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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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Well, its cold and dark outside, so it must be December. The waning days of 2017 are upon us. Since it is mid-month, it’s time to release our latest round of add-ons and give you the latest eMathInstruction news. But, first, let’s do the add-ons.

For Common Core Algebra I Add-Ons this month we bring you two new lessons, both in Unit #7 on polynomials. We added lessons 7 and 8 which look at both multiplying and factoring polynomials with the help of area models. The second lesson specifically looks at how to factor trinomials by essentially using the AC Method of factoring, but in an area array so that students can more easily see how this factoring relates to the previous lesson where we multiply binomials using area. We do plan to eventually make videos for these two lessons as we feel they are a great addition to the curriculum.

As usual, our Common Core Geometry additions this month are in the form of a Unit Review and a Unit Assessment. This month it is Unit #7 – Dilations and Similarity. We’ve put together a huge packet of problems on this unit that should give your students lot of extra practice on these tricky concepts and how they link together. It does look like, at this rate, that we should have the last Unit Review and Assessment for Geometry in the March add-ons.

Our Common Core Algebra II Add-Ons this month include one video and one new lesson. We made a video for a lesson we released last year in Unit #6 – Using Structure to Factor Expressions. This is a great lesson where students need to recognize the structure of complex algebraic patterns in order to efficiently factor them. We’ve updated the lesson to add the QR code for easier access to the video. Our new lesson comes from Unit 8 (Radicals and the Quadratic Formula). The lesson is on A Closer Look at Extraneous Roots and should be taught after Lesson 2 on Solving Square Root Equations. This lessons takes an in-depth look at why certain square root equation have extraneous roots introduced and why squaring an expression is an irreversible algebraic manipulation.

Finally, for our Algebra 2 and Trigonometry Add-Ons we have two nice new resources. First, we have a Unit #7 (Trigonometric Functions) mid-unit quiz, Form B. Last year we put out a Form A for this quiz and we decided it made sense to create a make-up for this quiz as well. We also created a large set of practice problems on graphing sine and cosine functions. This is a nice resource that gives students lots of extra practice in terms of graphing sine and cosine functions (without a horizontal shift) and also coming up with the equations based on the graphs.

That’s it for add-ons. Besides those, we’ve been hard at work on other projects. Just this week I went down to Long Island and visited Ward Melville High School in the Three Village School District. They had won our contest earlier this year with the dubious prize being my teaching at their school for the day. It was a blast!!! Hopefully we will eventually have video and pictures to share. I got to teach in a black box theater (definitely a first and maybe a last time for me). I mainly taught a Geometry lesson on using linear functions to model the following (mathematical) doodle:

It was a nice activity because it necessitated the use of both the slope-intercept (red portion) form of the line and the point-slope form of a line (blue portion). We also used the online graphing program, Desmos, to create the doodle. Of course, my tendency to take it way too far lead me to create a Desmos graph that would allow the user to vary the number of lines plotted so that graphs like this could be created:

Here’s that Desmos sheet if you want to play around with the doodle yourself:

Mathematical Doodle with Adjustable Line Count

And just because we are on the topic of Desmos, here are some other Desmos graphs I created that are particularly fun to play around with. Feel free to open these and play them as eye-candy for your students as they walk into the door.

Logarithmic Spiral with Rolling Ball

Complex Ferris Wheel

Lissouj Figures

Dynamic Polar Roses

Rotating Spiral

Well, I think that is longer than what anyone wanted to read. It’s time for me to get back to creating curriculum and stocking up the wood stove (did I mention it’s cold in upstate New York today?). Have a wonderful holiday season everyone. Enjoy the long break coming up!

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## Common Core Algebra I Scale Maintenance and Lake Wobegon Syndrome

So, the Common Core Algebra I exam was given this morning and the conversion curve was released as well. We had received advanced warning, about a week ago, that the state had done some “Scale Maintenance” on the Common Core Algebra I conversion scale. The memo was, as usual, filled with technical jargon out of NYSED, but one line caught everyone’s attention (all five of us that read it). The line went something like this:

With the curve maintenance, we expect more students to pass the Common Core Algebra I exam and more students to achieve higher grades.

