53 Funny Teacher Memes to Brighten Your Day!

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53 Funny Teacher Memes to Brighten Your Day!

53 Funny Teacher Memes Every Educator Can Relate To

Get Ready to Laugh Out Loud with These Funny Memes About Teaching!

Ready for Some Funny Teacher Memes?

Being a teacher is one of the toughest—and often most under-appreciated—careers a person can have.

And, while teaching can be an incredibly rewarding job with tons of positives (like making a difference in the daily lives of your students), there are also some negatives and frustrations that accompany the task of educating students for a living.

In the spirit of taking the bad with the good when it comes to be a teacher, it can fun be to celebrate the quirks of the profession, many of which only yourself and fellow teachers can truly understand.

So, let’s take a moment to celebrate the craft that is being a professional educator in a fun and humorous way by sharing the best and funniest teacher memes that the internet has to offer!

Below you will find our collection of the 53 best teacher memes, many of which are all too relatable to those who work inside of a classroom. Each teacher meme shines a light on some of the more frustrating and/or perplexing aspects of being a teacher at any grade level.

Whether you are dealing with rowdy children, out-of-touch administrators, delusional parents, or never-ending meetings and conferences that obviously could have been emails, this page surely has a meme or two that will have you rolling on the floor laughing in no time!

A hysterical teacher meme or two is just what you need to make it through your day!

Before you jump into our collection of 53 funny teacher memes, remember that each teach meme is meant to be playful and they are meant to be taken light-heartedly. Also remember that laughter is often the best medicine and it’s totally fine to laugh out loud at some of the vexing aspects of being an educator.

Whenever you are ready to laugh, scroll down to start enjoying our funny teacher memes and, if you find any memes to be exceptionally hysterical, then feel free to share this page with your fellow teachers to spread some much-needed joy and laughter :)

Funny Teacher Memes #1-10

1.) This can happen to the best of us.

 

Teacher Meme #1: When you forget to remember…

 

2.) I swear, I was only gone for two seconds!

 

Teacher Meme #2: 😬

 

3.) When the classroom telephone starts ringing the tenth time today…

 
 

4.) Yes, yessssss….

 

This may be the best teacher meme of all time!

 

5.) Your students doing anything to avoid actually doing their classwork…

 

Funny Teacher Meme via Reddit User u/aRabidGorilla

 

6.) All of the moisturizer in the world couldn’t save us!

 

Teaching Memes Every Educator Can Relate To!

 

7.) Is this even written in English?

 

Funny Teacher Memes #7

 

8.) Your reaction to accidentally overhearig your students’ personal conversations…

 
 

9.) You can not possibly be even remotely serious…

 

Teaching Memes #10

 

10.) When you’re in the middle of an awesome lesson and the fire alarm goes off…

 
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Funny Teacher Memes #11-20

Are you ready for the next ten hysterical teacher memes that will have you and your colleagues laughing out loud?

11.) We’re all thinking it…

 

Funny Memes About Teaching: What does the principle even do?

 

12.) When you start handing out rulers to your students…

 
 

13.) It’s sad—I mean, funny—because it’s true.

 

Teacher Memes: Sad, but True.

 

14.) May I laugh at this funny teacher meme?

 

Funny Teacher Memes #14

 

15.) You shall not pass!

 

Teacher Meme #11

 

16.) Good riddance!

 

Funny Teacher Memes #16

 

17.) When April Fools’ Day falls on the weekend….

 
 

18.) Dream on, dreamers…

 
 

19.) We actually just sat around and waited….

 

This teacher meme hits hard!

 

20.) If looks could kill…

 

53 Best Teacher Memes #20: Always show your work!

 

Funny Teacher Memes #21-30

Let’s keep the good times going with our next ten funny teacher memes!

21.) Every day is important!

 

Funny Teacher Memes #21

 

22.) Is anyone even listening to me?

 

My favorite teacher meme of all time!

 

23.) When you find out that you have to waste your off period sitting through another meeting…

 
 

24.) Just smile and nod…smile and nod…

 

Teacher Meme #24: Is this relatable to you?

 

25.) Some say that she’s still waiting…

 

Funny Teacher Memes

 

26.) This one is all too real!

 

Funny Memes About Teaching!

 

27.) Just gotta’ keep on truckin’…

 

This teacher meme is a little too real, isn’t it?

 

28.) When the copy machine is broken again…

 
 

29.) How sweet it is!

 

Funny Teacher Meme #29: Gotta savor the good stuff!

 

30.) When a student asks you how old you are…

 
 

Funny Teacher Memes #31-40

And now for ten more funny memes teacher edition.

31.) Let me just rest my eyes for a quick second…

 

Funny Teacher Memes: Teachers at home at 7:38pm…

 

32.) When a past student tells you that you were their favorite teacher…

 
 

33.) There can only be one…

 

Teacher Memes #33: The Teacher’s Dilemma.

 

34.) You couldn’t use the telephone and go on the internet at the same time!

 
 

35.) When a student’s math homework is written in pen…

 
 

36.) Wink, wink…

 

This is my favorite teacher meme of all time!

 

37.) Whatchu’ want me to say?

 

Teacher Meme #37: This one is spicy, we know!

 

38.) Back in my day….

 

Funny Teacher Memes #38

 

39.) Don’t pop the Champagne too early!

 

I have this teacher meme posted in my classroom!

 

40.) When you get an email telling you that your after-schooling meeting was cancelled…

 
 

Funny Teacher Memes #41-53

Our funny teacher memes collection wraps up with 13 more super funny teacher memes that will have your sides hurting!

41.) Feelin’ hot, hot, hot!

 

Can you relate to this funny teacher meme?

 

42.) Ya gotta’ love it!

 

Funny Teacher Memes #42

 

43.) When your class gets interrupted by a knock at the door…

 
 

44.) I guess it just doesn’t work that way…

 
 

45.) When you already explained something five different ways and students are still saying that they don’t get it…

 
 

46.) It takes two to Tango….

 

I also have this teacher meme posted in my classroom.

 

47.) When you find out that your students were well-behaved for the sub…

 
 

48.) If only a Panera Bread platter could solve all of our problems…

 

Is teacher meme #48 a truth bomb?

 

49.) No, I will not cover hall duty right now…

 
 

50.) The Parent-Teacher Conference Day experience in a nutshell…

 
 

51.) Most of us will probably go this way…

 
 

52) I’m not crying, you’re crying!

 

Funny Teacher Meme #52

 

53.) Every teacher after the last day of school before summer vacation…

 
 

That wraps up our list of the 53 funniest teacher memes that the internet has to offer! We hope that you these memes brightened up your day, and that you had a few laughs along the way. If you are looking for a few different ways that you can share and enjoy these teacher memes, here are a few ideas:

  • Revisit this page whenever the demands of teaching are weighing you down and you need a good chuckle or two to restore your sanity.

  • Share your favorite teacher memes in your teacher group chat or email chain to indulge in some humorous commiseration!

  • Post a funny teacher meme on social media to connect with fellow teachers, parents, and administrators.

  • Print and post a few funny teacher memes in your classroom to share some insight and humor with your students. This can be a fun way to give your students an idea of some of the challenges of being a teacher and working with students for a living.

  • Use these memes in meeting and/or professional development presentations to serve as an icebreaker or to simply break things up by injectiing some light-hearted and topical humor into the mix.

(Do you want more free K-8 math resources and activities in your inbox every week? Click here to sign up for our math education email newsletter)

Did you laugh, cry, or both? Share your reaction in the comments below!

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Quadratic Formula Examples—Solved Step-by-Step

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Quadratic Formula Examples—Solved Step-by-Step

Quadratic Formula Examples Tutorial

Step-by-Step Guide: Examples of How to Find the Roots of a Quadratic Function using the Quadratic Formula

 

Step-by-Step Guide: Quadratic Formula Examples Solved

 

Are you ready to work through a few quadratic formula examples to gain some more practice and experience with solving quadratic equations using the quadratic formula?

In math, the quadratic formula, x= (-b ± [√(b² - 4ac)]) / 2a is an incredibly important and useful formula that you can use to find the solutions (also known as roots) or any quadratic equation of the form ax² + bx + c = 0 (where a ≠ 0), whether it is easy to factor or not!

If you know how to use the quadratic formula, then you can solve a variety of algebra problems involving quadratic equations, and learning how to use it correctly is something that you can easily learn with some practice and repetition.

This free Quadratic Formula Examples Step-by-Step Guide includes a short review of the quadratic formula as well as several different practice problems that we will work through and solve using the quadratic formula with a step-by-step explanation. The guide is organize by the following sections, and you can click on any of the hyperlinks below to jump to any particular spot:

Before we dive into any of the quadratic formula examples, let’s start off with a quick review of the quadratic formula and why it is such a useful algebra tool.

 

Figure 01: The Quadratic Formula

 

What is the Quadratic Formula?

Before you can learn how to use the quadratic formula, it is important that you understand what a quadratic equation is.

Definition: A quadratic equation is a function of the form ax² + bx + c = 0 (where a does not equal zero). On a graph, a quadratic equation can be represented by a parabola. The x-values where the parabola crosses the x-axis is called the solutions, or roots, of the quadratic equation.

For example, consider the following quadratic equation:

  • x² + 5x + 6 = 0

Notice that this equation is in ax² + bx + c = 0 form, where…

  • a=1

  • b=5

  • c=6

If we want to find the solutions, or roots, of this quadratic equation, we have a few options.

First, we could factor this quadratic equation by looking for two values that add to 5 and also multiply to 6, which, in this case, would be 2 and 3. So we could say that…

  • x² + 5x + 6 = 0 → (x+2)(x+3) = 0

We could then solve for each factor as follows:

  • x + 2 = 0 → x = -2

  • x + 3 = 0 → x = -3

Now we can conclude that the solutions of this quadratic are x=-2 or x=-3.

 

Figure 02: What are the solutions (or roots) of a quadratic equation?

 

Another option for finding the solutions to a quadratic equation is to look at its graph. The solutions, or roots, will be the x-values where the graph crosses the x—axis. Note that quadratic equations can have two roots, one root, or even no real roots (as you will see later in this guide).

As for the equation x² + 5x + 6 = 0, the corresponding graph in Figure 02 above confirms that the equation has solutions at x=-2 and x=-3.

But what do we do when a quadratic equation is very difficult to factor or when we do not have access to a clear graph? Well, this is where the quadratic formula comes into play.

Definition: Any quadratic equation of the form ax² + bx + c = 0 (where a ≠ 0), can be solved using the quadratic formula, which states that…

  • x= (-b ± [√(b² - 4ac)]) / 2a

Why is the quadratic formula so useful? Because, as the definition states, it can be used to find the solutions to any quadratic equation. While the quadratic equation that we just looked at, x² + 5x + 6 = 0, was pretty easy to work with and solve, it is considered extremely simple. As you move farther along your algebra journey, you will come across more and more complex quadratic equations that can be very difficult to factor or even graph.

However, if you know how to use the quadratic formula, you can successfully solve any quadratic equation. With this in mind, let’s go ahead and work through some quadratic formula examples so you can gain some practice.

And we will start by using it to solve x² + 5x + 6 = 0, because we already know that the solutions are x=-2 and x=-3. If the quadratic formula works, then it should yield us that same result. Once we work through this first simple example, we will move onto more complex examples of how to use the quadratic formula to solve quadratic equations.

 

Figure 03: To use the quadratic formula, start by identifying the values of a, b, and c.

 

Quadratic Formula Examples

We will begin by using the quadratic formula to solve the equation shown in Figure 02 above: x² + 5x + 6 = 0

Example #1: Solve x² + 5x + 6 = 0

First, notice that our equation is in ax² + bx + c = 0 form where:

  • a=1

  • b=5

  • c=6

Identifying the values of a, b, and c will always be the first step (provided that the equation is already in ax² + bx + c = 0 form).

