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30 Ways to Say “Show Your Work” (Without Saying “Show Your Work”)

If you’ve ever told a student to show their work and been met with blank stares, scribbled-down numbers, or complete avoidance, you’re not alone. The truth is, many students don’t actually know what show your work means—or why it matters. To them, it sounds like just another rule, a hoop to jump through. But what if we reframed it?

The key is helping students see that showing their work isn’t about writing things down just because we said so—IT’S ABOUT MAKING THEIR THINKING VISIBLE! It’s about leaving a trail so they can check their reasoning, catch mistakes, and explain their process. And sometimes, the phrase show your work just doesn’t connect.

So, let’s rethink the way we ask students to document their thinking. Here are 30 different ways to say ‘show your work’ that might resonate more with your students:

Continue reading 30 Ways to Say “Show Your Work” (Without Saying “Show Your Work”)
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What Unfolds in Your Math Class When the Bell Rings?

The bell to start class just rang. Now what? Let’s talk about those classroom openers that go by many names – “bell ringers”, “warm ups”, or “do nows”. After over 35 years in the teaching game, I’ve had my fair share of experiences with these little classroom kickstarters. You could say that bell ringers (or your preferred name) and I have a bit of a “frenemy” relationship. Why? Let me elaborate on the advantages and challenges I’ve experienced with bell ringers throughout my career.

As we head into a new school year, I’ve been thinking about what still works — and what needs a refresh. Bell ringers are one of those things that can either work for you or they can be a challenge. It’s important to know how to use them properly and to realize the purpose.

The Value of Bell Ringers

First things first, let’s acknowledge the credit bell ringers deserve. They can truly elevate your teaching game. Once seamlessly integrated into your daily flow, most students will fall in line. When students enter the room, they dive straight into the bell ringer activity. This gives you some precious moments to tackle all those initial tasks that need attention – like attendance, catching up with absentees, and the never-ending quest for missing assignments.

Wondering how to make this streamlined approach a reality? It’s all about setting the groundwork from day one. Here’s the deal: let your students know that the next time they walk into the classroom, there will be a bell ringer or directions on the board waiting for them, and they should start on it right away. Consistency is key here – when you establish this routine early on, students will come to expect it and know exactly what’s coming their way.

But that’s not all. Having them dive into the bell ringer gets their gears turning. It’s like flipping a switch that says, “Time to learn, folks!” The activity itself helps reel in their focus, and guess what? It prevents those precious minutes from vanishing into thin air. Trust me, math teachers know how to squeeze every ounce of learning time from the clock.

What adds to the charm of bell ringers is their versatility. They can serve specific purposes within your lesson plan. Whether reviewing a topic, accessing material that might otherwise be overlooked, or even acting as a captivating lesson hook – a purpose-driven bell ringer provides valuable insights to educators while aiding students’ comprehension of topics and sparking their interest.

I often used bell ringers to prepare students for upcoming exams such as in-school ACT, SAT, or state tests. Additionally, I found value in conducting reviews of past topics and addressing areas where I knew many students have learning gaps.

Let’s Talk Challenges Now

It’s important to know that bell ringers don’t always go as planned. One big issue is treating them as just something to pass the time. If students think they’re not important, they might not take them seriously. Have you ever had a student ask, “Does this count for a grade?” That’s their way of saying, “I’ll only do it if it matters.” So, the trick is to make sure they have a clear purpose. Even if grades aren’t involved, helping students understand how the bell ringer helps their learning is key. It is also important that students know that once they are finished with the bell ringer, there’s a good chance that someone in the room will have to explain how to work the problem or even go to the board and work it. If students feel like they might get called on, they will not want to get caught off guard.

There were times when I was in a pinch and had to create a bell ringer on the fly, without much preparation. It’s no secret that students can sense when things are a bit disorganized. You see, the whole “Fake it until you make it” idea doesn’t work well in teaching. You can’t pretend to be organized. With a classroom full of around 28 students, there’s just too much happening. You’ve got to be on your A-game. Teaching requires real organization and being genuinely ready for what’s ahead. So, take it from someone who’s been through it – staying organized is a true game-changer and that applies to having a prepared bell ringer.

There have been times when I decided to stop doing bell ringers altogether, or at least in some classes. During remote learning, my bell ringers didn’t translate well online, so I paused them for a while. The important thing is, it’s okay to change things up when needed.

