tag:blogger.com,1999:blog-31599550064789355042024-02-07T00:21:45.607-08:00Ms. McHugh's Corner: Where Mathletes Come to TrainMs. McHughhttp://www.blogger.com/profile/14304467530751870803noreply@blogger.comBlogger36125tag:blogger.com,1999:blog-3159955006478935504.post-8529792854945390652013-09-17T13:38:00.000-07:002013-09-17T14:26:38.771-07:00Interactive Math Notebook: Factors and Multiples<span style="font-family: Arial, Helvetica, sans-serif;">Welcome to our Math Corner! Please come back often and leave a comment below to let me know your thoughts or any other ideas you have to add! Also, I would love a follow! :) Thanks!</span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;">We have been busy working on determining whether one number is a factor or multiple of another number. We started by building arrays both with tiles and on centimeter grid paper to determine a number's factors. Becoming proficient at building arrays has really helped some of my struggling students feel successful in finding factors even when they aren't proficient in their facts or have many strong strategies to use to determine a fact. After practicing many many times, I gave each student a pair of die (some were six sided, some were more for my kids who are proficient in their facts and wanted a challenge!) and grid paper and instructed them to roll the die and create an array with dimensions that match the numbers on the die. We then added this page to our notebooks. Below is an example. </span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;">Next, we used our Math Handbooks and its Table of Contents (oh hello, Language Arts skills! See....I'm learning how to incorporate it all!) to find the definition and examples of factor, prime number, composite number, and square number. We used this information to create a foldable to glue into the right hand side of the page. An example is below!</span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;">We are also learning about multiples. After many days of discovering, discussing, and applying this knew knowledge, we finally were able to put the information into our notebooks. I always try to wait until I feel they understand it to put it into the notebooks. We used a hundreds chart to choose a factor, then highlighted all of its multiples. We also used this factor to create a basic real world problem to show how to apply it to multiples. </span><br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi6QzTClxwzNc0QaIE2zgWcW3piTybsimVkoVTH03mKB3wDO7bls3Q7wIf0SuVtsMPLYncpNnSxYZJA-jAXwb1cxkZeC_0NoUvotMEjEBh-M6CIu0zldF-VA4KzhbEgy2HL_zXuyFHwUpEn/s1600/photo+2.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><span style="font-family: Arial, Helvetica, sans-serif;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi6QzTClxwzNc0QaIE2zgWcW3piTybsimVkoVTH03mKB3wDO7bls3Q7wIf0SuVtsMPLYncpNnSxYZJA-jAXwb1cxkZeC_0NoUvotMEjEBh-M6CIu0zldF-VA4KzhbEgy2HL_zXuyFHwUpEn/s320/photo+2.JPG" width="239" /></span></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-family: Arial, Helvetica, sans-serif;">This student chose the factor two, and wrote the problem: A store has CDs for $2 each. She then drew a picture to show that one CD would cost $2, two CDs would cost $4, three would cost $6, and so on. This shows that the price of buying CDs are multiples of 2</span></td></tr>
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<tr><td class="tr-caption" style="text-align: center;"><span style="font-family: Arial, Helvetica, sans-serif;">This student chose the factor four. His problem is about video games costing $4 each, so two would cost $8, three would be $12, and so on. He goes on to begin to write a question associated with it!</span></td></tr>
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<span style="font-family: Arial, Helvetica, sans-serif;">Lastly, I really wanted to make sure we understood the difference between factors and multiples, as it can get very confusing. We used markers to circle all the factors in a list and all the multiples associated with it. Students were allowed to pick their own factor, or for those who are still not feeling comfortable with multiplication, were permitted to use the factor four as I did in my example. Then, they showed an example of an array that shows one of their listed factors and multiples, as well as a non array (just to make sure they understood that an array is a rectangle and cannot have any pieces sticking off the end!!). These last two pages might be my favorite! </span><br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjVpJf9neeZ7w8uYbhyphenhyphenMo_Bi7RJ8UCNzoTXo5nG1tEWE1Z1RkyURnxxPskOeBa34hXiRPagx7UcG1xWDXS6ZIBVGycCIlpgP2w7m9Bj_84ZmhQGAQIYXcJHtW2T13fwcVnu0UWfwDahW7-1/s1600/photo+3.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><span style="font-family: Arial, Helvetica, sans-serif;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjVpJf9neeZ7w8uYbhyphenhyphenMo_Bi7RJ8UCNzoTXo5nG1tEWE1Z1RkyURnxxPskOeBa34hXiRPagx7UcG1xWDXS6ZIBVGycCIlpgP2w7m9Bj_84ZmhQGAQIYXcJHtW2T13fwcVnu0UWfwDahW7-1/s320/photo+3.JPG" width="239" /></span></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-family: Arial, Helvetica, sans-serif;">This student wrote all the problems for the number four. He circled all of the fours to show that is the factor. He wrote: 4 is a factor of any whole number that it divides evenly. He also circled all the multiples to show that you can multiply any number by four to get a multiple of four.</span></td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgy32dlWw8aKm-Ciu3h70rbfCf8AA4oiCQBWqdeDPL-hd_QdlL2pRiGv7slGvs04gBLxn9Fq6O1SCbCGRXFCfbxYxWpn9b6OT03Yf3We5CvPdsou8synX17LwebR5bZqMblKXfrp4eTSTsE/s1600/photo+5.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><span style="font-family: Arial, Helvetica, sans-serif;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgy32dlWw8aKm-Ciu3h70rbfCf8AA4oiCQBWqdeDPL-hd_QdlL2pRiGv7slGvs04gBLxn9Fq6O1SCbCGRXFCfbxYxWpn9b6OT03Yf3We5CvPdsou8synX17LwebR5bZqMblKXfrp4eTSTsE/s320/photo+5.JPG" width="239" /></span></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-family: Arial, Helvetica, sans-serif;">This student did an excellent job of showing the difference between an array that four is a factor of one of its multiples, as well as a non example saying "21 is not a multiple of 4" and using his array as proof!</span></td></tr>
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Ms. McHughhttp://www.blogger.com/profile/14304467530751870803noreply@blogger.com2tag:blogger.com,1999:blog-3159955006478935504.post-61286949228566189312013-09-10T16:04:00.001-07:002013-09-10T16:04:55.255-07:00Arrays: The Gateway to Multiplication Our first unit is all about factors, multiples, and arrays. I know from teaching 5th grade that if students don't understand what multiplication truly shows, they are missing the foundation to a deeper understanding of numbers, as well as the key to success with many many other parts of math. That is why I plan on really spending time this year developing a deep understanding of multiplication, how numbers are related, and strategies students can use to help them if they get stuck. <br />
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We first began, as always, using manipulatives. We have these wonderful one inch tiles that are perfect for creating arrays, but connecting cubes work as well. We discussed what the word "dimensions" mean when looking at the lengths of each side. We started by practicing arrays with smaller numbers and built our way up. Once I felt they understood, I put them in pairs and gave them each two numbers to find all the arrays for. An example of our work is shown below! (Please ignore the fact that the array she has showing shows 4x5 and is not an array for 18! She was actually building for their next number: 39)<br />
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This activity led into a discussion about why certain numbers had only one array, like 17. It was a "prime" time to talk about prime numbers! We displayed the posters throughout the room and refer to them often, especially when discussing multiples, factors, and special numbers!<br />
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If you have any suggestions for other awesome activities, or ways I can improve, please leave a comment below! Thank you!Ms. McHughhttp://www.blogger.com/profile/14304467530751870803noreply@blogger.com1tag:blogger.com,1999:blog-3159955006478935504.post-38489103177853254142013-08-19T16:49:00.000-07:002013-08-19T16:49:10.290-07:00New Beginnings<span style="font-family: Arial, Helvetica, sans-serif;">Is it really that time again?! <b>SO SOON?</b> August has truly flown by, and all of a sudden we are starting school. Except this year is going to be different. You see, last year, and the three years prior to that, I drove over an hour each day to my school (68 miles!!). While I loved my job, coworkers, students, and families, I needed to make a change. I couldn't continue using up two hours of my day (and all my extra cash for gas!) so I accepted a job closer to home. With this job is a different grade level (a 3-4 split....yowza) <b>AND</b> I get to teach all subjects (not just math as before)! I haven't figured out yet how this will affect my blog, but I'm sure that will come in due time. I look forward to doing math notebooks again, this year catering to 4th grade, while making many adjustments and improving it. I am also learning a new math curriculum, Investigations. Hopefully there will be lots of new and exciting ways to teach MATH! And perhaps, if I feel ambitious, I will broaden the blog to include all the wonderful things we will be doing in Language Arts. We shall see..... :)</span>Ms. McHughhttp://www.blogger.com/profile/14304467530751870803noreply@blogger.com0tag:blogger.com,1999:blog-3159955006478935504.post-54920861181241053982013-06-07T12:50:00.002-07:002013-06-07T12:50:35.647-07:00Wrapping up Notebooks: A time for ReflectionLast week was our last full week of school, so when Friday rolled around, we used our last full class together to wrap up our Interactive Math Notebooks. When I told my students it would be our last entry, some loudly groaned and others said audible "Noooooo!'s" I'll admit, I was sad too. We had all grown fond of the days we would add a new entry. They were all very excited that our last entry fell on page 100, which had been our goal for a while. "Ms. McHugh! We wrote a book that is 100 pages long!" And it's true, we did write a book. Who says Math and Language Arts don't go together??<br />
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Before adding our last page, I had created a word scramble page from<a href="http://www.superteacherworksheets.com/" target="_blank"> SuperTeachers</a> (currently a free feature). Each of the words were math terms that could be found in their table of contents. This was just a fun way to sum up our year together. Next, we all sat on the floor (Kindergarten style, as I call it) and slowly flipped through each page of our Notebook. This was by far the best part of that entire week. They couldn't believe all we had learned and how far we had come! Some mentioned that when we entered certain pages, they still had not understood it completely, but now at the end of the year, they "got it." This was a great lesson to learn. It doesn't always "click" for all our students at the same time. But with a little bit of hard work and a lot of perseverance, most students understood everything by the end of the year. Our Notebooks were a great reminder of that. <br />
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After we reflected on the year as a class, I let them make their very last foldable. This was a reflection on what they thought they were good at in math, things that were difficult or easy for them, and times that they had the most fun. I must admit, most said they had fun when their teacher got distracted or off track. What? I have no idea what they are talking about......<br />
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Here are some of my favorites from that last day:<br />
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<tr><td class="tr-caption" style="text-align: center;">This one makes me smile :)</td></tr>