Now, why would the curve need maintenance? Well, when the Common Core Algebra I exam was first given in June of 2014 a curious thing occurred. NYSED decided that they would make the percent needed to pass the test (scaled to a 65) pretty much the same as it had been on the Integrated Algebra exam. This raw percent was right around 35% of the test points earned. So, they made the test still relatively “easy” to pass.

But, the seismic change that happened to the conversion curve was the score a student needed to earn an 80. As any teacher or parent can tell you, the difference between a 79 and an 80 isn’t a point. It is a chasm. An 80 feels good. An 80 feels like you accomplished something. A 79 just seems not quite good enough. And a 72? Well, it’s better than failing, but, especially for an 8th grader taking the exam, it will likely feel like failing it.

So, what did it take to get an 80 on the old Integrated Algebra exam? Right around a 60%. So, a student who knew 60% of the credit on the older Algebra exam felt like they got a good grade. What did a student need on the June 2014 Common Core Algebra I exam, to get an 80? Well, they basically needed an 80. It was actually a 78%, but that’s splitting hairs. Here’s a graph that shows all of this:

35% raw = 65% scaled

80% raw = 80% scaled

Why is this a problem? Well, try to cram 45% of the raw score scale (35% to 80%) into only 15% of the scaled score scale. That leads to all sorts of problems. For instance, a kid who scored a 47 out of 86 points earned a scaled score of 72. But a kid who scored a 58 out of 86 earned a scaled score of a 75. That second student scored 11 points more (its actually 13% points more) than the first student, but only went up 3 percent points. What????

But, the real issue that many, many schools faced were kids who did quite well during the school year, many of them advanced 8th graders, and then scored a 78, a 75, or maybe even as low as a 72 on the Common Core Algebra I exam. But, how bad is that 72? Well, a 72% on the June 2014 CC Alg I exam corresponded to a raw percent of 58%. What would 58% raw earn you on the Integrated Algebra exam? Oh, right around an 80% scaled.

So, a little “scale maintenance” was certainly in order. And, boy did they do some!!! Let’s start with the most important number, the raw percent needed to pass. For comparison:

June 2014 Integrated Algebra exam: 35% raw score needed to pass

June 2014 Common Core Algebra I exam: 35% raw score needed to pass

June 2016 Common Core Algebra I exam: 31% raw score needed to pass

So, they lowered the percent needed to pass. To give you some perspective, it basically means a student could miss two additional multiple choice questions and still pass. But, now the question of the 80. Again, the comparison:

June 2014 Integrated Algebra exam: 59% needed to scale to an 80%

June 2014 Common Core Algebra I exam: 78% needed to scale to an 80%

June 2016 Common Core Algebra I exam: 59% needed to scale to an 80% (sound familiar?)

Here’s a graph to show all three conversion curves:

What’s fascinating is that they basically took the two June 2014 curves (red and blue) and spliced them together to create the one for this year (green). Notice how the green curve basically follows the red curve (the June 2014 CC Alg I exam) until the pass mark. Then, it follows the more traditional Integrated Algebra curve the rest of the way.

There are a lot of thoughts I have on all of this once I get past the math itself. My initial thought is how arbitrary it all seems. Right? It used to be that a kid who got an 82 got an 82. But, not anymore. My second thought is that there can now be absolutely no comparison that schools can make to previous year results. You could really only compare raw scores. The scaled scores are meaningless in year over year comparisons. Finally, given that all of this is arbitrary, it certainly seems like this is another case of what I’ve now decided to dub Lake Wobegon Syndrome.

We want our kids to learn more, we want them to be more challenged, but when they don’t live up to those challenges, then we change the metric that we use to make it seem like all kids are above average. But, the plain fact is, with an arbitrary scale such as this one, as a society we can manipulate the results in any way that we want to show any result that we want. So, what is the point exactly? And, how will we really know if our kids are actually learning more math if we can’t even agree on how to measure their progress?

Don’t misconstrue my commentary. I applaud that NYSED listened to voices of parents and teachers around the state and changed the conversion curve. Many students who worked very hard for the last two years felt like complete failures whereas if they had taken math a few years prior, they would have had scores in the 80’s. So, I think this is an excellent start. But, I still think it opens a lot of questions. I will also be extremely curious to see what the curves look like on Common Core Geometry and the brand new Common Core Algebra II.

For now, I need to go watch some soccer! Go U.S.A.

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