Had someone on the wiki ask quite a few questions and thought I would throw them out here for some more answers.
mrlongscience Today 10:02 am:
I'm slightly late in the game with my students coming tomorrow but still have tons of questions.
I only have 39 minutes a period so I often struggle to get through an entire lesson, and still have time for the students to work on practice problems from the book.
1. How many practice/homework problems do you assign for kids to work on?
I have 45 minutes class periods So I kind feel your pain. What I do is alternate between explaining a concept/group discussion to them working at their seats. So maybe will do 2-3 examples together and I will say do 1-4 on your paper now. They compare with their partner and then I call on random students for answers. Then we will do 2-3 nmore examples and then they will do 5-8, and so on. My goal is to make it all the way through one practice worksheet front and back and then depending on their understanding, assign (parts of) a worksheet for homework.
2. Do you just give suggestions on what problems to do since homework isn't graded and students have different needs as far as how many problems they need to do to develop competence with a skill?
I give them all the same worksheet and suggest they work on the ones they had the most trouble with. Our low level students have an extra math support class and so their teacher works through the entire sheet with them. Other than that, I leave it up to them.
3. Do you spend time going over the practice problems in class?
We do problems together throughout class so that they have a good grasp on what to do. The homework I correct and give feedback on individually.
4. Do you just go over the answers and ask for questions on practice problems or do you post the work and answers for practice problems on the board?
I haven't done either yet but I like the idea of posting them on the board. Actually, I'm thinking about printing them out with the answers on them so that they can make sure they know the correct process to get the correct answer.
5. What do you do with the kids who didn’t do any/all of the practice problems while you’re going over the answers/work in class?
I don't go over them in class.
6. How often do you include old skills on a quiz?
I plan to asses, for examples, 1234, then 1234567, then 45678910, so each skill is assessed twice. Still debating about doing a cumulative/retention test.
7. With skills, whenever students see an old skill on a quiz are the questions related to the skill progressively more difficult each time it's assessed?
I assess each skill twice and yes, the second time is harder.
8. Do grades carry over from quarter to quarter i.e. A student gets a 3/5 on the skill of Adding a fraction for the 1st quarter. Is that same skill inputed on the 2nd quarter? If the student re-assesses and receives a different score, do you change the grade only for the 2nd quarter or go back and somehow change the grade for the skill on the previous quarter's grades.
This depends on your admin and gradebook policies. My plan is to change it until that grading period is over. After that, I can't go back. So then I will input it as a new skill in the grading period they are reassessing in.
9. Does anyone haave written criteria for the score scale for each skill? I'll be the first one in my district to implement SBG and I have a feeling my administration/myself will want something to refer to when parents want to talk about their child's grade.
Check out the grading page of the wiki and there are some blog posts and sample rubrics explaining this in more detail.
8.29.2010
SBG: Questions Per Skill
I gave my first sbg skill quiz over 4 concepts in both Algebra 1 and Geometry on Friday. I also gave my first vocab quiz. We went through all the vocab words from the first section together and filled in each square of the Frayer model: Definition, Characteristic, Example, Nonexample. Then in the second section they looked up the definition in the book themselves and I mentioned the other 3 as we went along. Friday was the quiz and here is the example for Algebra 1 and here for Geometry. I reviewed a few minutes during our warm up and gave them 2-4 minutes to study on their own. The results were pretty terrible. The few that did well surprised me. One student missed about 3 out of the 5 days of instruction but told another teacher that we underestimate his abilities because he studies a lot at home. Touché. Another girl assured me that she would flunk it and I believe she has/d a learning disability or just low math scores. They were my top scorers. Yay!
I have to say I am pretty happy with the process even though I'm disappointed by the results. I like the Frayer model and I feel like the questions came straight from the information I gave them without being matching or multiple choice. The question I gave about 'modify the expression so it can be evaluated' was too hard and most didn't know what to do. That one was my fault. I felt like the others were within reach. My colleagues told me to stand my ground. It was only the first quiz and now they know what to expect. They will either rise to the challenge or fail. That sounds harsh to me but I will be curious to see what happens at the end of week two.
Now my first sbg skill quiz...
