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 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. 

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.

Geometry basics (and a cute baby)

And I am back. After a baby that was suffering from an ear infection and then turned out to be allergic to amoxicillin, I can truly say I am glad to have time to blog again. So this post will have several goodies, just because it has been a while.

First, I have been searching through sites such as issuu and flipsnap in hopes to find a way to present my work in one cohesive document (and for cheap).  I found one site which I will share my review at the end of the year. This is only because you must upload everything at once, but it is free.  In the meantime, I am using google presentation to post my notebooks online for students who may have missed a day of notes.  It seems to have no limit and now parents/students have access to the notes from class!  Problem of the absent student is solved. 

Math Tech 3 is a geometry based course with a slower pace. So having a matching activity for the terms guarantees that they will make it to the notes, but as one student pointed out "it feels like a game."  To this I respond by shrugging shoulders nod asking, "Who knew, that definitions in class could be fun?"

 This foldable needs tweaking prior to me posting it. After 15 minutes of trying to keep the copier from shifting my pages, I was able to get the front and back aligned. 

As stated earlier, geometry at a slower pace. Don't worry, I will have them doing proofs, just in a disguised manner.

My posts for Algebra 1 will go up tomorrow. I just could not stand going without posting. 

Compound Inequalities

My students only worked on compound inequalities that shaded between the two points if it was a "and" inequality and outside the two points if it was an "or" inequality, but I felt that it was misleading.  My kids had recently mastered no solution and all real numbers in the previous section, so why should it not carry through to compound inequalities.  I felt like I had misled them if I didn't show them other compound results.

First, we started off with a review sheet, I had noticed that some kids were struggling.  Thank goodness all my classes had an even number today otherwise my plan may have had more kinks.  There were four sections on the worksheet I had in class.  The first part was just interpreting the graphs.  The kids chose their best friend as their partners as usual.  Before moving to the next section, they had to find another partner.  Typically my low level students don't work with a higher level  math student in fear that someone may find out that they can't solve the equation.  This forced my levels to mix by the third and fourth round.  Haha, math teacher won out.  The kids worked the hardest they have worked in a while.  I praised them and then threw in the monkey wrench...

I started with the statement "Raise your hand if your grandmother is older than 50 years old."  Then, I said "continue to raise your hand if your grandmother is older than 50 and younger than 10."  I had a few "what?!" faces, but the hands quickly went down as I began to explain a no solution equation.

For all real numbers, I asked them to raise their hands if they were older than 14.  Then, I said raise your hand if you are older than 15 or younger than 17.  They all raised their hands.  This was an example for all real numbers, I begin to see ah-ha faces.

We'll see after their homework tonight if they grasped the two concepts.

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.

Taking the problem out of word problems...

As a teacher when I write my lesson plan for word problems I quiver at the thought of the frightened faces in my class.  Somewhere along the way word problems become a problem for students.  Oddly enough on my quizzes and tests most of my students can answer the word problems better than the multi-step equations.  Yet if you ask any of them about a word problem, they begin to almost hyperventilate.

Today's lesson will be to try and take the fear away by providing the students with a word problem toolkit.  I wanted to make sure the students didn't fear word problems and could find the key words to solving multi-step equation word problems.

First, we underline what the equation is looking for.  Next, we highlight the important information and mark out the unnecessary.  Third, we identify the indicators for operations and for the equal sign.  Finally, set up and solve.

The kids seemed to do a great job with the assignment and had a grasp of multi-step equations better than they did previously.  They still were tripped up by consecutive numbers, but until they see the answer they can't grasp why we are adding something to x.  Also, as always we had a discussion of when you need to go a step beyond solving for the variable.

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. 

Two step equation notes

So I had an epiphany.  Equations become smaller as you solve them so why not make a trapezoid shaped foldable. I tried to make the notes as easy to follow as possible. My kids seemed to grasp the concept better when they separated the terms. Thank you to the other teachers who taught it that way previous to me teaching this lesson. 

I am still trying to figure out how to do the equations with variables on both sides, but I think the snow will help get the creative juices flowing. 

Oragmi Envelopes might be cool, but never again!

We're still reviewing since the kids took a pre-assessment for my class and bombed it!  The kids are truly coming to me at a low level.  I wanted the check for an understanding of 8th grade math skills.  I chose easy to difficult level problems.  The students did well on order of operations since I had already covered this topic in our review, but other areas were poor. 

Today in response to the scores, we reviewed adding integers today.  We used algebra tiles that the kids cut out from card-stock.  We used them with a worksheet from Cooperative Learning & Algebra 1 by Becky Bride.  It's a great resource to have in any Algebra class.  

We then followed the oragami envelope steps, but it did take more time than usual.  I figured with Valentine's day coming up it would be neat for them to learn, plus it holds all of their algebra tiles in something they created.  We also used a foldable and blank number lines for our notes today.  Overall, they grasped the concept and we can move on to the next issue on the assessment.