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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

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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

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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

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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

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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

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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

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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.

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Unit #1.Lesson #5.Equivalent Expressions

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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Unit #1.Lesson #4.The Distributive Property

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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Unit #1.Lesson #3.The Commutative and Associative Properties

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

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Unit #1.Lesson #2.Variables and Expressions

O.k. So, this lesson is mainly about expressions and not so much about variables. At this point, I make the assumption that students are comfortable representing unknown quantities with variables, so not a lot of discussion occurs with them. Leave your thoughts and comments, please!


CCAlgI.Unit #1.Lesson #2.Variables and Expressions