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.

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.

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!

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. 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 working on the geometric sequence activity now and hope to finish in a week or so. The second resource 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. It’s a freebie, so take advantage and download from my store!