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Unit #2.Lesson #2.Seeing Structure to Solve Equations

This lesson is all about reversing order of operations to solve linear equations. I believe this is probably the most important equation solving technique in algebra and I want to establish it early on so that students understand that equation solving techniques, at their root, are all about undoing what has been done to the variable.

Here’s the lesson: CCAlgI.Unit #2.Lesson #2.Seeing Structure to Solve Equations

And the video (please pardon the rough nature of the video – it was one of the first that I did):

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Unit #2.Lesson #1.Equations and Their Solutions

In this lesson we make sure that students understand the basic concept of what a solution to an equation is in terms of truth values. This is emphasized up front, as opposed to bringing in checks at the end. I like this approach because I want students to understand the forest of equations before we start wading through the trees.

The Lesson: CCAlgI.Unit #2.Lesson #1.Equations and Their Solutions

And here is the video:

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Shipping Information

Hello Customers of eMathInstruction,

We continue to send out answer key CDs each day as soon as we get orders for them or that include them. The workbooks, those have more of a lag time. My great printers at NetPublications in Poughkeepsie, New York, are working tirelessly to get these things printed, packaged, and out the door.

The latest timeline is as follows:

1. If your district got me the order before August 15th, then the books are shipping today and should get to you by tomorrow (August 26th) or Thursday (August 27th).

2. If your district got me an order for workbooks after the 15th, but before today, those start to go into production soon. They will ship on or before 9/9/2014, but that still leaves you at least the first week without the books. Sorry about that! Consider copying the first two weeks from this site.

Email me at if you have questions about the status of your order. I’ll always give you the best information that I have.



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The Start of School is at Hand

Hello All,

Well, we have our first couple of days of professional development next week at Arlington (the 97th largest high school in America). This week for me is full of all sorts of fun stuff. I get to catalogue all of the supplies that came in over the summer, make sure all calculators have batteries that work, create list upon list to help teachers know who is teaching the same courses, who has prep which periods, etcetera. This on top of whatever right before the year begins surprises crop up. For a department of 25 math teachers teaching 23 math courses, this constitutes a lot. And I’m still on “vacation.”

But, I’ve also been trying to organize this site into as convenient of a discussion forum as possible. I want to thank Benjamin Kirk from Ithaca High School for giving me many suggestions as far as organizing the site.

Right now I am putting up a post for each lesson. I am categorizing these posts by unit, so it should be super easy to find a particular lesson that you might want to comment on/give suggestions on, or ask a question about. Right now you have to leave a username and an email in order to leave a comment. For those of you who know me, you know that any emails submitted would never end up being distributed to third parties.

For each lesson, I am leaving a very short blurb about my thinking and feelings on the lesson. I could probably write an entire page about each lesson, but don’t have the time, as I’m sure many of you can appreciate.

Click here to link to the Unit #1 Discussion Page

For now, take care all and enjoy your last days of summer. Remember how beautiful fall can be and how much fun it will be to meet all of your new students.

Best to all!


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Unit #1.Lesson #11.Algebraic Puzzles

So, this was another lesson that I always dreamed about doing. I love the idea of describing a sequence of manipulations that always work out to some cool pattern that you don’t see coming. Then, to me, it is fun to see why this pattern always holds by working through the manipulations on a generic variable. I loved doing this (with the help of some rational algebra) to my friends in college. I would have them pick an integer and then walk them through some set of manipulations that would always result in the number 7. That one will have to wait until Common Core Algebra II.

The Lesson: CCAlgI.Unit #1.Lesson #11.Algebraic Puzzles

Click here to watch the video.

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Unit #1.Lesson #10.Translating English to Algebra

Well, we all know we need a lesson like this. I tried to give plenty of examples for students to practice on the key phrases that we know are important in algebraic word problems. All of the typical ones are there. The question still becomes is this enough practice? Maybe not. Maybe the practice really lies in when they begin to set up these problems later on to solve modeling problems.

The Lesson: CCAlgI.Unit #1.Lesson #10.Translating English to Algebra

Click here to watch the video.


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Unit #1.Lesson #9.More Structure Work

So, in this lesson we set the stage for factoring by grouping. I want students in this lesson to “reverse” the distributive property where the common factor is a binomial. This will be challenging for some, but will pay dividends later in the course when they are better able to see structure in a variety of different ways. Still, the difficulty of this lesson early on may be a factor.

The Lesson: CCAlgI.Unit #1.Lesson #9.More Structure Work

Click here to watch the video.


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Unit #1.Lesson #8.More Complex Equivalency

So, I thought that since we now had exponents, the ability to multiply monomials, and the distributive property, there was no reason not to introduce multiplying binomials. I do stick with the traditional double distribution method, with some discussion later in the course on FOILing and other ways to think about this process. Here, I wanted to stress again the importance of equivalency between two expressions. I still wonder if it is too much, too soon. Let’s hear from all of you.

The Lesson: CCAlgI.Unit #1.Lesson #8.More Complex Equivalency

Click here to watch the video.

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Unit #1.Lesson #7.Exponents as Repeated Multiplication

I wanted to be able to work with functions involving exponents early in the course. So, I thought a day of review and practice with fundamental exponent ideas was warranted in the first unit. It’s always debatable to me where this should first be introduced, but I think students coming out of 8th grade Common Core mathematics should be able to handle this lesson, which culminates with students multiplying monomials.

The Lesson: CCAlgI.Unit #1.Lesson #7.Exponents as Repeated Multiplication

Click here to watch the video.


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Unit #1.Lesson #6.Seeing Structure in Expressions

This was a lesson that I dreamed about writing before I ever started this crazy venture. I wanted students to understand how the three primary properties of numbers could be used to manipulate algebraic expressions enough to solve riddles. So, I build a variety of exercises that force students to manipulate an expression to find its value based on the value of a related expression. I love this lesson and really want to encourage teachers to let me know how it went.

The Lesson: CCAlgI.Unit #1.Lesson #6.Seeing Structure in Expressions

Click here to watch the video.

On a funny side note, this was one of the first videos I had ever made. So, I had a terrible background, no theme music, and couldn’t see very well because I wasn’t wearing my glasses.