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<tr><td class="tr-caption" style="text-align: center;">Who...me? No!</td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiUTUQhDK3JB5BKHQWWB3gCA6gfRJRCOG2c9BHSbkSoCKXdHv8xLfc_ssP5vw6DJCHD0D26Ppb0W1muvbzJk9i1ubtGhC23uGd2dxQJP7_NKo28GonwLY3b6ntxnopJRao0RCsGV0KVWww3/s1600/IMG_3049.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="239" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiUTUQhDK3JB5BKHQWWB3gCA6gfRJRCOG2c9BHSbkSoCKXdHv8xLfc_ssP5vw6DJCHD0D26Ppb0W1muvbzJk9i1ubtGhC23uGd2dxQJP7_NKo28GonwLY3b6ntxnopJRao0RCsGV0KVWww3/s320/IMG_3049.JPG" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Fun is a theme in our room. When we have fun, we are learning and it sticks!</td></tr>
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Ms. McHughhttp://www.blogger.com/profile/14304467530751870803noreply@blogger.com3tag:blogger.com,1999:blog-3159955006478935504.post-91108436629697410412013-05-25T12:04:00.001-07:002013-05-25T12:05:55.875-07:00Interactive Math Journal: Fractions of Fractions<span style="font-family: Arial, Helvetica, sans-serif;">I've been promising my kids all year that I was going to teach them how to multiply fractions, and now with only 5 teaching days left, I can finally get to it. Thursday, I introduced the lesson by giving each student multiple half sheets of paper. Our first task was to find what 1/2 of 1/2 was. We folded the paper in half vertically, colored half with one color crayon, then folded it in half horizontally and colored that half with a different color crayon. The piece that had the two overlapping colors showed us what 1/2 of 1/2 was, or 1/4. We then did the same activity again, but this time wondering what 1/2 of 1/3 was. I kept recording our findings on the board. At one point, I heard a gasp from Abbie. She looked at me excitedly and kind of started bouncing in her seat. I knew she had discovered something, but I asked her to hold on to her thoughts just a little longer. As we kept going with the paper, I heard more and more gasps and "oh!!!!!" coming from the class. I could tell some kids were getting frustrated that the others were discovering something they were not, so I finally let Abbie tell us what she first discovered. Of course, she saw that we were making arrays with our papers, and noticed that all we had to do was multiply the denominators. It was a different student that noticed that in each of our examples, the numerators were also multiplied. It was an exciting moment for the class!! </span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;">Then, someone raised their hand and asked, "Are we going to put this in our notebooks?" To be honest, I hadn't thought of that, but they had such a great idea! They actually wanted to add to their notebooks on their own! YIPEE!!! Since this activity took so long, we had to wait a day to enter it into our notebooks, but that gave me a chance to type up some blank rectangles to record our drawings in. Here is the end result: </span><br />
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<tr><td class="tr-caption" style="text-align: center;">This student chose pink and yellow to color with, so the overlapping piece is orange and shows the end result!</td></tr>
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<tr><td class="tr-caption" style="text-align: center;">This student showed that 1/2 is shaded in yellow, while 3/4 is in pink. The orange shows that 1/2 of 3/4 is 3/12!</td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgyOFEYsnVS4crCCi7BLiBBiDOH8VgRBGgcHbcAodZT523E8iq30PNO6RZWYLV7W-oafK9A5Ll305gSmBqAfIIvde8tKfzzdg6-Sce-MHWvUsBCYRbnTh-sFovdjnroPLIn1SUhDTKu-lls/s1600/IMG_3027.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="298" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgyOFEYsnVS4crCCi7BLiBBiDOH8VgRBGgcHbcAodZT523E8iq30PNO6RZWYLV7W-oafK9A5Ll305gSmBqAfIIvde8tKfzzdg6-Sce-MHWvUsBCYRbnTh-sFovdjnroPLIn1SUhDTKu-lls/s400/IMG_3027.JPG" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">This time, we included a "What I know" and "What I learned" section. It should be on the left hand page, but oh well. We are still learning!</td></tr>
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Ms. McHughhttp://www.blogger.com/profile/14304467530751870803noreply@blogger.com0tag:blogger.com,1999:blog-3159955006478935504.post-17245952958857665662013-05-23T13:35:00.000-07:002013-05-23T18:28:04.044-07:00Interactive Math Notebooks: Adding and Subtracting Negative Numbers<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">With testing over, and the end in sight, we are working working working hard to stay on a routine and make sure we are ready for 6th grade! We just finished a quick unit on negative numbers. Manipulatives are great to use here and serve as a constant reminder of what is going on. </span><br />
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<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">First, we spent a couple days adding positive and negative numbers. We used green counters for positive numbers, and red for negative. We use these two colors throughout our unit. I really putting an emphasis on the fact that adding is PUTTING TOGETHER. This would later help with differentiating between the rules for adding negative and the rules for subtracting negatives. After doing a few sample problems, the students were able to come up with their own rules for adding positive and negative numbers. They quickly caught on and all was well in the world! (Don't worry.....subtracting is next....that's a WHOLE different ball game!) Here are our notebook entries for adding:</span><br />
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<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">Next, we began working on subtracting. This time, I used a clear bucket to show what we had in the container, and what we needed to subtract, or take out. Before giving them any tricks, we practiced many many times with counters. For example, if the problem read: 8- (-4), I would fill the container with 8 green tiles, or 8 positives. Then, I would ask if we were able to take out 4 red tiles. Obviously, there were only green tiles in the container, so I couldn't take any out. We had discussed earlier how the opposite of every number added together equals zero, so I demonstrated putting in groups of one red and one green tile at a time, until I had 4 reds to take out, all the while emphasizing that I wasn't changing the value of the container since I was just adding zero to it. Then, I was able to take out the red counters, leaving only green behind. This was not an easy concept to teach, and there were some frustrating looks around the room, but we kept at it until it slowly started clicking. That's when I introduced Mr. Minus. </span><br />
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<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">Who is Mr. Minus, you ask? It's more of a "what". Mr. Minus is a poem my mother, Mrs. McHugh, also a 5th grade math teacher, made up years ago. I owe her A LOT this year! It goes like this:</span><br />
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<span style="letter-spacing: 0.0px;">Mr. Minus, Mr. Minus</span></div>
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<span style="letter-spacing: 0.0px;">Learn you I must</span></div>
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<span style="letter-spacing: 0.0px;">But I think I’m going to turn you into a plus,</span></div>
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<span style="letter-spacing: 0.0px;">Now change the second number to its opposite sign,</span></div>
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<span style="letter-spacing: 0.0px;">Add them both together and life will be fine! Yeahhhhh!</span></div>
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<span style="letter-spacing: 0.0px;"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif; font-size: small;">It's catchy and the kids love it! Here is our notebook page on subtracting. Again, the pictures are of containers holding what we need to take out and the step by step change it goes through. </span></span></div>
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<br />Ms. McHughhttp://www.blogger.com/profile/14304467530751870803noreply@blogger.com1tag:blogger.com,1999:blog-3159955006478935504.post-65326286555864216412013-05-06T18:38:00.000-07:002013-05-07T12:55:10.985-07:00Mother's Day CraftsLet's take a break from math for just a moment to honor those amazing women in our lives: our mothers! We took a moment after testing was over to create these wonderful plates. Most students decorated the plate for their mother, but some included their dads and still others included their entire family. I left it entirely up to them. I purchased the plates from the Dollar Tree (a teacher's best friend!) after each student donated a dollar (one boy, Ben, donated $4 "in case someone else can't bring you the money." Who said kids aren't compassionate?! I melted!). I had them create a rough draft first, but once they realized baby wipes would wipe away mistakes, they lost all fear of messing up and got really creative! This is an easy, awesome project and is all over Pinterest. Just color your plate with Sharpies, and bake for 30 minutes at 350....and viola! A personalized gift :) Check them out!<br />
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<tr><td class="tr-caption" style="text-align: center;">Allison chose to include her entire family with a descriptive word about each starting with the same letter as the first letter in their name; I love majestic mom! :)</td></tr>
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<tr><td class="tr-caption" style="text-align: center;">They had so much fun displaying their love for their mothers!</td></tr>
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<br />Ms. McHughhttp://www.blogger.com/profile/14304467530751870803noreply@blogger.com0tag:blogger.com,1999:blog-3159955006478935504.post-11731996862316836262013-05-03T13:32:00.001-07:002013-05-04T08:14:59.726-07:00Numerical Expressions: Common Core<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">Now that the OAA is over with and testing season is behind us, we are going to start focusing on some of the things that are included in the new CCSS that were not on the Ohio Standards, as well as touch on some things that I think they need more exposure to to make sure they are ready for 6th grade. </span><br />
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<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">We have two great activities for numerical expressions today! We learned about numerical expressions already, but I didn't feel like I covered it deep enough. The Common Core is all about going deep with the concepts and really applying them to their lives. We began by practicing oral expressions and displaying them numerically on their slates. Here are some examples:</span><br />
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<span style="letter-spacing: 0.0px;"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif; font-size: small;">Twice a number, decreased by twenty-nine</span></span></div>
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<span style="letter-spacing: 0.0px;"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif; font-size: small;">Five times a number <i>y </i>increased by 3</span></span></div>
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<span style="letter-spacing: 0.0px;"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif; font-size: small;">Multiply three by two, then subtract one</span></span></div>
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<span style="letter-spacing: 0.0px;"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif; font-size: small;">Once we did enough practice and most of the kids had caught on consistently, we moved toward some independent work. They didn't have a lot of problems, just ten, and most were asking the kids to analyze the expressions without evaluating them. As they finished, there was an assignment on the projector waiting for them: our performance assessment. I always find that if I ask them to write their own problem, I can really see if they understand what's going on. </span></span></div>
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<span style="letter-spacing: 0.0px;"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif; font-size: small;"><b>The CCSS is: 5.OA2: Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. </b></span></span></div>
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<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif; font-size: small;">The performance assessment asked them to create their own real world problem that could use an expression, write the expression, and draw a picture to match. Being able to see math in REAL LIFE situations AND create their own problems is a HUGE skill that is SO important! Here were some of the final products: </span></div>
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<tr><td class="tr-caption" style="text-align: center;">A basketball game ticket cost $17. Hot dogs are $5.00. If Molly and 6 friends go and all get hot dogs, how much money will they spend? --Submitted by Molly K.</td></tr>
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<tr><td class="tr-caption" style="text-align: center;">A ticket to the school dance costs 15 dollars. A picture costs 10 dollars. El and three friends each buy a ticket and each get a picture taken. How much did they spend? --submitted by Shante J.</td></tr>
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<tr><td class="tr-caption" style="text-align: center;">Ms. McHugh's class bought her 3 bags of chocolates. Each bag has 10 pieces of chocolate. Then, Mrs. Haught bought her 7 bags of hard candy. Ms. McHugh ate 20 pieces of chocolate and hard candy all together. How many pieces does she have left? --Submitted by Ashley M. (can you tell I LOVE candy??</td></tr>
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<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif; font-size: small;">Next, I had a challenge for them. I found this idea on <a href="http://www.k-5mathteachingresources.com/support-files/numercialexpressionswallclock.pdf" target="_blank">K-5 Math Teaching Resources</a>, except I modified it for our purposes. The task was to use only the digit 4 (the original says only four 4's, but we just stuck to 4s) to create problems equaling the numbers 1-12 so that you could place those numbers on a blank clock face. Once they figured out a couple (4/4=1, and so on), they were unstoppable! It was one of those classes where kids asked "can I finish this over the weekend??" even when it wasn't a required assignment! Check out some of their clocks!! </span></div>
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<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif; font-size: small;">Truly, they learned the most from having to write their own problems. We did a similar activity with <a href="http://msmchughscorner.blogspot.com/2012/12/digging-into-common-core-deep-division.html" target="_blank">division</a> back in December, and I will definitely incorporate this task more next year! It's just a great way to really see how they look at and see problems! Hope you enjoyed! </span></div>
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Ms. McHughhttp://www.blogger.com/profile/14304467530751870803noreply@blogger.com0tag:blogger.com,1999:blog-3159955006478935504.post-20955077691174772652013-04-11T13:43:00.000-07:002013-04-16T09:59:14.096-07:00Technology: Finally!We have Technoooooolllloooogy!!!! (Said in my best "Oprah's Favorite Things" voice). Because we were able to build all new schools, we also received all new interactive whiteboards, as well as speakers in our ceilings and MICROPHONES! If you know me at all, you know I love to sing, so my poor students always catch me singing into the microphone. It always lightens the mood, especially during testing prep when things can get a little tense. <br />
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Today, I decided to slow things down a bit and let the students use the interactive whiteboard to show their answers on their homework. Normally, I would just slide their paper under our document camera, but he's been feeling a little under the weather lately, so we've had to do without (I feel LOST without it, but we make do!). We have been doing a lot of reviewing lately, as well as making connections between all the different areas of math, so last night's homework involved circle graphs, fractions, and percents. We can ALWAYS review that! They were given four frequency charts with information that they had to put into circle graphs using the fractions given. Here are some pictures of a few of the students recreating their graphs;<br />
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<tr><td class="tr-caption" style="text-align: center;">Ben was the first brave soul to give it a try! Pretty good!</td></tr>
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<tr><td class="tr-caption" style="text-align: center;">Paige and TeShon hard at work!<br />
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The last class of the day seemed to have a hard time deciding which fraction was larger; 3/8 or 1/4, so we decided to use the highlight feature on the interactive whiteboard to give us a better visual. As we were highlighting, I heard lots of "ohhhhh!!!!!!" The visual really helped, and it was so much easier with the interactive feature. Check out the picture below!<br />
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I can't wait to start utilizing our new technology in the future! Woo!<br />
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<br />Ms. McHughhttp://www.blogger.com/profile/14304467530751870803noreply@blogger.com0tag:blogger.com,1999:blog-3159955006478935504.post-14471979282228241592013-04-09T14:12:00.001-07:002013-04-09T14:12:42.056-07:00Probability: Math NotebooksToday's Math Notebook was inspired by the WONDERFUL Mrs. Runde over at <a href="http://www.rundesroom.com/2012/06/math-journal-sundays-probability.html" target="_blank">Runde's Room</a>, although, I catered it to our needs. I really liked how she had her students write out the learning goals and task before starting, so I decided to try it. I always let the kids know what our goals for the day are, as well as have our "I Can" statements posted clearly in the room, but this is the first time we really put it in writing as a class. We have been working with probability, so I decided to make a spinner as well. I also liked how she had the kids figure out a way to divide their circle in ten equal pieces as a nice review on dividing as well as remembering how many degrees are in a circle! We also love working with protractors, so it was a nice review. (We also had the chance to review equivalent fractions AND percents! All in one activity! YAY!) Below is our page:<br />
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Because our goal was to compare theoretical results with actual results, and to make predictions, our notebooks ends up steering away from Runde's a little bit. We have been having trouble creating frequency tables lately, so here was a great opportunity to do so. I was going to have them do their experiment 20 times instead of just ten, so we based our theoretical results off of 20 (and reviewed equivalent fractions at the same time!) I also had them come up with a prediction of what they thought would happen, based on their theoretical results. Then, it was spin time! They recorded their results in their frequency table and wrote out their conclusions based on their actual results. <br />
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Lastly, we met to talk about the reasonableness of certain results. We used our theoretical results to determine if the actual result was reasonable or not. Before this lesson, only 50% of my students answered a "reasonable or not reasonable" question correctly. After this lesson, we were up to 87%! I would say we succeeded! :)Ms. McHughhttp://www.blogger.com/profile/14304467530751870803noreply@blogger.com0tag:blogger.com,1999:blog-3159955006478935504.post-68980981770792994062013-04-09T13:57:00.002-07:002013-04-09T13:57:33.453-07:00Algebraic Expressions and Math NotebooksWe covered <a href="http://msmchughscorner.blogspot.com/2012/11/interactive-notebooks-algebra.html" target="_blank">Algebra</a> way back in October and did a really great foldable for the four steps to follow when solving a problem with unknowns. We came back to it today, both as a review, and to extend our thinking to expressions and patterns. Our <b>learning target</b> for today was to introduce the use of algebraic expressions to represent situations and describe rules. First, we watched this StudyJam on <a href="http://studyjams.scholastic.com/studyjams/jams/math/algebra/function-tables.htm" target="_blank">Function Tables</a>, as well as one on <a href="http://studyjams.scholastic.com/studyjams/jams/math/algebra/add-sub-equations.htm" target="_blank">Addition and Subtraction Equations</a> and <a href="http://studyjams.scholastic.com/studyjams/jams/math/algebra/mult-div-equations.htm" target="_blank">Multiplication and Division Equations</a>. We also did a sample problem in our notebooks, as shown below. The problem reads:<br />
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<b>Joe and Maria are 5th graders. Joe is two inches taller than Maria. </b></div>
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I asked the students to put this information into a function table and give me some measurements for Joe and Maria. I reminded them to make them reasonable measurements for 5th grade students. Of course, everyone had different answers, and all were acceptable as long as Joe was two inches taller. Next, I recorded some of their measurements on the board and asked them to explain how they came up with Joe's height. We also noticed that our function table was similar to the In and Out boxes they have become so familiar with using Everyday Math. I asked them what the rule was for this table. Of course, they all said "add 2!" Then, I encouraged them to tell me the rule for finding Joe's height based on Maria's if we use <i>m </i>for Maria. This was a little tricker, but with a little prompting, they said "<i>m</i>+2!<i>" </i>Now we're talking!<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgGFtPKOeKt_csbyBPLCcUU2-u7fUozWb4uoa_mV4Z-MbOOkokw4-mUgu0jCfB7oKvw3-5YgWN5WOOxJOFhLGjgMAYM3jferzgBKa6zc-FZu8DIBAQ3RYib0rWvjJ0wpeFJyu_EPz55-ZaZ/s1600/Algebra.JPG" imageanchor="1"><img border="0" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgGFtPKOeKt_csbyBPLCcUU2-u7fUozWb4uoa_mV4Z-MbOOkokw4-mUgu0jCfB7oKvw3-5YgWN5WOOxJOFhLGjgMAYM3jferzgBKa6zc-FZu8DIBAQ3RYib0rWvjJ0wpeFJyu_EPz55-ZaZ/s1600/Algebra.JPG" width="400" /></a></div>
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Next, we wrote some sample problems in our notebooks and came up with expressions to describe the problems (EDM 10.3):<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhP9oo9bgyqOuCtRNRH4oYpw8d_JcbmpypA3v2aD3TzEaVqvCkNRgAwN0UfMsOA9Mv8pQ8pvQ_i6AFhh7KaGaTxW1Uy39O9hMV7EfjxPejFWuV4G6tAGcoEv4cLAaWG26xfh739KbV-AWjb/s1600/photo.JPG" imageanchor="1"><img border="0" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhP9oo9bgyqOuCtRNRH4oYpw8d_JcbmpypA3v2aD3TzEaVqvCkNRgAwN0UfMsOA9Mv8pQ8pvQ_i6AFhh7KaGaTxW1Uy39O9hMV7EfjxPejFWuV4G6tAGcoEv4cLAaWG26xfh739KbV-AWjb/s1600/photo.JPG" width="400" /></a></div>
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After some more practice independently, I gave the students an opportunity to write their own problem situations that would require the use of a variable. I forgot to capture this in a photo, but they did a really great job! Being able to write their own, and accurately, made me feel confident in their understanding of expressions. Ms. McHughhttp://www.blogger.com/profile/14304467530751870803noreply@blogger.com0tag:blogger.com,1999:blog-3159955006478935504.post-76449016096655525492013-04-09T13:21:00.001-07:002013-04-09T13:21:48.147-07:00Capacity: Interactive Math NotebooksCapacity is always fun! Unfortunately, when moving to our new building, all the containers I had saved for this day were tossed thinking it was trash! Can you believe it? Someone thought our old milk cartons and jugs were trash! Anyway, I'm lucky to have a mom who also teaches 5th grade math (you should hear our phone conversations....very animated!) and because she had taught capacity the week before, she was willing to lend me her collection. Saved by mom (again!). After a lot of spilled water and "do you predict this container will hold two or three of these?" we moved into our notebooks to record our thoughts. <br />
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First, we wrote down the Big G. Why didn't we have this when I was a kid?? I never remembered what the Gallon Bot was and it was way too difficult to recreate, but the Big G is EASY! It's truly how I remember my conversions. Here is a picture:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjxXlwP29b1lOoymt69ItvzwhTWvElMDAdOTqKEeHjWK-AqXmuE5MdVHCxaUu2pZGjqqrfzGv59ZLGf0urxswyQvrekhme16R94gbaBnO7IzeSyOrNa261er_IPZZPpxXMBNqTJvglSguOr/s1600/Capacity2.JPG" imageanchor="1"><img border="0" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjxXlwP29b1lOoymt69ItvzwhTWvElMDAdOTqKEeHjWK-AqXmuE5MdVHCxaUu2pZGjqqrfzGv59ZLGf0urxswyQvrekhme16R94gbaBnO7IzeSyOrNa261er_IPZZPpxXMBNqTJvglSguOr/s1600/Capacity2.JPG" width="400" /></a></div>
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Next, I gave them a moment to free write. I really wanted them to write down everything they knew about capacity, so each student's page is very different, but many chose to write down conversions based on the Big G. I walked around making sure that they understood how to read it. Here is one example:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj3PVtKBLNqe2x3Erv9fzPHnksdkaQLIXQoQKTFULddWA3KGTFk0-DINapVXlZ_fJ21nucoVsuGeMkGIKO4oP0npfH3LyI_3Im0LZ9PDQgn5Tha8S9vyKBpYVa0sWBKIEyaEVIoFRVjzYCb/s1600/Capacity.JPG" imageanchor="1"><img border="0" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj3PVtKBLNqe2x3Erv9fzPHnksdkaQLIXQoQKTFULddWA3KGTFk0-DINapVXlZ_fJ21nucoVsuGeMkGIKO4oP0npfH3LyI_3Im0LZ9PDQgn5Tha8S9vyKBpYVa0sWBKIEyaEVIoFRVjzYCb/s1600/Capacity.JPG" width="400" /></a></div>
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Of course, there's also an anchor chart hanging in our room of the Big G that we refer to often, but I didn't feel the need to post it here because it is the same as the notebook page :)Ms. McHughhttp://www.blogger.com/profile/14304467530751870803noreply@blogger.com0tag:blogger.com,1999:blog-3159955006478935504.post-86030652598647260162013-04-09T13:09:00.000-07:002013-04-09T13:16:34.589-07:00Measurement and conversions: Interactive Math NotebooksAgain, I'm behind on posting this! Where does the time go? We did measurement back in March, and while we did a lot with it, I'm just going to outline what we did with our notebooks in this post. We began by discussing the two systems of measurement. We decided the best way to organize this information was in a T chart (we REALLY like those around here!) and we wanted to keep all the types of measurement (length, capacity, weight) together as well. Here is the list we came up with:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgMHnr-4KyNPeXq93bxdcp_Sim22cqYT6taVidM08xs7A1ysh79yzLUc2Eht0c2wE3Awo27N9WwuSX1adKICO87_A-bW6mCwI5tHGf-z7h8t6IsypCyLVz0fXrQEuVXt_NDoS8iiVcB3I-h/s1600/Measurement.JPG" imageanchor="1"><img border="0" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgMHnr-4KyNPeXq93bxdcp_Sim22cqYT6taVidM08xs7A1ysh79yzLUc2Eht0c2wE3Awo27N9WwuSX1adKICO87_A-bW6mCwI5tHGf-z7h8t6IsypCyLVz0fXrQEuVXt_NDoS8iiVcB3I-h/s1600/Measurement.JPG" width="400" /></a></div>
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Next, we brainstormed some of the basic conversions we remembered for length for each system and wrote them down. Lastly, we took notes on an easy way to convert between units of measurement. A <b>BIG</b> "thank you" to my coworker Adrienne, the 4th grade math teacher, for sharing her mnemonic device! Some of my students remembered it from last year! She taught us that there are two ways to change units: to multiply or divide. When converting from a <b><u>B</u></b>ig unit to a <b><u>S</u></b>mall unit, you <b><u>M</u></b>ultiply, so we think "<b><u>B</u></b>est <b><u>S</u></b>occer <b><u>M</u></b>om." When converting from a <b><u>S</u></b>mall unit to a <b><u>B</u></b>ig unit, you <b><u>D</u></b>ivide, so we think "<b><u>S</u></b>illy <b><u>B</u></b>abies <b><u>D</u></b>ancing." We always giggle at "Silly Babies Dancing!" <br />
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Below is the anchor chart hanging in our room to serve as a reminder. Another "thank you" to Adrienne! I got this straight from her! Thank goodness for kind coworkers willing to share and kick around ideas with!<br />
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<br />Ms. McHughhttp://www.blogger.com/profile/14304467530751870803noreply@blogger.com1tag:blogger.com,1999:blog-3159955006478935504.post-90408422629645979552013-04-09T12:52:00.000-07:002013-04-09T12:52:03.434-07:00Surface Area: Interactive Math NotebooksWe didn't spend a lot of time on Surface Area after all the time we spent on area, perimeter, and volume. I really just wanted the kids to understand the concept of it, not necessarily how to find it. We will get to that later in the year. So, in order to demonstrate the idea of surface area, I wrapped a box in wrapping paper to show that we needed to know how much paper to use to cover the box. I also gave each student a net for a rectangular prism and asked them to color just one side to represent wrapping paper. Then out came the interactive math notebooks! We creased each net and glued them into our notebooks so that when they flip to that page, they can easily fold it back up to look like a 3-D shape! Here is an example:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEimqq0bfNBfqXHqjDJIZiLVBuOEbz_UshLXEICArP9QZM9AKdWrZuVUXsVqnnoebFFrvjn4-l1H6BqH3YJFNFLQhzc4Feo2u6eE7MvIEv1t9obXE5SJmgwR4fR8rpI884Cyio1-xCyb_UlH/s1600/Surface+area2.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEimqq0bfNBfqXHqjDJIZiLVBuOEbz_UshLXEICArP9QZM9AKdWrZuVUXsVqnnoebFFrvjn4-l1H6BqH3YJFNFLQhzc4Feo2u6eE7MvIEv1t9obXE5SJmgwR4fR8rpI884Cyio1-xCyb_UlH/s1600/Surface+area2.JPG" /></a></div>
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Because we just finished up volume, we made a T chart in order to make comparisons between volume and surface area. I told the kids to think about a tool box or toy box to tell the difference. Here is what we came up with as a class:<br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjuBsyqTs20f-6GQudzscAC-zX267Z4nJX1VdKuiSaoNs3XqKLFBMvzl4K5CyzDOySwbJ7NK0UfuodySAO-OZt3_baFhPYRXei1OVJC2PhHwpmeT4ZpNjL9HmMpEQ3Q1acUYdmgIsIp-egO/s1600/Surface+area.JPG" imageanchor="1"><img border="0" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjuBsyqTs20f-6GQudzscAC-zX267Z4nJX1VdKuiSaoNs3XqKLFBMvzl4K5CyzDOySwbJ7NK0UfuodySAO-OZt3_baFhPYRXei1OVJC2PhHwpmeT4ZpNjL9HmMpEQ3Q1acUYdmgIsIp-egO/s1600/Surface+area.JPG" width="400" /></a></td></tr>
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Well, there ya have it! A quick and easy day! Thank goodness for math notebooks!<br />
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<br />Ms. McHughhttp://www.blogger.com/profile/14304467530751870803noreply@blogger.com1tag:blogger.com,1999:blog-3159955006478935504.post-59358042169677742392013-04-03T10:13:00.000-07:002013-04-03T10:13:21.129-07:00Pi Day!March 14. Finally. An ENTIRE DAY dedicated to MATH! And it's PERFECT for 5th grade! I started getting the kids excited about Pi day early in March. Some knew that pi = 3.14, but they really didn't know much more than that. I could feel the excitement as they entered the room that Thursday morning. I only had 90 minutes with each class and each minute was accounted and planned for, so we got right to business. Here is an outline of our activities for the day!<br />
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<b><span style="color: blue;">1. Quiet morning activity: Write as many digits in pi as you can around a paper plate</span></b><br />
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I used a paper plate for two reasons: I have 75 kids and they are CHEAP! And, of course, it's a circle. The directions were on the projector when the kids walked in and they quickly figured out they needed to sit as close to the board as possible so as not to miss a single digit. I only gave them about ten minutes to make their paper plate. I wanted them to have something to take home to show their parents as well as something to study from for our Pi contest. More on that later! This activity also got them wondering what the heck pi was! Here are some paper plate making shots:<br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg7_uSINpCedewT13wdVX2bUSn5xT5F6ZwVYRBXp9543g4d7DmC4MDa9HsOD2KA7US-6NE9QGTe4jFiBcFEJIYUEMM_SAA-BSXfoqJ8kRU8K4V97f65PIG4FbXp8RqfLyGNBDR9-Wj-OFwG/s1600/IMG_2591.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg7_uSINpCedewT13wdVX2bUSn5xT5F6ZwVYRBXp9543g4d7DmC4MDa9HsOD2KA7US-6NE9QGTe4jFiBcFEJIYUEMM_SAA-BSXfoqJ8kRU8K4V97f65PIG4FbXp8RqfLyGNBDR9-Wj-OFwG/s320/IMG_2591.JPG" width="239" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Allison ended up getting 4th place in our pi contest!</td></tr>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhqFNjYl5e6TaoIbZbFIHP5vrroJ1mj8TEAupuJieiSwuz3FS_HINVoJwtmvtcSFs8bLPXchfi6ZbHI4CzBNoXjB9cYJD7htdAOFYkVVtC3zMmaoTv3SwE6WvvB9pLFHmlXVJTZgIcv_4Xy/s1600/IMG_2590.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhqFNjYl5e6TaoIbZbFIHP5vrroJ1mj8TEAupuJieiSwuz3FS_HINVoJwtmvtcSFs8bLPXchfi6ZbHI4CzBNoXjB9cYJD7htdAOFYkVVtC3zMmaoTv3SwE6WvvB9pLFHmlXVJTZgIcv_4Xy/s320/IMG_2590.JPG" width="239" /></a></div>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEipf8298hDPToIhQA07rx8oR14-F9HD4kR5QyF3NZx01oUZcNBsqJmmtomX06ANDyw3lK3VwHrfWzxJmpcAb0vhSJNOLWs2GEDGs5jn915bV65vjHPqwhpoZy3ajejSQKM3m1CtddJsdmmS/s1600/IMG_2599.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="298" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEipf8298hDPToIhQA07rx8oR14-F9HD4kR5QyF3NZx01oUZcNBsqJmmtomX06ANDyw3lK3VwHrfWzxJmpcAb0vhSJNOLWs2GEDGs5jn915bV65vjHPqwhpoZy3ajejSQKM3m1CtddJsdmmS/s400/IMG_2599.JPG" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Busy at work making their paper plates!<br /><br /><br /><br /><br /><br /><div style="font-size: medium; text-align: start;">
<b><span style="color: blue;">2. History of Pi</span></b></div>
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We found a short history of pi in our books, and discussed it briefly. Many kids were fascinated by the fact that the definition of pi has changed so much throughout history (their teacher was fascinated too!). I could feel the excitement building now!</div>
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<b><span style="color: blue;">3. Measurement of circles and discovery of pi</span></b></div>
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We briefly discussed using centimeters in our measurement and getting right down to the exact millimeter so that our measurements were as accurate as possible. This was just a review for them. We also discussed measuring diameter as going right down the center of the circle as well as reviewed what ratio meant since we were finding the ratio of circumference to diameter. We did one example together, and off they went about the room. I had a table full of circular objects for them to choose from, and a chart from superteacherworksheets.com to fill in as they went. While they worked, I walked around and discussed findings, as well as helped troubleshoot when I could tell their measurements were off. </div>
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<tr><td class="tr-caption" style="text-align: center;">All the lovely objects we have to measure! Yes, that is my soap from my bathroom, and my coffee mug :) </td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiswkLrR2LMetN5w9uafGNS3LnUuFR1JB_DUWFMrYcrJczPNRQqDsWEe65ueSChrGw68IQlNEeP5hoHKhPc5j6-c3UB5g4RaxRsxMaVB3eFEb3mLB61ImjlCGT1TWMFU8uEMXPM_O1gBIii/s1600/IMG_2593.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="239" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiswkLrR2LMetN5w9uafGNS3LnUuFR1JB_DUWFMrYcrJczPNRQqDsWEe65ueSChrGw68IQlNEeP5hoHKhPc5j6-c3UB5g4RaxRsxMaVB3eFEb3mLB61ImjlCGT1TWMFU8uEMXPM_O1gBIii/s320/IMG_2593.JPG" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">"Ms. McHugh, did you even wash out your mug?" </td></tr>
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<tr><td class="tr-caption" style="text-align: center;">Pretty accurate I would say! </td></tr>
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<tr><td class="tr-caption" style="text-align: center;">Partners hard at work measuring and loving every moment of it!</td></tr>
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<tr><td class="tr-caption" style="text-align: center;">What a great day!</td></tr>
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<b><span style="color: blue;">4. Discovery</span></b><br />
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Once we were finished, we had a lengthy discussion about what we learned. Ultimately, I wanted them to see that the circumference of a circle was about three time its diameter. We used our knowledge of finding the unknown (all our algebra work is paying off!) to figure out that if you don't know the circumference, but you do know the diameter, you can use pi to help you find it. There were a couple ah ha moments at this point. I literally saw the understanding unfold on Ivy's face! It was neat to see her go through the process of understanding using our measuring activity and finding 3.14 was (about) the ratio each time, to knowing that she could always use that to find circumference. These are the moments people! The ah ha moments! :)<br />
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<b><span style="color: blue;">5. Short video</span></b><br />
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We always try to wrap up with a short video from StudyJams, and today was no different. It gives them a chance to listen to someone else talk about what we learned and they do a great job of putting concepts into real world situations. If you haven't checked out StudyJams yet, I encourage you to do so!<br />
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<b><span style="color: blue;">6. Cookies</span></b><br />
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On a day like today, you have to have a fun treat! Every student received a cookie, but don't worry, we found its diameter and circumference first! YUM!<br />
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<b><span style="color: blue;">7. Contest time!</span></b><br />
Lastly, I held a digit reciting contest. I gave them until the next day to see how many digits they could memorize in pi. It was completely optional and just for fun. I was so impressed by how many students really got into it, and memorized WAY more digits than I ever could! Our winner was Cale: he memorized 78 digits! WOW!<br />
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All in all, this will stand to be one of my favorite days of the year. I think my students would have to agree!<br />
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<br />Ms. McHughhttp://www.blogger.com/profile/14304467530751870803noreply@blogger.com0tag:blogger.com,1999:blog-3159955006478935504.post-84517559074833572402013-04-03T09:38:00.000-07:002013-04-03T09:38:00.147-07:00An Exploration of VolumeOk ok....So it's April and I taught volume almost a month ago. Things can get pretty hectic this time of year, what with preparing for the OAA and making sure my kids are in tip top shape to show what they know! Now that we're on Spring Break, I can finally sit back and reflect on what we've been learning and where we need to go after this. <br />
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I truly feel that math should be a hands-on experience for kids of all ages. It shouldn't stop in 3rd grade. All too often, we get caught up in making sure they know how to do it on paper and apply formulas, but kids need to be able to touch and feel what they are learning to really grasp it and understand it. I always try to give them thorough hands-on experiences before teaching them the "math" part: formulas and equations. So far, I think we've been pretty successful. But, as in most cases, time is always an issue. We just have to keep moving, moving, moving!<br />
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As will area and perimeter, we did an exploration of volume. Many of my students had remembered the formula for finding the volume of a rectangular prism from 4th grade, but I wasn't really sure they understood or remembered WHY you multiplied LxWxH. Thanks to Everyday Math, each student had the net of two different open rectangular prisms in the back of their math journals. We made predictions for how many cubes we thought would fit into each. These predictions actually gave me pretty good insight as to where each student was in their understanding of volume. Then, of course, we began filling! <br />
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We started by just filling the base of the prism and finding out many cubes that was. I wanted them to see this as the area of the base: of course, some did, some didn't. We will keep working on this idea of area! (Too often, their idea of area is just a rectangle on a page....must change that thinking!!). Then we added another layer, and finally a third. This allowed them to see that we were adding the area of the base however many times tall it was. For the second prism, we only filled the base and predicted what the volume would be based on the results of the first prism. From this, we developed the formula for finding the volume of a rectangular prism!<br />
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As an extension, and because we had a couple extra minutes at the end of class, I had each student build a rectangular prism on their desk with a volume of 24 cubic centimeters. I didn't give them any more specifications than that. After a minute or two of building, I began recording different lengths, widths, and heights that I saw around the room. Once they saw all the possibilities, hands flew in the air. They remembered what we had learned about multiplication being part of the commutative property and knew they could use the factors of 24 to build many many different prisms, all with the same volume. Ah ha moments are the best :)<br />
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Lastly, here is the anchor chart we came up with. They wanted me to point out that volume is "all about the threes":<br />
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<tr><td class="tr-caption" style="text-align: center;">Volume! </td></tr>
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<br />Ms. McHughhttp://www.blogger.com/profile/14304467530751870803noreply@blogger.com0tag:blogger.com,1999:blog-3159955006478935504.post-7202826736529616872013-03-12T13:43:00.001-07:002013-03-12T13:45:12.535-07:00Measurement: Perimeter and Area <span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">Teaching perimeter and area is one of my favorites because it can be so hands on (oh but just you wait until volume, surface area, and circumference!) Because our 4th grade teachers did such an excellent job in this area (pun completely intended!) I didn't feel the need to dwell on perimeter and area of rectangles for long. Thanks to Pinterest, I found an easy, hands-on way to review area and perimeter of rectangles that wasn't just a worksheet to complete. After watching a couple <a href="http://studyjams.scholastic.com/studyjams/index.htm" target="_blank">StudyJams</a> videos, we went straight to work with some grid paper, two dice, and our pencils. Students were to roll the dice and create an array to display the numbers on the dice. Then, they were to find the area and perimeter of the array. We discussed either counting the squares, or using the formula they used in 4th grade for area. I worked with a couple struggling students. I had them highlight the outside of the array in one color to find perimeter, then color the inside of the array with another color to find the area. This really seemed to jog their memory! Below is a picture of Aaliyah's arrays (although, I'll have to remind her that area is measured in square units....or squAREA!)</span><br />
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<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">The next day, we moved on to finding the area of parallelograms and triangles. This proved to be much more difficult, they concluded. The triangles and parallelograms were drawn on centimeter grid paper, and at first, some students were trying to shade whole squares, then put together pieces to create more wholes. When we shared answers and found that we all had something slightly different, we need we needed a better solution. I asked them why finding the area of a rectangle was so easy for them, but these polygons were so much more difficult. The conversation went something like this:</span><br />
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<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><b>Student 1</b>: Because with rectangles you just count the squares and that's the area!</span><br />
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><b>Me:</b> Ok.....so why are triangles and parallelograms so much harder?</span><br />
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><b>Student 2:</b> There are sometimes all these little pieces of squares that you have to put together. Sometimes they are easy, like if it's just a half of a square. But other times they are harder.</span><br />
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><b>Me:</b> What is it about rectangles that make it have just whole squares or half squares then? <silence in the room></span><br />
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><b>Student 3:</b> It....has....right angles?</span><br />
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><b>Me:</b> And....?</span><br />
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><b>Student 3:</b> Right angles are squared off....so they are easier to count!</span><br />
<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><b>Me:</b> So what if we made our parallelograms into rectangles so that they are easier to count?</span><br />
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<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">We went on to change each polygon into rectangles and go from there. I let them struggle with this method for homework: not all of the polygons were easy to change accurately. On day 3, we went at it again. Many students came in frustrated and unsure if their answers were correct. And this is how we led into the discovery of the formula for finding the area of triangles and parallelograms!</span><br />
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<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">We began class by looking at a scalene triangle and trying to find its area. I had them do what they did before.....divide it into 2 rectangles and find the area of each, then add them together. This time, however, they had to add up a bunch of half squares and quarter squares. It took them forever and they were frustrated (yet again). After all that, they knew they still had to divide it in half because it was only a triangle. That's when they saw that they were really just finding the area of a rectangle and dividing it in half! We tried this method, which was much simpler to multiply the length by the width, then divide in half, rather then count up all these pieces of squares. I actually had one student's face light up as she yelled out "OhMyGosh! That is SO much easier! Can we ALWAYS do it like that?!" To which I happily replied, "Yes, Ivy, because you just figured out the formula for finding the area of a triangle!" They were so relieved, and shocked, that it was THAT easy. We did a similar discovery lesson with parallelograms, cutting them in half and making them rectangles. </span><br />
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<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">The last 15 minutes of class were spent updating our notebooks and reflecting. We used the right side so show sample problems and made sure to highlight the base and height of each polygon in separate colors to help out our brains. Then, on the left side, I allowed them to write whatever they wanted on area of parallelograms and triangles. They were told they could use words, pictures, examples, formulas, or a combination to reflect on what they had learned. I think they did a great job! They even asked for more time! Here are some examples on the work we've done in our notebooks for area and perimeter:</span><br />
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<tr><td class="tr-caption" style="text-align: center;"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif; font-size: small;">Each student received two random arrays. They were asked to find the perimeter of one, use it to define perimeter, and think of examples. Then, we did the same with area of the other. Great visual! </span></td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgOlv1XUTImejrpGkBEzL_40Iz1-JuSoJC4NhbHTZgtVTiE_Yt-oLaFsr8VUZUq9XVI8vNd3Q0ibDy3OVGfb0XvkrAsdq1RTbgvPByNm_Y-TcBLertjxUCFFjP26eR1PPMfhxXK67umAP63/s1600/Allison+Right.JPG" imageanchor="1"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><img border="0" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgOlv1XUTImejrpGkBEzL_40Iz1-JuSoJC4NhbHTZgtVTiE_Yt-oLaFsr8VUZUq9XVI8vNd3Q0ibDy3OVGfb0XvkrAsdq1RTbgvPByNm_Y-TcBLertjxUCFFjP26eR1PPMfhxXK67umAP63/s1600/Allison+Right.JPG" width="400" /></span></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif; font-size: small;">Here is the right side of Allison's notebook. They used one color highlighter for base, and one for height to help them see that they come together to form a right angle.</span><br />
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<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">Here are a couple of the left side thinking from my students. Again, they were able to write their own notes on area. Each are a little different, but reflect how each student prefers to receive their information. </span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhGubfXmtyYx1Rmp01d_jSQlhP51B7SwV8XhitJfBByVHY8wRaTib7BPnzjbZUaPPMf43MqM9zJ2vWjGj6fzI6He6mpDKvYG3TTbZxfPdj1TWpYvF6jNO3mMxJrWSUL01G4pUEX75NRog3a/s1600/Allison+Left.JPG" imageanchor="1"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><img border="0" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhGubfXmtyYx1Rmp01d_jSQlhP51B7SwV8XhitJfBByVHY8wRaTib7BPnzjbZUaPPMf43MqM9zJ2vWjGj6fzI6He6mpDKvYG3TTbZxfPdj1TWpYvF6jNO3mMxJrWSUL01G4pUEX75NRog3a/s1600/Allison+Left.JPG" width="400" /></span></a></div>
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<span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">And lastly, as usual, we always make an anchor chart after we have learned something. Perhaps, if they glance at it enough, the information will stick!!</span><br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhXAXXjsJc0eliisG-jnLVtLrvP0_8Komml6M9tqOuu52lyDon884h5f9MYi2IQsi9I2UuwTXQJpLQ6owQ8XM5_IVpXlC4SX9BTVXyyzLqFCqNi6iFS88LOLzG6HV-y-djLkUvyh2tdCs1s/s1600/Area+Anchor+Chart.JPG" imageanchor="1"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><img border="0" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhXAXXjsJc0eliisG-jnLVtLrvP0_8Komml6M9tqOuu52lyDon884h5f9MYi2IQsi9I2UuwTXQJpLQ6owQ8XM5_IVpXlC4SX9BTVXyyzLqFCqNi6iFS88LOLzG6HV-y-djLkUvyh2tdCs1s/s1600/Area+Anchor+Chart.JPG" width="400" /></span></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif; font-size: small;">Area of Triangles and Parallelograms Anchor Chart</span></td></tr>
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<br />Ms. McHughhttp://www.blogger.com/profile/14304467530751870803noreply@blogger.com0tag:blogger.com,1999:blog-3159955006478935504.post-76672936605799934102013-03-04T13:53:00.000-08:002013-03-04T17:04:25.900-08:00Fun with P.E.M.D.A.S!Teaching the order of operations is fun because the kids really put together all they have learned about multiplying, dividing, and exponents into some really difficult looking math! They really feel smart and successful! I took to the Internet to find some really creative ways to teach order of operations and to get my students something to look forward to. After first reviewing the use of parenthesis in expressions, I taught them all about my dear Aunt Sally. We also took advice from <a href="http://www.rundesroom.com/2012/04/taking-math-outside.html">Runde's Room</a> and created hopscotch squares as a kinesthetic way of learning. Unfortunately, we couldn't go outside, so we improvised and used painter's tape in our own classroom. (They even practice at indoor recess!) Check out our video!<br />
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After this, they really got into it. They even came up with their own mnemonic devices for P.E.M.D.A.S. Some of them were hilarious! My personal favorite was: Please Excuse My Dad's Awful Smell!<br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhCf58kdBgwgEcze-XjoC6MWPSyzP5ax33BBLUQA5kpOMPgd2LqeDeW34C84Hc8f76Xk-f4XXegREv3OY5LIg-jxZNTfEOHax9FNov6ixVTueCC6NNc4f4KKQpoLF3xKohha6TlPvOfB4iu/s1600/photo+1.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhCf58kdBgwgEcze-XjoC6MWPSyzP5ax33BBLUQA5kpOMPgd2LqeDeW34C84Hc8f76Xk-f4XXegREv3OY5LIg-jxZNTfEOHax9FNov6ixVTueCC6NNc4f4KKQpoLF3xKohha6TlPvOfB4iu/s1600/photo+1.JPG" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Please Excuse My Dear (Students') Awful Spelling! ;)<br />
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And of course, we just had to update our Interactive Math Notebooks. These are really turning into something special. We added a foldable that showed what P.E.M.D.A.S. means and the symbols we can look for for each. We also used the left side to duplicate our hopscotch squares (we can do finger hopscotch!) and to add our own thoughts about order of operations. Some students chose to write a letter to their future selves explaining it, while others chose to write out the steps in their own words, and still others chose to show examples. I'm really trying to embrace the left side thinking into my notebooks more. Here's to another try!<br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiBJCYixb1Dys3Xj_XxtNGgjbIoUqoMYuy4vWZ4BYEpKEN2cVESLI4HdS7lQVrmIep9zHRxgSHYI9bA1Mk9y-KR9EE9GpM45jKUzeS8c6FAXbZG3GrNcFloSTIYB9PVLa5r1tXevjF3IbgN/s1600/photo+3.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiBJCYixb1Dys3Xj_XxtNGgjbIoUqoMYuy4vWZ4BYEpKEN2cVESLI4HdS7lQVrmIep9zHRxgSHYI9bA1Mk9y-KR9EE9GpM45jKUzeS8c6FAXbZG3GrNcFloSTIYB9PVLa5r1tXevjF3IbgN/s1600/photo+3.JPG" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Check out the I <3 Math add in next to her foldable! YAY!</td></tr>
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<br />Ms. McHughhttp://www.blogger.com/profile/14304467530751870803noreply@blogger.com0tag:blogger.com,1999:blog-3159955006478935504.post-75820664973120365062013-03-04T13:29:00.000-08:002013-03-04T17:12:53.876-08:00Choosing the Appropriate GraphAs mentioned in my last post, we wrapped up our Data Analysis and Graphing unit with a project to show off what the students learned. I put the students into groups of four for this project. Also, as a change up from previous projects we have done together, I put my "high" kids all together in one group and gave them a more open project where they made more independent decisions. Then, I mixed up the rest of the kids into groups. This forced some of my other students to really step up and be leaders! They learned they don't always have to rely on the "smarties" of the group! We will have to try that more often! <br />
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Each problem provided the students with a situation and data. It was their job to figure out the most appropriate way to display the data in a graph, explain why they chose the graph they did, create the graph including a title and labels, and create analysis questions to go along with the graph. Here are some pictures of the final products! I think they did a great job :)<br />
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Here is a link to the PDF file of the project: https://docs.google.com/file/d/0B3J8ikuadOFIQ290OUgwMDdCalE/edit?usp=sharing<br />
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<tr><td class="tr-caption" style="text-align: center;">I happened to overhear my students talking about their data when one asked, "What is oldies? Like, music from the 90s?" Sigh.....</td></tr>
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<br />Ms. McHughhttp://www.blogger.com/profile/14304467530751870803noreply@blogger.com0tag:blogger.com,1999:blog-3159955006478935504.post-55631511290512432802013-02-24T14:59:00.000-08:002013-02-24T14:59:21.348-08:00Interactive Notebooks: Data Analysis<span style="font-family: Arial, Helvetica, sans-serif;">It was nice to follow our unit on fractions with a unit on data analysis and graphing. It gave ALL of our brains a nice little break! Our 4th grade teachers really did an excellent job of teaching our kids all about bar graphs, line graphs, and data landmarks. In Ohio in 5th grade, we move toward more complicated graphs such as double line graphs, double bar graphs, and circle graphs, as well as being able to look at a set of data and decide which graph would best show that data. Going into this unit, I knew I didn't want to just show my students a bunch of graphs and have them analyze them. I wanted to get them really involved and care about their data, which meant that we had a LOT of data to collect! We began with a survey:</span><br />
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<tr><td class="tr-caption" style="text-align: center;"><span style="font-family: Arial, Helvetica, sans-serif;">Each student got to pick their survey question and had to survey 20 people</span></td></tr>
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<span style="font-family: Arial, Helvetica, sans-serif;">Next, we created a frequency chart to organize the data we collected. Because we just finished our unit on fractions, we were able to change our totals into fractions, then percents. This allowed us to display our data in a bar graph as well as a circle graph. To create the circle graph, we colored a strip of centimeter grid paper in the same fashion we colored our bar graph. For example: in the picture below, Allison colored 12 squares purple because 12 people voted for math as their favorite subject (YAY!!!!), 6 squares pink for science, and so on. We cut the strip out and taped the ends together to create a circle, and made our circle graph based on the outer edge of the circle. That way, the regions in the circle graph were accurate. It also gave us a great visual for how to create a circle graph. The result is below:</span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;"> Next, we moved into double line graphs. I had assigned one student to be in charge of taking the morning temperature and afternoon temperature everyday for a week. Then, we organized our data into a chart. Next, I asked my students what they could tell from the data. It was difficult for them to come to any definitive conclusions because it was difficult to visualize how the temperature changed from morning to afternoon and day to day. So, of course, we plotted our data onto a line graph. Once all the data was in a line graph, the students were really able to see what happened to our temperature from day to day. Some conclusions they made were:</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">"It is more likely to be warmer in the afternoon than the morning."</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">"The sun doesn't have time to warm up the earth at 8 a.m. in February, but by 3 p.m. it had a chance to warm everything up."</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">"Ohio weather is really unpredictable, Ms. McHugh!"</span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;">Welcome to Ohio, kids! Allison's notebook is below:</span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;"> Next, we collected data on 4th graders who wrote with their left/right hand and 5th graders who wrote with their left/right hand so that we could create a double bar graph. I left them in charge of coming up with a title, labels and a scale. They also dictated how they wanted their chart to look. Each class had a slightly different title and slightly different charts, but their bar graphs were spot on! We also decided that while a scale of 10 wasn't optimal, it was our best choice for the size of the grid paper. The students concluded that the data would probably be pretty similar if we asked the 2nd and 3rd graders too, since the 4th and 5th were so similar. Poor lefties! </span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;"> We created foldables to show the definitions of our data landmarks. I let them use a glossary but asked them to use their own words that would make sense to them and create an example. They really know these well! (Thanks 4th grade teachers!!!!!) We will wrap up our unit on graphing with a project this week. Thanks to Friday's snow day, we had to push it back. Stay tuned!</span><br />
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<span id="goog_989610230"></span><span id="goog_989610231"></span><br />Ms. McHughhttp://www.blogger.com/profile/14304467530751870803noreply@blogger.com0tag:blogger.com,1999:blog-3159955006478935504.post-36452898284253445582013-02-24T14:10:00.003-08:002013-02-24T14:10:58.040-08:00Fun With Fractions<span style="font-family: Arial, Helvetica, sans-serif;">Fractions! It's always that time of year that requires the most focus and stamina out of my students. I really get to see their true colors and get to see just how far I can push them. We started with a pretty basic understanding of what fractions really are. We busted out the fraction squares and explored how they worked and what they showed us. This really helped, not only for my lower kids, but for my higher kids too. My high kids love to be able to show me they know the numbers, but I also like to see that they really understand what's happening, and what better way than through the use of models?</span><br />
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<tr><td class="tr-caption" style="text-align: center;"><span style="font-family: Arial, Helvetica, sans-serif; font-size: small;">Allison was kind enough to let me borrow her notebook. These fraction bars gave us a great visual to start our unit on fractions!<br /><br /></span></td></tr>
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<span style="font-family: Arial, Helvetica, sans-serif;"> We really utilized our interactive math notebooks during our fraction unit. Because this is my first year with notebooks, I haven't done a stellar job implementing the traditional left page/right page setup of notebooks. That's something I plan to tweak for next year. You'll notice that in the pics :) Anyway, back to fractions. We began by using our fraction squares to find equivalent fractions. In fact, we used fraction squares for just about everything before moving into the numbers of the problems. Once we had the models down, we talked about what was actually happening with the fractions. The visuals really helped when making that transition! Below are some of the pages we entered into our notebooks on simplifying fractions and finding equivalent fractions. </span><br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgFR6U-Q1Elo-HILZPLU9PAV9DxDWt777NkChwL_xPZEUDc14GeP6j0g9WQ7fndjnPrphtlV2vyVk2yHLj3hLu4JFV4_RADZzcU3tNvzAqtDxqvCMbwGBibmf4As8eGgXFGLZo6N_RiuuWC/s1600/photo+1+(4).JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><span style="font-family: Arial, Helvetica, sans-serif;"><img border="0" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgFR6U-Q1Elo-HILZPLU9PAV9DxDWt777NkChwL_xPZEUDc14GeP6j0g9WQ7fndjnPrphtlV2vyVk2yHLj3hLu4JFV4_RADZzcU3tNvzAqtDxqvCMbwGBibmf4As8eGgXFGLZo6N_RiuuWC/s400/photo+1+(4).JPG" width="298" /></span></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-family: Arial, Helvetica, sans-serif; font-size: small;">Step 3 is KEY! If they can't prove their work with a model, then they don't really 'get it'! We also learned how to use prime factorization as a way to find the GCF.</span></td></tr>
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<tr><td class="tr-caption" style="text-align: center;"><span style="font-family: Arial, Helvetica, sans-serif; font-size: small;">I did ask this student to go back and change what she was dividing by to look like a fraction rather than a whole number. !</span></td></tr>
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<tr><td class="tr-caption" style="text-align: center;"><span style="font-family: Arial, Helvetica, sans-serif; font-size: small;">This is one of my favorite foldables. It took us a while but it was worth it!</span></td></tr>
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<span style="font-family: Arial, Helvetica, sans-serif;"> The fraction squares were perfect for teaching how to add and subtract fractions with unlike denominators. It really was an 'ah-ha' moment for them when they saw that they could use other fraction pieces and replace them so that the result were squares of all the same size and color. </span><br />
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<tr><td class="tr-caption" style="text-align: center;"><span style="font-family: Arial, Helvetica, sans-serif; font-size: small;">Here is our foldable on adding and subtracting fractions with like and unlike denominators. </span></td></tr>
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<span style="font-family: Arial, Helvetica, sans-serif;">Here are some of the other things we did with fractions. Phew....it was a long unit!</span><br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhWIAntFLzGYjArQaN7Krh55Bve4TLV8QTBsnUBtTqExl-fpizX_GgGRLh8zWMo_hCyFpvtVlQFOhcogggIMSNbJFQTOh9_0ffMYO_orb219Z-VH2NNJff2Afofw0u57PqA3xQp_lPZ7d1D/s1600/photo+1+%25282%2529.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><span style="font-family: Arial, Helvetica, sans-serif;"><img border="0" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhWIAntFLzGYjArQaN7Krh55Bve4TLV8QTBsnUBtTqExl-fpizX_GgGRLh8zWMo_hCyFpvtVlQFOhcogggIMSNbJFQTOh9_0ffMYO_orb219Z-VH2NNJff2Afofw0u57PqA3xQp_lPZ7d1D/s400/photo+1+%25282%2529.JPG" width="298" /></span></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-family: Arial, Helvetica, sans-serif; font-size: small;">This page was totally independent. Up until this point, I had written up notes for them. Starting now, they are coming up with their own notes and steps! I think they did a pretty good job on their first try!</span></td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhH_l7cV-izxoQ0qI3QsZrgSU6xZJBkzNuRlVz9vlbq1iIT2VPN3q1IunGZtSBJzG4lZo_cOIqKQUHMHINieVg4fjtuiTTBJksMhKPi3Ogvdo6sdnRTYvcfRWTVTX4XzFBqNKo4OEDw8esI/s1600/photo+2+%25282%2529.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><span style="font-family: Arial, Helvetica, sans-serif;"><img border="0" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhH_l7cV-izxoQ0qI3QsZrgSU6xZJBkzNuRlVz9vlbq1iIT2VPN3q1IunGZtSBJzG4lZo_cOIqKQUHMHINieVg4fjtuiTTBJksMhKPi3Ogvdo6sdnRTYvcfRWTVTX4XzFBqNKo4OEDw8esI/s400/photo+2+%25282%2529.JPG" width="298" /></span></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-family: Arial, Helvetica, sans-serif; font-size: small;">Here is a sample problem adapted from a former OAA test question. I wanted to see if they knew to change the fractions to percents and the percents to fractions. Most got it!</span></td></tr>
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<tr><td class="tr-caption" style="text-align: center;"><span style="font-family: Arial, Helvetica, sans-serif; font-size: small;">Fractions -->Decimals --> Percents foldable</span></td></tr>
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<br />Ms. McHughhttp://www.blogger.com/profile/14304467530751870803noreply@blogger.com0tag:blogger.com,1999:blog-3159955006478935504.post-55541883267524792912012-12-17T12:43:00.002-08:002012-12-17T12:46:31.328-08:00Digging into the Common Core: Deep Division!<span style="background-color: white; font-family: 'Lucida Sans Unicode', 'Lucida Grande', sans-serif; font-size: 14px;">We are just wrapping up our unit on division, and I wanted to know if they really understood what it is, so I decided to have them create their own problems. In order to get their best work, I told them we would be compiling our problems into a book to be given to our principal for Christmas. <a href="http://www.k-5mathteachingresources.com/5th-grade-number-activities.html">K-5 Math Teaching Resources </a> is a fantastic site for problems and activities aligned to the Common Core Standards. I found a problem aligned with 5.NBT6: Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. The students were asked to:</span><br />
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<span style="background-color: white; font-family: 'Lucida Sans Unicode', 'Lucida Grande', sans-serif; font-size: 14px;">1. Create a word problem that could be solved by dividing a three digit dividend by a two digit divisor.</span><br />
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<span style="background-color: white; font-family: 'Lucida Sans Unicode', 'Lucida Grande', sans-serif; font-size: 14px;">2. Estimate the answer to your problem. Explain your strategy.</span><br />
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<span style="background-color: white; font-family: 'Lucida Sans Unicode', 'Lucida Grande', sans-serif; font-size: 14px;">3. Solve your problem. Show all your work.</span><br />
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<span style="background-color: white; font-family: 'Lucida Sans Unicode', 'Lucida Grande', sans-serif; font-size: 14px;">4. Use a different method of solving your problem to check that your answer is accurate. Explain your strategy. </span><br />
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<span style="background-color: white; font-family: 'Lucida Sans Unicode', 'Lucida Grande', sans-serif; font-size: 14px;">I was really looking to see if they knew the difference between the operations. We have discussed clue words here and there but not in depth. Most students were on the right track; only a couple did an addition or subtraction problem. I made them peer edit their problems before putting them on good paper. The front showed the problem, while the back showed their estimate and solution. We had a blast! They are really proud of their problems, and most included me eating cookies....I wonder where they got that idea? :)</span><br />
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<span style="background-color: white; font-family: 'Lucida Sans Unicode', 'Lucida Grande', sans-serif; font-size: 14px;">Here are some fantastic examples of our work!</span><br />
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<span style="background-color: white; font-family: 'Lucida Sans Unicode', 'Lucida Grande', sans-serif; font-size: 14px;"><br /></span>Ms. McHughhttp://www.blogger.com/profile/14304467530751870803noreply@blogger.com0tag:blogger.com,1999:blog-3159955006478935504.post-47141899370823025942012-12-15T12:30:00.000-08:002012-12-15T15:09:07.878-08:00Number Talks: Division <br />
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<span style="font-family: Arial, Helvetica, sans-serif;">We've been doing a lot of division lately and I began to notice that the preferred method is the traditional algorithm, mainly because that’s what parents are more comfortable with at home when helping with homework. Because of this, I was noticing that if students made a mistake in following the steps, they really didn't notice they were making a mistake, let alone that their answer was not reasonable. So, I decided to encourage more mental math. We did this through some number talks and the use of slates. In previous Number Talks, I didn't allow my students to write anything down to force them to do work mentally, however, for the division number talks (at least at first) I allowed them to write down their thinking on slates so they wouldn't confuse themselves. The only stipulation was that they weren't allowed to divide the “normal way.” No “houses!” </span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;">We started with smaller, simpler numbers: 25 ÷ 4. Here is a picture of their thinking:</span></div>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhPJUCp8Iu9m0Bpyhj5Xje5sng2c8rluX3sEscubUGXSzZ94ayL-P_jk9X8oh6leAxger9EfSdxV5Cv5BhEzkLIWizfwp9QpD0qls_21iv17xVm4MOW-4MzLoYxzZarLeF7tP25zOoLXBAM/s1600/IMG_1934+(2).JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><span style="font-family: Arial, Helvetica, sans-serif;"><img border="0" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhPJUCp8Iu9m0Bpyhj5Xje5sng2c8rluX3sEscubUGXSzZ94ayL-P_jk9X8oh6leAxger9EfSdxV5Cv5BhEzkLIWizfwp9QpD0qls_21iv17xVm4MOW-4MzLoYxzZarLeF7tP25zOoLXBAM/s400/IMG_1934+(2).JPG" width="298" /></span></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-family: Arial, Helvetica, sans-serif; font-size: small;">Molly began by saying, "I know that 4 x 5 = 20 , and that was too small, so I added another group of 4 to get to 24. Then, I knew I just had to add one more to get to 25. So I had 6 groups of 4 with one left over."</span></td></tr>
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<span style="font-family: Arial, Helvetica, sans-serif;">Once some students saw how others were using basic facts to help them, they began to catch on. More and more students began volunteering their thinking. This is something we will continue to build a knowledge base of. My hope is that this will lead my students to a greater understanding of division and answers that are reasonable.</span></div>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhoOz70ClUPOPDV3Pusc3Z11PU9GcEtIxIsNc4OXPqtY6dfQZYJoJnQu5_RvdbP2iofiRYKIpahfO6bl6_KdORBuBVvAWsWYMZ6e8QKQO2HX7krWbNnjANkpnefu3cAF06NVHGopTs38FaN/s1600/IMG_1917.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><span style="font-family: Arial, Helvetica, sans-serif;"><img border="0" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhoOz70ClUPOPDV3Pusc3Z11PU9GcEtIxIsNc4OXPqtY6dfQZYJoJnQu5_RvdbP2iofiRYKIpahfO6bl6_KdORBuBVvAWsWYMZ6e8QKQO2HX7krWbNnjANkpnefu3cAF06NVHGopTs38FaN/s400/IMG_1917.JPG" width="298" /></span></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-family: Arial, Helvetica, sans-serif; font-size: small;">Blake is one of my students that has an amazing sense of numbers: he does almost all of his calculations mentally. I always try to see what he is thinking to guide the other students. </span></td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjntMU0Q97uptbpW8C3mL9iSrtbFIXZ8AmWM_i_LztwVLb8z-bD4SwqqkTdP3CQAqU_7FtkOnjdTwZzIpL7W9r3cBu6g1c26HKSOpN6qJ6GtcGmAb3OSwhDs3s0fYzKcptg8gUKQFiC0CoL/s1600/IMG_1933.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><span style="font-family: Arial, Helvetica, sans-serif;"><img border="0" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjntMU0Q97uptbpW8C3mL9iSrtbFIXZ8AmWM_i_LztwVLb8z-bD4SwqqkTdP3CQAqU_7FtkOnjdTwZzIpL7W9r3cBu6g1c26HKSOpN6qJ6GtcGmAb3OSwhDs3s0fYzKcptg8gUKQFiC0CoL/s400/IMG_1933.JPG" width="298" /></span></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-family: Arial, Helvetica, sans-serif; font-size: small;">This was a great example of two students building from something they already knew: multiples of ten. I love how one counted up from ten and the other counted down from 20!</span></td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgmINGHVhJDn5uS5atBIfXdOx8eX7VDxdUBZNVfWUOqu5XOHJnFojURHJAy7KoHsl-2iY1kKTs83eAab4IKN51bPng56J7BU5LvFd0cdY9QLt4ybOz4K6PJEbev3AjLeKOuxxosjh9b5ODz/s1600/IMG_1934.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><span style="font-family: Arial, Helvetica, sans-serif;"><img border="0" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgmINGHVhJDn5uS5atBIfXdOx8eX7VDxdUBZNVfWUOqu5XOHJnFojURHJAy7KoHsl-2iY1kKTs83eAab4IKN51bPng56J7BU5LvFd0cdY9QLt4ybOz4K6PJEbev3AjLeKOuxxosjh9b5ODz/s400/IMG_1934.JPG" width="298" /></span></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-family: Arial, Helvetica, sans-serif; font-size: small;">Jillian wasn't afraid to say she started with a fact that was too low and built her way from there! I always encourage them to admit when they make a mistake and tell us how they found it and fixed it! Chances are, they aren't the only one making that mistake!</span></td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgU2aRYmEhcJIViW7drcrFkbOlIiM2Er6LSib2ufMeLQiVLLGoXcFWXvQB9h7VKQLByh3xLQk7l9lnW57m1zZBEEa6k-Np-U7KqASgpDFOODovXHdc0VPYU8vLA64eR56BFLbCSK9MVSKLF/s1600/IMG_1935.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><span style="font-family: Arial, Helvetica, sans-serif;"><img border="0" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgU2aRYmEhcJIViW7drcrFkbOlIiM2Er6LSib2ufMeLQiVLLGoXcFWXvQB9h7VKQLByh3xLQk7l9lnW57m1zZBEEa6k-Np-U7KqASgpDFOODovXHdc0VPYU8vLA64eR56BFLbCSK9MVSKLF/s400/IMG_1935.JPG" width="298" /></span></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-family: Arial, Helvetica, sans-serif; font-size: small;">We are really improving and they are finally telling me how much they love math!</span></td></tr>
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Ms. McHughhttp://www.blogger.com/profile/14304467530751870803noreply@blogger.com0tag:blogger.com,1999:blog-3159955006478935504.post-34970216578510614742012-12-03T18:19:00.000-08:002012-12-03T18:19:07.124-08:00Division!Oh the joys of division! For whatever reason, my students are afraid, deathly afraid of division. From their pre-assessments, I could tell they weren't really thinking of the actual numbers being divided, but more concerned with the PROCESS, and because of this were making silly, careless errors and their answers made no sense! So, I decided to start at the basics: the concept of division and how it relates to multiplication. We soon moved on to estimation and using compatible numbers (multiples of ten) to help us solve. On Friday, we explored three different ways to divide.<br />
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We began by using base-ten blocks. We are pretty good at using them after using them for modeling decimals as well as multiplication. They knew that if they didn't have enough flats (100's) to fill in the groups evenly, they would have to break one into ten 10's and go from there. I was extremely happy that they were so fluent in this from adding and subtracting decimals! They had no idea they could divide this way. I chose some of my struggling students to model this in front of the class. They were extremely successful and were proud to show the class even they could divide large numbers. Here are some pics of Sam and Bobby dividing using models:<br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjt5Mk1lx38-xglyV8ZU7AYhYVozhZhnHBJdwIUgIYsqmKqytnASd-W09fWTiwhV1qDGqXMqVg_dOfo4f-JhsZ7fncqMnoE6CZOCOyuN3i7gyZV5cm1wBk-Hy1kszyVEE-q1tEQ6GRhOOnt/s1600/IMG_1853.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjt5Mk1lx38-xglyV8ZU7AYhYVozhZhnHBJdwIUgIYsqmKqytnASd-W09fWTiwhV1qDGqXMqVg_dOfo4f-JhsZ7fncqMnoE6CZOCOyuN3i7gyZV5cm1wBk-Hy1kszyVEE-q1tEQ6GRhOOnt/s400/IMG_1853.JPG" width="298" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Sam had to break a long into 10 ones! He did a great job!</td></tr>
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Next, we moved on to using the distributive property and expanded notation to divide. The kids are pretty proficient in writing numbers in expanded notation, so we really just had to take it a step further to create the area model. Here is Allison using her whiteboard to solve. You can see she broke 248 into 200+40+8, then divided each part by two, and finally added her quotients. Her area model is below, except I caught her before she had completed it, but you get the idea!<br />
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Below: Max bypassed drawing the model and opted instead to just divide each part by three. Then, he added up the quotients.<br />
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Lastly, we learned the partial quotients method for division. Personally, this is my favorite. It allows kids who aren't as proficient in their math facts to still be successful in division. It also really shows the value of the numbers, something my students clearly struggle with. Here is a shot of Keegan flying through a problem with ease. I think he's found his favorite way to divide!<br />
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Today, after a long, warm weekend of fun, we spent some time going back over each method for division. I split the kids up into partners: a student who "gets it" with a student who doesn't. They really worked well together and as I circulated I heard the helpers saying things like "how many times does 3 go into 400-some? Does it go in at least 10 times? Do you think we can go higher?" Sometimes, all it takes is some guidance from a peer rather than teacher lady. I'm OK with that! <br />
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Lastly, we created anchor charts showing the ways for division. We added a fourth way, the traditional way. I found that my "high" kids like the traditional way, and I'll let them use it as long as they can explain each step using place value! (Muahahahaha!) Don't forget to check out our <a href="http://www.youtube.com/watch?v=ICQOkKM_tyM">division math rap on YouTube!</a><br />
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<b>Common Core Connection</b>: Standard: Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.<br />
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<b>Mathematical Practices</b>: Make sense of problems and persevere in solving them.<br />
<br />Ms. McHughhttp://www.blogger.com/profile/14304467530751870803noreply@blogger.com0tag:blogger.com,1999:blog-3159955006478935504.post-82501690547730870532012-11-21T13:00:00.002-08:002012-11-21T13:00:41.919-08:00Number Talks<span style="font-family: Arial, Helvetica, sans-serif;">As previously mentioned, our district has the fortunate opportunity to train teachers on the CCSS. In addition to discussing RICH problems and how they can be used in our own classrooms, we conduct Number Talks. We use the book <u>Number Talks: Helping Children Build Mental Math and Computation Strategies, Grades K-5</u>, by Sherry Parrish as a resource. Number Talks were designed to improve students' mental computation skills and number sense. <a href="http://www.insidemathematics.org/index.php/classroom-video-visits/number-talks"> Inside Mathematics</a> is another fantastic resource that shows how different teachers in varying grade levels apply Number Talks to their lessons. In fact, this is a wonderful website that allows you to see teachers in action applying the Common Core Practice Standards! Woo! </span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;">Anyway, we have been doing our best to introduce these talks into our classroom. In my room, students sit together right in front of the board. I tell them to summon their inner Kindergartner, which they giggle at. We have only had time for a couple "formal" Number Talks, but we are beginning to apply it in all aspects of our day when answering questions verbally. Here is an example of how my students were able to solve a basic addition problem using mental math and their process for doing so: </span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;">Are they stellar? Probably not. My students were looking at me like I was a crazy person that day. They didn't quite understand why understanding how to compose and decompose numbers is so important. Many said, "I put them on top of each other and added. I also carried the one." My point was that I wanted them to know what "carrying the one" actually meant. As we do more, they do improve, and I can see it translating in other areas of math. They are really starting to think about the VALUE of the numbers. </span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;">I plan on doing more complex problems as we go and seeing how they improve. I told them I would keep their original posters so we can compare them to how they are doing in a few months. They have already drastically improved! If you don't do Number Talks in your classroom, I highly recommend you look into incorporating them every now and then, especially in younger classrooms!</span>Ms. McHughhttp://www.blogger.com/profile/14304467530751870803noreply@blogger.com0