Tag: Algebra

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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:

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Points of Concurrency: Connecting Geometry & Algebra

As educators, we’re always juggling – trying to cover a mountain of curriculum while making sure our students really understand the core concepts. And sometimes, we stumble upon those topics that make us wonder, “Is this really essential?” Points of concurrency and special segments in triangles often fall into this category. They can seem a bit intimidating, and let’s face it, we’re often pressed for time. So, should we teach them? Skim them? Skip them entirely?

Let’s explore this geometric puzzle, considering curriculum needs, the value of these concepts, and some practical strategies for teaching them effectively.

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10 Practice Questions for the Math Portion of the ACT

ACT math prep is essential for students looking to improve their scores and enhance their college applications. The ACT math section covers a variety of topics including algebra, geometry, trigonometry, and statistics. Effective preparation means not only practicing problems but also grasping the underlying concepts and mastering test-taking strategies. Using resources like practice questions, study guides, and prep bundles can help students identify their strengths and weaknesses. Consistent practice builds familiarity with the test format and can increase accuracy and speed. Teachers provide valuable support by offering guidance and resources to help students reach their highest potential

If you’re a teacher or a student gearing up for the math portion of the ACT, I’ve got just the thing for you—10 practice questions that mirror the ACT format with five multiple-choice options each. This set includes a mix of algebra, geometry, and probability to help gauge understanding and proficiency. An answer key is provided at the end to check the answers and see if students are on the right track. If more practice is needed, there’s a list of additional resources at the bottom of this post. Go ahead and take a look!

  1. What is the value of 3x2 – 5x + 2 when x = 2?
    A) 4
    B) 6
    C) 8
    D) 10
    E) 12
  2. In a right triangle, one angle measures 45 degrees. What is the measure of the other acute angle?
    A) 30 degrees
    B) 45 degrees
    C) 60 degrees
    D) 75 degrees
    E) 90 degrees
  3. Solve the equation: 2(x+1) = 16
    A) 2
    B) 3
    C) 4
    D) 5
    E) -2
  4. What is the area of a circle with a radius of 5 units?
    A) 15π square units
    B) 20π square units
    C) 25π square units
    D) 30π square units
    E) 35π square units
  5. Simplify the expression: √12⁄27
    A) √2⁄3
    B) √3⁄2
    C) 2⁄3
    D) 3⁄2
    E) Not Here
  6. If f(x) = 2x2 + 3x – 5, what is the value of f(4)?
    A) 17
    B) 23
    C) 29
    D) 35
    E) 39
  7. What is the y-value for the system of equations?
    2x + 3y = 7
    4x – y = 0
    A) y = 2
    B) y = 1
    C) y = 0
    D) y = -1
    E) y = 1⁄2
  8. A box contains 5 red balls, 4 blue balls, and 3 green balls. If one ball is randomly selected, what is the probability of selecting a blue ball?
    A) 1⁄3
    B) 1⁄2
    C) 4⁄11
    D) 3⁄10
    E) 8⁄9
  9. The sum of three consecutive even integers is 42. What is the smallest of the three integers?
    A) 10
    B) 12
    C) 14
    D) 16
    E) 18
  10. A triangle has side lengths of 5 cm, 8 cm, and 10 cm. What type of triangle is it?
    A) Equiangular triangle
    B) Acute triangle
    C) Obtuse triangle
    D) Right triangle
    E) Isosceles triangle

If you would like to have a PDF copy of these questions, then I will provide the link to the resource in my store. The store copy is slightly different. Question 4 has been changed to a higher difficulty and there are three bonus questions. The resource link is the last resource on this page. Scroll to the bottom.

Here’s an answer key with explanations:

  1. To find the value of the expression, substitute x = 2 into the expression:
    3(2)2 – 5(2) + 2 = 12 – 10 + 2 = 4
    Therefore, the answer is A) 4
  2. In a right triangle, one angle is always 90 degrees. The sum of the angles in a triangle is 180 degrees. Therefore, the measure of the other acute angle would be:
    180 – 90 – 45 = 45 degrees
    Therefore, the answer is B) 45 degrees.
  3. One way of solving this equation is turn 16 into 24, then set up the following equation and solve: 2(x+1) = 24 x+1 = 4 x = 3 Another way of solving this equation is by taking the logarithm (base 2) of both sides, we get:
    (x+1)log2(2) = log2(16)
    x+1 = log2(16)
    x+1 = 4
    x = 4 – 1
    x = 3
    Therefore, the answer is B) 3.
  4. The formula to find the area of a circle is A = πr2, where r is the radius. Substituting r = 5 into the formula, we get:
    A = π(5)2 = 25π square units
    Therefore, the answer is C) 25π square units.
  5. To simplify the expression, we need to find the square root of the fraction. Simplifying the fraction first, we get:
    √4⁄9
    Taking the square root of the numerator and denominator, we get:
    √4⁄9 = 2⁄3
    Therefore, the answer is C) 2⁄3.
  6. To find the value of f(4), substitute x = 4 into the function:
    f(4) = 2(4)2 + 3(4) – 5 = 32 + 12 – 5 = 39
    Therefore, the answer is E) 39.
  7. To solve the system of equations for y, we can use the method of substitution or elimination. By eliminating the variable x, we can find the value of y:
    Multiply the first equation by -2:
    -4x – 6y = -14
    4x – y = 0
    Add the two equations together:
    -7y = -14
    y = 2
    Therefore, the answer is A) y = 2.
  8. The probability of selecting a blue ball can be found by dividing the number of blue balls by the total number of balls:
    Probability = Number of blue balls / Total number of balls
    Probability = 4 / (5 + 4 + 3) = 4⁄12
    Simplifying the fraction, we get:
    Probability = 1⁄3
    Therefore, the answer is A) 1⁄3.
  9. Let’s assume the smallest even integer is x. The next two consecutive even integers would be x + 2 and x + 4. The sum of the three consecutive even integers is given as 42. Set up an equation:
    x + (x + 2) + (x + 4) = 42
    3x + 6 = 42
    3x = 36
    x = 12
    Therefore, the answer is B) 12
  10. Use Pythagorean Theorem to classify the triangle. If a2 + b2 = c2, then the triangle is a right triangle. If a2 + b2 > c2, then the triangle is an acute triangle. If a2 + b2 < c2, then the triangle is an obtuse triangle.
    52 = 25, 82 = 64 and 102 = 100
    25 + 64 < 100 or 89 < 100
    Therefore, the answer is C) Obtuse Triangle

Here’s a BONUS Question for Trig Practice that I grabbed out of my ACT 5 Week Test Prep:

Students should remember SOH CAH TOA in order to tackle this problem. If the question asks for cosine, then look adjacent to A, which is 8, and then look at the hypotenuse, which does not have a measurement. Since TA needs a measurement, use the Pythagorean Theorem to find that the answer. 62 + 82 = TA2. Square the 6 and 8 then add them to get 100. The square root of 100 = 10, so TA = 10. Now, Cos(A) would be 8⁄10 and would reduce to 4⁄5, which is answer choice D.

I hope these practice questions prove helpful. Consistent practice is key to improving skills and boosting confidence for the ACT. For additional resources, check out the links provided. Good luck on preparing!

All these individual resources are part of the ACT Math Success Prep Bundle. Whether you need to focus on specific objectives or want comprehensive practice, I’ve got your covered.

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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!

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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.

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Teacher Hack: Using File Folders for More Than Filing!

Over the years, file folders have proven to be versatile tools beyond their traditional use. They’re sturdy, easy to label, and even come in various colors for added flexibility. Let me share some practical applications I’ve discovered in my classroom.

Organizing for a sub:

When it comes to ensuring seamless organization during my absences, especially for longer periods with multiple substitutes, I rely on file folders. They provide a simple yet effective method to ensure that substitutes have all they need and can keep everything in order. What’s more, the sub can use the folder to ensure that materials find their way back to me.

Game Boards:

Another innovative use I’ve found is utilizing file folders as a durable game board. One notable example is my “Graphing Lines Games,” which I designed to withstand the test of time. By placing the game components inside the folder, it becomes a portable and storable game board. You can find this game in my store!

Projects:

File folders have also been indispensable for various class projects. For instance, I’ve adapted them to create unique booklets for projects like the “If/Then Statement Project Book” and the “Parallel Lines Cut by a Transversal Park Project.” While the “If/Then Statement Booklet” concept isn’t originally mine, I’ve customized it by cutting a folder in half and folding it like a fan, providing each student with a convenient booklet to work on. This approach ensures that everyone has the necessary materials, and it’s quite resource-efficient, with one folder serving two students.

One of the most beloved projects among my students is the “Parallel Lines Cut By a Transversal Park Project.” While I’ve typically used poster paper for this project, one year, I decided to experiment with file folders. This switch allowed students to easily transport their projects between school and home. Despite the unconventional material, the manila folder’s color works exceptionally well for students to express their creativity with various colors. The end result is a project that’s both practical and visually appealing.

The video below shows the project in the folder!

Sturdy Holder:

Here’s one last way that I used a file folder as a tool. This was a desperate attempt to teach some of my low level students how to solve equations. I made it a station.

In conclusion, it’s amazing how a simple file folder can transform our teaching and organizational methods. Whether it’s ensuring smooth sailing during your absence, creating durable game boards, or facilitating engaging class projects, these unassuming tools have proven their worth time and time again. As educators, we’re constantly adapting and innovating, finding new ways to make learning more efficient and enjoyable for our students. So, don’t hesitate to explore the possibilities of file folders in your classroom. Who knows what creative solutions you’ll discover? Thank you for joining me on this journey, and I look forward to sharing more insights and tips. Don’t hesitate to comment and below and share some of your own unique ideas!

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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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From Roots to Fruits: An Engaging Journey for Your Algebra Students

I’m thrilled to introduce a versatile algebra resource that will take your students on an exciting journey through the world of algebra. At the beginning of the year, I like to introduce students to the origins of algebra, give them some idea of why they need it and to give them some relief that they are prepared for this moment because of their background in math. In the past, I’ve addressed this in a disconnected manner. For the first time, I’ve actually created a resource that takes students on this journey in a fun and organized fashion. I’m excited to give you an opportunity to use it in your classroom this year.

The presentation is offered in several ways so that teachers can choose the option that fits their needs. Do you want a teacher-led presentation or do you want self-directed work? Would you rather the students work through a Boom Card activity? The teacher-led journey and the student self-directed exploration are included in one resource. The Boom Card activity is in a separate resource since not all teachers are familiar with this type of application. Check out the descriptions of each below:

  • Teacher-Led Journey:
    The teacher-led journey is captured through a PowerPoint. To make it easy on the presenter, I’ve included a teacher guide that provides clear instructions, ensuring a seamless experience as you navigate the presentation. Your students will participate in the reading of the slides, answering some math questions along the way and they will be creating a picture of a fruit tree that represents their journey. (Roots – origins of algebra, soil and rocks – the foundational skills needed and so forth.)

  • Self-directed Exploration:
    Recognizing that every classroom is unique, I’ve also included alternative options for student-led exploration. The Google Slides version allows your students to take control of their learning, engaging in a “scavenger hunt-style” activity at their own pace. Teamed up with a Google Forms companion, your students can answer questions, solve math problems, and reinforce their understanding while enjoying the freedom to explore independently or collaborate with a partner. While progressing through the Google Forms, students will have the opportunity to simultaneously create the picture of the fruit tree.
  • Boom Card Adventure:
    To add an interactive twist to the learning experience, I’ve created a Boom Card activity. Your students can embark on an exciting adventure through a series of engaging digital cards, answering questions and deepening their understanding in a fun and gamified format. The Boom Cards offer an exciting way to reinforce concepts and keep your students motivated as they progress on their algebraic journey. No tree is created in this activity, but the slides are basically the same as the presentations referred to earlier with the addition of some mulitple choice and matching questions. This self-graded option is perfect if you are fond of Boom Cards and you want your students engaged. They can work through the cards as many times as you will let them.


This resource addresses common student questions, such as “What is algebra?” and “When will I ever need it?” By launching this algebraic adventure, your students will gain a deeper understanding of the subject’s origins, its practical applications, and its relevance in their daily lives. Through a combination of visual aids, interactive activities, and thought-provoking questions, this resource aims to introudce algebra in a fun and eye-opening way. The Algebra Journey Activities are below. The poster is a freebie and fits well with the activity. Go take a look and good luck this year!

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Stay Organized and Minimize Distractions with Supply Boxes in the Classroom


I want to let you in on a little secret that was a game-changer in my classroom: supply boxes (pencil boxes used for supplies). I used these handy boxes for years, and let me tell you, they are a teacher’s best friend when it comes to reducing disruptions and keeping things organized. My largest classes were usually 28 – 30 students, so I kept 6 – 7 supply boxes. If we were not in groups, I kept them scattered around the room, so that students could share the supplies. I liked to use plastic pencil boxes, but a gallon plastic bag would do the job as well.

Benefits of Supply Boxes:
Let me start by saying that this teacher hack for material organization was a total lifesaver for me. Picture this: all the materials your students need for group work right at their fingertips, without having to get up and rummage around the classroom. It’s a game-changer! With supply boxes, you can say goodbye to constant disruptions and wasted instructional time. Engagement increases because students can get right to work and focus on the lesson. (You know how long it takes to get some students started just because they don’t have a pencil or some material they need.)

Another amazing benefit of supply boxes is the cleanup process. No more chaotic scramble to collect materials at the end of a lesson. Students work together to make sure all items go back into the box, making cleanup a breeze. Trust me, it’s a small change that brings big results. I can’t begin to tell you how much time this has saved!

As you can see in the picture below, I had a place in my room for supplies and the supply boxes when I needed to clear the desks for various reasons. This is also the area where I restocked and added or took away materials.

Essential Materials for Supply Boxes:
Now let’s dive into the must-have materials for the supply boxes. I do not keep all these items in the boxes at all times. I periodically change out what they contain. Here’s my top twelve list with links to build your cart on Amazon:

  1. Pencils and pens ensure that students have the tools they need to work so that there are no excuses. A good idea if you like your students to grade papers, is to stick some red pens in the box. Here’s a link to some assorted colors.
  2. Pencil sharpeners. How often do students get up in the middle of a lesson to sharpen their pencils? This disruption does not have to happen if they have access to some small pencil sharpeners.
  3. Erasers. Mistakes happen, and having erasers readily available allows students to correct errors without hesitation.
  4. Scissors are versatile tools that come in handy during activities involving cutting and are great if your classes have interactive notebooks.
  5. Patty paper is a thin, translucent paper that is invaluable for math exploration. It allows students to trace shapes and transformations, making it an essential tool for hands-on investigations.
  6. Notecards offer a versatile way for students to jot down key concepts, vocabulary words, or important information. They can be used for individual or group review activities, making them an effective study aid.
  7. Sticky notes are fantastic tools for collaborative brainstorming and organizing ideas. Students can jot down their thoughts, stick them to a board, and easily rearrange them to create a visual representation of their collective thinking.
  8. Tape or glue sticks are essential for securing papers, attaching visuals, or creating interactive displays.
  9. Colored pencils add a vibrant touch to collaborative projects and presentations. They encourage creativity, differentiation, and visual appeal in various subjects such as art, graphs, diagrams, or illustrating concepts.
  10. Protractors are indispensable tools for measuring and drawing angles accurately. They enable students to explore geometry concepts, and they’re also great for drawing straight edges. I also like that they come with an inch ruler and a centimeter ruler. I keep rulers in my classroom, but since protractors fit well in the box, they are my go-to measuring tool.
  11. Highlighters allow students to emphasize important information, key details, or highlight specific parts of a text.
  12. How about placing Task Cards or a special piece of an activity in the box before class? I’ll change out an activity such as task cards so that the students already have what they need to start the lesson.

By providing students with well-stocked supply boxes, containing essential materials like pencils, erasers, scissors, rulers, and other items mentioned above, you will be able to cut down on time wasters and discipline issues. It makes the room more productive and less chaotic.

If you don’t have the budget to purchase these items yourself, then add them to the student supply list. One thing that runs out fast is tape. Put items such as tape, notecards and colored pencils on the student supply list so you can stock up and have plenty for the rest of the year. Good Luck and I hope to hear from you after you start using your supply boxes.

You will also notice I have dry erase markers, erasers (these erasers are awesome and are magnetic) and dry erase boards. It’s great to keep these out so you can use them at any moment. (All of these items come as a set if you’d rather purchase them together.)

Disclaimer: This blog post contains affiliate links. That means if you make a purchase through these links, I may earn a small commission at no extra cost to you. I only recommend products and resources that I personally find valuable and believe will benefit my readers. Your support through these affiliate links helps me continue to provide helpful content for educators. Thank you for your support!

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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: