Mathematical Bakery

Working with generalized proofs today, we ran into a problem that said (a+b)(a+b)...we were using the distance formula. Oh the crazy answers I heard from my Geometry students!! Sure, we haven't done a lot of multiplying of binomials this year, but still....I was a bit frightened. I explained to them that at the end of this year we're going to do a pretty hefty Algebra review to make sure they're in shape to take Algebra 2 next year. I told them "factoring is cake compared to what you'll see there!" The following conversation ensued:

Student 1: "So....you're saying Algebra 2 is like a scone?"

Me: "What??"

Student 1:" Well if factoring is cake, Algebra 2 is a scone....it's a little harder."

Student 2: "Pre-Calculus must be like a stale scone!"

Student 3 (from across the room): "And Calculus is like a really hard loaf of bread!"

Student 1: "Good thing we have studying...that's our coffee! We can dip our scones into it and it will soften them and make them taste better."

Student 3: "I don't think I'm going to study in Calculus."

Me: "Why not?"

Student 3: "Because....old bread dipped in coffee? Gross."

Groups of kids like that remind me why I love my job, especially on the days when you're ready to hide under your desk.

What do Hercules, Kings, and Exponents all have in common?

Just introduced exponential functions in Algebra and I wanted to find an engaging way to get them hooked. I proposed this question to the students and asked them think & discuss with their groups:

A king has offered you a handsome reward for all your service to the kingdom. You may choose either:

- $1,000 on each square of a chess board until it is filled

- $0.01 on the first square, $0.02 on the second, $0.04 on the 3rd, until the board is filled

Which do you choose and why?

Naturally, most of them picked the $1000 deal- because obviously it will yield more money! Only one student bothered to actually do some calculating...like by the 17th square you'll start getting way more than $1000 per square. 

I had two students come to front of the room and handed them an envelope with the amount they would receive in it. They went nuts. Why would this happen? They thought & discussed. Geometric vs. Arithmetic sequences.... counter-intuitive but captivating!

I then showed them this clip of Hercules fighting the hydra. They then broke into 5 groups and each had a different type of hydra- one that loses one head and grows 3 back, one that loses one head and grows 4 back, etc. They had to make a table of the number of heads in each round, then write a function equation for it. This, of course, led easily into graphing and seeing the growth. Which hydra would you least like to face? The one with the biggest common ratio/rate of growth! Vi hart wrapped it up beautifully for the day with her binary trees video. Fun day!

Higher Level Confidence

Despite 4 weeks of practice and warnings over and over that I would never just give them a question like "find the slope between these 2 points," my Algebra class was still flabbergasted that I had the nerve to give them a world problem on a test. And let's just say....I gave them pretty much all word problems.  As you may have guessed, it was our first real, honest to God, Common Core aligned test. For everyone's testing pleasure- no questions below comprehension level here! And as of today, I have 26 new enemies.

The tests are graded and the students did wonderfully, but ohhhhhhhhh baby are they mad. I had 4 angry emails right after...all from the same parent....whose student got a 93% on the test. It's not that my kids don't know the material, but any challenging question shakes their confidence. They have had their hands held and been given knowledge level tests and quizzes for so long....I don't even think they know that they're capable of applying their knowledge!

Does anyone have some tips for helping to build students' confidence with higher level thinking? I always thought the challenge would be helping them be capable of it, but we've done so much practice that they've demonstrated to me that they can handle it. I know as we practice more, confidence will build. But, really, how do you break the "this should just be regurgitation" mindset? 

Giving back the tests tomorrow will be fun, though. That should help in the confidence department! 

The Wonderful World of....Foldables?

I am like my middle schoolers in some sense....there are "cool kids" in the "class" with whom I really, really want to hang out. Go to the mall, braid each other's hair, share secrets....you know? I just haven't quite figured out how to infiltrate their world yet. Obviously, I am talking about foldables. I see teachers who do these elaborate interactive notebooks and I think....those are SO COOL!!! But do I have time for them? Will they be helpful or are they just a bigger waste of time? How do I get a class of 28 to listen to elaborate directions for a foldable without wanting to pull my hair out? 

So today, I decided to go over to the cool kids lunch table and sit right down. We tried a (very simple) foldable for slope intercept form in Algebra. My students spent extensive time last year studying the topic, so I'm not dwelling on it for long. A foldable seemed like a good way to re-establish our relationship with good old m & b, then do some practice. Thanks to Sarah at Math=Love for the idea!

The kids LOVED it. To some extent, it was the "anything different than what we normally do is AWESOME" syndrome. But I genuinely think the found it informative and useful. 

My geometry class recently finished their own "foldables" project....making pop-up cards using triangle vocabulary. We established what an altitude is and what properties it has without even cracking a textbook. It was a nice transition to a really dense chapter (Euler line project, anyone?). 

Came out pretty cute, right?

The turkey card was from a pattern the students followed.  The Easter card was one the student designed on their own, then wrote out directions using chapter vocab.

I've seen tons of foldable ideas, but anyone have any that really hit the ball out of the park for Pre-Algebra, Algebra, and Geometry? 

Anyone have any tips on how to make and use them most effectively in class?

In the meantime, I'm going to keep creeping on their lunch table. Cool kids, here I come!

I hate...

I have a weakness. I know it. Everyday I fight it, but I just can't sometimes. Here it is...I got into teaching to teach concepts. I love the exploration lessons that engage students in problem solving and showcase their critical thinking skills. I did not go into teaching with a heated passion for standardized test review, nor did I go into teaching with a strong desire to be asked the same question 15,000 times in a 42 minute period. My students know that a multiple choice test from me means that either myself or a family member is deathly ill....or the Giants are in the Super Bowl and I just can't pull it together to write a thorough test. All of this sounds like a good thing right? At certain times....it is. But what my students do not know is that I dread almost every test and quiz review day.   So my goal has been to find activities that are engaging, provide good practice , and can somehow lessen the mass hysteria known as a room of 28 seventh graders. 

I am strictly anti review packet. The classroom I took over during my first year of teaching left me with students who relied so heavily on these they never learned how to study. I've tried what feels like a million strategies since- with mixed success. One of my favorites is having the students write their own version of the test, complete with answer key. Not only do they get some practice with the concepts, but I get to see what they view as important. I try to sneak the best question or two from the kids' tests on to the actual test....an added bonus for doing good work on the review. 

Cue this wonderful Row Game from Molly Kate at Mathemagical Molly. I adapted it for my Pre-Algebra students. Anytime I heard, "Ms. F, I don't get it!" from Student A,  I would ask Student B if they could tell me A's question. They couldn't? Guess they better work together on it first! This eliminated 98% of the questions and allowed me to move seamlessly from group to group, helping and encouraging. Goodbye gaggle of question-askers, hellooooooo critical thinking and correction of mistakes! 

Anyone have more fun ways to practice that don't make me want to say, "But Mommmm, I don't want to go to school today!"?Any other brilliant ideas for self-checking activities? Happy sharing!