Chicken Nuggets :)

Sorry Ya'll... Another Grad School Post! 

Here is the scenario ...

McDonald's sells chicken nuggets in boxes of 6, 9, or 20. Obviously one could purchase exactly 15 nuggets by buying a box of 6 and a box of 9. Using only combinations of boxes of 6, 9, and/or 20 nuggets:

1) Could you purchase exactly 17 nuggets? 

2) How would you purchase exactly 53 nuggets?

3) What is the largest number for which it is impossible to purchase exactly that number of nuggets?

4) Let's say you could only buy the nuggets in boxes of 7, 11, or 17. What is the largest number for which it is impossible to purchase exactly that number of nuggets? 

So ... 

#1: I could not come up with a way to purchase 17 nuggets. You could by 20 and throw 3 away, or you could purchase 3 boxes of 6 and throw 1 away. Purchasing just 17 is not possible. 

#2: To purchase 53 nuggets you could purchase 1 box of 20, 1 box of 9, and 4 boxes of 6. 

OR 

1 box of 20, 3 boxes of 9, and 1 box of 6. 

#3: The largest number that cannot be purchased is 43. I used excel to list all the multiples of 6, 9, and 20 and then combinations of numbers. I then put the numbers in order from least to greatest, eliminated the duplicates and found that 43 is the largest number not listed. 

#4: I solved this problem in the same manner. Using excel, I came up with 54 being the greatest number that you could to purchase exactly. 

Thoughts...

For my class this week, I was asked to watch a video and reflect on the use of reform based mathematics curricula. 

Personally, my school does not have a "text" book or a given math curriculum. When I started teaching 3rd grade we were introduced to a program called KEMS through the National Training Network. KEMS started in the third grade and worked up. This program started with a pictorial representation and practice, then moved to concrete and then to abstract. I am now in 1st grade and we do not have a math program. Teachers develop their own lessons using ideas, each other, TPT, and of course Pinterest. Our 3-8 just started a new program that I am not familiar with all all. I know very little about this program, other than it is being referred to as "Project C3M." 

Although I do not have a set curricula, I can see where these types would be an issue. If the standards state that students need to learn the algorithm, they will be tested on the algorithm. Not to say we need to teach to the test, but at this day in time the test is a HUGE deal. 

If a program teaches students so many different methods, how does one have time to master that one method? I can see students getting confused and wasting time deciding which method they would like to use for that problem. Just like the standard algorithm, each of those other methods requires you to memorize a set of steps. I have always said it is important for students to understand the why, before they begin to use an algorithm. This is where the teacher before comes into play. If a student in third grade masters the basic concept of division and how it works using pictures or models then will then be ready for the algorithm. I would never take time in my day to day life to draw out a "lattice" in order to solve a division problem. I have the standard algorithm memorize and can usually see the numbers in my head enough to complete the division in that manner. 

Another issue I see is the push for calculators! Is it important that a student know how to work a calculator? OF COURSE IT IS.. but should they be so dependent upon it they can't do anything else? NO! I remember in college taking a few math classes where calculators were not permitted? Allowing students to rely on a calculator is setting them up for failure! 

What are your experiences, thoughts, ideas, loves, hates of this curriculum? Do you use it? Do you not? 

Who Am I? Where Am I? How Do I Lead?

For my Teacher Leadership class this semester we were asked to answer these three questions. It could be an essay, a multimedia presentation, a photo essay, etc. I chose to use Powerpoint to make an image of each question, with a combination of quotes, pictures, and text. I encourage all teachers to ask yourself these three questions and jot down your thoughts, then go back to them at the end of the year and see if you answers remain the same. 

Storage Unit Exploration

Storage Facility

The owner of an empty building wants to construct walls to divide the building into individual storage units. All the space in the building will be used for the storage units. Each storage unit will have a door on the outside (perimeter) of the building.

Part A

Design the Storage Building

The grid that follows represents the rectangular floor of the building. Draw lines on the grid to divide the floor into 9 individual storage units.

The following rules apply:

• Each unit must have a rectangular floor.
• Each unit will share one side with the outside edge
  (perimeter) of the building.
• The storage units must not overlap.
  The sizes of the storage units and the number of each size that must be included in the drawing are shown below
  
  
  1- 5 X 5 
  2- 5 X 10
  1- 5 X 15
  2- 10 X 10 
  1- 10 X 15 
  1- 10 X 20
  1- 10 X 25
  
  
  For this problem, I started off with the largest piece and put it in place first. I then started adding the smaller pieces that equaled that large piece. I was able to put all the pieces in buy continuing to work from largest to smallest and added pieces that would equal the next biggest piece.
  
  
  
  
  
  When I finished, all my pieces were in place and met the criteria ! 
  
  

Mentoring A Fellow Teacher

I am almost finished with my Masters degree in Elementary Mathematics!! For one of my classes this semester, I am required to choose another teacher at my school and serve as their mentor in the area of mathematics. (I am also required to document my journey through this course on a blog and did not feel I could handle two different blogs, so I will be posting about my everyday classroom adventures, and my graduate school mathematics adventures here). I chose to mentor my teammate! This is the second year we have worked together and are both in our fourth year of teaching. From the start, I have felt more comfortable teaching mathematics and she feels more comfortable with the ELA aspect of the classroom. We work very well together and balance each other inside and outside the classroom. This is the second year in a row my teammate has taught a combination class, had I had more experience in the lower grades it would have been my honor this year. This year she is teaching a K-1 combo, but only 7 of her 24 students are Kindergarteners. Due to this, most of her class will be mastering the same standards and my 21 first graders. We both have high, average, and EC students in our classrooms. We will focus a lot on small group math instruction, while using lesson plans from engageny.org. I anticipate that with a combo class, and the wide ability levels I have in my own classroom, small group instruction will be more beneficial to all students, as opposed to a long period of whole group instruction. In order to measure our student's growth we will use county benchmark testing, as well as the mid-module and end of module assessments that accompany EngageNY. We will use standards based grading to ensure that our students are meeting all of the first grade standards for mathematics. 

September Currently

Hello All! I'm linking up with Farley for the September Currently :) 

Listening: My group of firsties this year are such chatter boxes when I come home I do not want to hear a sound. Luckily for me, the hubs had to jet off to work right about the time I walked in the door. I haven't had the TV on at all tonight! 

Loving: I am almost done with our reading benchmark testing, only 8 more students to go! We do not do a beginning of the year, county wide, math assessment- CRAZY I know, so I have my students working on one while I am pulling others! 

Thinking: WOW I AM EXHAUSTED! On Wednesdays, my students do not go to a special, they only have PE in the morning, not getting that afternoon break makes a HUGE difference! I'm still trying to get back in the swing of things as well! 

Wanting: A Yeti cup! My Teacher Assistant has one and I am so jealous of it! We only have one teachers lounge and it is at the other end of the school, a cup that kept ice all day would be a dream come true! 

Needing: I should be doing laundry, or getting ahead on some graduate school work, but blog stalking just seemed to happen :) While I'm on the subject of Graduate School, don't be alarmed if you see talk of different math task for school uploaded in the coming weeks. One of my classes required us to have a blog and I knew managing two would be TOO MUCH! 

3 Goals: 1) Be patient: I have to keep reminding myself that this first graders are still babies, they haven't reached the point of my group at the end of last year. I feel like it is taking so long for them to learn the procedures and start to follow the rules. I have incorporated some aspects of Whole Brain Teaching and we started our "practice cards" today. I'm hoping after a few days of missing their free time they will understand I mean business! 

2) Lose Weight: I have been "dieting" off and on for a while now and every time I have a few good days or weeks something happens and I fall off. I'm trying to keep a steady healthy eating kick going. I'm hoping as school starts to settle in my sister in law and I can work out a gym schedule! 

3) Be positive: I have a bad habit of speaking my mind, even when my opinion isn't such a positive one. Another teacher at my school is working on this goal along with me. It's hard to break a habit you've had since you were young, especially when you get it so honest from a parent! I'm trying though. My teammate is keeping me one the right track, we balance each other so well!! 

What are you up to ? Link up with Farley !