unit Quiz Form B. This quiz should be given after Lesson #8 in that very long unit. With two forms of this quiz now available teachers can mix and match or just give the new one for the year. We’ve also created a Unit 4 (Radicals and the Quadratic Formula) Form B Unit Assessment.

Well, a short newsletter for this month. I need to get back to writing. But, writing what?!? We plan to have a very exciting announcement in the next month or two regarding exactly that. I know my 5th grade daughter Evie is very excited to share the news. As always, if you have any suggestions for add-ons or questions about anything, feel free to contact us at: Info@emathinstruction.com

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It’s mid-September, which means classes have started and both teachers and kids are getting back into the school groove. We’ve been super busy here at eMathInstruction handling orders, sorting through technical issues (lost codes, lost codes, and more lost codes), writing books, and creating add-ons. We’ve got those up and ready for you, so let me lay out what’s new in September.

For Common Core Algebra I Add-Ons we’ve got two new Unit 1 resources. First, we have a new Skill Building set. This is our second for Unit 1 and we added it because it is so crucial that students establish these early skills, most of which should be a review from 8th grade and earlier. We’ve also brought you a Unit 1 Assessment Form C. That’s right!  This is our third assessment for Unit 1. We’ve heard from teachers that these additional assessments are critical, so we are committed to creating more of them for all of our courses.

Common Core Geometry is our “youngest” course and thus has the least add-ons so far. For this month’s Common Core Geometry Add-Ons we bring you two resources for Unit 3 (Euclidean Proof). First we have a Lesson 6 Warm-Up on parallel line terminology and properties. This is a great resource to use to review all of the terminology associated with parallel lines (alternate interior, exterior, same-side, corresponding). Use this if you think your students need this terminology review before higher-level work with parallel lines. We’ve also brought you the Form B (second) Unit 3 Assessment. We will get out a second assessment for each of our Geometry units this year, hopefully having them all done by February.

In Common Core Algebra II Add-Ons we bring you a couple of Unit 1 resources. We created a skill building set for Unit 1 similar to the ones we have for Algebra I. This set of problems gives students extra practice on some basic skills that they will need in order to be successful throughout the course. We also bring you the Form C of the Unit 1 Assessment. So, now you have three assessments for this unit to mix and match.

Algebra 2 with Trigonometry is our oldest course having been created in 2008, well before the Common Core Standards were adopted in New York (just a little history). For this month’s Algebra 2 with Trigonometry we bring you a Form B exam for Unit 3 (Quadratics). For Unit 4 we have a really nice Quadratic Modeling Extended Problem that has students play around with some projectile physics.

I don’t know about anyone else, but I’m pretty happy it’s Friday as I write this. As a teacher, you always sort of forget how good a Friday feels over summer break. But, once schools begins again, there isn’t anything quite like it. For now, enjoy your classes, your kids, and your beautiful fall weekends (Winter is coming).

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

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

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

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

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

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

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

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

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

@emathinstruction

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

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

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

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

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

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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.