Parallel Lines, Perpendicular Lines and Transversals

Why are parallel lines, perpendicular lines and transversals so important in Geometry? Have you thought about it? Why is this taught early in the geometry curriculum? Geometry is the study of shapes. How are shapes made? Yep, with lines or line segments to be more exact.

The whole time I’m teaching students about parallel lines and transversals, I’m constantly saying that this idea will return when we are dealing with future topics. One of my activities in fact, puts the converse of the postulates and theorems learned during this time into perspective. I ask the students to draw over the segments that make up the shapes to notice how parallel lines and transversals are involved. See below:

The resource with the above worksheet has a ton of hands-on activities. Students measure angles and discover which types of angles are congruent and which types of angles are supplementary. Parallel Lines and Transversals {with Project} is the name of this activity. It has a ton of engaging worksheets, notes, proofs and comes with a project and a short quiz.

Before I give my quiz over this lesson, I have the students do a Boom Card review. If you know me, then you know I love Boom Learning. This activity has 20 problems and students can redo them as many times as you will allow. It’s a great way to reinforce learning.

After the project, I specifically focusing on parallel and perpendicular lines. I love this lesson and the one over parallel lines and transversals so much because it gives me insight into the algebra skills of my students. After the transversal lesson, I have a good idea of who struggles solving equations. After the parallel and perpendicular lesson, I have a good idea on who struggles with the following major algebra concepts:

  • graphing
  • solving for y and understanding slope-intercept form
  • slope
  • using the slope formula,
  • plugging into point slope-form

It’s nice to help students with their algebra skills, but as far as geometry goes, why do they need to know when lines are parallel and perpendicular? The answer is the same as previous…shapes. This time we are learning about lines on a coordinate grid. If we notice lines are parallel or perpendicular, then in future lessons, we will know if a shape is a parallelogram, rectangle, square or even a right triangle. This Parallel Lines and Perpendicular Lines lesson could be used in an algebra class or a geometry class but I love how these two contents come together in this lesson!

I have a set of Boom Cards for this lesson too that I call: Parallel, Perpendicular or Neither?

This activity usually falls around Halloween for me, so I’ve also created a Halloween activity that is super fun. It comes without the Halloween theme if you prefer. It’s a nice way to reinforce this learning!

This unit is so important because it plants the foundation for many future topics. I think that it is so important that we as teachers understand where topics are headed. Sometimes, it is not related to anything else in our subject, but it needs to be taught for future years. If you have only taught Algebra or Geometry, I highly suggest that you reach out to your principal and ask to teach Algebra 2 and Pre-Cal and even Calculus if you get a chance. It is eye-opening! Algebra and Geometry are so important in these other subjects. I learn new things and how they are applied all the time. I see things that I teach my students right now and how useful they are in my son’s college engineering classes. It’s exciting to see how important our teaching really is.

If you are interested in all of these resources in one bundle, click on the picture below. Thank you for all you do and have a great school year!

Algebra STAAR Review Plan For Algebra and Geometry Teachers

***Please read further, but I recently found out that students that took Algebra and passed in the 2019-2020 school year are exempt from ever taking the STAAR test. When I wrote this, I did not know that. Here it is on the TEA website:

In waiving the required performance on academic assessments under TEC, §28.025(c) and §39.025(a) for spring 2020, the following applies: If a student is on schedule to complete instruction in the entire curriculum in spring 2020 for a course that has a corresponding STAAR EOC assessment, the student is not required to pass that specific test to fulfill graduation requirements. If a student is on schedule to complete graduation requirements in spring 2020 but does not have the opportunity to retake a STAAR EOC assessment prior to graduation, the student is not required to pass that specific test to fulfill graduation requirements but will need to complete the IGC process. For students graduating in future years but taking one of the five courses with a corresponding STAAR EOC assessment this year, those students will not be responsible for meeting that EOC assessment graduation requirement if they earn course credit this year.

This changes my thinking, but I am going to incorporate as much of the Algebra that I’ve listed below through bell ringers in Geometry since they are going to be weak. This will help them in their future math classes! At least now, I don’t have to do it all in one semester. I can spread it out over the year.

Here is this original post:

About 4 years ago, I created an Algebra STAAR Review that covered the newly established Algebra TEKS. Each of the Algebra TEKS is covered on a page of its own. At the top of each page, I put the objective practiced on that page. My thinking was if a teacher wanted to individualize the work, or just cover a certain standard in class, then this would make it easy for them.

Most people love the review, but some people complained that it was too much material. It is too much to try to cover in 2 or 3 weeks before the test. It is a detailed review with a short quiz at the end of each section. Each objective would probably take two to three (or more in some cases) 50 minute class periods to get it done. My mistake was that I did not give the teachers that purchased this review a suggested plan of action. With the craziness of school last year, I feel like it’s time to help teachers with a plan of action for the STAAR test. I have many questions from my district and the state that cannot be answered until we get closer to the school year, but I still want to forge ahead with a plan and I’d like to share it with you.

I am constantly studying the Algebra STAAR Exams. Recently, I took the tests from the last 3 years and put together an analysis. I wanted to see any patterns or trends. TEA has said how many questions come from each category, but when you figure out the details yourself, it’s eye opening. I’m going to teach all of the TEKS, but this helps me know which ones that I really need to emphasize. I took each objective and broke it into each standard within the objective and made tables and graphs for each objective. Below is the one I made for all of the objectives. The columns represent the number of questions in that category for that year.

*You can get a copy of the whole analysis at the end of this blogpost.

Before I share my plan, I wanted to discuss more about how to use the resources. For instance, Objective 2 has nine standards. There is no way to do all nine standards plus the quiz at the end right before the test if you want to review other topics. A suggestion is to use parts of the review during the school year to spiral the information. Pull them out when you need to review for a test or use them as bell ringers. Teachers have no time and before they know it the test is right around the corner. The best time to plan is as early as possible. My review bundle can be used throughout the year AND at the end of the year, so get the review now, print it off, put it in a binder and start thinking about how you can use the material. Also, if you purchase this and see something that needs to be added, just give me a shout out and I’ll see what I can do. (That’s the best part about purchasing from Teachers Pay Teachers. We can revise and edit as needed!) One thing that I really love about creating resources and lesson planning is being able to help other teachers that do not have the time to do it themselves, so here’s my Algebra STAAR TESTING PLAN for 2020-2021. I’m using the dates set by Texas as of July 2020. If things change, then I’ll adjust. I will be teaching both Algebra 1 and Geometry next year. Both groups will be taking the Algebra STAAR at some point since the STAAR testing was cancelled last school year.

EOC BEll Ringers – 10 Weeks, 120 Problems

All of the plans below are based on my Algebra STAAR Bundle and the EOC Bell Ringers-(I’ve changed the title to “Algebra Bell Ringer Review” but it is the same as previous.) The one thing not incorporated into my plan as of now are the quizzes at the end of the objectives. These could be used as pretests, posttests, homework, tutorials etc. I’m sure times will arise that I’m not thinking of right now, where I can use them.


TEST PLAN – December Test

(Testing Window – December 8 – 18, 2020)

Who is the Test For? Students that did not pass the Algebra STAAR in previous years and geometry or other math students that did not pass the Algebra STAAR or never took it because of COVID-19.

*If you see red Algebra TEKS in my descriptions below, they are readiness standards which means they are more of a focus on the test. (Go Look at the Algebra TEKS on the TEA website.)

**Note to Geometry Teachers – Let’s face it, Geometry will not be the same. You will need to focus on Algebra when you can. Some Geometry topics will not get as much attention this year!!! Some good news is that we do cover Algebra naturally in Geometry. While we are working on Parallel and Perpendicular lines, we can cover these Algebra Standards: 2B, 2E, 2F, 2G. When we are working with segments, segment addition, angles and angle addition, we can cover the solving equations standard: 5A.

  • Start the 2nd Week of School and do:
  • Pick days before Thanksgiving to work specifically on these topics: (***Side Note – My Algebra EOC Review covers all the TEKS and at the top of each page the objective is written, so you can easily pull the TEKS you need!)
    • Linear Topics – Writing and Graphing Equations Slope and Key Features of Graphs (2C, 3A, 3B, 3C)
    • Writing, Graphing and Solving Linear Inequalities (2H, 3D, 5B)
    • Quadratics – Writing, Graphing, Key Features, Transformations (6B, 6C, 7A, 7C)
    • Factoring and Solving Quadratics by Factoring (10E, 8A)
    • Writing and Solving Systems (2I, 3F, 5C)
  • Week of November 30:
    • Laws of Exponents (11B)
    • Exponential Functions (9B, 9C, 9D)
    • Domain and Range (2A, 6A, 9A)
    • Any other last minute details

TEST PLAN – May Test

(Testing Window – May 4 – June 4, 2021)

Who is the Test For? Students in Algebra 1 and students that did not pass the previous Algebra STAAR test.

For the Algebra I Students: (Use the Algebra Review STAAR Bundle)

  • Use these objectives as Bell Ringers OR add them to your homework/classwork starting the 2nd Semester. Each of these objectives is covered on a page in the bundle for that objective:
    • 1st Week: 2B, 2D
    • 2nd Week: 2E, 2F, 2G, 2H
    • 3rd Week: 3A, 3H
    • 4th Week: 4A, 4B, 4C
    • 5th Week: 12A, 12B, 12E
    • 6th Week: 9A, 9B, 9E,
    • 7th Week: 10A, 10B, 10C
    • 8th Week: 10D, 10E, 10F
    • 9th Week: 6A, 6B, 6C
    • 10th Week: 8A, 8B, 11B
    • 11th Week: 12C, 12D
  • End of March: (March 22, 2021)
    • The 3 Quizzes and Task Cards – (This is part of the bundle!) This takes a while to complete. I usually start the Task Cards at the end of March. Last year, I used the Task Cards as flash cards and put them in rings for each student.
  • 2 Weeks Before the Test:
    • First Week:
      • 3B, 3C, 3D, 3E
    • 2nd Week
      • 5C, 9C, 9D, 11B
  • 1/2 Day of Camp :
    • Use the worksheets and the task cards to do: 2A, 2C, 2I
    • Use the matching cards to practice: 3F, 3G, 3H
    • Use the task cards to do: 5A, 5B
    • Use the worksheets to do: 7A, 7B, 7C

For Students that did not pass in previous years or in December:

  • Invite to 1/2 Day Camp
  • Individualized Packets – Use their test results to create individualized packets.

I have a link to the plan and analysis below so you can have your own copy. To sum up what you will need to follow this plan:

Here’s a free sample of the Bell Ringers: Bell Ringer Sample

Diving into the First Unit of Geometry Headfirst!

Sometimes you’ve just got to get started and quit worrying about the perfect way to do something! As teachers, we tend to overthink. We want everything to be perfect. In teaching, there is no perfect. Just dive in and GO!

There is no better place to start in geometry than with the three undefined terms: point, line and plane! First, I like to see what students remember from past geometry lessons so I’ll ask them to list as many things as they can think of from their past math classes that had to do with geometry. I am amazed at how many students just sit and stare when I ask them to create that list. Sometimes I’ll have to prompt them by saying, “Do you know any shapes?” If they say yes, then I say, “Then you know some geometry.” I’ll ask again, “Do you know what a right angle is?” They usually say yes, so this is a nice way to get the ball rolling.

Now that the students realize they have an idea of some geometric concepts, I begin my lesson. We talk about how hard it is to define a point without giving an example. I go on to talk about line and plane and we discuss how in real life, there are no lines that go forever on this earth so we have to use examples that come close.

Next, I bring up some other important objects to see if students know what they are, such as segments, rays and angles. Students usually remember these from the past, but they are not familiar with how to name them using symbols. We discuss how to use a combination of letters and symbols to name things and how sometimes, you can use multiple ways to name the same object. Students struggle with writing names of geometric objects the correct way, but they get better as the year progresses.

When I talk about angles, I like to bring out the patty paper. This really gets the definition of an angle across. I like to have students draw two different rays on separate pieces of patty paper. They call one Ray CA and the other Ray CB. We then work on creating different types of angles and then they tape it into their notebook. Regular paper would work for this as well. You can see through regular paper well enough to do this exercise. ***Side note – If you are in a distance learning situation, think about materials that students should have on hand and tell them ahead of time! You might need to get creative.

Another geometric concept that students usually know before entering my class is supplementary and complementary angles. If they struggle on knowing the difference, I use this little trick seen on the left. After I show the students this visual, they never forget the difference!

I finally finish up the lecture part of the lesson by discussing adjacent angles, vertical angles and linear pairs. We also need to spend time on collinear points, noncollinear points, coplanar points and noncoplanar points. This lesson is packed full of vocabulary so students need to start an interactive notebook to keep all of this information. ***Play-Doh is a great visual when explaining some of the vocabulary! Imagine three Play-Doh balls place in a line with a pencil or a straw place on top of them. This would show collinear points!

We do some practice worksheets to make sure they are starting to understand. The next time we meet, we will work on the postulates that use these basic terms and try to use as many real-life objects as we can when discussing them. Here’s an example of my Google Slides presentation of one of the postulates:

I like to give a quiz over this lesson after students have completed the work. I give them a warning that the quiz will happen the next class. To make sure they do well on the quiz, we grade each other’s classwork and homework and make corrections and then give it back to the owner. ***In a virtual lesson, have students grade their own. Call on individuals to give their answers. I usually just give a completion grade over this because it’s not usually a pretty grade 🙂

The second big lesson of the year that I cover is segment addition and angle addition. This lesson has everything: measurement, setting up equations, solving equations and more postulates. It’s also great for continuing to discuss the correct way to name segments and angles. I love having students measure things because even in high school, they struggle on this. I find that they have misconceptions on how to measure inches. Students will try to measure something that is 1.125 inches as 1.1 because they are confused on the precision and do not understand that inches are not broken into tenths like centimeters are. (WHEW! Yes, sadly this is true.)

I’m ready to do this lesson virtually or in a live classroom this year by having rulers and protractors ready to go on my digital lessons. I’m anticipating some fun with this and I do expect some questions about accuracy. I know some students will round to whole numbers which is not what I want.

I love love love the equations involved in segment and angle addition. Students get practice on setting up equations correctly and then solving and plugging back in to find the segment or angle. It’s so important to use Algebra in Geometry as much as possible. ***Side note: If you are from Texas, your Geometry students will likely be preparing for the Algebra STAAR that they missed last year, so be sure to cover equations every chance you get.

I made a video preview of the digital version of this lesson if you’d like to take a look:

Before I give a quiz over the segment addition and angle addition material, I want to review all the things that we’ve done so far. I’ll give my students the Boom Cards that cover the first and second lessons. If you have not used Boom Cards, you need to start! I love Boom Cards. You can join for super cheap and there is even a free version, but you’ll want to upgrade after to you use it!

After all this practice, the students are ready for the next quiz. I like to give a lot of quizzes in Geometry because there are so many details and this is a great way to see how students are doing.

The last lesson in my first unit of Geometry covers distance and midpoint. This activity requires the student to be active! Students will discover both methods and see that they would probably figure out how to find these lengths and points or locations on their own using logic. Students should have learned Pythagorean Theorem in the past and I like to show the students how the distance formula was derived from the Pythagorean Theorem.

The last part of this activity is a silly made up story that I call the Zombie Turtle Problem. (Have you ever heard the Tom Petty song, Zombie Zoo? This song inspired me to do this problem. The song is silly but I love it.) I’ve placed some items on a map and the students have to find different distances and midpoints and then I tie in perimeter. Here’s a snippet of the problem:

I’ve recently made all three of these resources ready for a virtual learning situation. Teachers Pay Teachers has made this possible for all resources that were originally downloaded as a PDF. I’m excited that no matter what situation I go back to in the fall, I’ll have these up and ready to use whether I’m in a live classroom or I’m delivering my lessons via a digital platform.

Before you leave, go check out the freebie that you can use for later in there year. It’s down below my resources!

All of these lessons are in Unit 1, but they come individually as well! Check out the links below. Good luck and I hope you’re excited for your first lessons in Geometry!

All 4 Resources in One!
1st Lesson in Geometry
2nd Lesson in Geometry
Review for the Quiz over 1st Two Lessons!
3rd Lesson in the Unit
All the Geometry Units!

One last thing, if you’d like a freebie for later in the year, click here: Special Right Triangle Freebie.

What else do you like to do in your first unit that you don’t see here? Feel free to leave me a comment below!

Inductive vs. Deductive Reasoning

One of my favorite Geometry lessons is the one introducing inductive and deductive reasoning. It’s fun and engaging. I like to open the lesson by showing the students a YouTube video: Monty Python Deductive Reasoning (Should be called Inductive Reasoning, but oh well!)

This lesson has many opportunities for discussions on how people reason and come to the wrong conclusions. You can bring up the media, social media, racism and many topics where people might come to the wrong conclusions. I also like to talk about predicting weather. The topics are endless.

My lesson from Teachers Pay Teachers has several handouts that can be added to the student’s interactive notebook. One of the activities is to have students cut out the examples seen below and place them with the correct headings: Deductive or Inductive.

The lesson also includes some 12 task cards. I like to group the students into fours and have them turn their desks together. They put the task cards in the middle of the tables and select a card, answer it on an answer document and then place the card back into the middle of the pile. Here’s a sample:

Finally, the lesson has a short 3 question worksheet that I like to use as a group quiz. I have the students work together through the quiz. They all have to write on their own paper. I assign each person a letter and they put it beside their name. After about 15 minutes or less, I spin a spinner that has A, B, C, or D on it. The person with the letter I land on, puts their paper on top and that is the one I grade for the group. I tell them this ahead of time. This gives them incentive to work and make sure everyone is participating.

Here is a copy of the resource that I have on TpT. Take a look. It’s also a part of a unit as well as in my Geometry Curriculum.