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New Units in N-Gen Math 6, 7, and 8

In 2010, the Common Core State Standards were introduced in order to provide some uniformity about what mathematics should be taught in each grade, at least up until high school coursework. For the most part, the states that adopted the CCSS, taught the same math topics in each grade level. Eventually, many states began to modify the CCSS to provide more clarity about the standards and to make them more grade appropriate. These modifications gave rise to many different, “Common Core Adjacent”, sets of standards. In New York, for instance, the Next Generation Mathematics Learning Standards are just such a set of standards, going so far as adopting the Common Core domain and numbering system.

eMATHinstruction’s N-Gen Math courses are aligned to the Next Generation Math Learning Standards. However, because the Next Generation standards are Common Core adjacent, most of the content is exactly the same as that laid out in the CCSS. In the NGMLS some of the content from the CCSS was either removed from the Next Generation standards or moved to different grade levels. Here at eMATHinstruction, we want to ensure that our courses are as flexible and adaptable as possible, and can be used in as many states as possible. In our effort to do so we are adding new units to the online version of our Next Generation aligned middle school courses. This new content includes units that align more strictly to the CCSS. Some of the content within our “cc” units is found in other units, while many of the lessons are brand new. Each new cc unit includes a review and assessment aligned to the content in that unit.

Here’s what’s new for each course

N-Gen Math 6

Unit 11cc – Statistics – In this new unit, we have students work with quartiles, the interquartile range, and box plots. They strictly work with populations and there is no discussion on how samples are taken from populations. Finally, students learn how to summarize their finding using appropriate statistics.

N-Gen Math 7

Unit 7cc – Statistics – In this new unit, students learn how to interpret the mean as a balancing point. Students are introduced to the mean absolute deviation as a way to measure variation. Students then judge whether the differences in sample means or medians is significant based on how the difference compares to a measure of variability in the data sets.

Unit 8cc – Probability – In this new unit, probability is developed from the basic concepts that are also contained in our N-Gen Math 6 course, i.e. simple probability. After simple probability is developed, students then move onto compound probability.

N-Gen Math 8

Unit 6cc – Functions – In this new unit, functions are analyzed without the addition of scatter plots and lines of best fit.

Unit 12cc – Statistics of Two Variables – In this new unit, students look at associations between variables that are both numerical and categorical. In the numerical lessons, students learn how to create a dot plot, draw a line of best fit, and informally assess the linear fit of the data. In the categorical lessons, students learn how to use relative frequencies and conditional relative frequencies to determine if there are associations between different categories.

At this time, these new units available online only. They will contain the full gamut of Add-Ons including Spanish translations, assessments and more.

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eMath September 2020 Newsletter

Now that it’s September, schools around the country, including New York State, are in full swing. Around New York, schools are experimenting with in school classes, hybrid models, and fully remote teaching. Each has its challenges and there are still a lot of questions about how the 2020-2021 school year is going to play out. At eMATHinstruction, we are doing our best to create materials that will help teachers navigate these challenging times.

For this month, we start by offering SMART Notebook files for the first three units in each of our middle school courses. These files can only be used by the program SMART Notebook, which is the standard software used by teachers who have SMART Boards. Because of how many teachers use this software and how many are in remote learning situations, we thought it would be wise to post them. I did want to mention that some of the presentations have animation in them and teachers should experiment with the presentations before using them in a remote situation. The files are located as the last resource under each of the lessons.

For our new additions in Common Core Algebra I this month, we bring you two new resources. First, we have published the Unit 4 Assessments, Forms A, B, and C, in Spanish. As I mentioned in last month’s newsletter, these tests are identical to the original English versions, but have been translated into Spanish. We hope that if your school has native Spanish language speakers that these tests will help you better understand what math they have learned and what still needs work. We also created a new lesson for Unit 2 (Linear Expressions, Equations, and Inequalities). This lesson is entitled “Using Structure to Understand Solutions to Equations.” It has students solve equations with integer solutions both algebraically and using tables on their calculators. Particular emphasis is placed on understanding how the structure of an equation can tell us whether it has no solutions or an infinite number.

In Common Core Geometry this month we bring you two new resources for Unit 2 (Transformations, Rigid Motions, and Congruence). First, we have a mid-unit quiz that can be given after Lesson #5. We provide you with two forms of this quiz for more flexibility. We also bring you the Form D assessment for Unit 2.

For Common Core Algebra II this month we have one resource for Unit 3 (Linear Functions, Equations, and Their Algebra) and one for Unit 4 (Exponential and Logarithmic Functions). For Unit 3, we bring you a mid-unit quiz and include two forms of the quiz. For Unit 4, we bring you an enrichment lesson on solving equations that involve logarithms. Please note, this is not a lesson on solving exponential equations using logarithms, but a lesson on solving equations that contain logarithms. We keep them relatively simple and do not involve log laws to combine logarithms. We emphasize solving these equations by applying inverse operations, including exponentiation. Some time in the lesson is also devoted to solving logarithmic equations graphically.

Finally, in Algebra 2 with Trigonometry we bring you a Unit 3 (Quadratic Functions and Their Algebra) enrichment lesson on “Using Structure to Factor.” This lesson requires students to see the structure in an expression and use it to factor more challenging expressions. We also bring you the Unit 3 Form D assessment.

This has been an “interesting” start to the school year. With students and teachers on Zoom, Teams, Classroom, Schoolology and other platforms just trying their best to make this learning thing work this year. I don’t know about anyone else, but I long for the days of having kids in a packed classroom five days a week. Good teaching and thorough learning was hard enough back then, and now it is so much more challenging. We don’t have a crystal ball here at eMATHinstruction, and we certainly don’t know what the New York State Department of Education is planning in terms of testing at the end of the year. Our ardent hope is that they will either cancel the testing, as they did last year, or will modify it and the standards that should be taught in a way that makes sense given the reduced instructional time that all students are experiencing this year. Oh, and we hope they do this soon and don’t wait until mid-March of 2021. Until next month, stay healthy, stay sane, and keep fighting the good fight. -Kirk

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eMath August 2020 Newsletter

Ah, 2020! As schools “re-open” around New York and the country, the learning environment has never been more strange or more stressful. We’ve been busy here at eMATHinstruction filling orders and creating resources to help with whatever teachers and students face this coming year. It’s our first year with middle school courses, so we have lots of new resources on that front as well as all new add-ons for our high school courses.

Before we get into the new middle school and high school materials, we first should mention the new way we are organizing resources for each course. We have now moved all resources for a given unit of a course in that unit’s page. We used to have only the lessons and homework sets for a given unit located there, with reviews, assessments, and add-ons located in other pages. We now have moved all of those into the individual unit pages. Generally, we have the standard lessons/homework sets first, followed by the unit review, unit assessments, quizzes, and additional lessons or activities that have been added-on. We have color coded these so that it is easy to quickly identify free lessons versus paid items, such as reviews, assessments, and add-ons. Here is an example from Unit 2 in Common Core Geometry:

Now that our resources are easier than ever to find, let’s discuss the latest additions to all of our courses.

In Common Core Algebra I this year we are adding Spanish versions of our first three forms of the unit assessments (Forms A, B, and C). We worked with three fantastic math teachers who were also bilingual in Spanish to create these translations for us. Each exam was translated by one teacher and then reviewed by another. For this month, we are releasing a number of these assessments so that teachers can begin to evaluate how they can use them effectively. We have included Units 1, 2, and 3, for a total of nine assessments. You will find these as an option under the unit assessments. Here is a screenshot of Unit #1 from Algebra I:

Notice that the PDF DOCUMENT – SPANISH is located immediately below the PDF ANSWER KEY for each exam. Please also note that we did not translate the answer keys into Spanish on the assumption that the person grading the student exams will be fluent in Spanish.

In Common Core Geometry this month we bring you two resources for Unit 1 (Essential Geometric Tools and Concepts). First, we have a mid-unit quiz with both a Form A and a Form B. Although this would be a very early quiz, we believe it is more important than ever to make sure kids are starting off with a solid understanding of the material. We also bring you the Form D assessment for Unit 1.

For Common Core Algebra II we bring you a mid-unit quiz for Unit 1 (Algebraic Essentials Review). We are committed this year to creating mid-unit quizzes in each of our high school courses for each unit. We know that many of these have already been created, but we want to make sure we have consistency in each unit with both a Form A and Form B mid-unit quiz. We also bring you an add-on lesson for Unit 2 (Functions) on Exploring Functions Using the Graphing Calculator. In this add-on, we give students problems that force them to experiment with their graphing window as well as tools like the maximum and zero command to find important features of real-world functions. We think this is an excellent resource for encouraging kids to use their calculators to explore the behavior of unfamiliar functions.

In Algebra 2 with Trigonometry, this month we offer up the Form D Unit Assessment for Unit 1 (Introduction to Functions) and Unit 2 (Linear Relations and Functions). Our general goal is to have four forms of each unit assessment for each course.

Our middle school courses are brand new this year, which means that we have a much smaller library of resources for them at this point. Right now, teachers will find in each unit the lessons for the unit and the unit review. As add-ons this year, we will be publishing the first round of unit assessments for each course. For this month, we have published the unit assessments for Units 1, 2, and 3 for each course. You will find the assessments as the last resource (for now) of each unit. For example, Unit 3 in N-Gen Math 6 looks as follows:

We will continue to publish the unit assessments each month as the add-ons for the middle school courses. Next year we plan to add Form B assessments, as well as quizzes and exit tickets.

I don’t think I’m going out on a limb to say that the fall of 2020 will be even more strange and stressful for teachers and students than even the spring of 2020. And that was no walk in the park. Teachers will need to be ready to move from fully in school to hybrid models to fully remote learning at a moment’s notice. At eMATHinstruction, we hope to be able to help with whatever transitions you have to make as a teacher this year. For now, take care of yourselves, stay healthy, and stay sane.

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eMath March 2020 Newsletter

What a crazy last few weeks it has been. School districts have been closing left and right for weeks or even over a month in order to “flatten the curve” as it is being called. We just posted an article detailing the steps we are taking here at eMATHinstruction to help districts as many move to a remote instruction model in the coming days. Part of how we are going to help, though, is by continuing to publish materials in our monthly add-ons and by continuing to record videos for our middle school series of courses. Let’s discuss the add-ons first and then I’ll give you an update on our middle school progress.

In Common Core Algebra I Add-Ons this month we have the Unit 8 (Quadratic Functions and Their Algebra) Form D Assessment. We also bring you the Unit 9 (Roots and Irrational Numbers) and the Unit 10 (Statistics) Exit Tickets. We will put out our last CC Algebra I exit tickets, for Unit 11, in April. I’m hoping that teachers might be able to creatively use the exit tickets in a remote learning situation. Maybe they could be used for informal assessment by the student.

For Common Core Geometry Add-Ons this month we have a few resources for Unit 8 (Right Triangle Trigonometry). First we bring you a practice set of exercises on solving for missing sides and missing angles in right triangles using the trigonometric ratios. This is a straight up fluency worksheet that gives students some nice practice setting up trig ratios and then solving them. We also have the Unit 8 Form C Assessment. Finally, we bring you the Unit 9 (Circle Geometry) Exit Tickets.

This month we are brining you a lot of resources in the Common Core Algebra II Add-Ons. CC Algebra II is a very long course, as anyone who has taught it knows. In order to keep pace with the Form D assessments and exit tickets, we bring you five resources in CC Algebra II this month. We begin with the Unit 8 (Radicals and the Quadratic Formula) Form D Assessment. We then have the Unit 9 (Complex Numbers) Exit Tickets. Of course, that means that we then bring you the Unit 9 Form D Assessment. We then have the Unit 10 (Polynomial and Rational Functions) Exit Tickets and Form D Assessment. We wanted to make sure we got all of these resources to you now, so that if you need them while students are learning from home, then you have them at your disposal.

In Algebra 2 with Trigonometry Add-Ons, we have a similar situation to CC Algebra II. In this case, we bring you four resources, starting with the Unit 8 (Trigonometric Algebra) Form C Assessment. We then have the Unit 9 (Trigonometric Applications) Exit Tickets and Form C Assessment. Finally, we also bring you the Unit 10 (Exponential and Logarithmic Functions) Exit Tickets.

We are coming along on our Next Generation aligned middle school courses. For those of you not in New York State, the Next Generation Math Standards are what New York is renaming the Common Core Standards (with slight modifications). We now have our N-Gen Math 6 and N-Gen Math 7 books done in their first editions, with sample copies available in early May. Our N-Gen Math 8 book is not far behind. We are busy also recording videos for all three courses. It looks like by the end of March we will finish all videos for both Math 6 and Math 7. Math 8 videos will be finished by mid-April. We hope that these videos will help with remote learning this year.

We are starting to receive orders for our middle school products. Although we are happy to get the orders, we won’t be able to process them until late June. Let us know if you have any questions by emailing [email protected]. We will be posting cleaned up version of all of the middle school files in June as well standards alignment documents this summer.

That’s it for now. I hope that everyone out there, teachers, students, administrators, and parents, all stay healthy and sane during these coming weeks. We can do so much for each other in our communities, large and small, that will help our country as a whole defeat the common threat we now face. Take care and be well.


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eMath January 2020 Newsletter

Hello 2020! What a start to this new year and (possibly) new decade. We’ve been roaring into the 20’s here at eMATHinstruction by making a lot of improvements to our website, including a new(ish) color scheme to make the text easier to read and resources easier to find. More changes will be coming soon that will hopefully make the site even more user friendly.

We’ve also been creating materials for our new middle school courses and for our high school courses. The latest round of add-ons have been posted. Let’s get into those before we come back to what’s happening in middle school.

Our Common Core Algebra I Add-Ons this month include a practice set of problems, a Form D assessment, and some exit tickets. First, we have a practice set in Unit 6 (Exponents) on Negative and Zero exponents. This is a fairly basic problem set, but it allows students who need extra time with these tricky topics some additional practice. We then bring you the Unit 6 Form D Assessment. Finally, we have the Unit 7 (Polynomials) Exit Tickets. We’ve been getting great feedback on the exit tickets. Many teachers are using them as designed and some are using them as warm-up problems the class following the lesson.

In Common Core Geometry Add-Ons this month we have two resources for Unit 6 (Quadrilaterals) and one for Unit 7 (Similarity and Dilations). First, we bring you a practice set of coordinate geometry proofs. This set includes some of the standard problems and also ones that include those unpredictable twists that can often turn up on Regents Exams. We then bring you the Unit 6 Form C Assessment. Finally, we have the Unit 7 Exit Tickets for our unit on Dilations and Similarity.

Common Core Algebra II Add-Ons for this month include three assessments, of various types. First, we have the Unit 6 (Quadratic Functions and Their Algebra) Mid-Unit Quiz. We’ve been trying to round out our unit quizzes this year in all of our courses. We also have the Unit 6 Form D Assessment. Finally, we bring you the Unit 7 (Transformations of Functions) Exit Tickets.

For Algebra 2 and Trigonometry Add-Ons we bring you two resources this month. First, we have the Unit 6 (Polynomials and Rational Functions) Form C Assessment. We also bring you the Unit 7 (Circular Functions) Exit Tickets.

We continue to move along on our middle school program. We’ve been working primarily on four things at this point: editing the text, creating the answer keys, writing unit reviews, and recording videos for each lesson. We plan to have all of these materials, along with the workbooks, available for use on July 1, 2020. And who knows? Maybe even sooner. But we like to be conservative with our timelines. For schools that need them, we can do formal quotes for all of our middle school products.

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

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

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

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

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

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

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


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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 eMATHinstruction 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 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 October 2018 Newsletter

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: [email protected]