I get so much out of creating lessons. When you deeply understand a concept, you can talk about real-life situations and the math behind it. I’ve never thought about it until now, but a revolving door is a perfect example of a solid of revolution. Taking a rectangle and revolving it around a pole, creates a cylinder. What a beautiful example!
The last time I was at an AP Calculus seminar, I learned that another awesome example of a solid of revolution is a honeycomb decoration used at parties. These are perfect examples because you can see the 2-D version before it is rotated. This is exactly what we want students to know. What does the 2-D version become with you rotate it? If they can visualize that, then they get it!
Here is something fun I did in my class recently. Students cut out a shape and taped it onto a straw. Students had a blast! Some students took video!
Another concept that goes hand-in-hand with 3-D figures is the idea of cross-sections. Everytime we slice an orange, apple, or a loaf of bread, we have created a cross-section. In Algebra 2 and Pre-Calculus, we discuss cross-sections of cones. Depending on how you slice the cone, you can get a circle, an ellipse, a parabola or a hyperbola.
A great hands-on activity for cross sections is to have the students create a shape out of play-doh. Take a piece of dental floss and slice the object horizontally, vertically or even at an angle. Be sure and have them make predictions before they perform the experiment! Students with phones can take a before and after picture so that other students can see.
I enjoyed creating my Intro to 3-D Figures resource. It’s amazing how after teaching math for many years, that I can still pick up valuable insights and ideas. Math is infinite. There is no end to what you can learn! Check out both resources below. They are the same except one is a printable and the other is a digital Google Forms format!
At certain times of the year, you may feel like you’ve lost control of your classes. Toward the end of the year, you’ve become lax and the kids are getting too comfortable. Students are talking while you’re teaching. You have a hard time getting their attention. Phones are visible along with earbuds inserted. You are miserable and little worried about how you are going to make it through the rest of the year. I have 5 easy things to try to get you and your students back on track. You will realize how easy these things are to do and wonder why you haven’t done them all along. Sometimes even teachers lose focus and go into survival mode. Survival mode is a hard place to stay. Try these 5 things and I promise you will be happy and you can finish the school year with a confident attitude.
I. A seating chart is a must!
It doesn’t matter what grade you teach. Seniors? Juniors? 7th Grade? Doesn’t Matter! You need a seating chart if you’ve lost control. Look at the seating arrangement of each class. Have they started sitting where they want to sit? Are they too comfortable with the students around them? Do you have them in groups? Have you ever had them in a seating chart?
My suggestion is to put your classes in rows for a while and decide where you want each student to sit. Who needs to be in the front? Who can sit in back? Who does not need to be by each other? Strategize! The kids will moan and groan, but ignore it because you’re going to see good results from this seating chart. You’ll probably have a few kids come up to you and say that they can’t see from their new seat or they can’t sit by a certain person. You will hear some excuses, no doubt. For right now, just tell them to sit where you put them. (You are in charge!) If you see a problem with where some kids are sitting, YOU DECIDE when to move them!
II. Getting Their Attention!
Now that they are in their new seats, it’s time for a discussion. You are going to explain that they will not have their phones out, unless they have permission. You do not want to see the phones or see the earbuds or you will take them up and either turn them into the office or not give them back until the end of class. Now, if you say this, you have to follow through. The first person that messes up needs to be made an example. This will get the attention of everyone. Don’t budge on this!
The other thing you are going to tell them is that since you’ve had problems getting their attention lately, you will put your hand up when you need their attention. When they see your hand up, they put their hands up too until everyone has their hand up and mouth’s shut! (Seniors can do this! Adults can do this! Kids can do this!) Tell them that you will not talk over them and until they are quiet, you will stand and wait. If they choose not to listen, then you will hold the class after the bell. (Yes you can do this. You don’t have to hold them long. 30 seconds to a minute will get your point across.)
III. Walk the Class!
From this day forward, you need to walk the class. Don’t stand in front of the room and teach. Be everywhere. Talk to the class, then walk around and see if they are doing what you asked them to do. You can teach from any part of your classroom. Let students go up to the board. You don’t have to always do it. If you’ve never walked your class, you will be amazed at how this will change your classroom. Try to talk to each student at some point during the class period. Don’t hover over any student for long though. Keep moving and act like you are really checking out what they are doing. If you really want to put on a good show, get a clipboard and act like you are writing stuff down that you see. You can even walk around and put stars, stickers or check marks on things that you see that are good! You will have fun and the kids will too. All kids like stickers, smiley faces and check marks!
IV. Calling Cards!
Another awesome trick to keep your students on their toes is to randomly call on people to answer questions. There are random selectors on the internet, but I like to use index cards. It’s very easy to do. Put each student’s name on an index card. Shuffle the cards and randomly select students to answer questions. When I’m having kids work an example problem, I’ll warn them and say, “I’m going to randomly call on someone in a minute.” If you call on a kid that sits and looks at you because they don’t know the answer, still make them give you something. You can give hints, or help them out, but don’t let them get away without answering the question. All the students are watching to see how you handle the kid that says, “I don’t know.” This will get your students engaged, because they don’t want to be the kid that doesn’t have an answer. If students give me wrong answers, I still praise them. I don’t want anyone to be afraid to answer a question because they are afraid of being wrong!
V. When it’s Time to Go!
Be in charge…even when the bell rings. Did you know that the bell doesn’t release the kids? YOU DO! I tell the kids that they are not allowed to leave the room, until they hear me say, “Have a nice day!” I keep them in their seats until I inspect the room. Is there trash on the floor? Did they put up any materials they used? One trick, I’ve learned to do and yes it works with any age, five minutes before the bell I say, “I’m inspecting the room and the cleanest, quietest, straightest row will get to leave first.” This works great on that rowdy class that always leaves your room in a mess. I usually walk around and point out trash on the floor and other things that need to be corrected. When the bell rings, I’ll pick one row to go. I don’t release another row until the first one is gone. When I’m down to 2 or 3 rows left, I usually say, “Ok, everyone can go now.” If you do this a few times, they respond well. If there’s one kid talking and keeping their row from leaving, I’ll say that everyone can leave, but “Johnny.” I’ll let everyone go and Johnny stays behind. It’s entertaining to say the least, but I promise it makes a difference.
Don’t be miserable, take charge. It’s never too late. Trust me, I’ve made every mistake possible. I’ve learned that being FIRM is the key. I left many days, almost crying because my day has gone terrible, but it was my fault. Take control. Kids will respond as long as they see you are firm and fair. I hope the rest of your year goes well. If you would like a complete discipline plan for secondary students, click the picture below:
Area is taught in early grades. The concept of adding up all the square units that COVER a figure is actually pretty simple. Students need to understand WHAT area is before really delving into using the formulas and then taking them a step forward.
In secondary grades, we begin to use the formulas and study how areas of composite figures can be found as well as finding shaded areas. These types of problems bring in the “real-life” and “problem solving” component. I tell my students all the time, “You must know how to apply the problem and you must know how to think about it forwards and backwards.” (If you are given the sides, find the area. If you are given the area and one side, find the missing side.)
To take area a notch further, we throw in algebra. Instead of a side being just 4, we might make it 4x. We will talk about how area is quadratic, volume is cubic and perimeter is linear.
Before students get to pre-calculus, they also need to how dimensional changes affect the area. If all dimensions change, the area changes by that amount squared! So if all sides are doubled, then the new area will be quadrupled (or doubled squared). If one dimension changes, then the area is only affected by that amount!
I’ve been hard at work creating my Geometry Curriculum. My most recent resource covers area. The resource practices finding area of rectangles, parallelograms, squares, rhombi, triangles, and trapezoids. These figures are combined into composite figures and problems are worked forward and backwards. There is a special emphasis on regular polygons. Regular polygons are a great way to practice special right triangle rules and trig! There are tons of notes, practice and quizzes in this resource. If you need something like this, then go to my TpT store and check it out.
A pattern that occurs over and over in nature is the Fibonacci Sequence. The pattern is this: 1,1,2,3,5,8,13,21,34,55… Do you know the next number in the pattern?
When you make squares with those widths, you get this cool spiral:
Look at these beautiful images that follow this pattern:
The pattern does not always appear in a spiral.
The Golden Ratio and Fibonacci Sequence go hand in hand…pardon the pun.
Divide 8 by 5, Divide 21 by 8, Divide 55 by 34… choose any two numbers in the sequence that are next to each other and divide larger by smaller.
This coloring activity is a fun way to practice area and circumference problems. There are 16 problems in all. The students are asked to leave some answers in terms of pi. There are some problems that area is given and the student has to find circumference and vice-versa. The back of the activity has adding, subtracting, multiplying and dividing with pi. The variety of problems makes this resource fun but challenging!
This was my very first resource that I put on TpT. I love this activity. (I made a version for digital learning too!) Students have fun making a poster and using multiple representations. They are given several exponential scenarios to choose from such as a basketball bracket, a cockroach infestation, a zombie takeover, friendship bread, chain letters and more. Here’s a sample poster of a football stadium after a game has ended:
After students look at their choices, they may come up with their own situation. This is what differentiation is all about…students making decisions based on interests!
When I was getting my masters, we were encouraged to study exponentials in depth. This opened my eyes to all types of situations that are out there. I was inspired to create Exponential Functions: 6 Stations. Look at the titles of the stations below. Have you ever played Tower of Hanoi? There are free phone apps and online math sites that have this interactive game. Click here to see what I’m talking about! The number of discs and the least number of moves to get all the discs to tower 3 is an exponential function! How cool is that! Kids love games, so when you introduce this they will want to play for hours. Some of my buyers have turned these stations into other activities. After you see them all, you can decide for yourself how it works best for your room. These are not quick stations, they are more like math centers!
I still was not finished creating exponential resources. I couldn’t get enough! I wanted a unit! I wanted that unit to be about multiple reps and I wanted it to include transformations, compound interest and compound interest where the compounding is continuous which would bring in the constant e. I wanted another data collecting activity because there needs to be practice writing exponential functions. At the end of the unit, I wanted an assessment. I believe in differentiation, so I created 5 assessments that cover the same thing but with different difficulty levels. The assessments are a part of my unit in my TpT store, but I also sell them separately. The unit also contains warm ups and cool downs.
I make the unit a booklet and let the students work through it at their own pace. There are a few places in the unit, when the teacher needs to stop the class and have some discussions, but for the most part, the students can work through this on their own. Once they’ve made it through the booklet, we trade and grade. Students will know exponential functions forwards and backwards by the time they are finished with this unit.
Here are the links to my Exponential Functions Unit and my Exponential Functions Bundle (which saves you money and has all the resources in it plus 20 task cards), but I’d like to leave you with a freebie. This is an exponential activity that I have done over the years. It’s fun, interactive and tasty! Enjoy!
Recently, I needed a digital version, because I was teaching my class from 2000 miles away. I was able to watch and interact with my students in this version of my Exponential Function Activity:
Are you preparing your students for college entrance exams? Do you know enough about the exams to help your students? I challenge you to start now by making a difference for the future of your students. You do not have to be a high school teacher to start this process. Make up your mind and let’s do this!
Challenge 1:
Learn more about the SAT/PSAT and ACT. Go to the CollegeBoard website and the ACT website and browse. See what those tests are like. Do you know what topics are covered on those tests? Learn the importance of the PSAT…it’s more than just practice! Do you know the purpose of the ACCUPLACER (or if you are from Texas it’s called the TSI)? The more you know about these tests, the better you will understand how you can help prepare your students.
Challenge 2:
If you teach 5th grade math, does it matter if you know what is on the math portion of the SAT? I challenge ALL math teachers (elementary, middle school and high school) to take the math portion of the SAT or ACT. If you do not teach math, I challenge you to pick any of the portions of the SAT or ACT and take them…especially if it’s been awhile since you graduated from college! If you are a science teacher, check out the ACT science test. WOW! It’s crazy all the reading involved on that test! Open your eyes to what is on these tests and how they ask questions.
Challenge 3
Implement one thing (a topic, a strategy, a visual) that will help your students be successful on college entrance exams. Here are some examples:
1)Pick a topic to focus on and spiral into your lessons every so often.
2)We all have important vocabulary that we cover, but Google SAT vocabulary list and create a word wall with some of these words.
3)Pick a testing strategy like timing your tests.
4)If you teach math, have calculator and non-calculator portions of your tests.
5) Use actual SAT or ACT or ACCUPLACER questions as bell-ringers. If you teach younger grades, simplify them slightly if needed.
6) Show your students how to get on Khan Academy. This site is awesome and has great college entrance practice.
Challenge 4
Talk about these tests in class. Start talking about them while the students are young so they know what’s coming and know what to expect. The great thing about this topic is you are starting the conversation about going to college. Some students do not get to have that conversation at home, so the only place they might hear it is from you.
Challenge 5
If you teach 9 – 11th graders, encourage your students to go ahead and take the ACCUPLACER or the equivalent in your state. It doesn’t cost much and they can take it as many times as they like. Have them bring the paperwork back to you and you can help them figure out their strengths and weaknesses. In Texas, the students must make a certain grade on the three parts so they do not have to take remedial college math and English classes. My next door neighbor took her 8th grade daughter up to the nearest community college last year and had her take the test. Guess what? She passed all three portions and she hasn’t even taken high school Algebra yet. My school encourages students to take the test when they are ninth graders. Many of them pass the first time, but most do not. This is when I step in and start reviewing them for the next time they take it.
I’ll have to admit, that I did not see the importance of learning as much as I could about these tests until last year. I was given a class full of seniors that had not passed the TSI yet and my job was to help them pass it before the end of the semester. I found very little help online when it came to work that I could give them. I had no choice but to create my own reviews. I had to research the topics and I came up with 7 packets. I offer these in my TpT store. I also bundled all 7 reviews. My son is a senior, so I decided to put his picture on the front of the packet. I have to brag on him, he passed the TSI with flying colors. He is a fast test taker. It only took him an hour and five minutes to take all three portions. It’s an interesting test. If you do not pass the first 2o questions or so, it gives you 4o more to do, so that’s why it takes some students forever to take it.
After most of the students in my class had passed the TSI, I couldn’t let them come to class everyday and do nothing, so I started reviewing for the SAT and ACT. Again, I created my own material. I’m glad I did because now I know so much more about those tests. I plan on making more SAT reviews when I get a chance. I have bundles and individual products. The bundles are seen here:
I basically had to write my own curriculum for a semester. That’s not easy when you are also teaching Algebra II and Pre-Cal. If you are in the same boat and need curriculum for a senior math class, then I’ve bundled all three entrance exam reviews into a MEGA bundle as seen below:
Please take this advice and start familiarizing yourself with these very important tests. See if you can add anything to your routine that might help your students. Be creative in your implementation and don’t reinvent the wheel. I hope I have motivated you to start your “College Ready Research.” Encourage your colleagues to do the same. Send me some of your ideas if you get a chance. Good Luck!
Parks and Rec has to be one of my favorite shows and Rob Lowe is very cute, STILL! If you’ve never seen the show, put this on your to-do list! You’ll think it’s weird at first but the characters are hilarious. Rob Lowe joins the show during the second season. He literally says literally 20 times a show…maybe I’m exaggerating, but he does say literally a lot! Watch it…you’ll love it. It’s a nice way to relax and get your mind off school.
So why am I thinking about literal equations? The physics teacher is telling me that the kids can’t solve literal equations! I could have told him that :), but why can’t they? I know my students can solve 4x = 8, but they can’t solve d = rt for r. What’s the issue? I think it’s several things:
They are solving 4x = 8 in their head. They know that 4 times 2 is 8, so x has to be 2. They aren’t thinking about inverse operations. I’m realizing some students still do not know that 4x means 4 times x.
When students see a problem with only letters in it, they automatically think that it’s hard. They are not making the connection that really all that is happening is that r is multiplied by t. If they knew the operation taking place in the problem, then they should ask what is the inverse operation.
Students are not understanding that all they are “UNDOING” the operations to solve for one of the variables…which leads me to wonder if anyone has ever explained that when you solve equations, you are actually doing PEMDAS backwards.
I’ve created a lesson that addresses all three of the issues above. At first, I think the student should analyze the problem by writing the equation in words so I can see if they understand what operations are taking place. I then ask them to circle the variable they are solving for so they can have a visual of what needs to be by itself. The notes below are what I give the students to get them started on this process.
I take them through a problem similar to the one above and then I let them practice 4 problems that are similar to this. Below is a sample:If you like collaboration, these problems would be good for a sage and scribe activity. The sage tells the scribe what to write. The scribe has to stay quiet for a while and let the sage describe the steps and what needs to be written. I eventually let the scribe have some input because sometimes they are dying to help the sage. We switch roles for each problem.
Next, I give them a worksheet that has a regular equation with a literal equation that looks just like it. They do the regular one first and then the literal equation (they are solving for c). I keep telling them to remember what they did on the regular equation and follow those same steps. Here’s an example:
The final activity in this lesson is to help the students in their science class. I give them some science equations mixed in with a few math equations. I’m hoping by now, these problems will be easy.
There is one more reason students do not understand literal equations and it’s our fault as teachers.
4. Teachers work on literal equations for one day maybe two and that’s it. How can they really get it?
Let’s not make that same mistake again. I plan on recycling literal equations back into my lessons. I plan on using them in bell-ringers and I plan on putting them on assignments and tests in the future. How many people can understand something, especially in math, after one or two days? Remember that when a student first sees a literal equation, it looks foreign to them. They are not going to make the connection that they are just equations (at first).
We can help make the student more successful in math and science if they learn to solve literal equations. Don’t take this topic lightly. Ask your science teachers what else students have a hard time with when it comes to math in their class. Bring something to write with, because you’ll get a list of items. Other things that my physics teacher has mentioned is conversions, graphing linear equations (knowing slope, independent and dependent) as well as being able to graph bar graphs.
Good luck and if you would like to purchase my literal equations activity, click below:
I have fun teaching inductive and deductive reasoning. I usually start the lesson by having students watch a YouTube clip of Monty Python and the Holy Grail. It’s a pretty hilarious demonstration of how drawing conclusions based on patterns can lead you to the wrong conclusion. This would be a great place to talk about stereotyping if you would like to go a little deeper into how people base information sometimes from the media or gossip. This lesson has 12 task cards to practice reasoning and knowing the difference between the two types.
Conditional statements is also fun to teach. I love it when kids say that it doesn’t seem like we are learning math. We discuss where the hypothesis and conclusions are in the conditional statement so the students can write the converse, inverse and contrapositive. We also discuss counterexamples and biconditionals. This lesson has some hands-on activities where students create if/then statements and the related statements and tape them into their journals.
The last part of this unit is spent on two-column proofs. This usually happens for me in October, sometimes earlier but close enough that I can show them a silly Halloween proof that I created. I made this up a long time ago after watching “It’s the Great Pumpkin, Charlie Brown.” It’s got all the elements of a real proof. I’ve used this as a bulletin board in past years. Feel free to use this in your classroom.
One thing that is in this lesson that helps my students is a set of matching cards. Students will match the property or definition with its name. I do this as a collaborative activity. Students enjoy this and it helps them to have some tools to use going into writing proofs. This is a beginning proof lesson. I only practice two-column proofs. In lessons that follow this one, I introduce the other types of proofs like paragraph and flowchart proofs.
If you are teaching online, no problem. I’m in the process of making these lessons more online friendly. Teachers Pay Teachers has a new tool that can take a PDF and transform it into an interactive worksheet. Look for the “Use as a Digital Activity” button on products that are available for this. You as a teacher can modify it as you see fit then assign it to your students.
I love this part of Geometry. It’s different from the norm in math. It’s always a fun time of year. If you’d like to use my lessons, then the best way to get them and save a little money is to purchase the Unit 2 Bundle.
Exponential Functions Activity
If you like collaboration, these problems would be good for a sage and scribe activity. The sage tells the scribe what to write. The scribe has to stay quiet for a while and let the sage describe the steps and what needs to be written. I eventually let the scribe have some input because sometimes they are dying to help the sage. We switch roles for each problem.
