Hey Friends,
I need a favor. I am teaching a class next year that falls in our sequence between Geometry and Algebra 2. It is to boost Algebra skills and preview a fair amount of Algebra 2.
So if you could make sure that your Algebra 2 students knew 3 things (or really any number I don’t care) coming in what would they be?
Thanks so much for your five minutes,
Soph.
a brand new line. 
Solid solving linear equation skills and understanding the process of solving
Factoring
Graphing linear equations and a solid understanding of the parts of a graph (intercepts, slope, transformations)
If systems of equations was taught – what does the solution mean? How can you find the solution?
I think those are the biggies for me.
–Lisa
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I was always frank with my Algebra 1 students. I told them harshly that if you don’t know the following then you deserve to fail.
1) Solving equations
2) Graphing any type of line given an independent and dependent variable. I forced my students to always create an x/y table.
3)Factoring (quadratic formula)
If you have acess to a graphing calculator, all students should know how to use it. I fully believe that courses that use calculators, should foster the use. If you hate calculators then don’t allow any of them, but if you do allow them, show students (can be after the fact) how to make their life easier.
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Oh boy, there is so much. Where do I start…
1) Knowing the difference between solving and evaluating
2) Understand what solving means (there can be more or less than 1 answer)
3) Factoring (Not just the procedure but an understanding of what a factor is as well)
4) Fractions (This one is really not just an algebra topic, but an earlier topic that should be reinforced strongly)
I’ll stop now while my list is still reasonable.
Good Luck!
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The ability to solve any equation: two step, variables on both sides, equations with fractions
Number sense: is my answer reasonable? Does it seem to fit? Where is my answer on the number line? Etc
Graphing a line in all forms: slope-intercept, point-slope, and general
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I agree with the earlier posts but,
1) Factoring…factoring…factoring!!! I believe it is the most important topic in A2 that is not covered at all in most Geometry courses.
2) did I mention Factoring… I spend all year stressing the importance of factoring and the need to be able to factor in many situations. I never feel like they get it!!!!
3) understanding the answer to the problem. For example a root/zero/factor all give us the same answer.
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FACTORING, especially factoring the GCF out first
Quadratic Formula
Solving and graphing equations and inequalities (including absolute value)
Solving systems of equations and inequalities
Functions: domain, range, function composition, evaluating functions, graphing parent functions, transformations
Flowing between multiple representations (graph, equation, word problem, table, etc)
[Average] Rate of change
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I have to echo @misscalcul8 — when I’ve taught Algebra 2, I’ve felt really ambushed by how weak most incoming Alg2 students’ factoring skills are and how urgently they need to strengthen and deepen their factoring skills and understanding.
Specifically, they need lots practice (and “wallowing” time) in (a) recognizing frequently-seen factoring patterns (difference of squares, etc), (b) honing their tinkering skills (including recognizing GCFs in polynomials), and (c) factoring the dreaded nonmonic quadratic trinomials.
Since I want my Alg1 students to be well-equipped for Alg2, I have determined that factoring is one serious “boot camp” area, and I’d agree again with @misscalcul8 that Function Basics is another. When I teach polynomials and rational functions, I have them do a lot of basic function analysis (domain, range, x- and y-intercepts, parent functions, and graph sketching, along with whatever else seems germane). As you know, most of the existing CA Alg1 curriculum only requires mechanical manipulation of polynomial and rational *expressions*, which serves students poorly. Giving them exposure and practice with polynomials and rational functions AS functions helps them to internalize the basics of the study of functions which is, after all, a big part of what the study of Algebra is about!!!
This coming year, I’m definitely going to steal/use Megan Golding’s Function Family Albums activity. I discovered it too late this year, but I think that it can give Alg1/Alg2 students (who are, after all adolescents) a richer understanding of how functions are related to one another through a highly relatable tangible metaphor. It’s one of those rare metaphorizing ideas that truly embodies the concept it is supporting in a very creative way!
Zap me if you want pointers to any specifics or any of my materials I haven’t yet organized and posted.
– Elizabeth (aka @cheesemonkeysf on Twitter)
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(1) Adding, subtracting, multiplying, and dividing fractions and rational expressions.
