Real-Life Exponential Functions

Exponential functions are right around the corner for my math classes. I always look forward to this time of year. The best part about exponential functions is the real-life aspect. Students are more interested if they can make a connection. Draw your students in and they will enjoy this topic without realizing how much they are learning.

One of the first real-life examples that I can think of right now, is COVID-19. Remember when the saying was, “Flatten the curve?” What an interesting thing to talk about with students. A flatter curve means what? A steeper curve means what? What a great thing to talk about!

Here’s a great research letter I found on the CDC website. This has some wonderful references to “doubling time”. The research brings in some formulas and if you look at some of the appendices, it gets pretty technical, but it is fascinating.

The Coronavirus is a topic that I’m sure will get the attention of your students. Another topic that students may not be as familiar, but it is definitely worth mentioning is the stock market. Let your students read this article from Forbes. They may not think the stock market is very exciting, but after reading this article, it might spark some students to consider how they can one day invest in stocks.

A really fun exponential growth activities is the paper folding activity. I’m sure most math teachers have used this when teaching exponential functions. I love that Myth Busters tried to fold a giant piece of paper to see how many times they could fold it. Check out this video below:

We’ve been focused on exponential growth, but what about decay? Carbon dating is a topic that is also fascinating. This article can help students and teachers alike to understand carbon dating a little better: What is Carbon Dating? This might help students understand how scientist can estimate the age of an object. Below is a nice video that explains carbon 14 and half-life.

If you’ve read my blog before, you know how much I love exponential functions. I’m always on the lookout to learn more and find interesting things for my students to do. Below, you’ll find some of my resources that I sell on Teachers Pay Teachers. I’ve got all kinds of exponential function activities to keep your students busy and interested. Go take a look and I hope that you will want to follow my store and join my email list!

Slope and Rate of Change

I was going through a review of slope that I made a couple of years ago. I love this resource! It was created for the 8th grade STAAR, but I feel like all Algebra teachers would love this. Students are supposed to come into Algebra with a concept of slope already! Why do students have such a hard time with it? Slope is a fun and interesting concept and of course ties to so many real-life situations. Let me tell you what this review contains:

Now remember that it is a review of slope! The first page gives the students a picture of a line with four points on the line. The students are asked to find the slope of two different segments along the same line, two different ways. The picture also has two right triangles drawn that were created from using the endpoints of the segments. Students that already have a concept of slope should be able to think of several ways to find slope. I love this so much. On top of that, shouldn’t the slopes be the same and the two triangles created are similar. Hopefully students will have that Ah-ha moment!

The next two pages have the students interpret the meaning of slope by matching a situation to a graph. The students are thinking of slope as a rate of change and having a proportional relationship. I love the different graphs. Teachers could ask the students to find the slopes of all of the graphs first before trying to match them to the situation. Students are asked to explain why the graphs they did not choose are incorrect. Having students explain their reasoning is always important in math.

The next four pages are a set of 24 matching cards. 12 of the cards have either a graph or a table. The other 12 cards display a slope, y-intercept or another way of identifying that it matches one of the graph or table cards. This activity is engaging and students have to know what they are doing!

Finally, the last page in this resource is something that I have consistently placed in every 8th grade STAAR resource. I call it Smath’s Problem. It is an activity that reviews several of the topics in the resource. It is interesting and students enjoy working through the situation. It can be used as an assessment or a group activity.

I think you’ll enjoy this resource. All of the answer keys are included. Take a look if this sounds interesting!

Texas Success Initiative Assessment in Math 2.0

The new version of the Texas Success Initiative comes out in January. As far as the math goes, there is nothing new on the test. Students will still get a 20 question test, but if they don’t score high enough on that part, they get a second chance to pass it during the diagnostic portion.

If you want to know more about the test, the best place to go is to the Texas Higher Education Coordinating Board. This site is full of information. The specific TSI part is hard to find, so click here and you’ll go right to it.

Why should high school English and math teachers be interested in this? Students must pass the TSIA to take college English and math classes. This includes dual credit math and English classes. The only way students do not have to take the TSIA is if they score high on the SAT or ACT before they are starting their college-level classes.

The math portion covers 4 main areas:

  • Quantitative Reasoning
  • Algebraic Reasoning
  • Geometric and Spatial Reasoning
  • Probabilistic and Statistical Reasoning

I’ve created 6 practice sheets that mimic the College Ready portion of the test which is the 20 question test. Each practice sheet has 20 questions. The first 6 cover quantitative reasoning, the next 7 cover algebraic reasoning, the next 3 over geometric and spatial reasoning and the last 4 cover probabilistic and statistical reasoning. If your students struggle on any part of them, then I have other TSI resources that will help them further.

Here’s a pic of one of the sheets:

If you are not a Texas teacher and just need some good overall reviews for your ACCUPLACER class or your junior or senior math classes, these practice sheets would come in handy!

Go check this resource out or if you are interested in getting all the TSI materials, then check out the bundle!

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!