Now that we know the values of a, b, and c, we can plug them into the quadratic equation as follows:

  • x= (-b ± [√(b² - 4ac)]) / 2a

  • x= -(5) ± [√(5² - 4(1)(6))]) / 2(1)

  • x= -5 ± [√(25 - 24)] / 2

  • x= -5 ± [√(1)] / 2

  • x= (-5 ± 1) / 2

Now we are left with x= (-5 ± 1) / 2. Note that the ± mean “plus or minus” meaning that we have to split this result into two separate equations:

  • Plus: x = (-5 + 1) / 2

  • Minus: x = (-5 - 1) / 2

By solving these two separate equations, we can find the solutions to the quadratic function x² + 5x + 6 = 0.

  • x = (-5 + 1) / 2 = -4/2 = -2 → x=-2

  • x = (-5 - 1) / 2 = -6/2 = -3 → x=-3

After solving both equations, we are left with x=-2 and x=-3, which we already knew were the solutions to x² + 5x + 6 = 0. So, we have confirmed that the quadratic formula can be used to find the solutions to any quadratic equation of the form ax² + bx + c = 0.

Final Answer: x=-2 and x=-3

The steps to solving the quadratic formula example is illustrated in Figure 04 below.

 

Figure 04: Quadratic Formula Examples Step-by-Step

 

Example #2: Solve 2x² + 2x -12 = 0

For our next quadratic formula example, we will again start by identifying the values of a, b, and c as follows:

  • a=2

  • b=2

  • c=-12

Make sure that you correctly identify the sign (positive or negative) as well, since this is necessary to using to quadratic formula correctly.

Next, we can substitute these values for a, b, and c into the quadratic formula as follows:

  • x= (-b ± [√(b² - 4ac)]) / 2a

  • x= -(2) ± [√(2² - 4(2)(-12))]) / 2(2)

  • x= -2 ± [√(4 - -96)] / 4

  • x= -2 ± [√(100)] / 4

  • x= (-2 ± 10) / 4

Our result is x= (-2 ± 10) / 4. From here, we can rewrite e the result as two separate equations by “spitting” the ± sign as follows:

  • Plus: x= (-2 + 10) / 4

  • Minus:x= (-2 - 10) / 4

Now we can solve each individual equation to find the values of x that will be the solutions of this quadratic equation.

  • x= (-2 + 10) / 4 = 8/4 = 2 → x=2

  • x = (-2 - 10) / 4 = -12/4 = 3 → x=3

We are left with two values for x: x=2 and x=-3, and we can conclude that the quadratic equation 2x² + 2x -12 = 0 has the following solutions:

Final Answer: x=2 and x=-3

Figure 05 shows the step-by-step process for solving this quadratic formula example.

 

Figure 05: Quadratic Formula Examples #2 Solved

 

Example #3: Solve 2x² -5x + 3 = 0

For the next of our quadratic formula examples calls for us to use the quadratic formula to find the solutions to a quadratic function where:

  • a=2

  • b=-5

  • c=3

The process of substituting a, b, and c into quadratic formula will be exactly the same as the last two quadratic formula examples.

  • x= (-b ± [√(b² - 4ac)]) / 2a

  • x= -(-5) ± [√(-5² - 4(2)(3))]) / 2(2)

  • x= 5 ± [√(25 - 24)] / 4

  • x= 5 ± [√(1)] / 4

  • x= (5 ± 1) / 4

Are you starting to get the hang of it? Now that we have simplified our equation, we are left with x= (5 ± 1) / 4. And, just like the last two examples, we can go ahead and split this result into two separate equations as follows:

  • Plus: x= (5 + 1) / 4

  • Minus: x= (5 - 1) / 4

Finally, we just have to solve each equation to get our final answer (i.e. the values of the solutions).

  • x= (5+1) / 4 = 6/4 = 3/2 → x=3/2

  • x= (5-1) / 4 = 4/4 = 1 → x=1

Notice that the result of the first equation ended up as a fraction (3/2). This is totally fine! It just means that the parabola will cross the x-axis in the middle of a box (rather than hitting directly at an integer coordinate).

Final Answer: x=3/2 and x=1

All of the steps for solving this example are shown in Figure 06 below.

 

Figure 06: Sometimes a quadratic formula will give you a solution that is a fraction.

 

Example #4: Solve 3x² + 2 = 7x

The fourth and final of our quadratic formula examples looks a bit different. The given equation 3x² + 2 = 7x is not in ax² + bx + c = 0 form.

Whenever this is the case, we will have to see if we can use algebra to rearrange the equation so to make into ax² + bx + c = 0 form. We can do that by using inverse operations to move the 7x to the left-side of the equation as follows:

  • 3x² + 2 = 7x

  • 3x² + 2 (-7x) = 7x (-7x)

  • 3x² + 2 -7x = 0

Notice that result, 3x² + 2 -7x = 0, still isn’t in ax² + bx + c = 0 form. However, the commutative property allows us to rearrange the terms as follows:

  • 3x² + 2 -7x = → 3x² -7x +2

Now we have an equivalent equation, 3x² -7x +2=0, that is in ax² + bx + c = 0 form, where:

  • a=3

  • b=-7

  • c=2

Sometimes you will be given equations that have to be rearranged in order to use the quadratic formula. If you can not rearrange an equation so that it can be expressed in ax² + bx + c = 0 form, then you can not solve it using the quadratic formula.

This example, however, can now be solved using the quadratic formula as follows:

  • x= (-b ± [√(b² - 4ac)]) / 2a

  • x= -(-7) ± [√(-7² - 4(3)(2))]) / 2(3)

  • x= 7 ± [√(49 - 24)] / 6

  • x= 7 ± [√(25)] / 6

  • x= (7 ± 5) / 6

Now we are left with a much easier equation to work with: x= (7 ± 5) / 6. Let’s go ahead and split it into two separate equations to solve it:

  • Plus: x= (7 + 5) / 6

  • Minus: x= (7 - 5) / 6

We can solve for x in each equation as follows:

  • x= (7+5) / 6 = 12/6 = 2 → x=2

  • x= (7-5) / 6 = 2/6 = 1/3 → x=1/3

Final Answer: x=2 and x=1/3

That’s all that there is to it! You can review of the steps to solving this quadratic formula example by looking at the illustration in Figure 07 below.

 

Figure 07: Quadratic Formula Examples: Rearranging an equation to put it into ax² + bx + c = 0 form.

 

Do you need more practice with using the Quadratic Formula?

Check out our free library of Quadratic Formula Worksheets (with answer keys)

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Log Rules Explained! (Free Chart)

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Log Rules Explained! (Free Chart)

Everything you need to know about the natural log rules.

The Natural Log Rules Explained

In math, log rules (also known as logarithm rules) are a set of rules or laws that you can use whenever you have to simplify a math expression containing logarithms. Basically, log rules are a useful tool that, when used correctly, make logarithms and logarithmic equations simpler and easier to work with when solving problems.

Once you become more familiar with the log rules and how to use the, you will be able to apply them to a variety of math problems involving logarithms. In fact, understanding and remembering the log rules is essentially a requirement when it comes to working with logarithmic expressions, so understanding these rules is essential for any student who is currently learning about logarithms.

The following free guide to the Log Rules shares and explains the rules of logs (including exponent log rules), what they represent, and, most importantly, how you can use them to simplify a given logarithmic expression.

You have the option of clicking on any of the text links below to jump to any one section of this log rules guide, or you can work through each section in order—the choice is up to you!

When you reach the end of this free guide on the rules of logs, you will have gained a solid understanding of the natural log rules and how to apply them to solving complex math problems. Let’s get started!

 

Figure 01: What is the relationship between the logarithmic function and the exponential function?

 

Quick Review: Logarithms

While this first section is optional, we recommend that you start off with a quick recap of some key math concepts and vocabulary terms related to logs.

The first important thing to understand is that logarithmic functions and exponential functions go hand-in-hand, as they are considered inverses of each other. So, make sure that you have a strong understanding of the laws of exponents before moving forward.

Since the logarithmic function is an inverse of the exponential function, we can say that:

  • aˣ = M → logₐM = x

  • logₐM = x → aˣ = M

The log of any value, M, can be expressed in exponential form as the exponent to which the base value of the logarithm must be raised to in order to equal M.

Understanding this inverse relationship between the logarithmic function and the exponential function will help you to better understand the log rules described in the following sections of this guide.

Learning natural log rules shared in the next section will help you to break down complex log expressions into simpler terms, which is a critical skill when it comes to learning how to successfully work with logs, how to model situations using logs, and how to solve a variety of math problems that involve logs.

What are the Log Rules?

The natural log rules are set of laws that you can use to simplify, expand, or solve logarithmic functions and equations.

The chart in Figure 02 below illustrates all of the log rules. Simply click the blue text link below the chart to download it as a printable PDF, which you can use as a study tool and a reference guide.

The section that follows the log rules chart will share an in-depth explanation of each of the log rules along with examples.

 

Figure 02: The Natural Log Rules and the Change of Base Formula

 

Each of the following log rules apply provided that:

  • a≠1 and a>0, b≠1 and b>0, a=b, and M, N, and x are real numbers where M>0 and N>0

Log Rules: The Product Rule

The first of the natural log rules that we will cover in this guide is the product rule:

  • logₐ(MN) = logₐM + logₐN

 

Figure 03: The product rule of logarithms.

 

The product rule states that the logarithm a product equals the sum of the logarithms of the factors that make up the product.

For example, we could use the product rule to expand log₃(xy) as follows:

  • log₃(xy) = log₃x + log₃y

Pretty straightforward, right? The product rule of logarithms is a simple tool that will allow you to expand logarithmic expressions and equations, which often makes them easier to work with.

Log Rules: The Quotient Rule

The second of the natural log rules that we will cover in this guide is called the quotient rule, which states that:

  • logₐ(M/N) = logₐM - logₐN; or

  • logₐ(M➗N) = logₐM - logₐN

 

Figure 04: Natural Log Rules: The Quotient Rule

 

The quotient rule of logs says that the logarithm a quotient equals the difference of the logarithms that are being divided (i.e. it equals the logarithm of the numerator value minus the logarithm of the denominator value).

For example, we could use the quotient rule to expand log₇(x/y) as follows:

  • log₇(x/y) = log₇x - log₇y

Notice that the product rule and the quotient rule of logarithms are very similar to the corresponding laws of exponents, which should make sense because the logarithmic function and the exponential function are inverses of each other.

Log Rules: The Power Rule

The next natural log rule is called the power rule, which states that:

  • logₐ(Mˣ) = x ⋅ logₐM

 

Figure 05: Log Rules: The Power Rule

 

The power rule of logarithms says that the log of a number raised to an exponent is equal to the product of the exponent value and the logarithm of the base value.

For example, we could use the power rule to rewrite log₄(k⁸) as follows:

  • log₄(k⁸) = 8 ⋅ log₄k

The power rule of logarithms is extremely useful and it often comes in handy when you are dealing with the logarithms of exponential values, so make sure that you understand it well before moving forward.

Log Rules: The Zero Rule

Moving on, the next log rule on our list is the zero rule, which states that:

  • logₐ(1) = 0

 

Figure 06: Log Rules: The Zero Rule

 

Simply put, the zero rule of logs states that the log of 1 will always equal zero as long as the base value is positive and not equal to one.

For example, we could use the zero rule to rewrite log₂(1) as follows:

  • log₂(1) = 0

This simple rule can be very useful whenever you are trying to simplify a complex logarithmic expression or equation. The ability to zero out or cancel out a term can make things much simpler and easier to work with.

Log Rules: The Identity Rule

The fifth log rule on our list is called the identity rule, which states that:

  • logₐ(a) = 1

 

Figure 07: Natural Log Rules: The Identity Rule

 

The identity rule says that whenever you take the logarithm of a value that is equal to its base value, then the result will always equal 1 provided that the base value is greater than zero and not equal to one.

