Factoring: The magic method

I typically teach the box method when factoring. You can find the link for the box resource here. But this year, I was introduced to what I call the magic method. First, I would like to state how peeved I am that I did not documents this method when I discovered it in high school. 

Follow this steps on the side and the scary, a does not equal 1, becomes simple again!  It is magic!  (At least that is what I tell my students).  Some still prefer the box, others prefer the gcf method using parentheses, but for most, this method stole the cake.

Geometry: Pythagorean Theorem

Always provide a leg example and a hypotenuse example. Man, did I learn from that mistake of assuming my first year as a lateral entry teacher. I need to go back and add some color, but the kids caught on pretty quickly. I do my notes and post them on my school webpage now. This totally reduces the number of questions in regards to how and where does this go for the foldable. 

By the way, the paper was part of the donorschoose package. Apparently, I must have been mentally ill when I wrote approximately as approxi"mentally". I left the mistake for the kids to see that I can make mistakes as well. In a class like my math tech 3 group they need to be assured that mistakes are okay. 

 I love the textbook for this class. It is one of the first that puts the distance formula with the Pythagorean Theorem. Thank goodness, the connection was already made!  Other than a few moans and groans about the distance formula and the requirement to draw the triangles, my class caught on relatively quickly. 

Geometry: Angle relationships

Angle relationships are easy visuals to teach students. Change the c into a 9 for 90 degree complementary angles. The s into a 180 for supplementary. You can see the others below. 

Again, color is super important in geometry for your visual learners. I also believe the act of coloring them helps the hands on learners. 

Finally, I have caught up on my tech/ geometry notebook. This week we will be covering congruent triangles. I look forward to sharing my hook for this lesson later on this week. 

Geometry: All things Parallel, with a transversal

Okay, while I enjoy teaching Algebra 1 my favorite class is geometry.  I cannot state this enough.  This includes all of my activities, notes, and games I use teaching parallel lines.  My students have have really impressed me with the projects and even the game (considering the lack of enthusiasm for the study guide, go figure).

Let's begin with the notes.  I always have students shade in the acute angles one color and the obtuse another color.  Then, we put that the angles that are the same color = each other and the opposite colors = 180.  This really helps drive home the main two concepts.  Then, we discuss the interior vs. exteriors.  I hint that same-side starts with an S and so does supplementary.  Trying to help them recall the terms as well.  The foldable helps them organize the congruent angle relationships compared to the supplementary.

We do a little practice on worksheets, playing review games to get the answers.  On to the first project!  Design your own city.  I love this project, because I get to go over my previous profession in architecture and review urban design.  I show them images from my portfolio of how they could one day take this project to design cities.  Ya know, get them as excited as I am about the project.  I get to even throw in a mini lesson about scale. You can find the rubric I used here.  This was not my activity, but I loved the rubric and why re-create the wheel?

Review. Practice.  Time for the review game!  I didn't want my students that would be all so tempted to keep my real dice, so I had them cut out a template out of paper for the next activity.  I had played one similar to this activity before, but this one seemed to work out great.  Again, why re-create the wheel?  My kids surprised me in how engaged they were.  They had the terminology down!  We shall see how they do on the test, but right now I am pleased as punch.

Geometry notes: Segment bisectors & midpoints

For students who struggle with the midpoint formula, I typically put a number line on the board, so we can count to find the exact middle. This visual typically helps. 

In geometry class, I require colored pencils. It is the only way for students to easily visualize the areas and how they relate to the part + part = whole. Or in the midpoint section how the part = the other part. 

Geometry Notes: Segment Addition

We have had a nasty virus spreading through the school and therefore I caught it along with my three children.  So, I have had plenty of material to post, just no time to post the information.  The positive, tons of interactive notebook goodies.  Tons of pictures and some good tips that I have learned along the way when teaching geometry. 

Segment addition and angle addition work well together in a foldable. I think it helps kids see the same applied math to different shapes. 

I was quite surprised my first year teaching how many students need a review of the yellow box. 

Breaking down problems in geometry as two parts and a whole really helps them set up equations. 

Systems using elimination

Let me just say, wow!  The Internet is amazing!  I posted that silly donors choose video and bam I have classroom supplies coming straight to my door.  The blog had taken to the back burner, but I am back with a few posts.  I am going to do two today, the first for my Algebra class, the second for math tech 3/geometry.

I find that substitution is a difficult method to follow out of the three.  Unless you are a math nerd like I was in high school and had plenty of experience with math relays.  So finally, we come to elimination!  I think out of the three forms, minus the calculator for graphing, that this is the easiest form to solve for students.  I showed the students how to find the lcm in the calculator (a trick I didn't learn until I went back to school for my master's degree).  Go to ALPHA then over to the right to NUM and voila!  This menu can factor using the gcd, find the lcm, and plug the absolute value into your calculator.  I mean really, why did I not know about this?!

So after teaching the method, I used these worksheets from online.  There was one error on the substitution package, but the elimination seemed to be perfect.  I had students do the cut out activity as the students homework after the notes were taken.  I love this packet because it breaks the material down into steps.  The second can be used as a gallery style activity (the way I presented it) or as a matching activity.  I loved it!  The kids seems to really catch on using elimination.  I heard a few complaints from them about the number of steps needed to solve the equations.  We are playing a review game and quizzing on the three methods prior to teaching them how to just use a matrix.  Man do kids always get mad.  "Mrs. P, why did you make us do the other forms?  The matrix is soooo easy."

Note: there are limits to using the lcm or the gcd...you can only plug in two numbers and you must keep them positive.

System of Equations: Substitution

I absolutely despise teaching my lower level students the substitution method.  But the state always puts a question on the state test about the elimination and substitution methods.  Does anyone else feel this frustration?  I tend to want to jump straight to the calculator for graphing and using matrices.  But in an attempt at tutoring the other day, I had a moment of genius strike!  It inspired a creation of a worksheet...to be shared at a later date.  Note cards served their purpose in class that day.

I made the student flip the card to the other side every time he crossed the equal sign.  He said it was still a lot of work.  You know because our students are professional whiners at times, but he said it did make more sense after doing several problems like this.  Will he more than likely solve systems using a different method?  Yes, but will he recall this activity with this method?  Yes.  For some more eye candy, I have posted my latest notebook additions below.  The yellow chart came from Holt McDougal's powerpoint.

Inequalities: Flipping the sign

So my kids love the interactive notebook and were pouting that I didn't have some cool new foldable for this most recent unit.  The first reason being that one step and multi-step equations are practically the same methods for solving inequalities.  But I knew that I wanted to find something awesome to drive home when to flip the inequality sign.  After searching Google for at least three days, I found it!

Changing Image Tutorial  They include images for a tutorial on how to put it together and include a template.

I am slightly afraid my children with ADHD will be lost for the rest of the day as they make the sign flip, but at the same time they should be brainwashed by the time is all said and done.

This took a bit longer than anticipated, but the kids really enjoyed the final product.

Snow catch up part two

So today my kids were foldable overloaded. We had to make up for four lost days of curriculum.

First, we started with a two step refresher  foldable. The kids solved two step equations on the inside and explained in their own words how they arrived at their answer. 

Next, I found an awesome foldable online on teachers pay teachers. I think it is by far the best step by step foldable I have seen yet. 

Then, we worked out a few problems using the foldable. This led to the discussion of when the coefficient in front of the variable is the same. 

Finally, we concluded with their homework, which originally would have been a classroom assignment. Four no solution, four all real number equations, and four with a solution. They had to solve each to determine which pocket to place the slips into. 

Cold and Flu..time to catch up!

We have covered the remainder of the review for Algebra 1 and finally cracked open the textbook today.  I don't believe in a textbook driving the curriculum for a class, rather I use it as a learning tool for my lessons.  I found myself disgusted today to hear a coworker say "Well if they don't get it the way I teach it, they need to just find a video online to learn it.  I am cannot be responsible for them not getting it, I taught it."  I can't count the number of times in just my five years of teaching that I have changed a lesson the next time I taught it or changed a method in hopes that my students understand the concept better.  (I'm off my soapbox for now.)

So here is what we have covered since my last post...

Fractions

This semester my pre-assessment pointed out that majority of my students understood fractions, so we did not spend a great deal of time in this unit as I usually do.  My creative juices must have been flowing this day, because I love how my word art turn out for Improper fractions and Mixed Numbers. 

Expressions

My kids seem to think that this is an easy unit until I ask them to write an expression into words in two different formats.  This is the first time, I really get them to see how notes can help them not only study, but understand how to do their classwork.  Thanks again to Mrs. Hagan for some foldable ideas. 

I was super excited to find a way for them to use their interactive notebook to do their expression homework. I gave them a sheet of sentences and they determined the operation for each.