Tag: Math

Math Events and Phenomenon in 2024 For Your Secondary Classroom

In our pursuit of enhancing math education, let’s look into engaging activities that bring real-world events into your classroom. I’d like to explore some noteworthy occasions in 2024—Leap Year, Pi Day, and the Total Solar Eclipse (to name a few) — and how to seamlessly integrate them into your math lessons.

Leap Year

Leap years serve the purpose of aligning our calendar with Earth’s orbit around the sun. Picture this: a year clocks in at around 365.25 days. Without those periodic additional days, our calendar would gradually veer out of sync with the solar orbit.

Leap Year is on a Thursday so it would be a perfect time to throw in some real-life math that day. Here are three suggestions:

  • Leap Year Calculation and Discussions: (I pulled this from https://www.almanac.com/when-next-leap-year) A year may be a leap year if it is evenly divisible by 4.Years divisible by 100 (century years such as 1900 or 2000) cannot be leap years unless they are also divisible by 400. (For this reason, the years 1700, 1800, and 1900 were not leap years, but the years 1600 and 2000 were.)
  • Average Year Length: Examine the average length of a year, accounting for those crucial leap years. For example, if we take a four-year period (which includes one leap year), the average length of a year would be: (365+365+365+366) divided by 4 = 365.25 days
  • Birthday Probability: Inject some practical math by examining the probability of being born on February 29th. The chances of a baby being born on Leap Day is pretty slim: about one in 1,461, as Feb. 29 only comes around once every 1,461 days. And if a baby is born during a Leap Year, the chance of their birthday falling on Feb. 29 is a one in 366 chance (but of course, it all completely depends on when the baby was conceived).

Pi Day and More

Another event early in 2024 is Pi Day. Each year math enthusiast celebrate this event because of the numbers on the calender: 3/14, but did you know about these other celebrated, but not as well known math days?

  • “e” or Euler’s day which would be on 2/7
  • Palindrome Days which will occur in April in 2024, such as 4/2/24 or 4/21/24 etc.
  • Fibonacci Day: 11/23

My neighbor worked at Lockhead Martin for years and it was a thing to bring pie on Pi Day each year. Of course the engineers at Lockhead would think of that! People in general have embraced Pi Day, so it’s a fun event to celebrate each year.

Here is the activity that I do for Pi Day to refresh area and circumference of circles: Area and Circumference of Circles Coloring Activity

A good activity for Euler’s Day would be one where compounding continuously is explored. I have this activity called: Compound Interest Activity. In my Log Unit, there’s a section on dealing with natural logs, so that would be a nice activity as well.

I have never celebrated Palindrome Days before, but it would be really great to do that in April of 2024. Palindromes’ in general could be explored: words, phrases or numbers.

  • Examples of word palindromes: racecar, level, rotator, civic
  • Example of phrase palindromes: A Santa lived as a devil at NASA
  • Example of a palindrome math problem: 121 X 11 = 1331

Total Solar Eclipse

Now let’s discuss the Solar Eclipse that occurs on April 8, 2024 in North America. The path starts in Mazatlan Mexico, passes from Texas to Maine and into the far east of Canada. You can view the path on the NASA site here.

April 8th is a Monday. Start now and think about how you can take advantage of this phenomenon. If you love STEM activities, the sky is the limit (literally)!

If you are planning to take your students outside to see the event, you might want to start journaling about the event. My husband created an Eclipse Journal. The journal helps students explore thought-provoking questions, research tasks, and engaging activities. My husband is a biology teacher and an eclipse enthusiast.

If you aren’t the journaling type, then what can you do on April 8th? Here are some ideas:

1) If you are in the path and have permission, take your class to watch. You must take safety precaustions. Either purchase eclipse glasses, or make eclipse viewer.

2) Not in the path, but still want to watch? Here’s where to see past eclipses and future ones: Exploratorium.

3) Here’s a math challenge called Pi in the Sky from NASA. I hope you find all of this interesting. I know your plate is full, but real life events are a perfect time to show students how math can be used outside of the classroom.

Let’s gear up for a an exciting year in our classrooms. We’ve explored Leap Year, Pi Day, and the Total Solar Eclipse in 2024, but there’s another cool date in the not so distant futre… mark your calendars for a unique mathematical celebration on July 24, 2025 – Pythagorean Theorem Day! No matter where in the world you are or how you write the date, the sum of the squares of the first two digits (7 and 24) perfectly aligns with the square of the year (25). It’s an opportunity to explore the wonders of Pythagoras’ Theorem in a fun and memorable way with your students.

Here’s to a year filled with hands-on learning, real-world connections, and the joy of discovering the wonders of math in everyday life. Wishing you and your students a fantastic and mathematically enriching journey!

Mental Math in Secondary Math Classrooms

Let’s talk about mental math, a skill that holds immense value for our secondary students. Elementary teachers work with students on mental math but in middle school and high school it becomes limited because we have such a broad curriculum to cover and time becomes an issue. As experts in the field of math, we have a unique opportunity to equip our students with the tools they need to thrive academically and in real-life scenarios.

As a high school math teacher, the lack of mental math can become apparent. Here are a few ways that I know a student struggles with mental math:

  • They reach for the calculator to do simple tasks.
  • They struggle with positives and negatives.
  • They do not know multiplication facts.
  • They do not have confidence and avoid responding.
  • They struggle with estimation.
  • They have a lack of number sense.

The SAT is removing its “no calculator section” in 2024, and calculators are becoming increasingly common in everyday life. So why should we still teach mental math?

  1. Mental math is a valuable skill that can help students in many ways. It can improve their speed and accuracy in calculations, and it can also help them develop a deeper understanding of mathematical concepts.
  2. Mental math can help students become more strategic thinkers. When they are faced with a math problem, they need to be able to decide whether to use a calculator or to solve the problem mentally. This requires them to think about the problem carefully and to consider the best way to solve it.
  3. Mental math can help students become more independent learners. When they are able to solve math problems in their head, they don’t need to rely on a calculator or on someone else to help them (this is a dream for a math teacher). This can give them a sense of confidence and accomplishment, and it can also help them become more self-reliant.
  4. Mental math can simply be fun. It can be a challenge to try to solve math problems in your head, and it can be satisfying to be able to do it successfully.

How do we convince students that mental math skills will help them beyond the classroom? The best way is to give them some scenarios of things they could face. The number one thing to get across is that if students do not have good mental math skills, then they can easily be taken advantage of. Mental math can be used in many situations. This is a list of 15 ways students might use mental math in their future endeavors.

  1. Shopping: When shopping, mental math allows you to calculate discounts, estimate total costs, and compare prices to find the best deals without relying on a calculator.
  2. Financial Transactions: Whether you’re receiving change at a store or checking your bank balance, mental math helps you verify that you’re getting the correct amount and avoid errors.
  3. Cooking and Baking: In the kitchen, mental math enables you to adjust recipe quantities, convert measurements, and quickly calculate cooking times.
  4. Budgeting: Mental math skills aid in budgeting finances, helping you track expenses, allocate funds, and plan for future financial goals.
  5. Tip Calculation: When dining at a restaurant, you can easily calculate tips based on percentages, ensuring accurate gratuity without the need for a calculator.
  6. Time Management: In time-sensitive situations, mental math allows you to quickly estimate durations, plan schedules, and manage your time effectively.
  7. Travel Planning: When traveling, mental math helps you convert currency, estimate distances, and calculate time differences between different time zones.
  8. DIY Projects: In home improvement projects, mental math allows you to measure and cut materials accurately and estimate the required quantities of materials.
  9. Fitness and Health: Mental math is useful in keeping track of workout routines, counting repetitions, and monitoring health-related data like calorie intake or heart rate.
  10. Navigation: When driving or navigating through unfamiliar places, mental math aids in estimating distances and travel times between destinations.
  11. Tax and Tip Calculation: While dining out or shopping, mental math helps you quickly calculate total bills, including taxes and tips.
  12. Sharing Expenses: In group settings, mental math facilitates the fair division of expenses among friends or colleagues.
  13. Home Management: In household chores, mental math assists in determining the appropriate quantities of cleaning products, cooking ingredients, or household items to purchase.
  14. Career and Business: In various professions, mental math aids in analyzing data, making financial decisions, and calculating costs, profits, or margins.
  15. Emergency Situations: During emergencies, mental math enables you to quickly assess situations, calculate available resources, and respond effectively.

Let’s talk about how to incorporate mental math into an already busy math curriculum. As a secondary math teacher with limited time, you can efficiently incorporate mental math into your classroom routine with a little planning. Here are a few suggestions.

  • Start each class with a quick mental math warm-up, offering a mix of problems to reinforce concepts and challenge students.
  • Engage your class with math game sessions that focus on mental math skills, making learning fun and interactive.
  • To make mental math relevant, integrate it into real-life scenarios such as budgeting and trip planning.
  • During lessons, include quick discussions and estimation exercises to promote critical thinking.
  • Add an extra station for mental math if you are already doing stations.
  • During transitions times, have students work on a mental math.
  • Talk about mental math on a regular basis!

By nurturing mental math skills, students become strategic thinkers and independent learners. They gain confidence, self-reliance, and a sense of accomplishment. Beyond the classroom, mental math equips them to handle real-world challenges and prevents them from being taken advantage of. From shopping to cooking, budgeting to travel planning, mental math proves indispensable in numerous situations.

Incorporating mental math into our already busy math curriculum requires thoughtful planning and creativity. Utilizing warm-ups, game days, real-life applications, discussions, and peer collaboration, we can seamlessly integrate mental math practice into our lessons. With these concise strategies, we empower our students to master mental math, making them more adept at handling mathematical challenges and better equipped for success in their academic and future endeavors. Let’s embrace the importance of mental math and inspire our students to unlock its power for their benefit and growth.

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.

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