Parallel Lines and Angles

Our first week went well even if I'm still not through Reasoning about Intersecting Lines and Angles, but we only had 40 minutes in each class every day this week.  Next week I should be able to really get going.

The next lesson is Reasoning about Parallel Lines and Angles.  I'm going to start that one focusing on vocabulary.  There will be a Poll Everywhere question where the students decide which angles are located interior from the picture below.  Each student will have a small printed copy of the figure.

Poll Everywhere is a very neat site where you can post a question and have the students answer via text or website and it will display the results in real time (or you can wait to show the results).   

  

When they decide what angles are interior (3, 4, 5, 6) we will discuss which angles are exterior (1, 2, 7, 8).  We will highlight on the small printout the Interior vs Exterior angles.  At this point we'll discuss what transversal, alternate, corresponding, and same side means. 

After this general discussion we will create a foldable to denote the different types of angles along a transveral.  I also include linear pair and vertical on the foldable.  

At this point we only focus on the terms and not the congruent/supplementary relationships on the outter flaps.  

Depending on time we will play a game 

The students then begin working through some reasoning questions where they make some assumptions about relationships between the angles when the lines are supplementary from their textbooks.  We will return to the foldable and add those relationships.  

Parallelogram Proofs

Things have been crazy the last couple of weeks as I have been trying to balance life between being the lead math teacher, the digital learning specialist, a mom, a wife, ect.  We went one-to-one in the last couple of weeks with iPads.

Today's lesson was not very awe inspiring on the surface, but it actually seemed to work.  First, I hate teaching proofs.  Like, how?  HOW do you teach students to think logically.  I frequently get asked for a list of alllllll the reasons you can use in a proof.  Imagine the doubt I get when I try to explain that there really isn't a comprehensive list that can reasonably be provided and there really isn't one particular 'answer' to writing a proof.  I did have my students add this webpage to their reading list in Safari and that seemed to somewhat appease them.

Tomorrow we will take a quiz so today we just practiced and practiced proofs.  I used this nifty little website for the students to individually go through.  There were 8 parallelogram proofs that I had them solve, but there are MANY more proofs that I will definitely utilize in the future now that we have iPads. 

This took about 45 minutes or so of students working and me meeting with them individually to go through the process.  As they finished, they continued to proofs about the five properties of parallelograms.  This was to be there homework and they were required to complete two. 

I hope to see the understanding from their quiz tomorrow.

Missing Work Log

So this is totally something I stole.  Why create the wheel when it's already been invented....or something like that.

Anyway, I have pink missing work logs in the front of my room for when students 'forget' to do their homework.  So far I haven't had anyone do the walk of shame to the front of the room for one, but today is the first due date for homework so we shall see.  I very rarely take up homework because I suck at getting through piles of things that need to be graded.  I always walk through the room while the students are working on something or checking their answers and grade out of 20 on how much they attempted.  To me, homework is practice so I'm not really looking for them to have it correct, but I can tell pretty quickly if they actually attempted the work.  This is something I will have to keep up with though, but it will be an awesome tool when a parent is wondering why their child's grade is so low.

You can find the download for this particular Missing Work Log at this link.

Curriculum planning for Common Core Math 3

I'm currently in my classroom a day early planning for CC Math 3.  Just snagged myself a nice new desk chair too!  Early bird gets the worm I suppose.  (I'm actually a day early because I don't plan to come tomorrow and sweat myself skinny since there's a possibility of no AC)

New Chair!

I just finished some posters for my 'I Can...' statements grouped with the Common Core Standards for Unit 1 (Geometry).  I wanted to go ahead and get those out to whoever may be reading my blog.  At a later date I may pretty them up some with pictures.  I'm printing them on different colors to distinguish between the lessons.  The first two pages will be lesson one, the nexttwo pages are lesson two, and the last page is lesson 3 of Unit 1.  *Picture does not show the last page

I'm also going to laminate them so I can use a white board marker and check them off as we go through the unit.