For example, we could use the identity rule to rewrite log₈(8) as follows:

  • log₈(8) = 1

Similarly, we could also use the identity rule to rewrite logₓ(x) as follows:

  • logₓ(x) = 1

Just like the zero rule, the identity rule is useful as it can sometimes help you with simplifying complex log expressions and equations.

Log Rules: The Inverse Property of Logs

The next log rule that we will cover in this guide is called the inverse property of logarithms rule, which states that:

  • logₐ(aˣ) = x

 

Figure 08: The inverse property of logs rule.

 

The inverse property of logs rule states that the log of a number raised to an exponent with a base value that is equal to the base value of the logarithm is equal to the value of the exponent.

For example, we could use the inverse property of logs rule to rewrite log₃(3ᵏ) as follows:

  • log₃(3ᵏ) = k

Again, this is another useful tool that you can use to simplify complicated log expressions and equations.

Log Rules: The Inverse Property of Exponents

The seventh log rule that we will cover is the inverse property of exponents rule, which states that:

  • a^(logₐ(x)) = x

 

Figure 09: Log Rule #7: The Inverse Property of Exponents

 

The inverse property of exponents log rule states whenever a base number with an exponent that is a logarithm equal to that base number, the result will equal the number in parenthesis.

For example, we could use the inverse property of exponents log rule to rewrite x^(logₓ(y²)) as follows:

  • x^(logₓ(y²)) = y²

Log Rules: The Change of Base Formula

The eighth and final log rule is the change of base formula, which states that:

  • logₐ(x) = (log꜀(x)) / (log꜀(a))

 

Figure 10: Log Rule: The Change of Base Formula

 

Conclusion: Natural Log Rules

In algebra, you will eventually have to learn how to simplify, expand, and generally work with logarithmic expressions and equations. The logarithm function is the inverse of the exponential function, and the corresponding log rules are similar to the exponent rules (i.e. they are a collection of laws that will help you to make complex log expressions and equations easier to work with). By studying and learning how to the natural log rules, you will be better able to understand logarithms and to solve difficult math problems involving logarithms. Feel free to bookmark this guide and return whenever you need a review of the rules of logs.

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Idea: How to Engage Your Students at the Start of Any Lesson

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Idea: How to Engage Your Students at the Start of Any Lesson

Image Credit: Mashup Math MJ

Capturing your students’ interest and curiosity during the first few minutes of class is the key to keeping them engaged for your entire lesson.

But not all math warm up activities are created equally.

Math teachers miss out on activating their students’ critical thinking and reasoning skills when they assign routine, lower-level practice problems during the first five minutes of class.

However, when you use the right mix of fun and though-provoking math warm up activities to start your lessons, student engagement spikes, as your kids will constantly be wondering about what is coming next.

You probably already have some awesome math warm up activities—like Which One Doesn’t Belong? and Think-Notice-Wonder—in your tool belt. But if you’re looking for another great strategy for mixing up your instruction and engaging your students, then get ready for:

Two Truths and One Lie!

I recently started using Two Truths and One Lie (2T1L) activities, where students are presented with three mathematical statements (only two of which are true) and they have to identify which statement is a lie and justify why their choice is correct. The results? Pretty amazing. 2T1L taught me that my students love to argue and state their case (in small groups or to the whole class).

In short, 2T1L is a fun way to spark deep mathematical thinking and open discussion at the start (or end—2T1L activities make great exit tickets) of any lesson.

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Image Source: Mashup Math ST

What topics/grade levels are 2T1L activities best suited for?

2T1L activities can be used for all grade levels and topics. The graphics should be topic/lesson specific and can include graphs, charts, and diagrams.

 

Here are some grade-level specific samples:

Imagine how your students would react to starting class with one of the following activities.

  • What kind of creative and mathematical thinking would spark?

  • What kind of small or large group discussions would occur?

  • How would a spike in engagement effect the remainder of the lesson?

▼ 3rd Grade ▼

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▼ 6th Grade ▼

▼ 4th Grade ▼

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▼ 7th Grade ▼

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▼ 5th Grade ▼

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▼ 8th Grade ▼

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Are you ready to give it a try?

Here are a few more free samples that you can download and share with your kids (right-click to download each graphic and save it to your computer):

Looking for more for grades 3, 4, & 5? Download your 101 ‘Two Truths and One Lie!’ Math Activities for Grades 3, 4, & 5 eBook!

Looking for more for grades 6, 7, & 8? Download your 101 ‘Two Truths and One Lie!’ Math Activities for Grades 6, 7, & 8 eBook!

Looking for more?

You can now share 101 Daily Two Truths & One Lie! Math Activities for Grades 3, 4, & 5 OR Grades 6, 7, & 8 with your kids with our brand new PDF workbooks!

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Read More Posts About What’s Trending in Math Education:

Do you have experience using 2T1L activities with your math students? Share your thoughts and suggestions in the comments section below!

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By Anthony Persico

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Anthony is the content crafter and head educator for YouTube's MashUp Math and an advisor to Amazon Education's 'With Math I Can' Campaign. You can often find me happily developing animated math lessons to share on my YouTube channel . Or spending way too much time at the gym or playing on my phone.

 
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Celebrate Pi Day 2025 with These Fun Facts

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Celebrate Pi Day 2025 with These Fun Facts

Pi Day Activities: Learn about the history of Pi and more fun facts with our free National Pi Day Infographic

Happy Pi Day 2025!

Pi Day 2025 is on March 14th and it’s time to celebrate the most mathematical holiday of the calendar year.

If you're looking for some awesome National Pi Day 2025 activities, check out our infographic that shares interesting National Pi Day fun facts that will blow your mind!

Below, you will find a Happy Pi Day 2025 infographic that shares interesting facts about the history of National Pi Day and some fun facts about pi itself, including…

You can click on the image of the National Pi Day Infographic or you can click here to download a printable pdf version.

Below, you can also find an animated Pi Day Fun Facts Video that accompanies the free infographic.

Looking for some Pi Day humor? Click here to access 11 Super Funny Pi Day jokes for all ages.

 

Happy Pi Day! When is pi day, what is pi day, and how can you celebrate? (Image: Mashup Math FP)

 

When is Pi Day 2025?

National Pi Day 2025 will be celebrated on Tuesday March 14th.

Pi Day is celebrated on the 14th of March each and every year. Pi Day is a national holiday that is celebrated in the United States and sometimes also around the world.

 

When is pi day? National Pi Day is held on March 14th every year. (Image: Mashup Math via Getty Images)

 

What is Pi Day?

National Pi Day is a mathematical national holiday that celebrates the mathematical symbol 𝝅, which represents the ratio of the circumference of any circle to its diameter. Since this ratio, no matter the size of the circle, always approximates to 3.14, pi is of the most important and interesting mathematical facts, which is why it has its own national holiday.

 

What is Pi Day? National Pi Day is a mathematical celebration of pi—the ratio of any circle’s circumference to its diameter.

 

Why is Pi Day Celebrated on March 14th?

Pi Day is celebrated on March 14th every year because the date 3/14 resembles to approximate value of pi, which is 3.14.

Again, pi represents the ratio of any circle’s circumference to its diameter, which always approximately equals 3.14, no matter how large or small a circle may be.

 

Why is Pi Day celebrated on March 14th?

 

What year was Pi Day first celebrated?

National Pi Day is a relatively new holiday. It was first celebrated in San Francisco, California, in the United States in 1988.

If you ever visit San Francisco, the Exploratorium Museum has a Pi Shrine that commemorates the founding of Pi Day in the Bay City, along with a Pi Has Your Number exhibit, where you can interact with a touchscreen to explore all of the numbers hidden within the first 3 million digits of pi!

 

Pi Day was first celebrated in San Francisco in 1988. Photo by Jamie Street on Unsplash

 

What famous people are born on Pi Day?

There are many famous people born on March 14th—National Pi Day—including world famous astrophysicist Albert Einstein, NBA superstar Steph Curry, and USA Olympic Gold Medalist Simone Biles.

National Pi Day Fun Facts Video

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Idea: How to Engage Your Students at the Start of Any Lesson
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Celebrate Pi Day 2025 with These Fun Facts
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