Algebra Skill 1 and 2 Skill 3 and 4
Geometry Skill 1 and 2 Skill 3 and 4
I didn't really have a clue what I was doing. Still don't. I know you are supposed to make your assessments first but I just don't get that yet. How do I know what to assess when I haven't taught it yet? I know, you're thinking "How do you know what to teach when you don't know what you're assessing yet?". Touché. I had 5 questions per 2 skills and only 4 skills on the quiz. So 10 questions. This really makes no sense. I see that clearly now. I don't know how to grade these. If there are 3 questions for 1 skill, how do I give them one score for that skill? What about when there are only 2 questions per skill? Does it change now? Is each question worth a 2 to achieve the maximum score of 4? I haven't looked at them yet because I have no idea how to assess them.
I know other people use Marzano's 3 levels of questions per skill but I need someone to explain that to me. And still how do you grade that? How do those 3 pieces work together to create one score? I'd like to ask one question per skill that is purely computation but then I don't know where they would get questions on a deeper level that synthesize, analyze, apply concepts, and you know, actually matter.
On a positive note, I'd like to brag on myself for actually running out of time to finish the lesson. More than once. That NEVER happened last year. I went from preparing 10-12 slide Powerpoints to 25 or more. No, it is not all direct direct instruction. Yes, I use pictures. What I've started doing is giving them a worksheet as notes. We do examples together on the board. Then they do 3-5 at their seat and compare with their partners. Then we go back to the board. I have them come to the board and draw examples or work out problems. While they are working I scout the room to check for understanding (oooh nice little sample of edu-jargon for ya) This way I am alternating their focus and while I am 'lecturing' they can actually pay attention instead of scrambling to write. (Yes I need more inquiry and a variety of other strategies and skills. It's week two of my second year. Work with me here people.) Then at the end, I created an overview sheet for them to summarize the important ideas associated with that skill. Hopefully that will be like a quick and dirty study guide refresher with the accompanying worksheet to provide examples. Hopefully.
I would like to explain that I am doing vocabulary separate from sbg skills because
Hopefully.
I have to say I am pretty happy with the process even though I'm disappointed by the results. I like the Frayer model and I feel like the questions came straight from the information I gave them without being matching or multiple choice. The question I gave about 'modify the expression so it can be evaluated' was too hard and most didn't know what to do. That one was my fault. I felt like the others were within reach. My colleagues told me to stand my ground. It was only the first quiz and now they know what to expect. They will either rise to the challenge or fail. That sounds harsh to me but I will be curious to see what happens at the end of week two.
Now my first sbg skill quiz...
Algebra Skill 1 and 2 Skill 3 and 4
Geometry Skill 1 and 2 Skill 3 and 4
I didn't really have a clue what I was doing. Still don't. I know you are supposed to make your assessments first but I just don't get that yet. How do I know what to assess when I haven't taught it yet? I know, you're thinking "How do you know what to teach when you don't know what you're assessing yet?". Touché. I had 5 questions per 2 skills and only 4 skills on the quiz. So 10 questions. This really makes no sense. I see that clearly now. I don't know how to grade these. If there are 3 questions for 1 skill, how do I give them one score for that skill? What about when there are only 2 questions per skill? Does it change now? Is each question worth a 2 to achieve the maximum score of 4? I haven't looked at them yet because I have no idea how to assess them.
I know other people use Marzano's 3 levels of questions per skill but I need someone to explain that to me. And still how do you grade that? How do those 3 pieces work together to create one score? I'd like to ask one question per skill that is purely computation but then I don't know where they would get questions on a deeper level that synthesize, analyze, apply concepts, and you know, actually matter.
On a positive note, I'd like to brag on myself for actually running out of time to finish the lesson. More than once. That NEVER happened last year. I went from preparing 10-12 slide Powerpoints to 25 or more. No, it is not all direct direct instruction. Yes, I use pictures. What I've started doing is giving them a worksheet as notes. We do examples together on the board. Then they do 3-5 at their seat and compare with their partners. Then we go back to the board. I have them come to the board and draw examples or work out problems. While they are working I scout the room to check for understanding (oooh nice little sample of edu-jargon for ya) This way I am alternating their focus and while I am 'lecturing' they can actually pay attention instead of scrambling to write. (Yes I need more inquiry and a variety of other strategies and skills. It's week two of my second year. Work with me here people.) Then at the end, I created an overview sheet for them to summarize the important ideas associated with that skill. Hopefully that will be like a quick and dirty study guide refresher with the accompanying worksheet to provide examples. Hopefully.
I would like to explain that I am doing vocabulary separate from sbg skills because
- My admin asked me to
- Test scores show our students don't understand standardized testing vocabulary
- I know they have the skills but don't know what the question is asking
Hopefully.
8.27.2010
First Days 2010-2011
So my first week of my second year in my second room.
I think it went pretty well.
In every class, every day this week, I kept the students busy until the bell rang. That is an accomplishment I am VERY proud of. Classroom management and procedures are my downfall and what I am really trying to work on this year. My principal has beat it into my head that keeping them busy minimizes disruptions plus it's my job and what the taxpayers are paying for. So...I did it!
I stole all my first day ideas from my Twitter peeps and they all worked out great.
The first day I had my algebra students stand, no assigned seat. I gave them mental math problems that they had to solve and then could pick a partner and a chair. Then my algebra students designed an index card with the numbers from -25 to 25 and we hung them up as a visual number line. After that I gave them a 'pop quiz' with multiple choice questions about me. I then had them create 5 of their own questions about themselves. I plan on using these questions as a guess-which-student-trivia on my warm ups. From there we did some lateral thinking puzzles and filled out Who I Am sheets.
Next day I discussed my syllabus with them. Then I handed out a copy for them to sign and to take home to their parents and sign as well. I mainly did this because of my not grading homework policy and attempting sbg. After that I handed out the Million Words assignment and had them write ANY 3 questions on an index card. I answer every question. I've had great ones like "What are your fears?" "Do you ever feel alone?" "Do you ever feel used by people you trust? as well as random ones like "Who invented baseball?", "What's the fastest rollercoaster in the world?" "What are the three stages of a tornado?" And keep in mind high school boys asking a young female teacher anything. I find a creative way to answer every question. Yes. Every question.
So on Friday I answered all of those questions in class. They are always very interesting and the students enjoying laughing at me and each other. I hope that it helps build a positive and fun environment as well proving that what they say counts and that I will answer any question they have. Then we did one of my favorite activities yet...a Murder Mystery. I split the students into groups of 4 or 5 and passed out the clues. I had them deal the clues like cards until everyone had some. They had to read aloud, not switch, not share, not show. As a group they had to organize and solve the mystery. I gave them a little sheet asking the 5 questions, Who did it, Where at, What time, What weapon, Why and they filled it out. I checked their answers and told them if they were right or wrong but not on specific parts. Out of about 15 groups, only 1 group actually got them right. I feel like the students really enjoyed it and some spent over 30 minutes solving this one problem. U used the discussion questions at the end and they really understood the point of why we did it. I'm also going to use this as blackmail when they want to give up: "Remember that time you worked for 30 minutes on ONE problem. You didn't give up then." Ha ha ha
I have to say I have a really good group of freshman. They are almost scared to death and will hardly move a muscle or talk at all. Also, a lot of the girls really wrote some personal things to me in their Million Words assignment. Some literally brought me to tears. I don't know if it's just because they are girls or if they are an emotional group. Either way, I love that they felt comfortable enough to share all that with me. I wonder how many times they have been invited to freely share their lives with an adult.
And that's all I have to say about that.
I think it went pretty well.
In every class, every day this week, I kept the students busy until the bell rang. That is an accomplishment I am VERY proud of. Classroom management and procedures are my downfall and what I am really trying to work on this year. My principal has beat it into my head that keeping them busy minimizes disruptions plus it's my job and what the taxpayers are paying for. So...I did it!
I stole all my first day ideas from my Twitter peeps and they all worked out great.
The first day I had my algebra students stand, no assigned seat. I gave them mental math problems that they had to solve and then could pick a partner and a chair. Then my algebra students designed an index card with the numbers from -25 to 25 and we hung them up as a visual number line. After that I gave them a 'pop quiz' with multiple choice questions about me. I then had them create 5 of their own questions about themselves. I plan on using these questions as a guess-which-student-trivia on my warm ups. From there we did some lateral thinking puzzles and filled out Who I Am sheets.
Next day I discussed my syllabus with them. Then I handed out a copy for them to sign and to take home to their parents and sign as well. I mainly did this because of my not grading homework policy and attempting sbg. After that I handed out the Million Words assignment and had them write ANY 3 questions on an index card. I answer every question. I've had great ones like "What are your fears?" "Do you ever feel alone?" "Do you ever feel used by people you trust? as well as random ones like "Who invented baseball?", "What's the fastest rollercoaster in the world?" "What are the three stages of a tornado?" And keep in mind high school boys asking a young female teacher anything. I find a creative way to answer every question. Yes. Every question.
