Interactive Student Notebook - Exponents

 

After dabbling in interactive student notebooks over the last two years, I have made a more dedicated commitment to using them with students. Here is our latest entry when reviewing exponents this week. We did a review of the content and took notes on the right side of the notebook page. The next day I gave the students this to fold in half and glue onto the left side as an independent activity that also served as an assessment while I worked with small groups. The cartoon idea was a hit with the creative side of the kids and a great reminder for the power of exponential growth!

Math Munch - My Latest Discovery!

In my early morning searches of wonderful ideas on the internet, I was delighted and a little intimidated when I came across Math Munch.  This is a wonderful blog which invites kids into the coolest math experiences outside of the classroom. As the authors point out, readers don't just read in class, they choose to read outside of class. There are places to go for more books to read - libraries, book stores, collections in the home.  There are book clubs and forums to share the sheer pleasure found in reading.  What is there for the hungry math student? This is a site dedicated to opening the world of math that is all around us.  I have so much to learn from reading this site! Be sure to check it out.

Math Munch TED Talk   

Prime Factorization Success!

Following the frustration this week was a deeply satisfying "ahhhhhhhh" moment on Tuesday. My students were learning about prime factorization. I pulled together a few pieces from several great lessons. One idea came from an ace teacher, Jen Runde!  http://www.rundesroom.com/

I started the lesson by holding up a bag marked with 300 on the outside. I asked the students to do an "I Notice, I Wonder" journal entry to spark some interest. After some sharing, I revealed the colored shapes/numbers in the bag.  More "I Notice, I Wonder" writing and sharing. I was hoping students would notice there were only prime numbers and the fact that you could use those numbers to get the product of 300.  Paydirt!  At least one student in each class came up with the primary ideas. Never say for the students something they can say!

I had more bags with other numbers: 18, 30, 48, 56, and 75. I had the students work with partners to figure out the prime numbers in each bag I held up. They recorded their ideas in their interactive notebooks. We also talked about how we could find all the other factors of each number by combining the prime factors. This part of the lesson came from an article, "Moving Beyond Factor Trees," by Terri L. Kurz and Jorge Garcia in Mathematics Teaching in the Middle School. This was a powerful lesson for students. Rather than starting with factor trees and teaching a procedure, the students were able to discover through their intuition and understanding of prime numbers, how to do the prime factorization! Today we'll add the exponential form to the factorization.

Thanks to my online colleagues for the great ideas!

 

Frustration....

Yesterday's experience was frustrating....oh, yeah...teachers feel it.  So many students are reluctant writers to begin with.  Now I'm asking them to write in math class. (Are you kidding me?)

My two classes yesterday turned in mixed results of their Cat Walk problem.  It was clear that those that had quite a bit of work on paper had adult guidance. That's ok with me as long as the student can explain. Not all could do that.  Many of them had no written explanation of their reasoning. If I look at their papers, it's up to me to put some logic and order to the scribbling of numbers and calculations to follow their thinking. We had a talk about why it is important to explain your thinking. It is an expectation to be clear in oral and written language in order to be college- and career-ready. If you can explain your thinking, you demonstrate deeper understanding. This is going to be a growth experience for us all.

How do you move students along in their ability to write in math class?  Ideas? Suggestions? Let's pick each others' brains!

Prime Time

The last two weeks have been incredibly busy - Open House, first progress reports, four new students and papers to grade. Getting back up to full-speed is really time-consuming!

I'm spending a great deal of time thinking through my lessons to make them top-notch. I'm still having a hard time estimating the amount of time I need.  On paper, it looks like there is plenty of time to accomplish all that I plan for the students.  In reality, I'm biting off too big of a chunk! I have forgotten about all the little things that are not "planned" parts of the class period that absorb all those precious moments.  Prime time gets shorter after attendance, passing out flyers, homework, picture packets, dress code issues, explaining progress reports, and handling all of the spur-of-the-moment student crises!

Today I am looking forward to a discussion with two of my classes on the Problem of the Week. They have had about a week to think over the Cat Walk problem from the Math Forum website. http://mathforum.org/ The problem is one of proportional reasoning - a cat takes a different amount of steps than a dog to cover the same distance. Students are to find the distance a cat will cover in 24 steps. I am curious to see the methods of approaching this problem.  The students are going to share their work and talk about their reasoning.

I wonder....
   How many students will have their homework.
   How many students communicated their thinking in writing.
   If I can lead this discussion by allowing the students to do most of the talking!
   If students will enjoy the process of tackling a more difficult problem without being led through
       the steps.
   If they will gain the ability to persist even when it is challenging.

I am prepared to keep at it! I know that my students can get better at solving problems. I need to persist even when the going gets tough just like they do! We are ALL in the learning process here.

The other task today is to continue our work with prime numbers in all classes. We're entering vocabulary into our math notebooks (Frayer Model) while I work with small groups.

I wonder.....
    If I have bitten off too big of a chunk today? All I can do is monitor and adjust, right?

Twist on the Penny a Day Problem

I had to share this with all of you. You probably have seen this problem in another form.....do you take the offer to earn money by doubling the amount you earn each day starting with a penny or do you take a million dollars for the month?  Muhhahahahahahah...

Taming the Dragon

There is a paper dragon snarling and breathing fire in a folder somewhere on my desk. It is known as THE PACING CALENDAR.  It roars a few times throughout my day and begs for attention. It reminds me at 2 a.m. that I'm not covering enough curriculum in order to do it all. I've fed it a few tidbits this week to keep the flames of stress to a flicker, but the dragon demands attention at the most inconvenient times.

What is all this talk about dragons? It is my greatest enemy in being an effective teacher: TIME. I don't feel I ever have enough of it in each class period, in the week, in the school year. Just not enough time to do it all the way "THEY" say it should be done. 

What I am relaxing into is the concept that digging deeper into student thinking and problem-solving takes time. If my students are to really benefit from that hour with me, I need to give them space, opportunity to make mistakes, find ways out of their misconceptions, and support to try again.

The sweetest sound that slays the dragon came yesterday....I could have cried or leaped into the air with a backflip! While working with a partner on the Arranging Tables problem, a fledgling of mine SHOUTED and threw his hands in the air, "I got it!!!!" I went over to him and his partner, and we talked through his solution. Although it wasn't quite correct according to the criteria, they persisted and persisted until they figured out one of the possible solutions! VICTORY! That really doused the whimpering dragon's fiery breath on my desk!

What I saw yesterday from all five classes was total ENGAGEMENT for ALL learners. I saw persistence. I saw students willing to record their thinking by using diagrams. I heard focused conversations about math problem solving.  Teacher Heaven. I took a deep breath and told them we would keep working on this problem on Monday. (The dragon backed up into the cave and let out a whimper...) We are about the work of developing our mathematical brains here. We are not in a race to some finish line. The lessons that these students are learning through this lesson are invaluable for the long-term.

My students are inspiring me. The damsel in distress is ME - thank goodness they are willing to come to my rescue!

Arranging the Tables

This morning we are going to dive into a review of factors and multiples through a task I found on the NRICH math web site. 

http://nrich.maths.org/964



The task is to find a way to seat those 44 people with no empty seats at any table. I want students to find a way to record their thinking and to explain their final answer in sentences as well. There are multiple ways to make the arrangement so early finishers will be asked to find more ways. Are there any patterns to finding the ways?  Does knowing the factors of 44 help you to solve this task? Why or why not? Are there factors of other numbers that are useful? What are they and why are they helpful?  We can have some group sharing of solutions with feedback from peers.

 

Students will add their solution to their notebooks, and we will also make a Frayer model of their vocabulary words - factors, multiples. I've got an exit ticket prepared to check on their understanding of factors. Sounds like more than enough for one lesson - probably two! Oh, yeah....some time today we're having our first fire drill! Thanks for letting me think through my lesson with you all.

Dodge Middle School - An "A" School for Another Year!

Just wanted to brag about our school this morning - we received an A grade for the hard work of our students and staff. We are so proud! I have the priviledge of being a part of this great group. We are the only middle school in our district to have an A rating. This is no easy task - we are a magnet program and our students are chosen by lottery. Our student body is "like a box of chocolates" - we never know what we're going to get! Some think that we get to pick and choose, and that's why our students achieve so much. Not so! It's a lot of effort, commitment, and focus by students, parents, and staff!  Here's to all of you!

http://dodgemagnet.weebly.com/

Interactive Student Notebooks

Interactive Student Notebooks are another great tool that I am implementing this year.  I have always had students keep a notebook, but it has usually just been a place to take notes and do a little practice. As I have been looking at all the amazing ideas on Pinterest and on teacher blogs, I have come to realize what a powerful asset an ISN can be in my class. My hope is that kids will take ownership of their notebook and see how it can help them deepen their learning. They may even use it for homework or studying. Ahhhh....a teacher's dream!

So we started by getting the basics pulled together in the notebook.  All of this takes time, and I am impatient. I feel like I should be getting "more" accomplished in the area of curriculum. I have to keep reminding myself that time spent on procedures, routines, and the basic structures for the year will pay off in the long run!

I have borrowed and stolen all the great ideas for my notebooks from other teachers who are so kind to publish on the web. Thanks to you all for sharing! I will post throughout the year to share my victories and a-ha's about this new process.  For today, we're putting the last of the pieces - a sheet to keep track of their progress on standards, an "iPocket" for those unglued pieces, a reference sheet for geometry formulas, and finishing two reflections. That ought to be enough to keep us busy today!

If you see that I have used your idea, would you give me a shout-out so that I can give you credit?
I must keep better track of where I have gotten these great ideas!

 

 

NUMBER SENSE

I never really understood or was taught or asked exactly what "number sense" was.  You see, I am a dinosaur. I left the university quite a long time ago, and teaching methodology didn't include all these important ideas that I am learning these days. Jo Boaler's class is opening up a whole new world to me!

