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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.

Kirk

 

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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.

Kirk

 

 

 

 

 

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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!