So on Friday I answered all of those questions in class. They are always very interesting and the students enjoying laughing at me and each other. I hope that it helps build a positive and fun environment as well proving that what they say counts and that I will answer any question they have. Then we did one of my favorite activities yet...a Murder Mystery. I split the students into groups of 4 or 5 and passed out the clues. I had them deal the clues like cards until everyone had some. They had to read aloud, not switch, not share, not show. As a group they had to organize and solve the mystery. I gave them a little sheet asking the 5 questions, Who did it, Where at, What time, What weapon, Why and they filled it out. I checked their answers and told them if they were right or wrong but not on specific parts. Out of about 15 groups, only 1 group actually got them right. I feel like the students really enjoyed it and some spent over 30 minutes solving this one problem. U used the discussion questions at the end and they really understood the point of why we did it. I'm also going to use this as blackmail when they want to give up: "Remember that time you worked for 30 minutes on ONE problem. You didn't give up then." Ha ha ha
I have to say I have a really good group of freshman. They are almost scared to death and will hardly move a muscle or talk at all. Also, a lot of the girls really wrote some personal things to me in their Million Words assignment. Some literally brought me to tears. I don't know if it's just because they are girls or if they are an emotional group. Either way, I love that they felt comfortable enough to share all that with me. I wonder how many times they have been invited to freely share their lives with an adult.
And that's all I have to say about that.
8.12.2010
Much Encouraged
Much encouraged.
That's what I am after this day.
I have not been excited about going back to school. I've had zero motivation to prepare. The reason being is that I felt that my principal hated me. I honestly felt that if I wasn't a math teacher that they would not have kept me. I have been discouraged thinking about a year of looking over my shoulder and constantly waiting for the other shoe to drop.
I am terrible at hiding emotion. You can easily see on my face when I am angry, annoyed, tired, bored or if I think you're an idiot. Which doesn't really work well with being in public...
I hate fake small talk. I would rather sit in awkward silence then ask questions you don't care to answer and that I don't care to hear the answer. In groups of people I tend to sit back and observe. I like to see how people treat others, what makes the laugh, what bothers them, and basically who they are. Then I feel like I know how to approach them. Unfortunately this comes across as me being stuck up and rude. My dry sense of humor and sarcasm are not useful tools in erasing those assumptions.
All that to say, I've felt...uncomfortable.
Today after our meeting I spoke with the principal about my ideas for the upcoming year. He liked every idea and said that I was on the right track with the trainings he had been going to and that he knew he had the right teacher in the right place.
He said I could not grade homework.
He said I could be SBG.
He liked my weekly vocab quiz and loved loved loved the Frayer model. (Thanks @graceachen!)
He liked the idea of me incorporating reading and writing.
He agreed that we don't care about points but that WE CARE ABOUT LEARNING MOST!
That 10 minute conversation rocked my world, gave me hope, and changed my entire perspective on the school year.
My schedule has changed as well:
Homeroom- Interventions/RTI
1- Algebra Remediation
2- Geometry
3- Algebra I
4- Algebra I
5- Geometry
6- Plan
7- Algebra I
I only have 2 preps! That's fantastical!!!
Algebra remediation is an extra math class that certain incoming freshman have to take. They have me for Algebra I in addition to the remediation class. These are students who are not college-ready and so they will be getting extra help, time for homework and review, etc. Basically an intervention class to prevent students from falling behind. Students are chosen based on test scores, GPAs, and teacher recommendation. But you know what that means for the SBG express....perfect time for retaking assessments. SBG goes perfectly with this. It's like I have built in time to do what you all have to do after-school! Na na boo boo :P And the class is pass fail so traditional grading is unnecessary. At this point it seems like a wondrous idea. I hope it plays out that way as well...
I spent the rest of the day re-arranging my classroom. Unfortunately, I decided to get motivated a teensy bit late and so now I might possibly be a little bit pressed for time. Possibly.
I would like to propose that I found the most random things in my classroom today: a crockpot and a box of sweet n low.
I kid you not.
Oh, and by the way this blog is brought to you by my very own school-issued Ipad!!
Ta-da!!!!!
Leave me some comments of super cool techie edu fun downloadable apps!
Sent from my iPad
Ha ha I typed that myself tricksters!!!
(See what a little encouragement can do?)
Much encouraged.
That's what I am after this day.
I have not been excited about going back to school. I've had zero motivation to prepare. The reason being is that I felt that my principal hated me. I honestly felt that if I wasn't a math teacher that they would not have kept me. I have been discouraged thinking about a year of looking over my shoulder and constantly waiting for the other shoe to drop.
I am terrible at hiding emotion. You can easily see on my face when I am angry, annoyed, tired, bored or if I think you're an idiot. Which doesn't really work well with being in public...
I hate fake small talk. I would rather sit in awkward silence then ask questions you don't care to answer and that I don't care to hear the answer. In groups of people I tend to sit back and observe. I like to see how people treat others, what makes the laugh, what bothers them, and basically who they are. Then I feel like I know how to approach them. Unfortunately this comes across as me being stuck up and rude. My dry sense of humor and sarcasm are not useful tools in erasing those assumptions.
All that to say, I've felt...uncomfortable.
Today after our meeting I spoke with the principal about my ideas for the upcoming year. He liked every idea and said that I was on the right track with the trainings he had been going to and that he knew he had the right teacher in the right place.
He said I could not grade homework.
He said I could be SBG.
He liked my weekly vocab quiz and loved loved loved the Frayer model. (Thanks @graceachen!)
He liked the idea of me incorporating reading and writing.
He agreed that we don't care about points but that WE CARE ABOUT LEARNING MOST!
That 10 minute conversation rocked my world, gave me hope, and changed my entire perspective on the school year.
My schedule has changed as well:
Homeroom- Interventions/RTI
1- Algebra Remediation
2- Geometry
3- Algebra I
4- Algebra I
5- Geometry
6- Plan
7- Algebra I
I only have 2 preps! That's fantastical!!!
Algebra remediation is an extra math class that certain incoming freshman have to take. They have me for Algebra I in addition to the remediation class. These are students who are not college-ready and so they will be getting extra help, time for homework and review, etc. Basically an intervention class to prevent students from falling behind. Students are chosen based on test scores, GPAs, and teacher recommendation. But you know what that means for the SBG express....perfect time for retaking assessments. SBG goes perfectly with this. It's like I have built in time to do what you all have to do after-school! Na na boo boo :P And the class is pass fail so traditional grading is unnecessary. At this point it seems like a wondrous idea. I hope it plays out that way as well...
I spent the rest of the day re-arranging my classroom. Unfortunately, I decided to get motivated a teensy bit late and so now I might possibly be a little bit pressed for time. Possibly.
I would like to propose that I found the most random things in my classroom today: a crockpot and a box of sweet n low.
I kid you not.
Oh, and by the way this blog is brought to you by my very own school-issued Ipad!!
Ta-da!!!!!
Leave me some comments of super cool techie edu fun downloadable apps!
Sent from my iPad
Ha ha I typed that myself tricksters!!!
(See what a little encouragement can do?)
Much encouraged.
8.09.2010
ABG: Algebra 2 Skills Draft
This will be my first year teaching Algebra 2.
I'm using the McDougal Littell 2004 edition textbook.
I went through and pulled objectives straight from the text. A lot of them had a second objective thrown in that basically said: Use ____________ in real-life problems. I didn't number those because they seem redundant. It did make me think, should I be including real-life/word problems in the assessment for every standard? If so, I consider that a form of assessment instead of a separate standard.
I made a few notes on standards I didn't understand and thought should be separated.
I stopped at Chapter 11. The last three chapters of the book are:
Chapter 12- Probability and Statistics
Chapter 13- Trigonometric Ratios and Functions
Chapter 14- Trigonometric Graphs, Identities, and Equations
I would love to get to Chapter 12 but I doubt it. Also, this book throws in one probability and statistics lesson near the end of every chapter. I'm debating taking those out and adding them into this chapter that I may or may not get into.
Chapter 13 and 14 seem to me an introduction to Trig which I have decided is not necessary. But then I'm thinking, this is the last math class the majority of my students will take ever and especially before the ACT. So, are there things I should be teaching out of those last two chapters that will benefit my students' ACT scores?
Without further ado:
Algebra 2 Obejctives
1 Use a number line to graph and order real numbers.
2 Identify properties of and use operations with real numbers.
3 Evaluate algebraic expression.
4 Simplify algebraic expressions by combining like terms.
5 Solve linear equations.
Use linear equations to solve real-life problems.
6 Rewrite equations with more than one variable.
7 Rewrite common formulas.
8 Use a general problem-solving plan to solve real life problems.
Use other problem-solving strategies to help solve real-life problems.
9 Solve simple inequalities.
10 Solve compound inequalities.
11 Solve absolute value equations and inequalities.
Use absolute value equations and inequalities to solve real-life problems.