Transitioning from one activity to another can make or break the classroom atmosphere. There were years when after the bell ringer, things got a bit crazy until I could get things back on track. Realizing the importance of fewer disruptions in certain classes, I chose to skip bell ringers to stay focused and keep my sanity intact. By the way, transitions can be smooth. If you give clear directions on what to do next and even set a timer, they can go better.

The biggest reason that I have a love-hate relationship with bell ringers is the significant time investment required to either source or craft them. It can feel counterintuitive to dedicate an hour to creating something that’s intended to occupy just around 10 minutes or less of valuable class time.

Purpose Matters

If you’re set on doing bell ringers, give them a purpose. Before going any further on your quest for bell ringers, stop and write the purpose the bell ringer will serve. Here are some suggestions:

  • It will be a hook for the lesson.
  • It will be a digital task.
  • It will be a review of the previous day.
  • It will be state testing review.
  • It will be college readiness review.
  • It will be spiral review.
  • It will be a writing task.
  • It will be a seasonal math task.

Once you lock in that purpose, you can hunt down the material. You need to think about how much time you want to spend on the bell ringer in class. That will help determine how many questions you want to have. I’ve listed some ways to come up with the problems:

  • Search real-life examples so the problems have meaning.
  • Use Desmos activities and spread them out over a week.
  • Write questions that are similar to the homework.
  • Use released test questions from your state tests or from college entrance exams.
  • Grab problems out of the math book at the end of units for spiral reviews.
  • Use AI generated questions. Beware! AI is not always great with math.

Now that you know your purpose and where your material is coming from, what format do you want to use? I’ve done different things, but one of my favorites is a three question approach where the first two questions scaffold for the third question. I’ve used this format in my ACT Bell Ringers as well as my SAT Bell Ringers. Day 26 from the SAT Bell Ringers is seen below:

Another option is “We Do, You Do”. Together with the class, the teacher works through 1 and 2 and then lets the students work by themselves on 3 and 4. In this format, the teacher will begin class working the problems. When students work the other two, she can go do her attendance and other tasks. This approach is good when you have students that have a hard time starting. The example below is from my Algebra Review Bell Ringers.

Recently, I’ve been developing a new style of bell ringers designed with differentiation in mind. Instead of every student working through the same set of problems, this format allows students to choose from multiple levels of challenge based on their confidence and readiness that day.

This approach keeps all learners engaged—whether they need a little extra support or are ready to stretch their thinking. It also builds student independence, since they’re making decisions about how to approach the task. These differentiated bell ringers aren’t uploaded just yet, but they’re on the way. I’m excited to share them soon!

Your Bell Ringer Investment

Most of us do not want to spend our precious teacher planning period on bell ringers, so we end up working on it at home. If you decide to create these bell ringers yourself, then by all means save them so you have them for the next year. Make your time investment work for you in the future.

If you decide that recreating the wheel is not for you, then you can look at what I have. I’ve bundled up my most-used bell ringers from over the years to save others some prep time. Whether it’s Geometry, Algebra, or even a sprinkle of Trig, there’s plenty of things to choose from. Check out the resource after the final paragraph. You can look at the individual items and purchase them separately too.

In closing, the journey with bell ringers is an exploration of balancing their benefits and challenges. As educators, we adapt and refine our approach, always seeking the best ways to engage our students. Whether you’re harnessing the power of purpose-driven bell ringers, navigating their quirks, or even deciding to take a break when necessary, remember that your dedication to creating a meaningful learning experience remains at the heart of it all. With purpose as your guide, you’re well on your way to transforming those initial moments into impactful stepping stones towards an enriched classroom experience. Keep up the incredible work, and keep those bell ringers ringing with purpose!

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Summer Reading for Secondary Math Teachers

Summer is almost here and teachers and their students cannot wait. I personally love summer and all that comes with it including time to read. Reading for pleasure is my favorite, but it’s equally fun for me to read about my interests. The last book I read was by math education expert Jo Boaler titled “Mathematical Mindsets: Unleashing Students’ Potential Through Creative Math, Inspiring Messages, and Innovative Teaching.” I love how Jo Boaler believes that all students can learn math and it really is about nurturing a growth mindset.

Here are a few suggestions for math books that will inspire and give you new insight into the wonderful world of teaching mathematics. These books were selected because they will be enjoyable and hopefully will not remind you of a boring inservice!

“Visible Learning for Mathematics: What Works Best to Optimize Student Learning” by John Hattie, Douglas Fisher, and Nancy Frey. (paperback version or Kindle version)

“What’s Math Got to Do with It?: How Parents and Teachers Can Help Children Learn to Love Their Least Favorite Subject” by Jo Boaler. (paperback version or Kindle version)

“It’s a Numberful World: How Math Is Hiding Everywhere” by Eddie Woo. (paperback version or Kindle version)

“Math with Bad Drawings: Illuminating the Ideas That Shape Our Reality” by Ben Orlen. (paperback version or Kindle version)

“100 Ideas for Secondary Teachers: Supporting Students with Numeracy Difficulties (100 Ideas for Teachers)” by Patricia Baptie and Sue Dillon. (paperback version or Kindle version)

Now that you’ve looked at the list, grab a cool drink, find a cozy spot, and dive into the world of math education through these inspiring reads.

If you will be teaching for the first time next year, I have a blog post that you should read called 1st Week of Math Class Ideas. Good Luck!

***Please be aware that as an affiliate marketer, I may earn a commission for any qualifying purchases made through the links provided in this blog post. This commission comes at no additional cost to you. I only recommend books and products that I genuinely believe will be valuable to you as a math teacher. Thank you and happy reading!

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15 End-of-Year Ideas to Keep Your Math Students Engaged

The end of the year is fast approaching and you’re probably wondering what you can do in your secondary math class to make the most of the time left. Here are some suggestions. See what will fit your situation!

  1. The obvious thing to do is review. You’ve covered a lot of topics throughout the year, so take some time to go over key concepts and formulas. Throw in some practice problems, games, technology, and hands-on activities to reinforce what has been learned. Reviewing is boring, so as you read down this list, use some of these strategies in your reviews.
  2.  Another idea is to assign a project that allows students to apply what they’ve learned to a real-world problem. This would be a great way to see math in action and flex their problem-solving muscles. An example would be to have students model real-world phenomena, such as population growth or temperature changes, using algebraic functions. This project would require students to apply their knowledge of function notation and graphing to real-world scenarios.
  3.  You will probably be giving exams, so another thing to talk about is test-taking strategies. Discuss how to read and interpret word problems, how to show work, and how to avoid common mistakes. Practicing these skills would be beneficial to show students how the strategy works. Teach your students how to make a brain dump. This is especially helpful for state exams.
  4.  Create a fun and engaging math competition for students to participate in. This can be a great way to end the year on a high note and showcase students’ math skills.
  5.  Offer individualized feedback to students on their performance throughout the year. This can help them identify areas for improvement and develop a growth mindset. If you have over 100 students, this could be a daunting task. Ask students to self-reflect first, then you could quickly add a statement or two and comment on what they felt were their strengths and weaknesses.
  6.  Recognize students who have excelled or improved in math throughout the year. This can be done through awards, certificates, or other forms of recognition. It’s also fun to give silly awards since, at this point in the year, you know the students so well.
  7.  Encourage students to set goals for themselves and create a plan to achieve them over the summer or in the next school year. It is a great skill to learn how to set goals. The great thing is that you don’t have to look at them. Have students type the goals in the notes on their phones and then encourage them to occasionally look at them to see their progress. 
  8.  Reflection activities can help students process their math learning and prepare them for future math classes. Some ideas are surveys, class discussions, journaling, writing a letter to their future self, and creating a portfolio with some of their best work.
  9.  Choose a math-themed movie or documentary to watch in class and use it as a springboard for discussion and learning. Some great options include “Hidden Figures”, “A Beautiful Mind”, “October Sky”, and “The Story of Maths”.
  10.  Create or have your students create math-themed board games that can be played in class. This is a great way to review key concepts while having fun with your students.
  11.  Group challenges encourage teamwork, foster critical thinking, provide a fun and engaging experience, build problem-solving skills, and promote healthy competition. Some group challenges are scavenger hunts, escape rooms, Kahoot, Quizizz, Jeopardy, debate, and so forth.
  12.  Take your students on a math-focused field trip to a museum, science center, or even a local construction site. This can help them see the practical application of math in the real world.
  13.  Bringing in a guest speaker would be a nice change and break up the monotony at the end of the year. It can inspire and motivate students, provide a different perspective, introduce new topics, build connections, and offer networking opportunities.
  14.  Peer tutoring is a great way to add something special to the end of the year in a math class. It encourages collaboration, builds confidence, reinforces learning, provides personalized learning, and promotes social skills.
  15.  Go outside if it’s feasible. Let students take their math notebooks and pencils and sit under a tree to study or take chalk outside and let students work on math problems on the sidewalk. Getting outdoors at the end of the year is a great way to refresh and rejuvenate yourself and your students!

It’s super important to plan out the end of the year for your math classes. You don’t want to bore your students with endless reviews and exams. Instead, make it fun with cool activities that connect what they learned to the real world. Personalized feedback is a must too, so get to planning and make the end of the year a blast for your students!

Here are some of my own resources that I tend to use at the end of the year:

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Digital Activities in Math Should Still Require Showing Work

One challenge math teachers face using digital activities in the classroom is that students put down their pens/pencils and don’t pick them up at all while working on the assignment. How many times have you given a digital test and students do not work problems on paper? Do you notice they sit and stare at the screen and try to answer questions without the aid of working the problem out by hand? I think this is a big mistake on our part as teachers. We need to train students to show work even if they are filling out answers online.

Most math teachers require a journal or a notebook for notetaking. I believe that this is the perfect place to show work. Require students to date and title a page in their journal and work problems in an organized manner in the journal. The page can be a part of the overall grade of the assignment. Showing work will allow students to show steps, explain reasoning and they will have the ability to go back and find mistakes. A teacher only needs a quick glance to confirm the students did what they were supposed to do. Here are three things to consider:

  • If a student has hardly any work done, that is a sign that the student may not know what to do.
  • If students miss all the problems and don’t show work, they are clueless.
  • If students get all the problems correct and don’t show work, they may be cheating.

There is a direct correlation between the amount of work shown and how much a student understands.

For example, I use Boom Cards in my class. My students know, when working on the cards, they have a page in their journal dedicated to showing work on the assignment. I allow students to work the boom cards as many times as they want to get the grade they want. When they show work, they are able to look back at the work and see if they can find a mistake. I haven’t tried this next part but, what if I took this a step further? Have the students highlight incorrect problem(s) and, if they find their mistake(s), they write a quick statement analyzing the mistake. How much better will the math “stick” if they analyze their own mistakes? If you’ve never used Boom Cards, click on the picture below:

The one time I would not use the journal to show work is for tests. I like to provide a colored sheet of paper for showing work on a digital test. The paper must be turned in when the test is completed. Even better is to have a piece of paper that has space for each problem. If you don’t have time to print one, then have students fold the paper in half, then in half again and then again if you need that many places for answers. When students open up the paper, it is separated into 8 boxes on the front and back if the paper has been folded three times.

I recommend taking up the paper after the test rather than have them take a picture and upload it. Here is why: students take a picture of their work to upload it. Now, they have that picture to send to whomever, like a friend in a later class.

A digital place to show work could be on a Google Jamboard. I used Jamboards alot during Covid. Students can easily open a Jamboard if they have a Gmail and use a separate slide for each problem. The Jamboard only comes with 20 slides, so think about this before having them use it. The Jamboard can also be shared with whomever so, be sure they put their name on it.

Example of a Jamboard

As math teachers, we tend to make a big deal about getting the right answer, but just as important as a correct answer is HOW to get the answer. If we constantly use digital activities in our classes and we are never looking at student work, then we have no clue if students really understand what they are doing. Looking at the work does not have to be time-consuming. You can quickly know if the work is legitimate or gibberish. You can catch cheaters by requiring work as well.

If we get away from having students show work, we are doing them a disservice. Our job as math teachers is to create problem solvers. It is hard to solve problems without going through steps or explaining how the solution is derived. Let’s change the way students think about digital activities and train them to show their work.

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Making Mistakes in Math

Say this to yourself: “I make math mistakes and it’s ok!” Most of the mistakes we make as teachers are probably because of being careless. Our minds are processing 20 different things while we are teaching. We are wondering if the students are understanding or if Susie is on her phone or if Johnny is ever going to come back from the restroom. 

Make it known from the beginning of the year that you WILL make mistakes and you need the students to catch those mistakes. If they catch the mistake, then give them bonus points or a sticker or some reward to let them know it’s important that they notice your mistakes. Also tell your students that you do not know everything about math. That might shock them. You need to show vulnerability so that the students feel comfortable about their own mistakes. When you make a mistake and a student points it out, say THANK YOU!

Something that I have said many times this year is that I want the students to be wrong… a lot. I want them to mess up. I want them to make mistakes. I want them to leave the class and say, “Well I made a lot of mistakes today in math.” Weird, I know…but if they can say that, then they worked hard in class. Mistakes are a part of learning. Mistakes mean effort. No mistakes will probably mean no work. 

Have you asked a student a question and they say, “I don’t know?” Tell them they can’t say that anymore. Do not let them write IDK for an answer on a paper. That’s a big no no. I tell the kids to “Fake it until you make it.” Act like you know. Put something down or give some sort of answer. Who cares if you are wrong! 

Next week when you are teaching, look at your students and see who is just sitting. Walk the room. Who has a blank paper. Don’t let this happen. Get the students involved and teach them to be ok with math mistakes. Mistakes are necessary! 

(Here is a gift to you. A digital display poster of Mistakes are Necessary. This is from my Google Drive… if you cannot open it, try from your personal email and not your school email.)

This post was a newsletter first. This is the kind of content that I like to write for my email subscribers. If you’d like to be a part of my email list, sign up here. My goal is to provide tips, ideas and resources for the busy secondary math teacher or tutor. If that’s you, please join.

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7 Reasons to use Bell Ringers in High School Math Classes

I’ve used bell ringers (sometimes called Do Nows or Warm-ups) my entire teaching career until the pandemic. For over a year, I quit using them. I was juggling too much to add bell ringers to the mix, but I’m happy to say that I’m using them again. I debated over whether to start using them because I do have a few cons that bother me.

One of my cons for using bell ringers is that it requires a transition from one task to another and sometimes transitions in a classroom are hard to deal with. Another con is that you have to think of what you want your bell ringer to be and that requires time which we as teachers have very little time.

The pros far outweigh the cons when it comes to bell ringers. I have 7 reasons why I feel like bell ringers are worth the struggle. It makes sense to me to continue using them because of what bell ringers provide.

  • #1 – Get the students busy from the start! As a teacher, the beginning of class is a chaotic time. We need to get the students settled and do attendance. If students are in a routine to come into the class and get started on the bell ringer, then the chaos is limited and the teacher has time to get organized.
  • #2 – Use bell ringers to recycle information or to review information. Maybe you want to review the first grading period during the second grading period using bell ringers. I’ve learned that 3 or 4 problems is the limit. A quick way to create something is to use material that you were not able to use during the first grading period. You might have run out of time to do a worksheet or maybe you did not get to go as deep as you wanted. Divide that worksheet into days and give it to your students at the beginning of the week. Students get the worksheet out at the start of class each day and work on it. (I have my students tape everything into their journal so they do not lose it.)
  • #3 – Use bell ringers as a quick check to find out what students know. For instance, before a lesson on the properties of exponents, you decide to see if students remember how to use integer operations or if they remember that 5^3 really means 5*5*5. Before any lesson, think about what might cause some issues. Do not assume that students remember their math from past grades. Give them some problems and see what they remember. This will guide you to take a moment to reteach some concepts before you get started.
  • #4 – Bell ringers can simply be a way to get your students thinking or “get the wheels turning” as they say. Some teachers call bell ringers warm ups. That’s a good name! Before you run, don’t you warm up. You want to get the blood flowing and the muscles stretched. The brain is no different. It’s great to have students focused and thinking before you begin a lesson.
  • #5 – This reason is related to #4 above… Use bell ringers as a lesson opener. To get the “wheels turning” use a problem to spark interest in the topic you are about to teach. Real-life problems are a great thing to use. It really doesn’t have to be anything but a picture or a simple question. For instance, before a quadratic lesson you could have a picture of a football player throwing a pass. You could ask students to predict if the throw is accurate or how many yards the ball will travel. The great thing about this kind of question is that anyone can answer it. All kids are on an equal playing field. All students can be successful on these types of questions.
  • #6 – Here’s a biggie… Use bell ringers to fill in gaps. Welp, we all know how important that is at this time. Think about the students you teach. What’s missing in their learning. What did they NOT learn the past few years that you can practice through bell ringers? You could literally pull material from the previous grade level and reteach it. If your state has standardized testing, go pull from old tests. You could even go back a couple of grade levels. Think of the good this would do!
  • #7 – Use bell ringers to prepare students for standardized tests. Not all math teachers think about preparing students for college entrance exams or college placement exams. Your students will be taking tests such as the ACT, SAT, PSAT, TSI or ACCUPLACER. Why not give them a taste of what they will see on these tests? Students are not familiar with the questioning used on these types of tests. What a great service you would be doing for your students if you helped prepare them for what they might see on college entrance exams.

I hope I’ve given you some ideas. To me, bell ringers are another learning opportunity. To provide the best thing for your students, you need to think about your particular groups. My Algebra students need something different than my Geometry students most of the time. The only time that I may give them the same bell ringers is if I’m in the mode of preparing them for the TSI or PSAT.

