You know when you give a quiz and students do well on one objective, but almost all of them completely bomb the other objective? That's when I know I did not effectively teach the second objective. So, back to the drawing board I go.
The quiz was on solving exponential and logarithmic equations. Most of the students clearly and easily solved the logarithmic equations. But, WHOA, those exponential equations really threw them for a loop!
I had taught the solving exponential equations lesson right before spring break. Normally, I write all of my own lessons, but this time I decided to use a lesson from a textbook (stupid, stupid, stupid!). In this lesson, the textbook had only shown how to solve exponential equations using logarithms as the inverse operation to exponentials. At the time, I didn’t think twice about it. I had already showed them in a previous lesson how to rewrite a logarithmic equation to an exponential equation and vice versa. I assumed they would apply that knowledge too. Ugh…bad assumption.
When we did the practice activities the day before the quiz, I also reviewed the property of equality for exponential equations. I think that is when I started to realize that I did not CLEARLY define the three methods to solving exponential equations, which is not like me at all. If you’ve read this post, you’d know I think one of the best ways for students to understand math is to compare and contrast different methods.
Anyway, the students seemed to be doing okay in the group activity, so I gave them the quiz the next day. Once I began grading them, I immediately realized they were struggling to solve the exponential equations. They were mixing methods all over the place. That’s when you get that pit in your stomach and think oh man, where did I go wrong with this lesson?!
It’s not the textbook’s fault, it’s mine. I so regret not taking a more critical eye to the textbook lesson. Maybe it was me being antsy for spring break or the fact that I had wanted to revamp some of my notes for that unit and I hadn’t had time to do so, so I was wanting an “easy” way out. Whatever the reason, it doesn't matter, I knew I had to fix it with my students.
I decided to create a graphic organizer that CLEARLY states each method and the proper steps to solve. I will be using this with my students tomorrow to review solving exponential equations and then giving a mini retake on this objective.
I’ll update you all soon on how it goes. I imagine it will be MUCH better!!!
In the mean time, I want to share the graphic organizer I created with all of you! Maybe it will prevent you from having an exponential failure like I did.
Click on the picture below to download the file. Enjoy!
UPDATE: Ummmmm, yeah, went soooooo much better!!!!
If you were to visit my classroom, you would see a lot of different ways students learn: guided notes, games, stations, activities, projects and more! Project Based Learning (PBL) is a great way for students to critically think, problem solve, and, in general, see math differently. Therefore, I try to integrate a project into every unit and make them as “real” as possible.
One of my favorites, and my students, is the Parabola Selfie Project. In this project, students take math outside of the classroom and explore the real world to find a parabola.
Let’s take a quick look at how this project is broken down…
Students find a parabola in the real world and then take a selfie with it. Why take a selfie, you say? Well, first of all, it makes it fun for them since selfies are something they do often and share on Facebook, Snapchat, Instagram, or some other form of social media. Second, I want to make sure they don’t just Google search a picture online. That would take all of the fun out of this project. There is so much in the world to investigate, so I want them to go out there and see math as much as possible.
Next we pop that picture right into Desmos, which is an online graphing calculator. Students adjust the scale of the graph to match the dimensions of the real life parabola. I’ve even created a video showing students how to do this, in case they are not familiar with Desmos. Then they write an equation for their parabola and analyze the parabola by finding characteristics such as the axis of symmetry, vertex, domain, range, etc.
In almost every project I try to create a fun little twist that involves students observing or reviewing each other’s project. In this one, I have students exchange their graphs with each other and use the Parabola Swap table to record their information. This will give students an opportunity to identify characteristics of another parabola and also receive feedback on the accuracy of their data.
I rarely have students complete a project and then individually present to the class. It takes up too much class time and sometimes it can be difficult to see and understand the data when in a slideshow. I’d rather students take their information and put it on a poster or in a report format. Then we do some kind of walk around to view all the projects up close.
For this project, since students already swapped parabola graphs with another group and filled out the characteristics table for that graph, I don’t have them fill out another form when they do the walk around. Instead, I have them view each project and then vote on who found the most unique parabola in the real world. I give out a prize to the first and second place winners. You could give out a homework pass, food, or anything that your students enjoy. This gives each student a little more incentive to really find a fun and unique parabola.
As with any project, I do use a rubric. I evaluate each project on the following criteria: neatness/organization, the parabola selfie, the graph, the characteristics of the graph, and the quadratic equation.
Here are some of my student’s Parabola Selfies:
Doesn’t the Parabola Selfie Project look like fun?!....and educational! Click on the project below that you'd like to try in your classroom:
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What I really wanted to title this is “How TpT for Schools Saved my Behind” because that’s exactly what happened.
Our school needed to purchase new math books for grades K-5. We use the Virginia Standards of Learning (VSOL), so it was difficult to find textbooks that covered these standards because most resources are aligned with Common Core. We had to carefully evaluate all of our textbook choices online. Why? Well, we are an international school, so shipping is both expensive and time-consuming. Even if samples could be sent to us, there would not be enough time to evaluate them and order books in time for the new school year. So, yes, evaluating books online was not an easy task. Regardless, we finally decided on one that we thought would work well for our program.
August came and the textbooks arrived. It didn't take long to realize that, not only were the books missing standards, but they were also missing pages that had been in the online version. To top it off, the workbooks were stamped "Common Core," which was also not on the online version. How could this happen? These textbooks were listed as Virginia aligned, so we assumed they were specifically designed around the VSOL and all standards would be included, but they weren't. I was devastated. As our school's curriculum director I felt responsible. I am in charge of leading the team and approving the resources. How could I have let this happen?
Long story short, we were able to get reimbursed for the insufficient resources by the publishers. Yay, problem solved, right?! No, we still had teachers with books that had missing standards and no resources to teach those standards. What were we going to do?
Ordering new books wasn't feasible. We needed an immediate solution. We decided to give each teacher a budget on Teachers Pay Teachers (TpT) where they could find high quality, standard aligned resources. Teachers could purchase resources to cover the standards they were missing. Another yay, right?! Yes and no. In order for our teachers to get the resources they would have to go through a very complicated process which included filling out a Google Form for each resource they wanted, approval of the resource by me, then approval by our financial manager and then finally the resources would be distributed to the teacher via hard copy or thumb drive. Clearly not an ideal process, but it was our best option until I saw that TpT was coming out with something called, TpT for Schools. I immediately applied and was thrilled when I received the email that we had been accepted into their early pilot program. They scheduled a video conference so they could explain the platform. It was exactly what we needed!
TpT for Schools was the perfect solution to all of my problems. The steps are so simple:
This process can happen in five minutes or less. We love this process and we love the wonderful resources we are able to purchase through TpT. This was so well received by the K-5 teachers, that we gave other teachers a budget and added them to our TpT account so they could order resources to supplement our curriculum. What had once been a curriculum catastrophe, turned into a long term victory, thanks to TpT for Schools.
Besides the convenience of TpT for Schools, they also have top-notch customer service! Anytime I have a question or suggestion, they quickly respond via email. They assured me that it is a priority of theirs to help make the platform even better for us. Also, they check in with me every other week to see how we are doing with it and if we have any other suggestions or ideas, etc. You can tell they truly want this to be the best solution for all schools, and it’s a team effort between them and us. The TpT team is outstanding because they are:
Sign up for TpT for Schools NOW
So, as you can see…..TpT for Schools SAVED ME! What does this mean for you?! It means that it can save you too. Maybe your school doesn’t have the same issue as we did, but teachers are ALWAYS in need of more innovative resources that books from publishers do not provide. Therefore, I highly recommend you reach out to your admin and ask them to sign your school up for TpT for Schools so that you can start enjoying the benefits too!
Share TpT for Schools with your administrator to begin the conversation:
Do you remember playing Battleship when you were a kid? How exciting was it to figure out where your friend’s battleships were and sink them?! Well, I’ve brought that fun and excitement into the math classroom. For those of you who have no idea what the game Battleship is, read below to discover a game that will keep your students asking for more!
BATTLE MY MATH SHIP?
Battle My Math Ship is a game for two players who try to guess the location of the ships each player hides on a grid that can't be seen by the opponent. Each player receives a page with two grids and sheets to identify the spaces they choose and show their work. The goal of the game is to sink all of the opponent's ships by correctly guessing their location and solving the problem.
HOW DO YOU PLAY?
Each player secretly marks the battleship grid on the TOP of their sheet with the number of battleships stated. They do this by drawing a ship, marking an X, shading the box, highlighting, etc. in the spaces they choose. The BOTTOM battleship grid is what they use to choose spaces and attack their opponent.
Each player calls out a letter and number that identifies a column and row from the BOTTOM grid in an attempt to name a space that contains an opponent's ship. Each player then solves the problem and states their answer to their opponent.
AFTER each player solves the problem, the opponent checks that space and states whether they “hit” or “missed” a battleship. Each player should cross off the spaces the opponent attacked and answered correctly and write HIT for the spaces that contained a ship. If they did not answer correctly, they can try attacking that space again on a different turn.
The first player to sink all of their opponent’s ships wins the game!
HOW MUCH TIME DOES IT TAKE TO PLAY?
The game can take anywhere from 30-60 minutes, depending on the math concept. I know class time can be limited for games. No problem! Often, I give my students a time limit to play the game. The winner is then determined by the player that sunk the most battleships in that time frame. Not needing a certain amount of time and the fact that my students LOVE sinking ships, is the reason this activity has become the most popular math practice activity I use in my classes.
HOW DID YOU CREATE THE GAME?
The idea came from the original Battleship board game made by Milton and Bradley. This was my favorite game as a kid, so I had to find a way to create an activity for my students that would bring them the same joy I had growing up and of course tie in some math learning! The Battle My Math Ship games cover many math topics from grades 6-12, so your students can play again and again.
DO STUDENTS REALLY ENJOY THIS ACTIVITY?
YES, it has been the biggest hit in my classroom! But you don’t have to take my word for it. Here are some reviews from other math teachers that have used it in their classroom as well:
Math games make math fun and this is no exception. My students loved playing this and repeatedly ask for it. – Sarah O.
Absolutely the most engaging game. My advanced kids were enthralled and asking for more!! – Colleen A.
This is a very creative way to get kids engaged in practice. – Katherine G.
I thought my kids would find this activity confusing, but they LOVED it! – Jennifer M.
My students had so much fun with this! Students who had struggled at the beginning of our linear equations unit, worked hard to master finding slopes to play this game. – Tiara W.
Students had a blast with this activity! – Amy H.
My students loved this! It was a very engaging way to practice slope, all in a self-checking activity! – Emily K.
Hoping you will keep creating more activities for more skills in this series -- my students have loved every one we have played so far! – Diane M.
Love all of the Battleship games and so do my students!! – Nicole Z.
My kids flipped over this! They LOVED it! They asked me to find more for them to do. – Harrison B.
Can’t wait to get your hands on a battleship?! Great! I have one waiting for you for FREE, just CLICK HERE.
OR are you already convinced that your students will LOVE this activity?! Click below on the battleship bundle that fits your classroom needs: