My students initially HATED logarithms. This surprised me because my Algebra 2 students LOVED them last year. This might have had something to do with the fact that I chose to introduce them on a day that most students thought we should have been out of school. Many of the schools around us had already closed due to the impending arrival of Cleon. But, we were in school. And, my students wanted to have nothing to do with learning something new.
|Introduction to Logarithm Notes|
This introduction to logarithms is basically a compilation of a lot of ideas I found on the Internet. The Loop Trick was stolen from Square Root of Negative One Teach Math. Another memory device was stolen from Zook Tutoring. Additionally, I stole Until Next Stop's Secret Method of teaching logarithms.
I made a booklet foldable for my students to introduce logarithms. I wanted to emphasize both converting between exponential and logarithmic form and evaluating basic logarithms.
|Logarithms Booklet Foldable (Outside)|
The inside of the foldable houses lots of practice problems that were stolen from a Kuta worksheet.
|Logarithms Booklet Foldable (Inside)|
After we came back from five days off due to snow, I decided that my students needed a LOT more practice with converting logarithms to exponential form and vice versa.
I had been trying really hard to not teach them the loop trick. I had been emphasizing the question: what exponent is required to go from a base of b to reach a value of a? But, my students were frustrated, and I was frustrated. Once I showed them the loop trick, it was like a whole new world. You mean, that's all we have to do? Students were in disbelief over just how easy logarithms were.
|Logarithm Loop Trick Notes|
Our notes were followed with lots and lots and lots of practice. We practiced for days. First, we played Log War. I printed and laminated decks of logarithm war cards. There are many different sets of log cards available online to download. I chose a deck created by An "Old Math Dog" Learning New Tricks. I chose this deck because the location of the x varied from card to card. (Some of my students discovered the log button on their calculators WAY before I intended them too. By varying the location of x, these students were still forced to convert the equation from logarithmic form to exponential form. I know, I'm mean.) Last year, I used a deck created by someone else. It had fractions and negative numbers as answers which I liked, but the variable location never changed. I didn't laminate these cards, and the card stock didn't hold up as well as I'd hoped. Maybe some day I will make my own deck of cards that has everything I'm looking for.
My students LOVED log war. I was surprised, though, by the number of students who said that they had never played war with a deck of cards. I had them play in groups of 3. Everybody flips over a card. Each person evaluates the logarithm before them. Whoever has the largest x-value gets to keep all the cards. If there is a tie, everybody involved in the tie flips over a new card. The winner of that gets to take all the cards that have been laid down. The goal is to end up with all the cards. As soon as 1 person ran out of cards, the other two players were declared victors. I did this to ensure that everybody was participating all the time. If we played until one person had all the cards, that would mean some students would not be participating. Even my kids who usually hate to participate in anything got into this activity!
I loved walking around the room and listening to the conversations taking place. They quickly caught on to which cards had negative or fractional answers. They were patient with each other for the most part. Explanations were given when needed from student to student. It was a beautiful lesson because it pretty much ran itself. It was fun and engaging. And, I can't imagine teaching logs with log war!
If you don't believe me, take it from one of my students: "I wish math class could be like this every day!"
|Log War Cards|
|Logarithm War Cards|
After playing log war, a student asked if there was any way we could play log bingo. Umm...I'm not sure if log bingo exists. Let me do some checking. Sure enough, log bingo exists.
|Logarithm Bingo and Logarithm Speed Dating Cards|
I found a version called MATHO on ILoveMath.org. (Apparently, this link is now broken, so I have uploaded the MATHO Bingo file below with my other files.) I immediately fell in love with it when I realized that it required students to create their own bingo boards. Filling out the MATHO board took longer than I realized. I realize I could have laminated these and used them for years to come. But, I decided that there would be less cheating if students actually wrote on the boards with pen/pencil instead of dry erase marker. The hardest columns for my students to fill out were the M and A columns.
|Blank MATHO (Logarithm Bingo) Board|
I was provided with a call sheet that has a logarithm question for every possible number students could put on their MATHO boards. If you scroll back up, you will see a bag full of slips of paper. Each one of these slips represents one of the possible questions on this call sheet. I didn't want there to be any accusation of my picking or not picking certain questions because I wanted a certain person to win. I would draw a slip and write the problem on the Smart Board for my students to solve on their mini dry erase boards.
|Logarithm Bingo Call Sheet|
My students had fun with this as well! The game took a lot longer to play than I anticipated. I had planned on getting through two rounds. But, we only made it through one. I hadn't picked up any bingo prizes, so I figured I would offer to buy the winner their favorite candy bar. I didn't even have to do this though. Before I could mention my intended prize, someone goes, "Can we get a sticker if we win?" Sure! I'll gladly give you a sticker if you win.
That was 2nd hour. When my 5th hour came in, I was told, "You better still have some of those stickers like so-and-so had. I'm going to win so I can get a sticker just like him." What can I say? My students love stickers.
On the same day that we did logarithm bingo, we also did logarithm speed dating. I printed off the log flash cards from Square Root of Negative One Teach Math. There were two levels of questions, so I printed them on two colors of card stock and laminated them. I introduced the idea by asking my students if they knew what speed dating was. A few of them did. But, most of them didn't. When I asked them if any of them had tried it, they looked at me like I was crazy and reminded me that they were only 15-16. Apparently, speed dating is only for the truly desperate, and they're not that desperate yet.
And, then they had to ask me if I had ever tried speed dating. No. No, I haven't. Instead of rearranging tables, I had students make two lines that faced each other. I let them pick their initial partner. I passed out the flashcards and instructed them to keep the answer facing themselves.
Speed dating is simple. Hold up your card so your "date" can see the question. When your date tells you what they think the answer is, you should either congratulate them on getting it right or provide coaching/feedback on what they did wrong.
"Ummm...If I'm on a speed date, and the guy across the table from me doesn't know what he's doing, I'm not going to coach him on how to be a better speed dater."
|Logarithm Speed Dating Cards|
My kids did eventually catch onto how to effectively coach one another. I was able to see several light bulbs go off during this activity. Then, the other person holds up their card, and the process repeats itself.
When we did this, I got to be both a participant and the person who gets to ring the bell that tells everybody to wrap up their conversation and move onto their next date. In actual speed dating, you exchange information at the end of the date so you can get in contact with one another if the date went well. In logarithm speed dating, we exchanged cards with our partner before moving on to our next partner. I had one line of students move down two spaces to reach their new partner.
Both class periods, I had an odd number of students. So, I got to participate in the speed dating process. I even got every question right. Imagine that! Overall, I think my students really enjoyed the activity. It was something different. It was fast-paced. It provided instant feedback. It gave students an opportunity to coach other students who were having trouble. And, I was able to eavesdrop on conversations and get a sense of exactly where my students stood in relation to logarithms.
My students' only complaint was that the cards were used were too small. In the future, I will make bigger cards for this activity. I'm curious what other topics I could use this practice structure for...
I've got more to post about logarithms, but I need to get a new digital camera. I've had the same camera since 2007, and I think it has finally died.
Oh, and I got this comment from one of my students. I think it's a compliment. I'm going to ignore the fact that they were probably insinuating that I would be terrible at non-mathematical speed dating.
"If mathematical speed dating were a real thing, you would rock it, Ms. Hagan."
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