12 Represents relations and functions.
13 Graph and evaluate linear functions.
16 Use the slope-intercept form of a linear equation to graph linear equations.
17 Use the standard form of a linear equation to graph linear equations.
18 Write linear equations.
19 Write direct variation equations.
20 Use a scatter plot to identify the correlation shown by a set of data.
21 Approximate the best-fitting line for a set of data.
22 Graph linear inequalities in two variables.
Use linear inequalities to solve real-life problems.
26 Use algebraic methods to solve linear systems.
Use linear systems to model real-life situations.
27 Graph a system of linear inequalities to find the solutions of the system.
Use systems of linear inequalities to solve real-life problems.
28 Solve linear programming problems.
Use linear programming to solve real-life problems.
31 Solve systems of linear equations in three variables.
Use linear systems in three variables to model real-life situations.
33 Multiply two matrices.
Use matrix multiplication in real-life situations.
34 Evaluate the determinants of 2 x 2 and 3 x 3 matrices.
35 Use Cramer’s rule to solve systems of linear equations.
36 Find and use inverse matrices.
Use inverse matrices in real-life situations.
37 Solve systems of linear equations using inverse matrices.
Use systems of linear equations to solve real-life problems.
EXTENSION Solve systems of linear equations using elementary row operations on augmented matrices.
39 Factor quadratic expressions and solve quadratic equations by factoring.
40 Find zeros of quadratic functions.
41 Solve quadratic equations by finding square roots.
Use quadratic equations to solve real-life problems.
42 Solve quadratic equations with complex solutions and perform operations with complex numbers.
45 Use completing the square to write quadratic functions in vertex form.
46 Solve quadratic equations using the quadratic formula.
Use the quadratic formula in real-life situations.
47 Graph quadratic inequalities in two variables.
48 Solve quadratic inequalities in two variables.
49 Write quadratic functions given characteristics of their graphs.
50 Use technology to find quadratic models for data.
51 Use properties of exponents to evaluate and simplify expressions involving powers.
Use exponents and scientific notation to solve real-life problems.
52 Evaluate a polynomial function.
53 Graph a polynomial function.
55 Factor polynomial expressions.
56 Use factoring to solve polynomial equations.
58 Find the rational zeros of a polynomial function.
Use polynomial equations to solve real-life problems.
59 Use the fundamental theorem of algebra to determine the number of zeros of a polynomial function.
60 Use technology to approximate the real zeros of a polynomial function.
63 Use finite differences to determine the degree of a polynomial function that will fit a set of data.
64 Use technology to find polynomial models for real-life data.
65 Evaluate the nth roots of real numbers using both radical notation and rational exponent notation.
Use nth roots to solve real-life problems.
66 Use properties of rational exponents to evaluate and simplify expressions.
Use properties of rational exponents to solve real-life problems.
68 Find inverses of linear functions.
69 Find inverses of nonlinear functions.
73 Use measures of central tendency and measures of dispersion to describe data sets.
74 Use box-and-whisker plots and histograms to represent data graphically.
75 Graph exponential growth functions.
Use exponential growth functions to model real-life situations.
76 Graph exponential decay functions.
Use exponential decay functions to model real-life situations.
77 Use the number e as the base of exponential functions.
Use the natural base e in real-life situations.
78 Evaluate logarithmic functions.
79 Graph logarithmic functions.
80 Use properties of logarithms.
Use properties of logarithms to solve real-life problems.
81 Solve exponential equations.
82 Solve logarithmic equations.
83 Model data with exponential functions.
84 Model data with power functions.
86 Write and use inverse variation models.
Use the graph of a rational function to solve real-life problems.
89 Graph general rational functions.
Use the graph of a rational function to solve real-life problems.
91 Add and subtract rational expressions.
92 Simplify complex fractions.
93 Solve rational equations.
Use rational equations to solve real-life problems.
101 Solve systems of quadratic equations.
Use quadratic systems to solve real-life problems.
EXTENSION: Find the eccentricity of a conic section.
102 Use and write sequences.
Use arithmetic sequences and series in real-life problems.
106 Find sums of infinite geometric series.
Use infinite geometric series as models of real-life situations.
107 Evaluate and write recursive rules for sequences.
Use recursive rules to solve real-life problems.
EXTENSION: Use mathematical induction to prove statements about all positive integers.
I'm using the McDougal Littell 2004 edition textbook.