Number sense is the ability to use numbers flexibly and creatively. Hmmmm....I was never taught this in school.  I was one of those students who learned procedures and algorithms. I knew my facts inside and out from multiple hours of drill and practice (all we had back then...). My teachers never showed us how to decompose numbers to solve problems. Manipulatives? That was my pencil. Group work didn't occur. It was me and the pencil and paper. I never intuitively figured math out either. I would always be amazed how other adults could tear apart numbers and add/subtract/multiply/divide so quickly without pencil and paper. How did they do that? Number sense.

My sixth graders are going to get lots of practice with this concept this year. I know that being able to strategically look at a math problem is where the meat of the mathematics lies. Yesterday I asked a straightforward question:  What comes next in the sequence 40, 48, 56, 64...and what is the rule? They all knew what came next (no biggee), but I was interested in the way they explained HOW they figured it out.  There were multiple answers - AMAZING! "They're multiples of 8." "I added 8."  "I subtracted to find out." We are off to a great start to opening up conversation about our thinking.

Today I'm giving them a dot pattern problem that I saw in Jo's class on video. I'm drooling with anticipation about our juicy conversation today.  We're also going to talk about "growing our brains" as well.  I'm so grateful that my teaching practice continues to expand - even after 34 years - there's always something new to learn!

Number sense....

New math book arrived yesterday. I can't wait to dig in.


P.S. Thanks, Sidney! You helped me be a little braver in the land of blogging!

Checkerboard Problem Re-Cap

The first day is over and the lesson was a success!  The "less is more" philosophy really paid off today. 

We did not take this problem to completion in one lesson.  I allowed plenty of time to wrestle with the idea, intersperse questions to assist in next steps, and left them dangling....I encouraged them to think more about the problem and to discuss it with their family but asked them not to Google this problem just to get an answer.

It was challenging for this teacher to not give away the answer and the procedure just to finish up the problem for the students! Letting them do the work means I need to ask thought-provoking questions and stay out of their way!

I asked students to complete an exit ticket and answer the following questions:

1. Something I liked about math class today...
2. Something I learned in math class today....
3. A question I have....

There was a pattern to their responses that was so gratifying and encouraging to me. Here are common responses to today's experience:

Students overwhelming said they liked the problem and found it fun, exciting, hard, and challenging. They liked working in groups and being able to talk the problem out with their friends and meet new students as well.

Here are some favorite quotes: " I liked that we really used our brain",  "we had to think", "it got me thinking real hard", "I had to really think, not guess", and "Our first problem was difficult and difficult problems help me learn."  WOW!  I did not prompt any of this thinking in them. They knew it all along no matter what their "level" of ability or achievement was.

In response to the second question, students commented frequently that they learned something about counting squares on the checkerboard, but they also remarked that they learned that you should "look closely for patterns," "you write down what you think", and "math can trick your brain."

Overwhelmingly, the students' question was all about finding the actual number of squares on the board (I've got them hooked for tomorrow!) and finding out if they were going to do more problems like this one.  My favorite comment: "How come math has so many cool things?"

I'd say I did my job today - get kids curious about math problem-solving, help them persevere, and make them beg for more! Need I say more - I'm eager for Day 2. The plan is to talk about the strategy of keeping an organized list, using a smaller case to help solve this bigger problem, looking at the emerging pattern of square numbers/square roots, and then predict how many squares on a 10 x 10 grid.

FIRST MATH LESSON OF THE YEAR

Do any of you teachers agonize over that first lesson of the school year as much as I do? I've decided that I want to spend the first hour with my new recruits diving into content more than yadda-yadda-yadda with my syllabus and class rules.  Let's get a taste of what this class is going to be like everyday! Then let's talk about how we're going to make that class operate like a well-oiled machine.

So, I've been agonizing about lesson plans. What to do? I want the lesson to be challenging, engaging, reflective, a learning experience, an assessment of general skills, and a little bit of fun as well. It's similar to the experience of Writer's Block - I just can't commit an idea to paper until I think it's "just right." This morning I'm taking the plunge.

 

After the usual attendance record-keeping, making sure the kids are in the correct class, and introduction of myself to those who didn't come to our summer school, we are diving into group problem-solving with Checkerboard Squares. The directions are simple: Find the number of squares on this checkerboard. Record your thinking. We're going to have our first math discussion and student display of their work. My objective is to see how my newbies work together and how they persevere in problem solving.

There are many descriptions of this activity online. Here's an interesting interactive model: http://www.donbeaty.com/CJHS/checkerboardmodel.htm. Or look at this: http://math.rice.edu/~lanius/domath/page2.html.  I might use these after students have quite a while to wrestle with this problem or as an explanation. Today I want to dive into allowing my kids the opportunity to struggle a little bit with some guidance a la Mathematical Practices.

It's going to be a great first day!