Thursday, August 05, 2010

Math 1 Concept List

I need help again.  I have done my Math 1 concept list.  Some background on Math 1:
  • These are students who are lower level freshmen and not totally ready for Algebra.
  • This is a new textbook for this course (McGraw Hill's Algebra Concepts and Applications).  It was chosen because we use the Geometry Concepts and Apps by the same publisher for Math 2 and we wanted to be working on Algebra 1 skills with these students.
  • Ohio standards for 9th grade are basically all Algebra-related.  Actually some of the 8th grade standards are also Algebra related.
  • This will be the first group of students who are required by the State of Ohio to have Algebra 2 or its equivalent to graduate.
  • These students will take Algebra 1 at some point (either next or after taking Math 2).
I know these students will not get all the way through my concept list.  I can't even reasonably say how far I think they will get.  However, I have gone through the book and made my list and done some beginning organization.  I don't like how they have inequalities at the back after quadratics - that made no sense to me.  Also, there were other concepts that were later in the book than I would have put them, so I have done some reorganizing.

I have not taught Algebra 1 in some time, let alone the basic level of it, so I need some help. Some issues I am looking for feedback on include:
  • Is it really worth teaching them the operations with rational numbers (fractions, mixed numbers, decimals)? When they get to any standardized test, they will have calculators available to them that will deal with the fractions, not to mention they've already seen (but probably struggled with it) the concepts multiple times.
  • They integrated in probability and data analysis stuff in the 1st 5 chapters - leave it as is or pull the sections out and lump them together?
  • They have adding/subtracting for rational numbers and equations in one chapter, multiplying/dividing rational numbers, equations, and the rest of solving equations in the next.  Leave it as is or put the rational number stuff together and the equation stuff together?  ***I really need input from those of you who have taught Alg 1 skills before - I have an Alg 2 perspective here.***
  • As we get to the later stuff (anything after graphing) - what becomes most important to teach?  Do I do systems of equations? Radicals? Exponents/factoring?  Once again, these kids will head to Algebra 1 and 2 and will see this again - I want to expose them to what material I can and give them a good solid foundation so that when they see it again, they can have greater success than had they just jumped into Algebra 1.
Please address anything in the comments.  If you want to download the file from and make your own tweaks, please feel free to do so - but rename the file when you save it and let me know how I can get it from you.  Thanks!

Math 1 Concept List
*** I have updated this on 8/8 after the comments.  I'm still looking for suggestions.  Thanks!


Andy said...

"Is it really worth teaching them the operations with rational numbers (fractions, mixed numbers, decimals)? When they get to any standardized test, they will have calculators available to them that will deal with the fractions."

I struggled with this when I taught Alg I but found that teaching operations on numbers paid off when we got to solving multi-step equations. Reinforced the order of operations early on and didn't make solving as daunting.

Kate said...

I'd say definitely do operations w/ decimals, fractions, mixed numbers. Chances of them getting it later is slim.

I'd pull the prob/data analysis stuff out and do in a lump. They'll lose too much from topic to topic.

Not sure about question #3 without seeing the book.

I think exponent rules and radicals are probably more important than systems of equations. Factoring would be great if you could get to it.

How is this different from what your school does for Algebra 1? Your skills list looks much like mine does for Algebra 1.

Lisa said...

Thanks for the feedback on the rational numbers skills Andy and Kate.

It should look similar to Algebra 1 - but I will be going at a slower pace with them. I don't honestly expect to get more than half to two-thirds of the list accomplished.

Dvora said...

I have taught lots of Algebra 1 on grade level and for struggling students.

I would definitely not do the prob and stats filtered in as it is just more confusing for them.

I would spend a bit of time with fractions and such, but don't make it punishing or suffering. You could also focus on teaching them how the calculator can be a tool to help with these types of problems. This serves them later on for SAT and such as well.

I have always grouped the rational number stuff together and then the equation stuff, but I see the validity of either method.

As for later stuff. I think systems of equations is a nice unit and you can show them graphing and calculator tools as well. This is also a good topic for a project. I have one I am happy to share if you like.

Exponents and factoring are also area that take some students longer to grasp so they might be good to see now and then again later in another course.

Lisa said...

Dvora - thanks for your feedback. I appreciate it so much. Just one question - did I understand your remarks on the rational numbers correctly that you focus on showing them how to use the calculator to do the operations rather than try to (re)teach the process? Thanks.

Mythagon said...

"Is it really worth teaching them the operations with rational numbers (fractions, mixed numbers, decimals)?"
I've found more success mixing this in with some basic equation solving. They've been learning number operations for a long time and though the fraction/mixed number aspect may be newer, I find they tend to think they know it (when they don't) so they tune out the class as the 'same-ol, same-ol.

I question dividing equations in a low-level algebra class. We don't do that in Washington till Alg 2 as it's like fractions, only scarier for them. Add/Sub/Mult are all good things for them (especially multiplying with the box method for those geometry-thinking kids!).

Systems are neat, but possibly stick with the easier ones? Things that are nice to graph, substitute, or eliminate just so they learn the process. Exponents and Factoring exposure and the basic rules are hugely important at my school as it helps a lot in later years. I like to mix those up with order of operations problems (go-go-gadget parentheses!).

Lastly, your skill list seems huge to me (we have around 60 for Algebra 1), but you have some things that are more pre-algebra and a lot more prob/stat, so I think it balances out. On #55, how do you plan to assess 'explore'? Are these skills lined up in the order they are presented in your book?

Thanks for sharing your list and good luck this year!

Lisa said...

Mythagon - I took the skills as they were in the book. I was looking for a place to start and wanted some feedback before I started culling and doing any more rearranging. I know that I won't get all the way through that list - I just wanted everything out there as a starting point. Later today, I'll go back through it and cut it down considerably based on what everyone has suggested.

Thanks for your suggestions!

Dvora said...

Lisa, I meant that I do review the skills with the students (you never know when it will make sense or you say something in a new way that work for them) but also show them how to use the calculator so if they still struggle it does nit hold them back from moving forward with other algebra and problem solving skills.

Lisa said...

Thanks for clarifying that Dvora - I appreciate it. So when you assess them, do you allow them to use the calculator or not? I know if I allow the calculator on that test, I'll end up assessing whether they can do it on the calculator rather than if they can do fractions/decimals by hand. And I'm not totally sure where I fall there. On the one hand, they should know how to do fractions by hand so I feel they should be allowed the calculator since they've done it 3-4 times already. But on the other hand, they should know how to do fractions by hand so I feel they should have to show me they know it. If I do that, however, I am afraid that I'm setting them up for failure for the 3rd or 4th time (well, I hope not - but I also know past history here). So, I'm still mulling that one - but I don't have a whole lot of time until I teach those sections.

Dvora said...

Lisa. For assessment i had a 2 part assessment. A small part with no calculator to see what they know without - this was only, 4 or 5 questions to see if they can add, subtract, multiply and divide fractions and the like. Then for part 2 they had calculator use to also show me they knew how to properly use the calculator including proper ( ) to solve problems. With this level of class I also assessment more often in smaller chunks with lots of practice I class that modeled what they would see in class. Homework was for practice and nothing we had not covered.

Lisa said...

Thanks for clarifying the assessment Dvora - that sounds like it would work well.