I went through and pulled objectives straight from the text. A lot of them had a second objective thrown in that basically said: Use ____________ in real-life problems. I didn't number those because they seem redundant. It did make me think, should I be including real-life/word problems in the assessment for every standard? If so, I consider that a form of assessment instead of a separate standard.
I made a few notes on standards I didn't understand and thought should be separated.
I stopped at Chapter 11. The last three chapters of the book are:
Chapter 12- Probability and Statistics
Chapter 13- Trigonometric Ratios and Functions
Chapter 14- Trigonometric Graphs, Identities, and Equations
I would love to get to Chapter 12 but I doubt it. Also, this book throws in one probability and statistics lesson near the end of every chapter. I'm debating taking those out and adding them into this chapter that I may or may not get into.
Chapter 13 and 14 seem to me an introduction to Trig which I have decided is not necessary. But then I'm thinking, this is the last math class the majority of my students will take ever and especially before the ACT. So, are there things I should be teaching out of those last two chapters that will benefit my students' ACT scores?
Without further ado:
Algebra 2 Obejctives
1 Use a number line to graph and order real numbers.
2 Identify properties of and use operations with real numbers.
3 Evaluate algebraic expression.
4 Simplify algebraic expressions by combining like terms.
5 Solve linear equations.
Use linear equations to solve real-life problems.
6 Rewrite equations with more than one variable.
7 Rewrite common formulas.
8 Use a general problem-solving plan to solve real life problems.
Use other problem-solving strategies to help solve real-life problems.
9 Solve simple inequalities.
10 Solve compound inequalities.
11 Solve absolute value equations and inequalities.
Use absolute value equations and inequalities to solve real-life problems.
12 Represents relations and functions.
13 Graph and evaluate linear functions.
14 Find slopes of lines and classify parallel and perpendicular lines. (Separate?)
15 Use slope to solve real-life problems.16 Use the slope-intercept form of a linear equation to graph linear equations.
17 Use the standard form of a linear equation to graph linear equations.
18 Write linear equations.
19 Write direct variation equations.
20 Use a scatter plot to identify the correlation shown by a set of data.
21 Approximate the best-fitting line for a set of data.
22 Graph linear inequalities in two variables.
Use linear inequalities to solve real-life problems.
23 Represent piecewise functions. (What does represent mean?)
Use piecewise functions to model real-life quantities.24 Represent absolute value functions. (What does represent mean?)
Use absolute value functions to model real-life situations.25 Graph and solve systems of linear equations in two variables. (Separate?)
Use linear systems to solve real-life problems.26 Use algebraic methods to solve linear systems.
Use linear systems to model real-life situations.
27 Graph a system of linear inequalities to find the solutions of the system.
Use systems of linear inequalities to solve real-life problems.
28 Solve linear programming problems.
Use linear programming to solve real-life problems.
29 Graph linear equations in three variables and evaluate linear functions of two variables. (Separate?)
30 Use functions of two variables to model real-life situations.31 Solve systems of linear equations in three variables.
Use linear systems in three variables to model real-life situations.
32 Add and subtract matrices, multiply a matrix by a scalar, and solve matrix equations. (Definitely needs to be split in separate standards!)
Use matrices in real-life situations.33 Multiply two matrices.
Use matrix multiplication in real-life situations.
34 Evaluate the determinants of 2 x 2 and 3 x 3 matrices.
35 Use Cramer’s rule to solve systems of linear equations.
36 Find and use inverse matrices.
Use inverse matrices in real-life situations.
37 Solve systems of linear equations using inverse matrices.
Use systems of linear equations to solve real-life problems.
EXTENSION Solve systems of linear equations using elementary row operations on augmented matrices.
38 Graph quadratic functions. (Shouldn’t this say more?)
Use quadratic functions to solve real-life problems.39 Factor quadratic expressions and solve quadratic equations by factoring.
40 Find zeros of quadratic functions.
41 Solve quadratic equations by finding square roots.
Use quadratic equations to solve real-life problems.
42 Solve quadratic equations with complex solutions and perform operations with complex numbers.
43 Apply complex numbers to fractal geometry. (Say what?)
44 Solve quadratic equations by completing the square.45 Use completing the square to write quadratic functions in vertex form.
46 Solve quadratic equations using the quadratic formula.
Use the quadratic formula in real-life situations.
