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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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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.

Kirk

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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™ 6N-Gen Math™ 7N-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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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.