Category: Math Education Discussion

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Next Generation Algebra I vs CCSS Algebra I

In September of 2022, schools around New York State will transition from the Common Core State Standards version of Algebra I to the New York State Next Generation Mathematics Learning Standards version of Algebra I. Although this transition could certainly be viewed skeptically as simply a rebranding of the Common Core standards, there are important changes that have been made to the course. At eMATHinstruction, we will be publishing N-Gen Math Algebra I to align to the Next Generation standards, but have also included material to make the text more broadly align to the CCSS. In this post, I’d like to discuss some of the changes to the CCSS that will occur with the Next Generation standards and how we will be treating them in our new text. As longtime readers of eMATHinstruction posts also know, I will add my own color commentary here and there.

The New York State Education Department (of NYSED) has a fantastic website devoted to the Next Generation Learning Standards for Mathematics. There are lots of helpful links on timelines, testing, and curriculum. Here are some vital links from this page:

New York State Next Generation Mathematics Learning Standards (nysed.gov)

Mathematics Learning Standards | New York State Education Department (nysed.gov)

New York State Next Generation Mathematics Learning Standards Algebra I Snapshot (nysed.gov)

New York State Next Generation Mathematics Learning Standards Algebra I Crosswalk (nysed.gov)

The first link takes you to the official Next Generation Math Standards in all of their glory. The second link is to the launching page for all of the math standards, a good place to start if you want to find information for all grade levels. The last two links are what we will concentrate on in this post. The Snapshot gives a very quick summary of the new standards, standards that have been removed, and standards that have their content clarified.

We can see immediately that one new addition to Next Generation Algebra I is the topic of linear-quadratic systems (AI-A.REI.7a). This is, of course, a topic that many Algebra I teachers have taught for years to their students. I love that the topic has been placed in Algebra I as it reinforces many of the big ideas and skills students have seen while still keeping the math relatively simple. We have included a lesson on this in our new N-Gen Math Algebra I text.

Besides that topic, the only other new content added in Next Generation Algebra I is the skill of rationalizing a denominator. I was sincerely hoping when New York State redid its standards it might throw out the idiotic rational/irrational number hooey that is contained in Algebra I, but I was sorely disappointed. Not only did they not get rid of it, they upped the ante by including rationalizing the denominator and even more rules about how rational and irrational numbers combine using operations to form either rational or irrational numbers. This is where the Crosswalk link above is helpful in really understanding how the CCSS math standards compare to the NGLS:

So, in addition to knowing the ever-so-useful fact that the sum of a rational and an irrational number is always irrational, they now must know that the sum and product of two irrational numbers could be either rational or irrational. I just cannot fathom in what universe it is important for a student who is taking Algebra I (typically kids who are as young as 13 and 14 years old) to know that when we have the following sum:

its result is a number whose decimal representation does not terminate nor repeat. I honestly think our entire treatment of irrational versus rational numbers makes no sense whatsoever. Irrational numbers are one of the amazing mysteries of mathematics. Yet, what we ask kids to know about them gets at none of the magic behind these numbers. More on that in a future post.

The Snapshot link above also gives us topics or standards that have been removed from Algebra I.

Some of these have been removed due to the ambiguous nature of the standard (yes, I’m talking about you N-Q.2). Others have been removed because there was redundancy in the standards (A-SSE.3a and S-ID.6c are good examples). And some have been removed because they are developmentally inappropriate for this level. A great example of this is the removal of residuals as a topic in Algebra I. I’ll be honest, after having taken three college courses in statistics, I had never even heard of residuals before the Common Core Standards, so I’m not crying to see them go. One interesting note in these subtractions is the fact that completing the square will not be used to transform a quadratic function into its vertex form. It will only be used as an algebraic procedure to solve quadratic equations. I’m a bit ambivalent to this particular change. I love the fact that they are keeping completing the square as a technique for solving quadratic equations, but am a bit sad to see it go in terms of the vertex form of a quadratic function. Be careful as some subtractions are not contained in this section of the Snapshot. A good example of this is the removal of the cube root function (a topic that has been moved to Algebra II).

Besides these additions and subtractions, the rest of the Snapshot and Crosswalk links above give us more specificity about particular standards. As a math teacher and curriculum creator, I very much appreciate this. One of the oddities of the Common Core Standards at the high school level was always the fact that they were not broken into courses the way the standards were at the K-8 level. Although I can appreciate the fact that the writers on the CCSS wanted to give states flexibility in terms of how the standards were arranged in courses at the high school level, it meant that the depth to which certain standards should be taught was not as clear as it should be. This is not a minor issue! Seemingly small changes in how generally a topic should be taught can transform it from being a one lesson topic to a one week topic.

A great example of exactly this is the topic of factoring. In the CCSS the topic is fairly vague, urging students to “use the structure of an expression to identify ways to rewrite it.” I do love the idea of students recognizing structure in expressions, but a standard that is this vague leaves a lot of guessing to be done by the teacher in terms of how deeply to pursue it. The Next Generation Standards clean this issue up nicely:

Notice now that specific types of factoring are required with other noted types being excluded, such as factoring by grouping and the sum and difference of perfect cubes. Additionally, we now see that students will only need to factor trinomials whose leading coefficient is equal to 1. Of course, this single additional specification takes a topic that might warrant four class days and cuts it down to one or two. In our own Next Generation aligned Algebra I text, we concentrate on factoring trinomials with lead coefficients equal to one, but also include one lesson on more challenging trinomials. Another nice example of where the Next Generation Standards become more specific is when using completing the square to solve a quadratic equation. In this case, they now specify that the leading coefficient of the equation will be equal to one and the linear coefficient will be an even number.

I love the fact that New York considered these two factors when specifying what kids will need to be able to do with completing the square, a procedure that is certainly within their ability to grasp. Students at the Algebra I level are being flooded with a level of abstraction and technique that is far above anything they experienced in grades K through 8. As every math teacher knows, lots of students enter 9th grade with only a tenuous grip on fractions. When we have them learn a process such as completing the square, we do not want their deficiencies with a topic like fractions to hinder their acquisition of an important new skill.

Another important change to the standards involves sequences. In the Next Generation version of the standards, sequence rules will only be given in explicit form, i.e. no recursion, and will only be given using subscript notation, not function notation.

This again seems like a minor change, but now teachers can feel free to bypass the enormous amount of confusion that occurs from the recursive definition of a sequence. My feelings are a little more mixed on getting rid of function notation for sequences, as I thought this was a good way to connect them to the overall concept of a function. I can live with that change, and our new N-Gen Math Algebra I will only include subscript notation when working with sequences.

One area with both subtraction and more specificity is the topic of transformations of functions.

Notice that the horizontal stretch/compression of a function has been removed. I very much support that move. I think the horizontal stretch and compression is far too difficult to understand at the Algebra I level, even if its basic mechanics can be mastered. I also like how very specific the standard now is in terms of what students should be able to do regarding the value of the transformation constant k.

The topic of statistics, even though amazingly out of place in this course, remains mostly unchanged. We have already mentioned that the topic of residuals is being removed. As well, the only type of regression that is studied is linear, with both exponential and quadratic pushed off until Algebra II. Finally, and I think this is an interesting one, a change in terms of what types of data sets kids will work with:

Notice that the Next Generation standards are very clear that data sets, when given, will be sample data sets only. There will be no population data sets. As such, only the sample standard deviation will ever be used. I love this for multiple reasons. One, it means we don’t have to constantly debate whether we should use the population or sample standard deviation. More importantly, though, it allows us to focus on what statistics is most often used for, making statements about populations based on samples. We are very happy with our new statistics unit in N-Gen Math Algebra I. We revolve this unit around using tools from statistics to answer statistical questions, including how we can compare samples statistics to make inferences about populations.

