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
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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
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
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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
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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.
So much of what we teach in algebra consists of how to rearrange one expression into another that is equivalent. But, I think I’ve often lost site of that forest for the trees that clutter all of the techniques and rules. So, I wanted to establish early on in this course the idea of two expressions being equivalent due to the properties of real numbers that we had just worked with. I try to keep the examples relatively simple and the number crunching appropriate.
The Lesson: CCAlgI.Unit #1.Lesson #5.Equivalent Expressions
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The distributive property is one of my favorites to think about as a math teacher. I think about how little I understood about the standard multiplication algorithm when I was in grade school. I try to introduce the property with real number examples, before jumping into the more algebraic approach. I also emphasize the distribution of division at the end of the lesson. I think most Algebra teachers would sympathize with my frustration that even high level students will fail to distribute with division, even when they have it down pat with multiplication.
The Lesson: CCAlgI.Unit #1.Lesson #4.The Distributive Property
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It is so unfortunate that the emphasis on the commutative and associative properties so often boils down to which property is being illustrated, versus what is being illustrated. That’s why I wanted to introduce this topic by having students add a string of integers that consisted of pairs that summed to 10. In that case, they naturally use both properties to rearrange the sum to make it easier.
The lesson: CCAlgI.Unit #1.Lesson #3.The Commutative and Associative Properties
So, the answer keys arrived yesterday. We printed an original run of 60 CDs and will run out of these quickly. Each CD contains the entire text, in both pdf and Word format, and the entire answer key, in both pdf and Word format. They can be copied to any district owned computer and any computer owned by a teacher in the district. Expect to see them arriving this coming week. Thank you everyone who ordered. Remember, books may not be there until the last week of August and if your business office is slow getting us the PO, you may not get them until the first week of school. Email me if you want to know if yours were ordered in the “first wave.”
Update: We shipped all answer key orders this morning!!! The Rhinebeck post office was a bit overwhelmed, but Mark at the desk was a trooper and processed all 35 orders. The expected delivery date for all locations in New York is Monday, August 18th. So, look for them soon. They will come in a small bubble wrap package. There will be two identical answer key discs. Email me if you have any questions about order status.
emathinstruction@gmail.com
Hey All,
Well, we placed the first round of PO orders that we’ve received to our printers yesterday. They are quickly creating the CD’s that have the answer key and text on them (both in pdf and in Word). So, those will probably be shipped out in the middle of next week. The workbooks will be heading out by the end of next week and will arrive in the last week of August. Sorry they couldn’t be there sooner.
Warning: Any PO for workbooks that I receive from now until the end of August will most likely not get there until after Labor Day weekend. Be prepared to photocopy the first few lessons from this website or our original emathinstruction site. Check with your business offices or send me an email to check. Orders of only the answer key will still get to you before Labor Day even if they arrive in the coming weeks.
On the browser issue. I continue to find that Chrome does not work well in terms of either this site or the original site. I just downloaded the most recent version of Firefox and it works great for both seeing this site, downloading files from it, and downloading from the original site. Internet Explorer has worked well for both all along.
Take care and continue to enjoy summer. Kirk
Well, the school year starts for many of us right after Labor Day weekend, less than three weeks away. For some, it starts even sooner. In anticipation of that, I’m making freely available the answer key compilation for Unit #1. You can download it by clicking on:
I hope this helps planning for the upcoming year easier. It’s never too late to start commenting. I won’t start making edits until it makes sense to make edits, i.e. as the year progresses and we see where this experiment leads us.
For now, download some Unit #1, get some photocopying done, and don’t forget to hit the Dutchess County Fair with your kids! It’s awesome.
