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!

Inequalities in Algebra

I’ve been fascinated by inequalities lately. I always find it interesting how students tend to get them backwards. I feel like they learn some bad habits and have some misconceptions about inequalities before they get to Algebra. It’s hard to get them out of those habits.

I’ve heard my students say that you always shade in the direction that the inequality is pointing. Because of this situation, I try to get them used to switching the inequality if the x is on the right side of it. This really is not an easy concept for them and I think it’s because they really do not understand what’s happening.

What is this sign? What does it really mean? Why do I switch it sometimes and not at other times? These questions are hard. I developed a lesson where the students do a discovery of what causes the inequality to switch directions. As they are solving problems in the Google Sheets activity a picture is evolving. The kids can’t wait to finish to see what the picture becomes.

The rest of the activity is setting up, solving and graphing inequalities. To see if students truly do understand, I ask them to either show work or explain their steps. This is really challenging for many students. It’s interesting to see if they truly know what they are doing.

I have several activities that go nicely with this one. Check out the resources below:

Holiday-Themed Math Activities

It’s always fun to incorporate a theme into a math activity. I thought it would be nice to have all of my Holiday activities listed together and I can come back and add things as I create them. Enjoy finding what you need! If you click on the item, it will take you to my store where you can read a description.

Expressions in Math

Dealing with expressions is the foundation of Algebra. The tricky part is the basic math that is involved. As a high school teacher, I love using expressions to have students practice their basic skills such as operations with positives and negatives and dealing with decimals and fractions. It doesn’t make sense to me to give my students practice problems that look like this: -5 + 8. I need them to know how to do that problem, but why not make it look like this: -5x + 8x. I also want students to use these expressions in a situation like a perimeter problem or an area problem. All of these things help prepare students for tougher problems and it gets them used to setting up problems themselves. I try to use a variety of resources through the first part of the year in Algebra. My daughter and I have both created expressions activities that can be useful for any math teacher that teaches expressions. Have a look below at two of our favorites: