Logarithm Clothesline

I have some typical activities that I use when I introduce logarithms (logarithm "war", Kate Nowak's great intro puzzle, laws of logs explorations, etc), but this year I was looking to challenge my kids and get them talking a little bit more. When I taught middle school, I always loved a good clotheslines activity. It made kids look at multiple representations and analyze them, all while interacting and getting some energy out. I decided to try it out this year. 

Stage 1: Get Them "Designing"

My juniors were out at the ACT, so I had a class of about 8 sophomores (who are obviously very accelerated in pre-calculus) for 90 minutes that I needed to amuse. As a part of that, I gave them the activity below. In it, I gave them the "answers" and they needed to design logarithm questions to match. They got WAY more into it than I thought they would and it actually turned into a pretty engaging activity on it's own

Logarithm "Design" Challenge

Stage 2: Clothesline

I took the outstanding questions from my sophomores and made them into a sorting activity for the clothesline. 

Logarithms Clothesline Sort

When kids walked in, I had clotheslines up through the center of the classroom, knowing I'd be putting them in small groups to have them work. I handed each group a baggie with the sort cut out and enough clothespins. I then instructed them to work as a group to order them (which was more of a struggle for some groups than others). 

What I liked most about this was that they actually had to think about a logarithm having a value- something which is usually a struggle for them. They had to work collaboratively and wound up answering a lot of each other's questions before I could. I always love when kids can answer each other in a different way than I can. I had another activity ready for early finishers, but some of them really engaged in it and took the whole time. 

Here was some feedback from the kids. Besides that they wanted candy as a prize and to work with whoever they wanted, they seemed to really enjoy it! 

Rational Functions Challenges!

I always find my Pre-Calculus class the most challenging to teach at this time of year. Yes, even more so than prepping for AP Calculus for the first time and teaching a blended class with 50 students and about 10,000 things to grade every night. 

Why, you ask?

We run on block scheduling and there are few things which I think are more of a challenge for mathematics teachers than the gaps in background knowledge that happen from skipping semesters (or YEARS) of math in high school. By the time the kiddos get to me in 11th or 12 grade, all those "must know" skills have been forgotten. My goal is to try to remind them of those skills without having to reteach the concept completely. I know it's in there....we just need to bring it back to the surface!

We are currently studying rational functions, a topic which is so vital to their study of limits and later calculus. The whole idea of discontinuities....so important! 

This year for some of the review topics, I'm using some classroom flipping (with videos I made with Educreations). Kids who remember the material can speed through these and demonstrate mastery while kids who need the extra remediation have the opportunity to get it. My kids had 2 "flips" last night- a brief video on holes vs. asymptotes and one on horizontal asymptotes. Having the preview of these topics allows me to group the kids strategically and have them really practice in class. 

Desmos PolyGraph Activity 

Think "Guess Who?" for functions (the one pictured above is quadratics)! I loved that it let me move around the room and assess the comfort level with mathematical vocabulary.

We had a big discussion about what questions would be considered appropriate for pre-calculus level students. Here's what we decided...

From the teacher perspective, I could follow each conversation and make sure they were using academic vocabulary. I was able to circulate around the room and listen and ask probing questions to kids who needed it. It was competitive, but fun! Every single one of my students said on their feedback form for the activity they'd want to do it again.

What the kiddos are saying....

"It made me really think about the characteristics of the graph/function."

"It was fun and helped strengthen my math terminology" 

"I like the fact that you can ask questions to better understand the topic and also get asked the questions. It's easier to understand and more fun with being partners with some random person :)"

"It was a fun, creative way to show what we know with out the stress of a quiz, or test."

Once I felt confident that they had mastered the vocabulary and were ready for more collaborative practice,  the students had to complete a graphing mini-project on my giant laminated graph paper! The first 2 questions were a mini-review from rational expressions and equations and the 3rd was the actual mini-project.

Now to grade them all....

(Is the domain and range bothering anyone else?? Have some more work to do with that group, still!)