(2) What does the graph of a function really represent?
Sounds like a great class! Best wishes!!
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Factoring…
Radicals….
Solving equations…
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1) Factoring (from binomials to polynomials with n terms)
2) Simplifying vs Solving (how to apply order of operations in either)
3) Functions (evaluating and graphing)
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order of operations (they get tripped up when there’s a substitution – like they think 2*x^4 when x = 3 is 6^4)
factoring (they tend to be pretty good on x^2 + bx + c but lousy with everything else)
operations on fractions (with algebraic expressions, but i’d take just with numerical expressions)
finer points of calculator use i.e. (-3)^2 vs -3^2
what other people already said about graphing
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1 – FACTORING!!!!
2 – solving linear and quadratic equations (also encompassing order of operations)
3 – graphing equations with AND without a calculator.
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Everything everybody else said. But my favorite three are
(1) Graphing: with/without a calculator, solving equations graphically, interpreting graphs with data
(2) Exponents stuff.
(3) And here’s a slightly unconventional answer: it would be awesome if students had some sophistication about irrational numbers. Teaching complex numbers is hard, and it would be easier if students saw irrationals as extensions of the number line and as genuinely weird numbers.
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I teach a class like this. I was told when I started that all I had to do was take a more watered down Algebra 2 book (I forget the edition, I can find it if you’re interested), take it slow, and make sure that they got all the basics down. It was okay that they couldn’t solve the toughest problems, as long as they understand the basics well, whether it was graphing parabolas, factoring polynomials, or solving linear equations. The fact is they will see these topics again in Algebra 2, so I’m allowed to focus on basics and make sure they understand before I move on. Also, if this is an “in between” class (as in, not all students have to take it, just ones that struggle in math) like mine, don’t stress about having low scores. I had a test where half the class flat out failed, so we had to take a step back and do some more before moving on.
Just my two cents. I can share more if interested.
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I advocated for and was allowed to teach a transition/bridge course between Algebra 1 and Geometry/Algebra 2. Here’s the very ambitious outline (I’ve modified it since last year to include even more Geometry and previews of Algebra 2 despite the fact that I didn’t even get to everything that I planned last year):
http://www.classconnect.com/app/filebox/5000a536c58216605e000003/
Feel free to use this as a starting point and cut as you see fit (probably a lot of the geometry as the class you are designing will be sequenced AFTER Geometry); if you do look/use it, let me know if you have any questions or feedback.
As for directly answering your question, I’m going to cheat and try to condense the major themes of algebra down to a few big ideas:
1. Evaluating Expressions (order of operations, variable expressions, defined operations, function notation)
2. Manipulating Variables (combine like terms, multiplying polynomials, simplifying exponents/radicals, factoring, simplifying easy rational expressions)
3. Graphing Relationships (tables of values, linear functions, parallel/perpendicular, easy non-linear functions including quadratics and exponential growth/decay)
4. Solving Equations (Linear, Proportions, Inequalities, Systems, squares/roots, by factoring)
5. Analyzing Geometry (Pythagorean Theorem -> Distance Formula -> Equation of a Circle, Trigonometric Ratios, Vectors) [I’m assuming we’re talking Common Core Algebra 2 here which includes significant amounts of trigonometry]
… I’d be pretty happy with a year where students master those five big ideas, can see the connections between them, and not be intimidated about trying to apply those skills to unfamiliar concepts – in fact, not sure if I can genuinely say I’ve had that year so change happy to ecstatic … what did I miss?
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Angela and Aaron,
What textbook are you using for your class? I teach a class similar to these and i’m looking for a textbook.
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sorry, no book – just the outline and I scavenge together things using books/resources I’ve used in other classes
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Solving multi-step equations, graphing/writing linear functions, factoring quadratics (when a = 1)
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We discuss this at length in my department and the Top 3 always come down to : solving equations, graphing linear equations, and factoring. With all the extra stuff that goes into our Algebra I course (domain and range, really? Is that necessary?) we often don’t hit factoring til late in the year when the kids have checked out and there are so many scheduling breaks for end-of-year activities that it doesn’t seem to stick. I’m thinking of rearranging the order of things this year.
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