My biggest concern for my Geometry students is how much Algebra they lost last year. I created an Algebra bell ringer resource just for them. When I’m doing these bell ringers with them, I’ll ask them to raise their hand if they remember certain things. It’s terribly disappointing how little they learned last year. I’ll link this resource below if you are interested, but here is a freebie related to those bell ringers. Each day there are four problems. I work two with them and then they do two on their own.

Your next question might be, should you grade bell ringers? I usually grade on completion. I have students keep the bell ringers in their journals, so sometimes during a journal check, I might refer back to certain bell ringers and ask them questions about them.

I’ve attached some of my bell ringers below that are in my TpT store. Half the battle is having time to create them. Remember, bell ringers do not have to be something you create. It can be an old worksheet that you didn’t get to or it can be review material that you have. I’ve used my TSI material a lot as bell ringers. I’ll pull a page out of a lesson and it will become my bell ringers for the week. The great thing about TSI or ACCUPLACER material is that it covers a variety of content that students should know from past math classes.

Here’s what I’m currently using with my Geometry Classes:

These next two resources are for college entrance exams:

I use any of my TSI resources to pull from for various reasons. I recently pulled from this activity for my Algebra class bell ringers to help recycle previous concepts:

I have all of my bell ringers including in one bundle so you can save:

If you like my ideas and tips, then consider joining my email list. If you chose to do that, then you will receive a free exponential function hands-on activity. Join Now!

Good luck with your bell ringers. If you are not on board, I understand. I have my reservations at times too. You need to do what is best for your situation.

Please follow me at my TpT Store so that you know when I upload new resources. All my new resources are 50% off for 24 hours.

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First 6 Weeks in Algebra 1

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:

# of Days Topic
2Pre-Algebra Review – PDF Version or Digital Version
1Patterns (Boom Card Lesson)
1.5*Setting up and Solving Equations and Inequalities
1.5*Solving Equations and Inequalities
1*Literal Equations
1*Review Equations and Inequalities
My First 6 Weeks Plan

*Get all of the resources above in a bundle: Equations Bundle

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!

Happy Teaching!

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Examples of Real-Life Arithmetic Sequences

One of my goals as a math teacher is to present real-life math every chance I get. It is not always easy, I have to admit. When I was in college and the earlier part of my teaching career, I was all about the math… not how I might could use it in real life. I’ve made it a goal of mine to find real-life situations. I’ve also tried to catch the situation in action, but it’s not always possible especially since sometimes I think of an idea while driving or when I’m falling asleep at night.

My recent thoughts have been about arithmetic sequences. Seems easy, right? They are linear. There are a ton of linear situations. Yes, but I want visuals! I also did not want the situation to be a direct variation or always positive numbers and always increasing or positive slopes.

Below are some of the situations I’ve come up with along with a picture. I’m happy for you to use these situations with your classes. When you are finished reading this post, please consider filling out this feedback form called: Understanding Our Visitors. Enjoy!

Stacking cups, chairs, bowls etc. (Stacking anything works, but the situations is different when one thing fits inside the other.) The idea is comparing the number of objects to the height of the object.

Pyramid-like patterns, where objects are increasing or decreasing in a constant manner. Ideas for this are seats in a stadium or an auditorium. A situation might be that seats in each row are decreasing by 4 from the previous row. I use this in one of my arithmetic sequence worksheets.

Filling something is another good example. The container can be empty or already have stuff in it. An example could be a sink being filled or a pool being filled. (Draining should also be considered!) The rate at which the object is being filled versus time would be the variables.

Seating around tables. Think about a restaurant. A square table fits 4 people. When two square tables are put together, now 6 people are seated. Put 3 square tables together and now 8 people are seated. I really love this example. You can use a rectangular table as well and start off with 6 seats.

Fencing and perimeter examples are always nice. Discuss how adding a fence panel to each side of a rectangular fence would change the perimeter. Figure one could have one panel on each side (or change it so it isn’t square). Figure two could have two panels on each side. Each time find the new perimeter. The possibilities for fencing are endless. But how fun would it be to get actual toy fence pieces and do this in your classroom?!

Even though this is not particularly a real-life situation, it’s still good because the visual is real life. The students can touch the objects or even create the pattern themselves! Use toothpicks, paperclips or even cereal to make patterns. If you’d rather set them up somewhere in the room for math centers, then that would be good too! The following is an idea with cereal. If you count total Froot Loops, it’s not arithmetic, so it’s best to stick with rows, perimeter, or sides of the triangle to stay with a linear pattern. (Counting all of them is an area problem, so that would make it quadratic.)

Negative number patterns are not as easy to find. Our thoughts usually go to temperature or sea level. There are some fascinating places on earth that are below sea level. I think it would be cool to do a study on some of them. Once you’ve talked about some of these places, then various situations could be created like, during a rainfall the surface of the water started at 215 feet below sea level and rose at a rate of such and such per hour.

Situations involving diving in the ocean could be used as well. Did you know that a diver should descend at a rate no faster than 66 feet per minute or ascend at a rate of no more than 30 feet per minute? I’m sure many students don’t know why and this could certainly create some great accountable talk.

I hope I’ve given you plenty to think about. It’s really fun to create these problems. Students need to know that their math is real and useful! I hope this encourages you to use some of these examples or make up some of your own. I’d love to hear some of your examples. Leave a comment if you’d like. We can all learn from each other!

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Some of the examples I used above are in my Arithmetic Sequence Activity seen below. When I was creating this resource, it really stretched my thinking. I wanted to create something that students could learn from and see how these patterns are involved in real-life situations. I’ve attached a couple more of my resources. I’m also have a Geometric Sequence Activity that you can go check out. The second resource below would be a great follow up after teaching arithmetic sequences. It’s a Boom Card Activity. The third resource is an arithmetic and geometric sequence and series game. It is really suited for Algebra 2. The resource at the bottom is a formula chart for geometric and arithmetic sequences and series. There are 10 different chart choices! Go take a look!

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9 Exponential Functions Activities That Are A Must!

I could do exponential functions all year. I really enjoy them and think they are super fun. When I got my master’s degree, I did a study on exponential functions. I learned so much and I found that I was really interested in them. I created this first lesson more than 10 years ago and have been using it ever since! Creating that first activity sparked me into creating more and experimenting with some other ideas. I’m excited to share with you my list of 9 Must Do Exponential Function Activities!

(1) Exponential Function Poster Activity:

This is my very first exponential function activity that I ever created. It’s not the first lesson I teach when I’m starting this content, but it’s my favorite. This activity is the ultimate collaborative and differentiable activity. There are so many interesting exponential function situations! It’s been tried, tested and tweaked. Basically this lesson is a collaborative activity where the students are given an exponential scenario. The groups must create a multi-rep poster where they collect data, draw a graph, write an equation and answer a question.

The lesson opener is a bacteria problem. I want every student to get a feel of how they should work through one of these scenarios. The bacteria problem talks about what bacteria are and how they can multiply very quickly. I help the students go through the multi-representations to make sure they know what is expected of them when they start their poster.

Next, I show them their choices which are:

  • A Chain Letter Problem
  • A Zombie Situation
  • A Tournament Bracket
  • A College Football Situation
  • Making Friendship Bread
  • A Lovely Cockroach Scenario

Every situation usually gets chosen. You can entice students to create their own situation too. The college football situation was a student idea from years ago that I have improved upon to make it work better. Your students are amazing and creative, so don’t think that they wouldn’t be able to make up a situation of their own. The student of mine that created the football problem was not one of my top students, but because he was the one that thought of the scenario, he was interested and did a great job of completing the task.

After the bacteria problem, I turn the students loose and let them start their work. They are told to be creative and display the information in a way that is interesting and pleasing. I tell them to title the poster and make sure every person in the group writes on the poster. I supply the poster paper, the markers and the scenario sheets.

I’ve learned to watch out for misconceptions. Some students when creating graphs, will take the exact y-values and place those numbers on the y-axis. Here is an example below that I didn’t catch until it was too late. I cringe when I see this! (Not a very creative poster either…ugh!)

Once the posters have been created, it’s time for the Gallery Walk! I want the students to check out at least 4 posters. I’ve created a page that students fill in while looking at the posters. They have to write the title of the poster, determine the domain and range, decide if the situation is growth or decay and then write down one thing they may wonder about the situation. The conversations that I hear are amazing. They love getting to look at the other posters and they love to critique them as well.

I’ve had feedback from teachers that have taken my activity and changed it to fit their needs. One teacher used a speed dating strategy where the students worked through a problem on their own and became the expert. The possibilities are endless. Each teacher has their own unique way of teaching and their own unique classroom situation. If you have a group of rowdy kids that you don’t want up running around, then let them do their own problem on notebook paper or graph paper. You could even let them create the table and graph in excel and present the problem in a PowerPoint.

Check out this activity in my store: Exponential Functions Activity

(2) Exponential Function Activity in Google Slides Form

Out of necessity last year, I created a Google Sides version of the lesson above. I’m having a hard time deciding which one to use this year. Instead of making posters, the students create the table, graph and equation in Google Slides. This doesn’t sound very exciting except that my whole class was in the same Google Slides all working at the same time. I was 2000 miles away monitoring the activity. They asked me questions and I could see them working in real time. I loved it so much that I’m honestly going to have a hard time deciding what I should use. Maybe I’ll let one class do the posters and one class do the digital form and compare the two. If you are big into digital resources you will love this. I now have this version in my TpT store: Google Slides Exponential Functions Activity. Below is one of the slides that I graded. Looking at this now, I should have asked the students if this situation was discrete or continuous.

(3) Tower of Hanoi

Find a Tower of Hanoi game on the internet or have the students download an app on their phone. The object of the game is to move the discs from one stack to another stack in the least amount of moves. You can never put a larger disc on top of a smaller one. The number of discs and the least number of moves is an exponential function. It’s fun to let the students play a while and get them to create a table of the number of discs and the least number of moves and then see if they can figure out the exponential function.

(4) Twizzler Decay Activity

Tasty and fun. This is a freebie I’d like to share with you! I love using this as a quick lesson opener. Students measure a Twizzler and jot down the data in a chart. The student folds the Twizzler in 1/2, cuts it and measures it. Each time the student continues this step until there is not enough Twizzler left to work with. They plot the table and then lots of discussions can take place about decay or even the concept of half-life. Click Here for the Freebie: Exponential Function Twizzler Freebie

(5) Exponential Function Unit

This is the first thing I start with when I introduce Exponential Functions in Algebra 2. I refuse to stand up and lecture over this topic so I let the students work through this unit at their own pace. I copy the pages as a booklet. Students can use a calculator and even partner up if they want to work with someone. I let them work through the unit and figure out most of the information by graphing and using the information that they have already learned earlier in the year about transformations and domain and range. I do have to talk about asymptotes because we have not discussed this concept much up to this point. I teach on a block schedule and it takes most students a good 2 class periods to get this packet done. Topics covered are transformations, e, compound interest, 1/2 life, growth, decay, domain, range, y-intercepts, asymptotes, an inverse problem, writing equations from tables, growth and decay model scenarios, a paper folding activity, assessments and bell ringers and lesson closers. There’s a ton of information. I usually get the students to trade and grade after all is said and done. I feel like they learn a lot by working through this on their own. Students need to see that they can work on their own and figure things out. If you are interested, click the link: Exponential Functions Unit.

(6) Exponential Function Task Cards

I have a set of 20 Exponential Functions Task Cards. For some reasons, students do very well with task cards. If you put these same 20 questions on a worksheet, some students will be bored or are overwhelmed with thinking about doing a 20 question worksheet and they will give up. Take the same 20 questions and put one on a card, now they will sit there and work through them. It’s amazing! This set of task cards would be a great review right before an assessment. The task cards cover recognizing growth and decay from an equation, transformations, key features of graphs, the growth and decay model and compound interest.

(7) Sierpenski’s Triangle

How do you get all of these activities done? Part of my strategy is to do them in stations. Really math labs or centers would be more accurate. It would be hard to time these stations and expect students to be completely finished with each task. The Sierpenski Triangle activity, the Tower of Hanoi and several more exponential phenomena are discovered and tinkered with during my Exponential Stations Resource.

I love the Sierpinski Triangle activity because not only do the students create beautiful art work, they have to collect data on the number of shaded or unshaded triangles. We then put all of the triangles together to make a giant Sierpinski Triangle!

(8) Compound Interest Study

Students are told that they have inherited some money but to receive it, they must follow some rules. Every student in the class will probably end up with a different situation. Each student gets 4 cards that tell them how much money they inherited, how long they have to invest it and 2 different compounding options to compare. They work through their problem and then share their information. This study sparks lots of good conversations and helps the students realize that compounding doesn’t make much difference but time invested does make a difference! Get the Compound Interest Study Here!

(9) Marble Slides Exponential Function Desmos Activity

If you aren’t using the Desmos Graphing Resources, you need to start. I love the Marble Slides Activities and so do the students. There are several Marble Slides Activities for various functions. The object is to change the equations so that when the marbles are dropped, they travel the correct route and hit all of the stars which means success. Students learn how to manipulate the equations so that the marbles do just what they want. Very fun and engaging!

So there you have it! If you can get most of these activities and lessons done, then your students will know tons of awesome math content. I have all of these activities bundled (except for the google slides activity) into one package for 20% off. If you are intersted, then click on the pic below. If there is something that you can’t find, please let me know. I’d love to add things that teachers are looking for. Thanks for visiting this article.

Happy Teaching…