47 Graph quadratic inequalities in two variables.
48 Solve quadratic inequalities in two variables.
49 Write quadratic functions given characteristics of their graphs.
50 Use technology to find quadratic models for data.
51 Use properties of exponents to evaluate and simplify expressions involving powers.
Use exponents and scientific notation to solve real-life problems.
52 Evaluate a polynomial function.
53 Graph a polynomial function.
54 Add, subtract, and multiply polynomials. (Separate?)
Use polynomial operations in real-life problems.55 Factor polynomial expressions.
56 Use factoring to solve polynomial equations.
57 Divide polynomial and relate the result to the remainder theorem and the factor theorem. (This confuses me.)
Use polynomial division in real-life problems.58 Find the rational zeros of a polynomial function.
Use polynomial equations to solve real-life problems.
59 Use the fundamental theorem of algebra to determine the number of zeros of a polynomial function.
60 Use technology to approximate the real zeros of a polynomial function.
61 Analyze the graph of a polynomial function. (…And that means what exactly?)
62 Use the graph of a polynomial function to answer questions about real-life situations.63 Use finite differences to determine the degree of a polynomial function that will fit a set of data.
64 Use technology to find polynomial models for real-life data.
65 Evaluate the nth roots of real numbers using both radical notation and rational exponent notation.
Use nth roots to solve real-life problems.
66 Use properties of rational exponents to evaluate and simplify expressions.
Use properties of rational exponents to solve real-life problems.
67 Perform operations with functions including power functions. (Separate?)
Use power functions and function operations to solve real-life problems. 68 Find inverses of linear functions.
69 Find inverses of nonlinear functions.
70 Graph square root and cube root functions. (Should these be separated? And how will students know if they have successfully graphed them?)
71 Use square root and cube rot functions to find real-life quantities. 72 Solve equations that contain radicals or rational exponents. (Separate?)
Use radical equations to solve real-life problems.73 Use measures of central tendency and measures of dispersion to describe data sets.
74 Use box-and-whisker plots and histograms to represent data graphically.
75 Graph exponential growth functions.
Use exponential growth functions to model real-life situations.
76 Graph exponential decay functions.
Use exponential decay functions to model real-life situations.
77 Use the number e as the base of exponential functions.
Use the natural base e in real-life situations.
78 Evaluate logarithmic functions.
79 Graph logarithmic functions.
80 Use properties of logarithms.
Use properties of logarithms to solve real-life problems.
81 Solve exponential equations.
82 Solve logarithmic equations.
83 Model data with exponential functions.
84 Model data with power functions.
85 Evaluate and graph logistic growth functions. (Separate?)
Use logistic growth functions to model real-life quantities.86 Write and use inverse variation models.
87 Write and use joint variation models. (Idk what joint variation is?)
88 Graph simple rational functions.Use the graph of a rational function to solve real-life problems.
89 Graph general rational functions.
Use the graph of a rational function to solve real-life problems.
90 Multiply and divide rational expressions. (Separate?)
Use rational expressions to model real-life quantities.91 Add and subtract rational expressions.
92 Simplify complex fractions.
93 Solve rational equations.
Use rational equations to solve real-life problems.
94 Find the distance between two points and find the midpoint of the line segment joining two points. (Separate?)
Use the distance and midpoint formulas in real-life situations.95 Graph and write equations of parabolas. (Separate?)
Use parabolas to solve real-life problems.96 Graph and write equations of circles. (Separate?)
Use circles to solve real-life problems.97 Graph and write equations of ellipses. (Separate?)
Use ellipses in real-life situations.98 Graph and write equations of hyperbolas. (Separate?)
Use hyperbolas to solve real-life problems.99 Write and graph an equation of a parabola with its vertex at (h, k) and an equation of a circle, ellipse, or hyperbola with its center at (h,k). (Separate many times?)
100 Classify a conic using its equation.101 Solve systems of quadratic equations.
Use quadratic systems to solve real-life problems.
EXTENSION: Find the eccentricity of a conic section.
102 Use and write sequences.
103 Use summation notation to write series and find sums of series. (Separate?)
104 Write rules for arithmetic sequences and find suns of arithmetic series.Use arithmetic sequences and series in real-life problems.
105 Write rules for geometric sequences and find sums of geometric series. (Separate?)
Use geometric sequences and series to model real–life quantities.106 Find sums of infinite geometric series.
Use infinite geometric series as models of real-life situations.
107 Evaluate and write recursive rules for sequences.
Use recursive rules to solve real-life problems.
EXTENSION: Use mathematical induction to prove statements about all positive integers.
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