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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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Ah, its the last week of classes here in New York before the big break. Kids and teachers here are restive, but happy that one of the longer break is on the horizon. Just last minute tests, office parties, and school concerts to get through. Maybe our hypercube logo in a Santa hat is just what you need:

Or maybe you also just need that vacation. I know I do.

We’ve got the typical add-ons to discuss but first I wanted to update all of you on the latest timeline for New York State switching to the Next Generation Math Standards. If you are not teaching in New York, you may want to skip to the add-ons. However, if you have been confused about when the Next Generation standards are going to be implemented, read on.

As most teachers in New York know, these standards are very close to the Common Core Standards. But, like many states, the political backlash against those standards, earned or not, has made them untenable, at least in name. The timeline for adoption of these standards, of course, is dictated on when they will be assessed. That timeline has been fairly transparent for quite some time at the K-8 level. Here’s the graphic and link from the NYSED.gov website:

http://www.nysed.gov/curriculum-instruction/next-generation-learning-standards-and-assessment-implementation-timeline

The most important part of this graphic is the final piece (with my horrible highlighting):

At eMath we have been working under the assumption that the changes due to the Next Generation Standards in Algebra I, Geometry, and Algebra II would all go into effect in the Fall of 2020 and then assessed for the first time in June 2021. NYSED hasn’t updated that graphic on their website for quite some time (at least 6 months) and to my knowledge has not made any solid decision. But, NYSED is speaking to math teachers, especially in the form of responding to question from the Association of Math Teachers of New York State (AMTNYS). Here is the relevant question (from AMTNYS) and the reply (from NYSED):

I love the fact that “new” is in quotes. Here is the full document:

2018 AMTNYS Math Questions

So, it looks like at the very earliest the changes at the high school level will be assessed in June of 2022 (which seems like a century away to me). And it seems like that will only be for Algebra I. So, those of you holding your breath for 3 by 3 systems to be taken off the New York State Algebra II Regents exam could be waiting until the 2023-2024 school year. Let that sink in for a minute (or more).That’s five years and countless numbers of Regents exams between now and then.

The upshot of all of this for users of eMathInstruction courses is that we will not introduce these changes to our texts until at least the Fall of 2021. This, of course, is subject to change should NYSED decide to implement changes to the assessments earlier, but that would be disastrous for them.

O.k. Onto the add-ons for the month.

In Common Core Algebra I Add-Ons, we bring you two Form C assessments, one for Unit 5 (Systems of Linear Equations and Inequalities) and one for Unit 6 (Exponents, Exponents, Exponents). We will continue to put our these additional assessments year in and year out since we get a lot of positive feedback on them. Of course, it never hurts to have makeups and alternate exams.

In Common Core Geometry Add-Ons this month we have two sets of practice problems. First, we have a Unit 5 Coordinate Geometry Formula practice sheet. This is a short set of problems that give students a chance to practice what they’ve learned about the three fundamental coordinate geometry formulas (slope, midpoint, and distance). This is a good extra assignment for the average student. For Unit 6 we bring you a nice set of quadrilateral practice problems. These aren’t proofs, just algebraic and numerical problems that ask kids to use facts about the various quadrilaterals they’ve been studying.

For Common Core Algebra II Add-Ons we again bring you two Form C Assessments. We bring you the third version of the Unit Assessment for Unit 5 (Sequences and Series) and the third for Unit 6 (Quadratic Functions and Their Algebra).

Finally, for Algebra 2 with Trigonometry Add-Ons we have an assessment and a practice set of problems. We bring you the Form B Assessment for Unit 6 (Polynomials and Rational Functions). We also have another resource for Unit 7 (The Circular Functions). We created a set of fairly basic trigonometric graphs (no horizontal shifts) and ask the students to create their equations based on either the sine or cosine functions. This is a nice sheet to give kids to practice immediately after they have learned all of the basic sinusoidal graph parameters.

So, in other eMathInstruction news, we will be paying a visit to Edward R. Murrow high school in Brooklyn, New York this spring for our annual school visit. I’m excited to meet the students and teachers at Edward R. Murrow and amaze and awe them with some math that’s more fun than serious. Next month we will have some exciting news regarding new courses coming to eMath just in time for those Next Gen Standards I was talking about before. So, I’ll leave you with this teaser of an image:

Have a great holiday season! Enjoy the break, the rest, your family, and your friends. 2019 here we come!

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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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## TI Inspire Directions for Algebra I – Units 2 and 3 by Jeanne Oliveira

Our good friend Jeanne Oliveira from Germantown sent us these fantastic TI Inspire direction for Algebra I Units 2 and 3. We do all of our video instruction on the TI-84+, but we know that many schools, including our own Red Hook, use the TI Inspire. Jeanne took the time to translate all of the eMathInstruction lessons in Units 2 and 3 that have calculator instruction into TI Inspire. Not every lesson has a calculator involved, but for those that do, these are fantastic resources.

Unit 2 – Linear Expressions, Equations and Inequalities

Alg I Unit 2 Lesson 1

Alg I Unit 2 Lesson 3

Alg I Unit 2 Lesson 8

Unit 3 – Functions

Alg I Unit 3 Lesson 1

Alg I Unit 3 Lesson 2

Alg I Unit 3 Lesson 3

Alg I Unit 3 Lesson 5

Alg I Unit 3 Lesson 7

Thank you to Jeanne for spending the time making these and for sharing them with our Forum readers. If you are a teacher who has a resource you would like to share, including assessments, please let us know.

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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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## TI Inspire Directions for Algebra I – Unit 1 by Jeanne Oliveira

Our good friend Jeanne Oliveira, from Germantown High School, is creating TI Inspire instructions to go with our Common Core Algebra I lessons. She has generously volunteered to share them with us so that we can share them with you. Last spring, we published Jeanne’s Inspire directions for Unit 10. Here’s a link to that post:

TI Inspire Directions for Unit 10 (Statistics) by Jeanne Oliveira

Now, she has created direction for Unit 1 – The Building Blocks of Algebra. Jeanne only creates these handouts if the lesson contains a significant amount of calculator work. Here are her files for Unit 1:

Alg I Unit 1 Lesson 1

Alg I Unit 1 Lesson 2

Alg I Unit 1 Lesson 5

Check these out if you primarily use the TI Inspire calculator and want students to have a great reference for which functions to use on the calculator and when to use them.

Thanks again to Jeanne for sharing these files!

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Wow! Is it already August 15th? For those of us living in New York, that generally means we have just over two weeks of summer break left before school begins. How time flies.

Speaking of the waning summer, if your school is still looking to purchase workbooks for this coming school year, make sure to do so as soon as possible. We’ve still got quite a bit of them in stock now, but by next week, the delivery times will start to push past Labor Day weekend. For New York City teachers, we now have all of our workbooks, including Common Core Algebra I in Spanish, on ShopDOE and the FAMIS ordering systems. Find all of the important information using the document below:

eMath Instruction ShopDOE and FAMIS List 2018

Now that the school year is almost upon us, we have new additions to each course. As always, please feel free to send us suggestions about what you would like to see as monthly add-ons to various courses. Always best to catch us with your suggestions at least a month ahead of time. Assessments are always in demand and we have a bunch for you this month.

In our Common Core Algebra I Add-Ons, we bring you a Unit 3 (Functions) Quiz. This quiz goes through Lesson 3 of the unit and we provide you with both a Form A and a Form B version of the quiz. This is the first year of our Common Core Geometry Add-Ons. For the Geometry Add-Ons this year we want to make sure you all have a Form B test for each unit. So, for this month we give you a Unit 1 and Unit 2 Form B assessment. These mirror assessments can be used as makeup for the typical exams or just as replacements.

For our Common Core Algebra II Add-Ons, this month we bring you a Unit 2 Quiz (Also Functions). This quiz should be given after Lesson 3. We provide both a Form A and Form B version of this quiz. In Algebra 2 and Trigonometry Add-Ons, we provide a Unit 1 and Unit 2 Form B quiz. In Alg2/Trig, the first two units are very short, so we did not write full unit assessments for them. Here we provide a Form B for the “quizzes” for each of these units.

This year we are going to have our eye on the changes coming due to the Next Generation Standards in New York State. For those outside of the state (or those out of the loop), New York decided, like many states, to massage the Common Core Standards and given them a less politically charged name (they’ve even taken it off of the NY standardized tests). These standards do not go into effect at the K-8 level until the 2020-2021 school year. They will first be tested at the 3-8 levels in the spring of 2021. Here is a graphic of the timeline:

Here’s a link to that page:

Next Generation Math Standards Implementation Timeline

Now, I get a lot of questions about when we will be incorporating the Next Gen changes into our Alg I/Geo/Alg II series of curricula/books. Well, New York State has been vague, at best, about when the changes will be implemented at the high school level. BUT, if you look at the fine print of the Timeline graphic above, you see:

Two things to note here: (1) NYSED has not yet decided on when these standards will be implemented, so we must assume the status quo in terms of the assessment content and (2) the implementation of the Next Gen standards on tests will not happen before June of 2021.

We plan to really start modifying our high school texts later this academic year and will continue to create lessons that fit these standards as add-ons. We do not plan on actually changing the workbooks until the 2020-2021 academic year. We also hope to release something for kids younger than 9th graders for the Next Gen standards as well. More on that later this year.

That’s it for now. Continue to enjoy the rest of summer. Get out to your local fairs, waterparks, and festivals. As for me, I’m looking forward to taking a long weekend to camp with the kids.