After the unit I will post them along my walls with illustrations.  During the unit they will be at a designated spot on my whiteboard.

Hope this makes someone's planning a little easier!

Stay tuned for the addition of other Units.

A New School Year

I go back to work tomorrow.
       But it's still July!    
       I KNOW!  Early College life man.

I will be teaching Common Core Math 3 for the second time.  The first time was difficult!  There just seems to be SO MUCH information in CC Math 3 and I definitely did not get through everything the first time.  This time I'm working my behind off trying to get everything organized so I can do a better job this semester.  I will also be working as the Digital Learning Specialist for my school as well as pursing National Board Certification.  Pray for me!

So Unit 1....I'm going to cover the Geometry stuff first.  I have to keep reminding myself to focus on the proofs.  It's easy (and more fun!) to get caught up in the activities that only require them to use the facts related to angle relationships.  The general flow of things will go like this...

   REASONING about intersecting lines (linear pairs and vertical angles)
   REASONING about parallel lines and angles
   REASONING about triangles (sum of interior angles, base angles of an isosceles triangle)
   Review Triangle Congruence Theorems
   Perpendicular Bisector Proof (i.e. any point on a perpendicular bisector is equidistant to endpoints)
   Similar figures (which I need to break down some more at a later date)


Day 1 - I plan to have the students solve a crime scene investigation from their textbooks (Core Plus Mathematics Course 3 Unit 1 Lesson 1 Investigation 1 #1)  The goal is to talk about using logic and supporting your conclusions.  I'm thinking 10 to 15 minutes on this activity.

Of course I need to go over the usual first day stuff (syllabus).  My students will already know each other so I can skip the get to know your neighbor activities.  Chances are they already know each other too well and I will spend the entire semester trying to regroup them back to the task at hand.

Then I want to jump right into REASONING about intersecting lines.  From their textbook that would be #1-3 of Unit 1 Lesson 2 Investigation 2.

The gist of this investigation begins with looking at a truck where the bed (?) raises and lowers.  Ah...just...here's a picture....

So we'll discuss what things change and what things stay the same as the bed raises and lowers.  We'll come up with the vocabulary terms 'Linear Pair' and 'Vertical Angles'.  I'm looking for a neat interactive notebooky way of getting the terms into their notebooks that they hopefully have on Day 1.

The first official problem are examples of solving for the other angles of the standard X (see picture below) when given one of the angles.

The next problem looks at a general proof of vertical angles using linear pairs.  The students follow through a complete proof showing one pair of vertical angles are congruent and then they create their own to show the other pair are congruent.

The final problem we'll work through now is a proof that if one angle is a right angle then all four angles are right angles.  This one is organized as a two column proof with all the statements filled in and the first few reasons filled in.  The students are to come up with the last few reasons.

I'll assign them the homework and everything will end with just enough time to assign an exit ticket ;)

We will have half days our first week which means each class will be about an hour.  Think I can fit it all in??

They actually ask to play it during their study hall! Mathonopoly

I brought this game in to review congruent triangle postulates and the students absolutely loved it!  I kid you not I had students ask to borrow the game to play during their study hall period.

I don't remember where I found this idea, but there are several lower level math monopoly boards out there.

There is quite a setup with it, but once you get your cards assembled it is a quick and fun go to for review of quick skills.  I wouldn't suggest using this for something like solving multistep equations, but something like very basic factoring would work perfectly (ie x^2 + 4x + 4).  I first used this with recognizing triangle congruent theorems from pictures.  

The cards from my templates are personalized to my classroom so should you decide to use it you may want to look through the chance and community chest cards to personalize to your classroom.  These are the cards that make the game so fun! 

