Algebraic Expressions

By the time students are in algebra, they should have experience with algebraic expressions. I never feel comfortable enough with this fact, so I always start the year with a refresher. Expressions are the building blocks of algebra, so it’s better to cover this topic and make sure students have a good foundation before heading into solving equations.

As I begin the year, I like to review operations with integers and rational numbers, order of operations, expressions and terminology. Terminology is key. Students must know what you are talking about when you use words such as like terms, coefficients, variables, distribute and constants. Also, never assume students know things like a fraction is really a division problem and all numbers have exponents of 1 when no other exponent is visible. Get all of this taken care of in the beginning and you will find out really quickly who has these foundational skills and who doesn’t. I will not get the calculator out until after all of this material has been covered.

Here’s the content that I like to make sure to cover during the expression lesson:

• Setting up expressions from phrases like: five less than twice a number
• Evaluating expressions by plugging in a number for a variable. It’s important to review order of operations at this point.
• Simplifying expressions using combining like terms and distributive property.
• Using applications with expressions.

If students are able to do the 4 items above, they will be in a good position for success when moving to solving equations. I will probably take a week to practice expressions, but I feel like this is time well spent.

My lesson plan will look something like this – (I’m on a block schedule, so I see my students 80 minutes two days and 50 minutes on Friday.)

Day 1:

• Bell Ringer – Operations with Integers
• Math Terminology
• Expression Opener
• Setting Up Expressions
• Evaluating Expressions

Day 2:

• Bell Ringer – Operations with Rational Numbers
• Simplifying Expressions
• Practice Writing, Evaluating and Simplifying with a Partner
• Application with Expressions – Digital Practice

Day 3:

• Quizizz Activity – (I have a Quizizz Activity that practices the skills used in the application activity.)
• Quiz – Short quiz that will let me know how well the students understand the concept.

I have a resource that covers all of this material. The expressions lesson that I created has a PowerPoint that goes through the terminology and example problems. I like students taking notes and following along, so I have note pages that follow the PowerPoint.

The lesson comes with a practice page that contains 12 problems covering the three categories: writing expressions, evaluating expressions and simplifying expressions. The quiz has a section where students fill in terminology and the rest of the problems are multiple choice for quick grading.

The application part of this activity is a Google Slides where students show that they understand what an expression is versus equations or inequalities. Students then see some perimeter problems where the dimensions are expressions. Students solve the problems two ways. There is a video tutorial that walks students through simplifying some expressions with the distributive method.

Expressions are the foundation of Algebra. Students start learning expressions early in their math classes, but variables are an abstract concept and tend to be something difficult for them. The more we expose our students to understanding the purpose of a variable, the better they will grasp it. Give your classes lots of examples of how expressions might be used and keep checking for understanding. See if they can come up with their own examples. If they can create their own expressions and tie it to a real-life concept, then you know they have made the leap to understanding this idea.

If you’d like to look further into my Expression Lesson, I have linked it to the picture below. Thank you for going through this thought process with me and good luck with your students.

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, Â§28.025(c) and Â§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.

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

Preparing Your Students for Math Portions of College Entrance Exams and a Bright Future!

High School teachers and their students should be aware of the ins and outs of both the SAT and ACT admissions exams. Both of these exams are used by colleges and universities to decide if a student is eligible to be admitted into their institution. My goal as a high school math teacher is to be aware of the testing dates and keep my students practicing the skills needed to be successful on either or both of these tests. For the upcoming year, here are the testing dates for both exams during the 2021 – 2022 testing season:

*Possible School Dates. Not all schools offer the exams.

When a student asks me which one they should take, I always say both. Some students do much better on one of them than the other. The students should also think about which colleges they are applying and look at the requirements to help them decide which test to take. More urban high schools are paying for students to take the tests during the school day. This is an awesome opportunity and the students should take advantage. Another thing for teachers to keep in mind is that 11th grade students have an opportunity for recognition and scholarships through the National Merit Scholarship if they do well on the PSAT in October.

If you’re wondering how the SAT and ACT math portions compare, take a look at my chart below:

Now that you know more about these two exams, it’s time to start thinking about how to prepare your students. Even 9th and 10th graders can take the SAT 8/9 and the SAT 10 if you school chooses to facilitate it. All levels of students need practice over these exams. These tests are not like what students are accustomed to. One of the best ways for a teacher to understand how questions are asked is to take some practice tests. Very quickly you’ll see how you need to up your game in your classes and ask questions in different ways.

In 2016, I became a teacher on an Early College High School Campus. This is when my interest in college readiness soared. I also felt bad that in my previous years I did not give much thought about these tests. In 2016, I was given a class of seniors that had never passed the TSI (comparable to the ACCUPLACER). I had no resources, so I started researching and soon found out that I was going to need to create my own. Once I got most of my students to pass the TSI, I began preparing them for the ACT and SAT. Again, I had to create my own lessons. I’m happy to say that I’ve got all of these resources in my Teachers Pay Teachers store. I’ve got them in various forms. You can purchase bundles or individual lessons. I’m still enjoying creating these resources and I’m adding things as I go. My current project is ACT bellringers. I’m also adding distance learning resources so that no matter your situation, you can find what you need.

I’m glad you made it here. This shows that you are invested in your students. They rely on us to use our knowledge to advance their knowledge! I wish you and your students success and a happy future. Please check out my resources if you are limited on what you have available!

Other Related Posts:

TSI – ACCUPLACER READY

Study Guides for Math Portions of College Entrance Exams and College Readiness Exams

GETTING READY FOR THE OCTOBER PSAT

Are Your Students College Ready? 5 Teacher Challenges!

Resources:

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 ðŸ™‚

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!

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!