One final note I’d like to mention is on the topic of exponent properties. Algebra courses, both Algebra I and Algebra II, often concentrate on exponent properties in order simplify expressions that might look something like this:

The Common Core Standards, and to a greater extent the Next Generation Standards, are more interested in using these properties to transform exponential expressions where the base is a constant into equivalent exponential expressions.

Notice that now students will have to work with exponential expressions whose exponents could be linear expressions (with integer coefficients). In other words, they might now have to solve problems such as:

This type of manipulation is included now because in Algebra II we want a student to be able to take a function like:

And rewrite it like this:

This type of manipulation allows us to transform an exponential function that is written in terms of doubling time (8 years) and to one in terms of annual percent increase (9.05%). This is an important skill and an important shift from how we have traditionally thought of using exponent properties. That’s not to say that a problem like the following won’t show up on a state assessment:

The New York State Next Generation Mathematics Learning Standards are based off of the Common Core State Standard. All public schools in New York will be aligning their Algebra I courses to this set of standards in the fall of 2022. Schools outside of New York who use the CCSS as the basis of their high school courses can have confidence that eMATHinstruction’s N-Gen Math Algebra I text will closely align to the CCSS, with some important changes as discussed above. Although the Next Generation Algebra I standards are certainly different from the CCSS, it is mostly in specificity and not content that they differ.

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eMath November 2020 Newsletter

November has hit and so has the chilly weather. Schools around our own area have been fluctuating between hybrid education and going completely remote as needed due to Covid cases. These are challenging times for students, parents, and educators. Here at eMATHinstruction, we continue to try to help in as many ways as we can, including creating and posting more resources.

Our new middle school resources this month include the Unit Assessments for Unit 6 in each course and the Unit 6 SMART Notebook files for each course. As I’ve mentioned before, we are going to be publishing one or two unit’s worth of assessments per month until all units have been covered. We plan to publish both the Unit 7 and Unit 8 assessments in our December add-ons. We’ve gotten some questions from teachers about the SMART Notebook files and being able to open them. These files can only be opened by SMART Notebook, the primary software used for SMART Boards. The software is very nice and includes some math tools, like rulers, compasses, and protractors, which are very nice for geometry related topics. A free trial version of the software can be downloaded at the following link

SMART Learning Suite

For this month in Common Core Algebra I, we bring you a nice extended problem on linear function modeling for Unit 4 (Linear Functions and Arithmetic Sequences). In this activity, students model populations of two towns using linear functions. They then graph their models and algebraically determine the year when one population will surpass the other. This is a nice two page lesson/activity that could be given as an enrichment exercise that reinforces many of the important ideas behind using linear functions to model constant rate applications.

In Common Core Geometry this month, its all about Unit 4 (Constructions) assessments. First, we bring you a mid-unit quiz, both a Form A and Form B version, that can be given after Lesson #3. We then bring you the Form D Unit Assessment.

Our new Common Core Algebra II additions for this month include multiple mid-unit quizzes and some additional practice problems. First, for Unit 6 (Quadratic Functions and Their Algebra), we have a problem set on Parabola Practice. In this problem set, students find properties of parabolas, including intercepts and turning points, algebraically. They then choose an appropriate graphing window on their calculator to visualize the parabola. Both the standard form and vertex form of a parabola are used. We then have the Unit 6 Mid-Unit Quiz, both a Form A and a Form B version. Finally, we bring you the Unit 7 (Transformations of Functions) Mid-Unit Quiz, Form A and Form B.

In our final additions of the month, we have some additional assessments for Algebra 2 with Trigonometry. First, we have the Unit 5 (Complex Numbers) Mid-Unit Quiz, Forms A and B. We then bring you the Unit 6 (Polynomials) Form D Unit Assessment.

In exciting news, we are finally beginning the rewrite of Common Core Algebra I for the new Next Generation Math Standards in New York State. For those not in New York, these standards are based on the Common Core Standards, with some slight modifications. These modifications are mostly in terms of the extent to which topics should be taught. For example, completing the square is still required in Algebra I, but only when the leading coefficient is one and the linear coefficient is even. We are tentatively titling the new book, N-Gen Math Algebra I. My hope is that we will have an evaluation version ready for next year, although the standards do not officially go into effect until the autumn of 2022 (wow!).

That’s about it for now. I’m hoping that everyone reading this email stays safe, healthy, and happy, especially over the coming Thanksgiving holiday.

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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 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.

Kirk

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eMath February 2020 Newsletter

Happy February my math teacher friends. Hopefully you all had a long Presidents’ Day weekend. I know many in my part of the state have this entire week off from classes. We’ve been working diligently at eMATHinstruction on our new middle school courses and on the add-ons for the high school courses. We’ll talk more about middle school in a bit. For now, let’s get into those add-ons.

In our Common Core Algebra I Add-Ons this month we have three new resources to share. To begin, we bring you the Form D assessment for Unit 7 (Polynomials). We also have created the Unit 8 (Quadratic Functions) Exit Tickets. Finally, we bring you a new lesson in Unit 8 on the factored form of a polynomial. We plan to eventually add this lesson to the Next Generation version of Algebra I, which we will begin to finalize next year.

For Common Core Geometry Add-Ons this month we bring you two resources for Unit 7 and one for Unit 8. In Unit 7 we created an activity where students explore the centroid of a triangle. Strangely enough, the topic of the centroid is not addressed anywhere in the Common Core Standards (easy enough to search the term centroid). We discuss the centroid in Lesson 10 of this unit when we look at the medians of a triangle. But, in this activity students find the centroid, cut out the triangles, and see how the centroid becomes its balancing point (center of mass). We then bring you the Unit 7 (Similarity) Form C Assessment. Finally, we have the Unit 8 (Right Triangle Trigonometry) Exit Tickets.

In Common Core Algebra II Add-Ons this month we first bring you a quiz for Unit 7 (Transformations of Functions). We are trying to round out unit quizzes in all of our courses this year (no matter how short the unit). We also bring you the Unit 7 Form D assessment. Finally we also offer the Unit 8 (Radicals and the Quadratic Formula) Exit Tickets.

Our Algebra 2 with Trigonometry Add-Ons for the month begin with the Unit 7 (Trigonometric Functions) Form C Assessment. We also bring you the Unit 8 (Trigonometric Algebra) Exit Tickets. Finally, we also have a Unit 8 Quiz for after students have completed Lesson #3 of the unit.

Besides working on the add-ons, we’ve been very busy with our three new middle school courses, which are aligned to the Next Generation Mathematics Learning Standards. We’ve been getting fantastic feedback from teachers about the courses and we’ve integrated some of that feedback into the lessons for each course. We are now very close to having both the Math 6 and Math 7 books done in their first edition versions. Unlike our high school courses, we will only be offering our middle school workbooks in a single binding that is both spiral bound and three hole punched. The sheets also have a fine perforation so that students can rip pages out and then place them in a 3-ring binder. Here are a couple of pictures of our N-Gen Math™ 6 book:

If you look very hard, you can even see the fine perforation in that second picture. We’ve designed the books to be as light as possible with lower weight paper. We are always trying to balance that weight issue with the quality of the paper.

Work continues on the supplemental materials for these courses, like the videos, unit reviews, answer keys, and assessments. We plan to have the Teacher Plus Answer Keys and workbooks available for use by July 1, 2020. Until then, we can certainly provide quotes for school districts interested in these for next year.

Well, that’s about it for now. Time to get back to work. Have a great rest of February. May it end soon and may spring be upon us again!

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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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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 February 2019 Newsletter

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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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