Why is domain and range so tough for students? I’ve really worked on slowing down and teaching domain and range in detail the past few years. The idea that students are asked to find all the x’s and y’s that belong to a graph or situation is overwhelming. I believe part of the problem is that the concept is abstract. It’s not physically possible to name all the points that exist on a line. Students are not digging deep and realizing what the line or curve is really displaying (or saying). We’ve got to get them to see the details on the graph. Where does it start? Where does it end? What is happening between? I’ve created some online items that have worked well recently, but I have some older resources that I like to use too.
It’s important that students distinguish between finite and infinite values and which type make more sense for the problem. Give students real-life situations and make them think about these situations and what the graphs would look like in detail. A great example of a continuous function is when someone is getting gas out of a gas pump. Here’s a video you can use as an opener. There are tons of questions you could ask students about what is happening.
The concept of a vending machine is a great example of input and output (which would be a finite situation). If you push a certain button, then you get a certain item.
Last year, I created the lesson below. It is a Google Docs with an embedded Google Drawings. Students can click on a Google Drawings and move pieces around or type. I have found this to be very interactive and useful.
Here’s a sample:
The one on the left is before the student has clicked on the picture.
In the same activity, before I start having student plug into a table, I have them work on a function machine:
Function Machines in Google Drawings
This activity has 3 parts:
Relations and Functions
Domain and Range
Infinite vs. Finite Domain and Range
Below is another useful activity that I think works well for students each year. This lesson introduces reasonable Domain and Range and we practice which variable is independent and which one is dependent. The worksheet seen below is a tiny look at this activity that contains 10 graphs where the students are asked to find the domain and range. There are 5 linear graphs, 3 quadratic graphs, one circle and a graph with only points. Another worksheet asks students to create graphs with a given domain and range.
I love Boom Cards, so I’ve got a couple of Domain and Range activities that are great for extra practice. The problem below is a sample question in this activity. The students do not know what a parabola is at this point, but I still give them all types of functions. We will come back to domain and range again when we get to quadratics and exponentials. If you click on the picture, you will be taken to a 4 page preview of this activity.
Finally an escape challenge is the ultimate fun activity to end Domain and Range. If students can get through this tough challenge, then not only do they understand domain and range as well as reasonable domain and range, but they are good at following directions, reading carefully, figuring out combinations and they have that finishing spirit!
Domain and Range ChallengeDomain and Range Challenge
In Algebra, teachers tend to start completely over with solving equations as if the students have never seen equations before. Students have been solving equations for a while at this point. I thought it would be nice to take a look at a few questions from the state assessments in Texas to show what the students should know before coming to Algebra. I am a stickler for understanding what students should already know before they get to me and what they will learn after my class. This helps us to know what and how to teach certain content. My advice to all new math teachers: Do not get stuck in one math subject. Move around above and below where you like to be so that you understand fully what students have learned and will learn. Take a look at the questions below to get an idea of what they are tested on in 6th and 7th grades:
2019 6th Grade Math STAAR Test – By the end of sixth grade, students should be able to set up one-step equations and solve them.2019 7th Grade Math STAAR Test – By the end of 7th grade, students should be able to solve 2-step equations.
I don’t think there is anything wrong with reviewing the material. If you read my last post about Algebraic Expressions, you learned that I still review this every year. I do think this means that we should not spend too much time covering material that they should already know. The Pandemic has caused some issues with learning gaps, so it’s important that we recognize that we might have to review, refresh and even reteach. Continue to look at the next set of problems to see the progression:
2019 8th Grade Math STAAR Test – By the end of 8th grade, students should be able to solve equations that have variables on both sides of the equal.2019 Algebra Math STAAR Test2019 Algebra Math STAAR Test
It’s obvious by the time students finish Algebra, they should be able to solve multi-step equations with variables on both sides that contain the distributive property and might contain decimals or even fractions. It is very important that students understand how to check their answers. If the test is multiple choice, they will be able to get the answer correct by plugging in the answer choices. (I don’t like that, but before the STAAR test I make sure they know all the tricks and tips.)
My progression on teaching students how to solve equations goes like this:
Review solving one- and two-step equations. Discuss how an x is really 1x. Discuss inverse operations.
Practice checking solutions.
Use the distributive property in equations. Show students how to distribute and other alternate methods depending on the look of the problem.
Solve problems with variables on both sides. Use combining like terms.
Solve more complicated multi-step equations.
Solve equations with decimals and fractions. Teach students to clear decimals and fractions. (This is a skill that will come in handy on the college entrance exams.)
Solve equations that have no solution or infinite solutions.
Setting up and solving equations from word problems.
You may end up spending more time in this area than you planned, but think about how much it will help the students in other areas. If they have a good foundation of solving equations with one variable, then solving inequalities, literal equations, linear functions, quadratic functions and exponential functions will be much easier.
The progression that I discussed earlier is contained in some lessons that you will see below. I bundled this material in a comprehensive unit that contains:
This will be what I’ll use this year in my Algebra classes. All of these activities come with a PowerPoint for notes, a PDF packet with notes, practice and a quiz. There are also a few digital activities dispersed among the resources. Good Luck and remember how important it is to give your math students a strong foundation!
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.
Expression PowerPoint
Note Page Example
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.
With COVID still going strong, it’s hard to know how to prepare for the Algebra STAAR exam. Teachers are sick, students are sick, campuses are closing or going virtual. How do you deal with all of this? First, don’t put pressure on yourself. You can only do so much. You can plan and teach the students that are there. That’s it. You are an awesome teacher. Never forget that!
It’s 2022 and we are headed into the second semester of school. I’m wrapping up linear functions in a couple of weeks and I feel pretty far behind. My plan is to give myself at least three weeks before the test to review. I still need to cover exponentials and quadratics. How do I get all of this done? I like to get a calendar and put the test dates on it and mark off the three weeks of review. I look at my school calendar and make sure I know when spring break is and when the English I & II STAAR will be.
***You can get a copy of my planning calendar, so you can make it fit your needs. I’ll attach it at the bottom of this post.
Something new that I’m doing this year is focusing on the free response questions. I’ve created activities that will help students build confidence on the types of problems that they will see on the griddables or fill-in-the-blank problems. My students will take the online STAAR, so I’ve got this Boom Card Activity for them: Algebra STAAR Review Free Response Practice
Feb 28 – March 4: Algebra Task Cards (These are in the STAAR Bundle) as Bell Ringers or Opening Activity. Polynomials – Mainly multiplying binomials and refreshers on combining like terms and distributive property.
March 7 – 11: Continue Task Cards and Factoring
March 28 – April 8: Start Taking Task Card Timed Quizzes. Start quadratics using my objective 6, 7 and 8 resources from the Algebra I STAAR Bundle.
April 11 – 15: Continue with quadratics and do quick reviews of objectives 4 & 12(combined these two objectives have only been 3 – 5 questions in the past)
April 18 – 22: Reviews of objectives 2, 3 and 9 – I’ll use my STAAR Bundle, but I will pick and choose what I want to use from these objectives. (Bell Ringers will be key features of graphs.)
April 25 – 29: Objectives 5, 10 and 11 – I’ll use my STAAR Bundle, but I will pick and choose what I want to use from these objectives. Bell Ringers will be Brain Dump Practice.
When all is said and done, I’ll reflect and see how it went.
Please don’t stress out Algebra Teachers! Do what you can. Have a plan and work through the plan. Things will be fine. The students will do as well as they can and we will probably be pleasantly surprised at how well most of them will do. Remember that YOU ARE AWESOME!
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!
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!
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:
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:
***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.
**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 Schooland do:
10 Weeks of Algebra EOC Bell Ringers. (Get a FREEBIE sample of the Bell Ringers at the end of this blogpost.)
Pick days before Thanksgivingto 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)
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.
Algebra 1 is a fun but challenging class to teach. So many thoughts run through my head when I think about the beginning of the year in Algebra. One of the biggies is how much do the students remember from their previous math class? This is especially a big question since last year our district went to a distance learning format. I’m not sure what to expect from the incoming students, so I need a plan.
This year will be interesting. Our district has decided to have both online learning and in class learning. I’m working hard to make sure I have plenty of lessons that will work for either scenario. I’m going to start the year off with a two day review of number sense, order of operations and basic operations with integers. I’ve used this in the past because I always get a range of abilities, so I want to know where the students are. I have a print version of what I use and I’ve recently made a digital version. After I do the two day lesson, I give the students 3 quizzes (yep 3… because I want the repetition and plus it’s a challenge). All the quizzes are similar to each other but ask slightly different questions. The quizzes contain 15 questions. To move to the next quiz, students must make an 80 or better. If they don’t, they retake it. (These are timed because I don’t want the students to take too long. Either they know it or they don’t.) This can last up to 3 weeks. It’s not hard to keep up with because I take a grade on each quiz. Here’s a peek at the print version of the quiz vs. the Google Forms version:
The majority of the six weeks should (and hopefully will) be spent on solving equations. The days in the plan are block-schedule days. We have classes every other day for 80 minutes except on Fridays when the classes are only about 35 minutes. Below is plan that I will follow with the activities:
I’ve linked the topics to some of my lessons and worksheets that I used in my TpT store, but as I see the need, I go find content in other places. My district uses a couple of resources that I pull from as well, but our students know how to find answers online for these assignments, so I don’t like to use them for homework.
If you’ve never used quizziz.com, you should try it. The kids really enjoy doing these. I like that the students can do them more than one time. I have the students show work in their journal. Basically it’s just a digital quiz with 4 answer choices. These are teacher-made and there are a ton to choose from on just about every topic.
One of my favorite digital resources is Boom Learning. If you like task cards, then you will love Boom Cards. Again, these cards are teacher-made. There are a variety of ways kids can answer questions. I started creating my own decks. I used two of my own creations the first six weeks. One set of Boom Cards covered patterns and how to write an expression from a pattern. The other set was for practicing solving equations and inequalities. The kids can go through them as many times as they want so they get a lot of practice and get the best grade possible. To use Boom Cards, you need a teacher account. The free account is perfectly fine, but you don’t get to see the reports. The best thing to do is to get a paid account which is only $15 – 35 dollars a year depending on which plan you choose. Make your own decks or purchase decks. There are free choices as well. Click here to go check out my store. I’m brand new at making these, but I can already tell that this will be something I work on because all of my classes love Boom Cards!
After I get used to my students and find out who has gaps in their learning, then it will be time to dive into tutoring. I will engage my students through online tutoring this year. It will be an interesting year to say the least. I know that I will need patience and I will need to be flexible. I’m ready for anything and I hope you are too. I wish you well in your new year!
