Week 33

So obviously I got kind of behind on posting my weekly recaps. I'll do my best to remember but it's basically going to be a bunch of links.

I mentioned last time a surface area lesson gone wrong. Here is the retake.

Scientific notation went not as well as I had hoped, especially when it came to multiplication and division rules. In division when you are supposed to subtract the exponents on the base 10, they also wanted to subtract the whole numbers in the numerator and denominator instead of dividing. While multiplying, they remembered to multiply the exponents but forgot to take the whole number to the power. Those pesky whole numbers...

Here is a sheet I created for review and here's the quiz.

Ok, I'm getting overwhelmed and there is no need for me to get panicky about my OWN blogging! So I will just make the rest of this post my algebra links for the rest of the year.

Polys Notes
Adding and Subtracting Polynomials, Notes
Monomial Polynomial Review Sheet, PPT
Monomial Polynomial Quiz Students had a terrible time labeling the type of polynomials.
Multiplying Monomials and Polynomials, Notes

I taught Box Method instead of FOIL and it worked much better. A couple students preferred FOIL but for the most part, Box Method was simple to understand. Now adding like terms was what tripped them up.

Box Method

I created this box method worksheet and I just loved it. The kids loved multiplying the 5 x 7 polynomials. it could be considered busywork but they loved seeing the patterns that emerged in the exponents and I think doing this one big problem really reinforced the box method itself. They still struggled with adding like terms to get the final answer though. Why is that???

Special Binomial Products, Notes I literally made them use the special formulas even though they begged to use the box method. I don't if it was a mistake to force them to use it or if I should have let them find the patten on their own using box method. But considering they can't add like terms, I don't think they would have ever found any pattern at all. The pitfall here is that they wanted to use a^2 - b^2 for everything.

Polynomial Memory Review Game My lower level class really liked this game.

Finally, the multiplying polynomials quiz.

P.S. I love polys and factoring!

I intro'd factoring with this diamond math puzzle. I made everyone work silently until they figured out the pattern and finished the sheet. A lot of students really struggled when I made them think for more than 30 seconds without giving them answers. I gave no hints, just told them yes or no. A few people literally took the whole hour so I finally gave them the hint along the lines of, what can you do to these two numbers that give you the top and bottom answers. From there, it was easy peasy, lemon squeezy.

Started with this GCF lesson (notes)- they loved it. Why? It was easy  and they already knew how to do it. I always believe that I can break anything down to where it is easily understandable. But can I?

Factoring, Notes

Factoring by Grouping, Notes  I've actually never heard of this method but it was mentioned in 2 of my 3 Algebra textbooks so I went ahead and taught it.

Factoring Negatives, Notes

I AM IN LOVE WITH THIS WORKSHEET. Seriously, I would make out with it. It's not even mine. Someone else thought it up and I would make out with them too. I used it all throughout our factoring unit and we worked on sections of it at time during class, at the beginning, at the end. And I even used activities that I talked about in this post to do it. How bout them apples

Factoring Quiz

The end. Algebra style


Week 32

Now that I've caught up on blogging, I kinda like actually doing it again.

I taught the easy part of scientific notation today, and the hard part (notes) is up tomorrow. Luckily, they have done this before and we just finished our unit on exponent rules, so hopefully we can wrap this up neatly. I like the lessons I've made but it's very much direct instruction and no inquiry, which I am so. so. tired of.

In geometry, this is my surface area lesson which went over like a lead balloon. I hate that class. Hate. It.

My other geometry class just finished sin, cos, and tan, and bombed the quiz. Three people got an A and the rest were below passing. They had 10 minutes to do 10 multiple choice questions and then the rest of the time to work in partners on 9 problems. I even allowed them to come in throughout the day to finish or correct. And they got to use notes. The three that came back are the three that got A's. So today I went through every single problem and worked every step out. I told them they could correct their quiz and use it tomorrow. Tomorrow I'm giving a totally different quiz to anyone who wants to make it up. The condition is, it can't be made up during class. They have to come in on their own time. I feel like they need to be responsible for learning and getting a better grade. But what worries me is if they all fail again, then I can't just move on with them not understanding. Can I?


8 Standardized Testing Strategies

I went to a meeting quite a while ago about 8 test-taking strategies. In Illinois, our state test is the ACT (please ask me how stupid this is) which is a college readiness indicator. Whose standards are totally different from the state standards we teach to.

But anyway, the ACT has 33 Algebra questions, 23 Geometry, and 4 Trig questions (do you know that I love Algebra so much that I always capitalize it, but not any other classes? Seriously, I just went back and capitalized Geometry and Trig). The majority of our juniors are at the Geometry level. Automatically, there are 4 Trig questions they don't know, plus the Geometry questions that we haven't covered by the test dates. So, aside from preparing them for the test by teaching the content on the test, these are strategies for the questions where they just don't know what to do. What do you do when you don't know what to do? Why, use a standardized test-taking strategy of course!

And because I too love to list, here are the 8 strategies:
  1. Ball-parking and the 10% Rule
  2. Proportion
  3. Hit the Middle
  4. P.I.T.A
  5. Calculator Shortcuts
  6. "Seeing" with Graph Paper
  7. Drawing and Knowing
  8. "On Your Toes"

Ball-parking and the 10% Rule
This strategy refers to questions that involve percents such as sales tax, discounts, percent of total population, etc. The 10% rule means that you can easily find 10% of the number and multiply times whatever number needed. Ballparking is basically estimating or rounding to help knock out answers that don't make sense and narrow it down to a realistic guess.

Again, this strategy can be used for percentage questions or any questions that are comparing or describing the relationship between two things on a different scale. Ex. "If it takes Chris 45 minutes to make 18 cherry tarts, how many hours will it take to nake 60 cherry tarts maintaining the same pace?" If students can set up the proportion correctly, they can usually cross-multiply and solve.

Hit the Middle
I honestly never noticed this before but did you know that the answers on the ACT are arranged in numerical order? Hit the middle means to start with the answer in the middle, plug it in and solve. Judging by the answer you get, you can usually knock out the answers that are too low or too high. Again, eliminating unrealistic answers helps those guessers.

This is the old-fashioned Plug In The Answer. Try picking answers and plug them into the problem to see which ones work and which ones. Also, when faced with problems including multiple variables, try plugging in numbers to see what happens and then generalize what's going on.

Calculator Shortcuts
Ex What is the value of 2x^2 - 3x + 2 when x = -2? By pressing the STO-> button on the TI-83 and then -2, enter. You can then type in the equation and the calculator will pull in the -2 and solve. Neat-o. Another shortcut is graphing equations to either see where the functions intersect, if there is any intersection at all, and finding equivalent functions.

"Seeing" with Graph Paper
Students can use graph paper to find distance between points, lines that pass through a specific point, and etc. While it's possible to do this on the calculator as well, it may be easier for students to draw out themselves than to try to use the trace or table feature on the calculator.

Drawing and Knowing
One of the things I loved most about my geometry teacher is that every time I had a question, she would pull out a scrap of paper, draw out the problem, and then ask, what do you know? This strategy can be used whether a drawing is provided or not. Draw and label all the given information and anything that you can deduce from what is given. Remember properties of congruency, similarity, special triangles, regular polygons, area, perimeter, diameter, radius, etc. Use your drawing to eliminate wrong answers.

"On Your Toes"
Beware of unnecessary information given in the problems. Also, notice the difference between the answer choices "No values of x satisfy the equation" as opposed to "There is insufficient information to answer the question". Always look for the oddball answers that can immediately be eliminated.

These strategies are courtesy of a professional development meeting by Dr. Tim McNamara.


Planning Ahead

While I haven't accomplished a ton over my spring break, I would like to list what I did accomplish.
  • Caught up on my blogging finally (reading and writing)
  • Cleaned out my closet and various other dark places
  • Fixed my itunes music
  • Ate a lot of candy
  • Watched a lot of movies
  • Slept in every single day
  • Irritated everyone on twitter with my endless questions
  • Set goals or at least a forward path for the rest of the year
  • Read some good books
Let's talk about my planning. Topics coming up in Algebra:

  • Scientific Notation
  • Exponential Growth/Decay
  • Polynomials (Adding, Subtracting, Multiplying)
  • Factoring (Diamond Math)
  • Quadratic Equations/Functions
  • Rational Expressions (if time allows)

Now for Geometry:

  • Circles
  • Jumping backwards to polygons
  • Then polyhedra, surface area/volume
Any ideas, comments, suggestions, resources, links, or anything at all you would like to share- please give freely. I'll take it all!


Week 25-31: The One With The Geometry

Apparently I just hate geometry. Algebra just comes so much more naturally to me. I have two different geometry classes and I've branched off and went two different ways with them. I think this may be causing more work for me but oh well. One class, I've been going by the book and following the order of topics. In the other class I jumped ahead two chapters to start using sine, cosine, and tangent in order to prepare for our state testing on April 28-29. We keep being pressured to prepare the students for state testing but no one is telling me how.

I don't think anything frustrates me more than to be told to do something and not told how. I can't work with nothing here. The only suggestion I've been given is to use ACT questions on my warm up. Which okay, I can do, but the point of the warm up is to review what we did yesterday and lead into what we're doing today. Finding ACT questions to fit that purpose is hard as heck. I use this site which gives an ACT question of the day, but of course that doesn't align with anything I'm doing. I went to a conference on ACT test-taking strategies and I've introduced a few of them in class but...that doesn't seem like enough. My teacher bestie teaches English and she gives her students short timed quizzes so they can get used to working under a time limit. I've tried that. Once. But I'm just not feeling prepared enough to prepare them. In my opinion, they need more content which is why I've skipped ahead to the back of the book to get more of the content covered by the ACT. That's my big nod to ACT prep.

Anyway, I don't know a good way to talk about my separate geometry classes except for separately. In one class, my students literally do not care at all about class or school, period. They don't do homework and copy as much as possible. I have totally failed this class. But, I digress. The way we do class now is that I lecture all period for one day and they take notes and then turn in their notes for a grade. By notes, I mean I print out Powerpoints as handouts and they fill in the blanks and work out practice problems on those. That is how I do notes in all of my classes. I grade the notes and then give them back the next day when they are quizzed and are allowed to use their notes. So lecture, quiz, lecture, quiz. This doesn't really work either. Only a few actually understand their own notes and the rest just blindly write down whatever I write with no sense of where the numbers came from or what to do with them. But I don't know what else to do and so this is where I'm at.

These Powerpoints were mostly copied and pasted directly from the textbook, so they aren't anything magnifical but I want to share everything I can to help as many people as possible. I am definitely a lesson-stealer. I steal everything I can get my mouse on for the classroom. There's really not a lot to discuss, so I will just link it up.

Convex and Concave Polygons, HW Quiz
Angles in Polygons
Area of Squares and Rectangles, HW Quiz
Area of Triangles
Area of Parallelograms/Rhombus, Notes, HW Quiz
Area of Trapezoids
Area and Circumference of Circles, Notes
Area and Circumference Part 2, HW Quiz
Polyhedra, Notes, Quiz

My other geometry class is the one where we have skipped ahead. We started with simplifying square roots which came with mixed reviews. I thought this was something easy to start with but they struggled a little with it. I think part of it comes from the fact that I let them off too easy one too many days and now they think the year is over and they should not have to do any work. But we press on. Next up was special triangles 45-45-90 and the cheat sheet I printed on colored card stock paper and allowed them to use on quizzes. Did the same for 30-60-90. Cheat. After begging for help on Twitter, Kate, directed me to her blog post on introducing right triangle trig. I stole this from her and modified a tiny bit. I gave them this and literally had them draw nested triangles directly on the protractor, using the black line on bottom as there bottom of the triangle. They had a LOT of trouble with measuring and writing the measurements in the right ratio.  I put the answers in the chart so I would remember, so make sure you delete those if you use this. It took two class periods to accomplish this and they didn't come up with exact measurements, but they did realize they had the same answers as other classmates with the same angle. This Powerpoint demonstrates it pretty well I think.

From there we transitioned from bottom, vertical, hypotenuse to opposite, adjacent, hypotenuse and introduced sine and cosine. We practiced on this and I just lightly hit on tangent. I didn't even have a powerpoint, we just discussed if we had already used sine and cosine, the only other ratio left for tangent would have to be opposite over adjacent. From there we went to the inverse trig functions. Here's a worksheet. Then I totally stole this review golf game from ilovemath.org and edited a bit for my people. Last but not least, the assessment.. I first gave them a 10 question standardized quiz that they have 10 minutes to work on. Then they worked in a team to complete this quiz. I had quite a few students who did not finish and had to come in later to finish on their own. I even let them use notes and cheat sheets. I may have sucked it up but oh well now!

I know this is the linkiest post ever but I had to catch up and this is just how I roll.

Feel free to steal any and all of this, edit, ask questions, etc.


Week 29-31

Somehow my timing got off in my weekly recaps so I'm just going to lump things together and hope it makes sense. It didn't really take me three weeks to do exponent rules but I've been lazy in my blogging and at least this gives me a general timeline to go by next year.

In my last post, I mentioned my exciting introduction to exponents. My 8th grade algebra class absolutely loved the activity and wanted me to hide post-it notes for the next week or so. My freshman algebra class thought it was stupid but went along with me. From there though, they really struggled with the concepts. I went to fast and when it came to applying the rules, they were lost. Figuring out the rule wasn't too bad but using them, especially more than one a time, was a disaster. So after uselessly practicing and practicing, I had to take a step back, break it down into separate lessons and separate days and take things one step at a time.

Now that I say that, I realize I never formally taught the division rule, but it was sprinkled throughout. Here is negative exponents rule and notes, multiplication properties, graphic organizer, and mini mini quiz. I also went here for homework worksheets and here for tons of review games.

After reading Riley Lark's post about team testing (literally like the day after I read it) I was intrigued and wanted to try it. So what had happened was....this was my original exponent quiz.  And consequently...I forgot to finish it. So I'm printing it out -.01 minutes before I'm actually giving the quiz when I panic at the sight of this backless monstrosity. Quick as lightning, I google exponent quiz and abracadabra- an experiment is born. I made this and passed it off as a team quiz. And apparently it was super easy because they asked if they could do every single problem for extra credit. I took a minute to think about this and decided that if they wanted to do extra work in order to completely convince me that they know what they are doing...I'm okay with that.