It's played very similar to Monopoly.  I use points instead of dollars and start everyone off with 200 points.  When a player lands on a number they pull that number card out of the stack and try to answer.  Someone else checks their answer from the back of the card.  If they get it right then they own that space and anytime someone lands on their space there is an exchange of points based on the number associated with that space.  If they land on a community chest or chance card then they chose a card from the appropriate stack and do as it says.  I used the other spaces (electric company and the train spots) as just safe places but you can set different parameters of course.  I usually let my classes decide if points should be lost for getting the wrong answer.  

I find it works best in groups of three or four.  

Besides the printouts, the other materials you will need are die and player pieces.  

The cards are meant to be manually fed front to back in a printer (ie not a copier).

Mathonopoly - Congruent triangles

A new way to give a worksheet...Question Stack

I have had the greatest opportunity of attending the Greene County Math Drive-In several times and each time I walk away with some really awesome resources.  If you have the opportunity to attend one I promise you will not regret it.  The concept is catching on in other subjects and other areas of NC.

So one activity I've taken away and used SEVERAL times is the Question Stack.  What you do is take a worksheet (I typically use kutasoftware worksheets with the answers) and put a problem on one side of a card with the answer to another problem on the back.

The students would work a problem, find the answer on another card and put the answer on top of the problem so that a new problem is showing.  They solve the new problem and continue to stack up the cards until they are all stacked.  The answer to the top problem should be on the bottom of the stack.

The students typically prefer this over just working through a worksheet...especially if there is some sort of incentive for the first group to finish.

I have made several Question Stacks for many different topics.  The templates are made to be manually fed through a printer (ie NOT in a copier).  I usually print them on bright cardstock and they have held up well over the years.  Laminating would probably last a lot longer (and discourage writing on the cards).

The Unit Circle

So I totally stole this from another blogger who stole it from a student (how cool is that?!?).

I used different methods with each of my three classes and the best method I thought was to work with one triangle (I used the 45-45-90) all the way around the circle filling in the degrees and the coordinates.  Then I filled in the first quadrant with the other two triangles and let the students work their way around the circle based on what we had in the first quadrant (again just the degrees and ordered pairs).  We then came back and worked with converting the degrees to radians.

The templates can be found at this link (thanks to the original blogger - Math Teacher Mambo!)  

The coolest trig foldable!

I found this style of foldable browsing around one day and just KNEW it had to be a part of my class somehow!  It is the coolest thing since sliced bread when it comes to foldables.....and what's even better is that the students think so too!!!

This is my adaptation of the foldable for trig functions.  On the outside you can see the basic SohCahToa with triangles where you set up the ratios (including it related back to the unit circle in the coordinate plane).  Then there's a section where you solve for missing sides in triangles...both where the variable is up high (multiply) and down (divide).  The last section is where you would solve for angles.  In the secret section (cue the shocked faces of your students) is where they look at the graphs of sine and cosine (tangent wasn't in our AFM standards, but I'm sure you could find a way to fit in if needed).

This would also be a good spot to refer back to function transformations and discuss how it all relates.

Secret Door Trig foldable front view

Secret door trig foldable inside view

The magic

 

Building up to The Unit Circle

Trig has always been one of my favorite subjects.  We have reviewed right triangle trig and I'm trying to work towards graphing, but first we are going to have to make a stop at the Unit Circle.  

My plan is to develop the side measures of the special right triangles using Pythagorean theorem and right triangle trig before discussing converting degrees to radians.  Below is the very beginning of this lesson.  Stay tuned for the rest.

Btw...I have a super awesome secret door trig foldable for this unit.

Function Transformations Foldable

I have a confession.  I love foldables!  If information can be organized into a foldable you can bet I will be on that bandwagon with my foldable loving flag waving. 

For this post I'm going to highlight a foldable I used in my Advanced Functions and Modeling class for transformations of functions.  I didn't think of adding the mapping notation on the flaps until after they had already taken their tests, but hey...there's always room for improvement next year right?

I chose a set up similar to this.  

And without further ado....