Thursday, July 24, 2014

Volume, Cylinders, Cones and Spheres

     This is a post that I just never finished from the end of the school year. It has been sitting in my draft box gathering dust so I'm going to share it as it is. These are some of my favorite lessons and videos for the 8th grade volume unit. I wasn't able to use them all because I just ran out of time, you  know how the end of the year just creeps up on you? Also, because it was the last unit of the year, I had no creativity left to make my own lessons so I used awesome lessons that were created by others. Thanks to all of you who shared this great lessons.

      I have to show a video clip for all my units. This Phineas and Ferb clip is fun.
Click here to go to the video: Phineas and Ferb volume cartoon.

  Phineas and Ferb

     This is the foldable that I used for volume from Lisa Davenport at teacherspayteachers.
                                              Volume of Cylinders, Cones, & Spheres (Foldable!)

      Love, love, love this lesson from Robert Kaplinsky. The kids really liked it and had fun trying to get as close as they could to the number of gumballs in the machine. I will do this again for sure next year.

Click here for Robert Kaplinsy's gumball machine  lesson.

      I haven't used this lesson but it looks good. It is on my list for next year.

Click here for Dan Meyer, you pour i choose 3 act.

                                                 Click here for Dan Meyer popcorn picker.
     I have actually done this lesson, Popcorn anyone ,  from illuminations. The kids have lots of fun with it and of course they get to eat the popcorn they use. The lesson has the students make rectangular prisms from notebook paper but I had them make cylinders because prisms are not 8th grade standards. The kids take a piece of paper, make a cylinder by rolling it with the longer side on the bottom, making a short cylinder. Then they take a second piece of paper and roll it with the shorter side on the bottom, making a taller cylinder. It always amazes me they don't realize that the volume will be the same. It is lots of fun but a little messy.

     OK, my students who are my most reluctant students love Andrew Stadel's trasketball. They all want to be the ones to make the baskets with the paper. The class gets wild and crazy and fun is had by all.

                                             Click here for Andrew Stadel-Trashketball

I love this lessons from NCTM the Ice Cream Puddle  It combines spheres, cones and cylinders. Perfect! Everything I need to go over all in one lesson.
                                                                                                                                   Click HERE to see activity sheet and lessons from NCTM.

I hope you enjoy these as much as I do. 
                                                                             Til next time,

Monday, July 21, 2014

Changes, Changes, Changes, Brain Dump number 1


      I have to admit it. This year I feel terribly overwhelmed with all the changes that we are expected to make, I don't even know where to start. So when I feel like this I have to do a, "brain dump." I just take everything that is floating around in my head and dump it onto paper. Once I do that I feel like I can get an idea of where to start or at least do something from each category. So here I go.
    1. My first priority is to make lessons that align to Common Core Standards.  I began with my 8th grade Pre-Algebra classes last year but did not change anything with my Algebra. Second semester is when I started feeling good about the changes I made to the Pre-Algebra curriculum, but my 1st semester lessons are not put together the way I would like them to be. I can not go into the school year, less than one month away, without having the first units ready to go. I have bits and pieces but I'm not there yet. Twenty-four days til school begins. Yikes!
     Algebra is another story. I have always used the Algebra book and then supplemented where needed. Now, not having a book to refer to is really a challenge for me. In Pre-Algebra, I haven't used the book in years, but the Algebra book has been great. Not any more! The curriculum is all over the place in the book as I am sure you all know. On the last day of school we were given the curriculum and told we could pull from the book or use Engage New York - Algebra and follow it day by day. I guess I am going to try Engage New York and fit it to the needs of my students. Looking at the first module is a challenge. I like to have a book to see how everything is laid out. This is so big that to print it all is ridiculous so reading it on the computer is what I am going to have to do. We will see how it works.
     2. Standards based grading and Common Assessments- My district did provide training on SBG this summer. See my post on SBG here. I've been reading blogs and I did go through the training but I am still having a hard time with writing assessments for this. 
    3. Interactive Notebooks. I want to use Interactive Notebooks with not only my Pre-Algebra classes, but also my Algebra classes. This is going to be a lot to do considering curriculum changes this year.Why not do everything at once? I may do a modified INB scattered with more traditional notes. We'll see. Last year was my first year using INB's with my Pre-Algebra classes. I want to improve on what I started last year. See my post on Reflecting on my first year using Interactive Notebooks . 
     4. Kagan strategies - My building is going to receive training from a Kagan instructor, four times this year. (See Kagan strategies) I know just a little about these methods but am excited to learn more. I am going to pick up a book from our library on this and do some pre-reading before the training so I have a better idea what this looks like. I will be implementing these strategies in all my classes but as far as getting everything organized before school starts in this area is going to be difficult. 
     5. Group work- The layout of my classroom is going to be different this year. I have always had rows in my room as another teacher comes in for two periods a day. This will be a new teacher this year so I am going to have groups of four around the room. The newbie will think it has always been that way. Yeah! Kagan strategies are going to be used to help with the group work. I'd better get reading soon to get a head start for the year.
     6. Technology and Geometer's Sketchpad - How do I add more technology to my classroom? I have a smartboard and am comfortable with that. I use graphing calculators once in awhile, they are 25 years old and I spend so much time fixing them. I plan on using Geometer's Sketchpad when we hit graphing in both Pre-Algebra and Algebra. Geometer's Sketchpad is going to be an amazing tool to use with transformations in Pre-Algebra. I can't wait to use it for that unit. If I can do that much this year with all the other changes I will be making I think that is a good start. (See my post on Geometer's Sketchpad .)
     7. PARCC testing. This will be our first year using PARCC assessments. My students need exposure to lessons and assessments that will prepare them for the types of questions they will see.
     8. Writing standards. In my INB's (Interactive Notebooks) I am going to have the students journal more. As part of my SBG I will have questions that are more like the extended response problems I have used in the past. These problems have the students writing out explanations and I will use our writing rubric to grade the students work. 
     9. Pre Tests. I don't always pre assess prior to starting a unit. As a department we have created pre assessments for the vocabulary for each of our units. It is a starting point in this process.
    10. Differentiation. This is the hardest thing for me to do. Last year Pre-Algebra classes had students that were in the 1st through 76th percentile on the MAP test. This wide range made it so hard to differentiate. I am going to work hard to do better in this area. One of the ways I plan to do this is in the group work. I've never used stations in my class but I'm going to give it a try this year.
     Wow, I knew there were changes this year but oh my goodness! I didn't think it was this much. No wonder I'm stressed. Thanks for reading my ramblings. I'll keep you posted on my progress attacking my new to do list.
                                                            Til next time,


Saturday, July 12, 2014

Reflecting on my first year using Interactive Notebooks

      Last summer I started reading about interactive notebooks and fell in love with the idea. I was familiar with foldables, by Dinah Zike, from the Glencoe math books we had at the time. Each chapter had a foldable that we made and the notes from the chapter were placed inside.  When I used foldables I noticed that the students loved them. They thought they were taking less notes but actually it was the same amount or more. (Fooled them!) Students who would forget their spirals for their notes on a daily basis, would not forget the foldables. They always had them handy. My special education  and ELL students really enjoyed them because everything was available to in one place in an easy to read format. So last year I jumped right  in full force with my 8th grade Pre-Algebra students. 
     The students liked the foldables and even my students who struggle were busy and engaged during the lessons. The only problem was they didn't use them as a study tool. So many of my students just left them in my room so they wouldn't forget them. That was good  but  they didn't use them for the reference that I was hoping they would. Next year the students really need to use them as I will be following Common Core Standards and our book does not follow that sequence at all. Their INB's will be their books. After reading several blogs, I am going to stress with the kids that this is their book and they need it with them everyday. I read a blog, (sorry can't remember who), that said all work was done in the spiral even homework so the kids always brought them. I might try that next year and see how it works. 
     There are some things that I am going to do differently next year. The first change is that I am going to have a table of contents. What was I thinking that I didn't have the kids put that in their notebooks and number the pages. I really like the unit table of contents page from math = loveI anticipate that I will have a beginning table of contents page at the beginning that will list the page for the unit table of contents. Then they can turn to the unit page index for a detailed listing.

Unit index page from math = love, notice nothing is filled in yet! Yikes!

     Vocabulary is important for all of my students but even more so for my second language learners. I am going to make it a major goal and really really stress it this year. So we are going to make Frayer model or other graphic organizers for all of the targeted vocabulary in the unit.(See Unit 1 Vocabulary post HERE.)

                                                        Frayer Models


                                              Vocabulary Foldable Unit 1  


      I am also going to have a word wall for the first time. I just need to figure out where to put it. There is not a lot of wall space in my room so it may have to go on a blackboard.
     Last year we used spiral notebooks for our Interactive Notebooks. The composition notebooks are sturdier but I write large and need more room. I liked the amount of space that the spirals gave us for each page but the pages did tend to fall out of the spirals easily. You just can't find spirals anymore that don't have the easy tear out pages! UGH! I've debated about using binders as well but I think I will stick with the spirals for one more year. I will give the kids the option to get a college rule composition notebook if they want to.
     I know that many people use the right hand side of the notebook for teacher input and the left side is for student input. I didn't really follow that rule at all last year. Sometimes I did it that way and other times not. I am going to try to have the kids do their homework on the left so they are using them everyday. We'll see.
     The right side versus left side, what to do? I read a blog where they had the foldable on the left and the class work or homework on the right. This prevented any clumping from the glue where the kids were doing their writing. Now that is something I hadn't thought about before. We did have issues when using glue of the paper getting wrinkly and it was hard for the kids to write on the other side. I have to think about this one. I like to place any foldables that have flip pages on the right hand side and have flat sheets on the left. I have found that the tabs flip over when they are on the left and stay neater on the right. So I will experiment and see which way I like better.

Beginning INB pages. 

      My first day of class I introduced myself using numbers about me that several people have discussed on their blogs. If you haven't seen it just google and you will find several. I did a power point where the kids had to guess why certain numbers were important to me. Like 3 is how many children we have etc. Then the kids did the Numbers about me page from math = love. I made different colors for each of the classes and then we hung them up. I may have them make 2 this year, one to hang and one for their INB covers.
      Click here for my classroom expectations sheet. I found the original for this at everyone is a genius and made a few changes. Check out Sarah's blog to see all the
great tips she has for starting your interactive notebooks.  I found this on someone's blog but cannot find out who or where it was. I love this page and would like to give 
credit to the author. Anyone know who made this? I like the way it shows the students exactly what a good homework paper should look like. You can't imagine how much time I spend with my students in 8th grade teaching them how to set up their papers. I really liked these two pages and will use them again this year.

      I've been toying with the idea from 4mulafun about doing unit foldables. I  like the idea of having the notebook in a two pocket folder and then maybe storing old folders in the classroom. I don't know, I have to think about what I want it to look like. One thing is for sure, I will be using Interactive Notebooks again next year! They were great.
      My classes used the interactive notebooks all the time. They were a great easy to read reference for them. I would love the hear about the different types of Interactive Notebooks you may use. I hope to post my first unit pages soon.
                                                                                    Til next time,

Saturday, July 05, 2014

Teaching number sense to my students

     I've always known that my students struggle with number sense and if I could improve their number sense that would increase their understanding of math in all other areas. But how to do that when my students are already in 8th grade? I can tell you the students in my classes that have strong number sense and which students don't. I don't need to look at a test to give me that information. My students with good number sense can pull numbers apart and put them back together in a number of different forms. For example, they know that 25 is the same 5 X 5, 10 + 10 + 5,  10/2 and √ 625. They can  recognize number patterns and can spot errors easily. They understand the order of numbers, can compare them and place them on a number line. They just "get" numbers where my struggling students just don't "get it" when it comes to understanding numbers. I know the math, I' m a good teacher so why can't I help those struggling students? What more can I do?  I need a template with a step by step process to use with my kids to develop these skills. Some type of check list or something like that to refer to so I am making sure I am covering all of areas the kids needed.
     So when I was doing my Action Research Project for my masters, I knew that I wanted to research how to improve number sense in my students. Most of the reading that I found on teaching number sense stressed the fact that you need to start young with developing these skills, giving these young children the opportunity to use manipulatives to understand the different forms of a number. I totally agree with this. However, my students are in 8th grade not pre-school so that doesn't help them at all. 

  •       Well, I finally found what I was looking for when I stumbled upon this article by Valerie Faulkner, The Components of Number Sense, an instructional model for teachers. (Read it, I found it fascinating.)  In this article, number sense is divided into seven categories,
  • quantity and magnitude, 
  • numeration,
  • equality,
  • base ten, 
  • form of a number, 
  • proportional reasoning and  
  • algebraic and geometric thinking.                                                                                            I love the chart that she gave. I am going to print this up and hang it in my classroom as a reference for not only the students but also for me. It will remind me to discuss all of these different forms as many times as possible each period. These are discussions that can be made in every math lesson and are applicable to the middle school classroom. I am going to work to address as many of these categories as possible in each and every lesson.

Here is a brief explanation of the different categories to address with students on a daily basis.

Quantity and Magnitude
Students need to understand that math is about quantity not just numbers. It is the amount of something whether it is a weight, measurement, sets of elements or symbols. These are all ways to show quantity. It is important for students to understand the magnitude of numbers and what they  mean in terms of a number line. I am always amazed when in 8th grade students can't place numbers correctly on a number line. This is very obvious when we get review negative numbers and the number line. Is this something I need to spend more time on with them? They should be able to show where quantities are positioned on the number line with placement to the right being a higher magnitude and to the left on the number line a smaller magnitude.   

Base Ten
 Students need to know that the numbers that we use are based on ten. To understand 16 students need to know that the one stands for one-ten and the six stands for six ones. This is a pre-requisite to then be able to compare numbers according to their  magnitude.  I need to ask for expanded forms of numbers and again watch the language that I use when teaching sections with tens. When I teach scientific notation I should say the number is in expanded form and have a conversation about this form. I need to stop giving shortcuts, they will figure those out, and have deep discussions about the forms of numbers. Understanding base ten leads to better estimating skills. When the student is a good estimator  (Estimation 180 site, love it.),they will be able to use many different forms of numbers to show their understanding of the problem.(Faulkner, 2009, p. 28) 
Numeration is the act of numbering, counting, or computing. Once again base ten is crucial to the understanding of the numeration system. I   need to take time when discussing numbers and say 23 is two-tens and three-ones and when adding and subtracting to include this type of discussion as well. Reflecting on my discussions in class, I am not sure that I spend enough time on this, assuming that my students understand this already. Again, I can't tell you how many times my students just stare at me as if to say I am speaking another language when we discuss the value of a number. 56 is not 5 and 6, it is 5 tens and 6 ones. In a class I took last month, the teacher said when she would ask students to show her the value of a number using base ten blocks, they would take 2 tens and 5 ones for 25 and say they value was 7! 
Equality does not necessarily mean the same as. Students need to understand that numbers have different forms with the same value. For example: 2/3 = 4/6 are equivalent but represent two different forms with the same value. Two out of three items and four out of six total items are different representations of the same value. (Faulkner, 2009) Teachers need to be aware of the language that they use with students instead of just showing the steps involved in solving a problem. “Two trucks may be equal in weight to an elephant, but they certainly aren’t the same as!"(Faulkner, 2009, p. 26). (I love this analogy.)

Form of a number
     The different forms of a number should be shown to be equal in value but shown in different forms. An example of 45% can be shown as 0.45 they are equivalent but different forms of the same value. It can also be shown as 45/100 and can be written as a ratio as 45:100.       

Proportional Reasoning
     When teaching, I should give a variety of activities that allow them to develop the proportional analogy themselves. (Geometer's Sketchpad will be great for this.) An example would be to have students measure the circumference of various circles and divide the circumference by the diameter and discover pi. This is a proportional reasoning activity that will be more meaningful then just plugging pi into a formula and solving without meaning attached to problem. (Faulkner, 2009, p. 27)     
Algebraic and Geometric Thinking
     I need to take time to “unpack” the concepts of algebra and geometry and place them under the previous components listed above. Pi becomes a proportional reasoning problem, X = Y is an equality problem showing different forms of the value. (Faulkner, 2009, p. 25). Similar figures and dilations and the list goes on ...are other examples.

   I love Andrew Stadel's site, Estimation 180and I plan on using it next year with my classes. There is an estimation activity for the students every day of the school year. Having the students pick a reasonable guess that is too high and too low is a great way to have students understand the ordering and magnitude of numbers. I can't wait to see the improvement in their estimating after a full year of doing this program.

     My goal for the upcoming school year is to use these seven components throughout the year the so students will have the building blocks of number sense. I am going to be mindful of the language that I use and give my kids more opportunities to use manipulatives to get a deeper understanding of the meaning behind numbers. The great thing about blogging is I know all of you will hold me accountable for this. Thanks. I'll try to regularly update this post.
                                                                                       Til next time,

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