tag:blogger.com,1999:blog-4357907418884172182016-12-26T05:46:57.463-05:00Math BrattSarahhttp://www.blogger.com/profile/15836775412858228674noreply@blogger.comBlogger18125tag:blogger.com,1999:blog-435790741888417218.post-70857484720187408332012-08-19T07:24:00.002-04:002012-08-19T07:25:34.003-04:00Stop.Start.Continue. #MSSunFunToday is my last day of summer. We are back tomorrow for a day of PD. Tuesday is a work day but I will have a few meetings that will eat up most of my morning. I'm heading in today to hopefully finish organizing my room. I moved over a room so I had to relocate a few things. We still don't have all of the results from our state testing. I find it frustrating to plan for this year, when I don't have data from last year. So much for data driven decisions...<br /><br />I'm not much for writing elaborate goals, but here are a few of the ideas that come to mind. After reading everyones' some others will come surely come to mind.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://3.bp.blogspot.com/-u9-m4HFb5i4/UCaqbp7Im5I/AAAAAAAAAEY/_gARWY_eCZo/s1600/MSSunFun.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://3.bp.blogspot.com/-u9-m4HFb5i4/UCaqbp7Im5I/AAAAAAAAAEY/_gARWY_eCZo/s1600/MSSunFun.png" /></a></div><br /><br /><br />STOP<br /><ul><li>Talking so much.</li><li>Worrying about everything.</li><li>Eating everything left in the teachers' lounge.</li><li>Holding on to hurt feelings for something that happened > a year ago (feeling less angry now - just hurt). I'm hoping to heal more this year. </li></ul><div><br />START</div><div><ul><li>Making videos for my YouTube Channel - for parents and students (more on this later)</li><li>Better defining the role of the intervention specialist in the classroom</li><li>Being better organized - (love my new teacher binder this year - thanks for all the great ideas)</li><li>Being more consistent with homework consequences.</li><li>Moving my grading back to SBG (got away from it last year)</li><li>Being a better listener. </li><li>Using students' technology (Socrative)</li></ul></div><div><br /></div><div>CONTINUE</div><div><ul><li>Working with my instructional coach.</li><li>Being flexible in my plans and adjusting to student needs.</li><li>Thinking differently about the structure of my class.</li><li>Think, Pair, Share - get students talking.</li><li>Finding time for small group instruction (just need to find more times for it)</li><li>Trying to be less helpful.</li><li>Blogging.</li></ul></div><div><br /></div><div>I am really excited to meet my new students on Wednesday!</div>Sarahhttp://www.blogger.com/profile/15836775412858228674noreply@blogger.com1tag:blogger.com,1999:blog-435790741888417218.post-72631864014950311852012-08-17T00:01:00.000-04:002012-08-17T13:27:15.512-04:00#MyFavFriday - My Instructional Coach <div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-jaiw9OeeWQk/UCTuX51qM_I/AAAAAAAAADw/pxkVSLpoHPU/s1600/MFF.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="220" src="http://2.bp.blogspot.com/-jaiw9OeeWQk/UCTuX51qM_I/AAAAAAAAADw/pxkVSLpoHPU/s320/MFF.jpg" width="320" /></a></div><br /><br />I love working with my friend and colleague Jonily. When I started teaching in my current school she was teaching at one of the other middle schools. My school district gave us many opportunities to work with teachers in the other buildings. 6+ years ago my district added instructional coaching positions at the elementary and middle school level. Jonily and I moved into the MS math positions so I had the opportunity to work even closer with her. She has really influenced how I think about teaching and learning. Kids always come first. She has an amazing ability to see how students build their understandings and connect mathematics. The coolest thing is that she is able to present things so that average people like me can also begin to see teaching and learning as she sees it. <br /><br />Check out her <a href="http://www.mindsonmath.com/" target="_blank">website</a>. You can sign up for a weekly newsletter where she shares some of her awesomeness. The latest newsletter is below. <br /><br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-GE3XeNFOPs4/UCpfm1N4UTI/AAAAAAAAAFA/AhDG8upHC7c/s1600/DSCF8240.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="240" src="http://2.bp.blogspot.com/-GE3XeNFOPs4/UCpfm1N4UTI/AAAAAAAAAFA/AhDG8upHC7c/s320/DSCF8240.JPG" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-7OKAZoLqzow/UCpgB4BEklI/AAAAAAAAAFI/e5fMfrI43ow/s1600/IMG_3344.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="213" src="http://1.bp.blogspot.com/-7OKAZoLqzow/UCpgB4BEklI/AAAAAAAAAFI/e5fMfrI43ow/s320/IMG_3344.JPG" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><blockquote><blockquote><table border="0" cellpadding="0" cellspacing="0" style="background-color: white; color: #0e5daf; font-family: Verdana, Arial, Helvetica, sans-serif; font-size: 12px; text-align: justify; width: 100%px;"><tbody><tr><td style="padding-bottom: 6px;"><blockquote class="tr_bq"><span style="color: #0e5daf; font-size: small;">Hello from "The Math Girl"!</span></blockquote></td></tr></tbody></table><span style="color: black; font-family: Arial,sans-serif; font-size: xx-small;"><span style="font-size: 12px;">To continue our theme of "Teaching with Questions," this week I will introduce the Candy Probem. I will refer to the Candy Problem all year and extend the amount of content that can be drawn from this single situation. The problem can be given to ALL ages from 1st grade through Algebra! Keep in mind that the questions we ask are the most important instructional pieces of any task or problem. These questions will guide the instructional process and will open the door for exploration of grade level content throughout the Common Core State Standards. The purpose of the questions we ask is to generate mathematical thinking. The more questions generated for each problem or task, the longer the problem can be extended (even while introducing additional situations, tasks and problems). </span></span><span style="color: black; font-family: Arial,sans-serif; font-size: xx-small;"><span style="font-size: 12px;"><span style="font-size: x-small;"><b>Brace yourself! This email is a long one this week!!</b></span></span></span>Begin by introducing the situation:<br /><u>The Candy Problem</u><b>Two boys share 80 candies in the ratio 2:3</b>Next, ask students...<br /><b>What math questions can you create for this situation?</b><span style="color: black; font-family: Arial,sans-serif; font-size: xx-small;"><span style="font-size: 12px;">Give students some time to generate creative math questions. Collect questions as a class and either answer some now or save for later!</span></span>Now ask students...<br /><b>How many candies will each boy get? How do you know?</b> To eliminate the discussion and instruction of "ratio" for students below grade 4, phrase the situation, Two boys share 80 candies with boy 1 getting 2 pieces and boy 2 getting 3 pieces. Emphasize that "sharing" is not always equal. Students can act out, use manipulatives and/or draw a picture of the situation. The pupose of this task for younger students is to begin building the ideas of ratio, proportional reasoning and algebraic thinking by doing and exploring mathematics.<br /> Do not give this alternative form of the situation to students in grades 4 and higher. One of the purposes of having students answer the question "How many candies does each boy get?" is to use student responses as an assessment. Maybe even have students put their initial "guesses" on a post it or index card with their name to turn in.<br /> Also for students in grades 4 and higher, do not initially define ratio as a class. Again, use this problem as an assessment of their knowledge of ratio.<br /> **Look for students who initially say that each boy gets 40 pieces of candy. These students have limited knowledge of ratio. Document these students names and move on.<br />At this point, a variety of next steps could happen based on the mathematical understanding of the students in your class, or the grade level you are teaching.<br />1. Teach a mini-lesson on ratio using the example "What is the ratio of boys to girls in this classroom?" (Emphasis on MINI - - - the lesson should be no more than 10-15 minutes) Discuss equivalent forms of that ratio. Could extend the discussion, now or at a later time, to ask "If the ratio of boys to girls in our school was the same as the ratio in our classroom, how many total students are there if there are _______ boys? For most students, especially struggling students, encourage the use of a variety of strategies to figure this out - NOT setting up and solving a proportion!<br />2. Discuss the possibility of each boy getting 40 pieces. If the boys end up with the same amount of candy, then they will always have the same amount of candy. What ratios are equivalent to 40:40? At one point both boys had 20 pieces - the ratio 20:20. Get students to continue to move toward how many pieces each boy would have gotten to begin with (1:1). Point out that the ratio 1:1 is not the same as the ratio 2:3. Show with drawings, manipulative or even actual candy what the "Passing out of candy" looks like for the ratio 1:1 and then for the ratio 2:3.<br />3. Give students time to explore the problem by acting it out, using manipulatives or drawing a picture. Have many discussions about what is happening and what is the mathematics involved.<br />4. Eventually, have students create a TABLE of the information and look for patterns.<br />5. Relate the amount of candies each boy has at each "passing outing" to the multiples of that number.<br />Additional Questions:<br />1. What fraction of the candies does boy 1 get?<br />2. What fraction of the candies does boy 2 get?<br />3. What percent of the total candies does each boy end up with?<br />4. What is the difference between a "part-to-part" and a "part-to-whole" ratio?<br />5. How is a ratio the same as a rate? How are they different?<br />6. What algebraic equation can you write to solve this situation?<br />7. At what rate does each boy get candy?<br />8. How many candies does boy 1 have after the 7th passing outing?<br />9. How many candies will boy 2 have after the 50th passing outing?<br />10. If the two boys still share candies in the ratio 2:3, what total candies can there be so that no candies are left over after all passing outings?<br />11. If the two boys still share a total of 80 candies, what ratios are possible so that no candies are left over after all passing outings? Is the ratio 1:4 possible? Is the ratio 1:2 possible?<br />12. (Another variation) If 2 boys share 90 candies in the ratio 2:3, how many candies does each boy get? **Look for students who say 45 and 45. Again, these students have a limited understanding at this point. Document these students names and flag for intervention.<br /><span style="color: black; font-family: Arial,sans-serif; font-size: xx-small;"><span style="font-size: 12px;">Do not worry about the levels of understanding of students!! Make sure to document levels of understanding and note which students need extention and which students need intervention, BUT just HAVE FUN engaging students in mathematics!! This will build the classroom culture and climate of THINKING and LEARNING!! Let students DO MATH themselves, not watch you do all of the math!</span></span>As teachers, let's reflect on these questions:<br /><b>What other math questions can be asked related to this situation?</b><b>What other variations of the situaion are possible?</b><b>What is all of the additional math content that can be drawn out from this situation?</b><br />-Jonily Zupancic<br />"The Math Girl"</blockquote><div style="background-color: white; color: #0e5daf; font-family: Verdana, Arial, Helvetica, sans-serif; font-size: 12px; margin: 5px 0px; text-align: justify;"><span style="color: black; font-family: Arial,sans-serif; font-size: xx-small;"><span style="font-size: 12px;"></span></span><br /><div style="margin-bottom: 14pt; margin-top: 14pt;"><span style="color: black; font-family: Arial,sans-serif; font-size: xx-small;"><span style="font-size: 12px;"><a href="https://email.gjps.org/owa/redir.aspx?C=f00dba02c55d4a3cb9aaedebd263e514&URL=http%3a%2f%2fclicks.aweber.com%2fy%2fct%2f%3fl%3d7LBKw%26m%3d3ZCN_TZ5D7HMBGr%26b%3d2abAjM7FV1XlA8eAYLbhug" target="_blank">www.mindsonmath.com</a></span></span></div><span style="color: black; font-family: Arial,sans-serif; font-size: xx-small;"><span style="font-size: 12px;"></span></span></div></blockquote><div class="paragraph" style="background-color: white; font-family: Arial, sans-serif; font-size: 12px; margin: 5px 0px;"><span style="font-size: x-small;"></span></div>Sarahhttp://www.blogger.com/profile/15836775412858228674noreply@blogger.com1tag:blogger.com,1999:blog-435790741888417218.post-11931169288954346722012-08-13T00:00:00.000-04:002012-08-13T00:58:31.748-04:00#Made4Math Address Labels<div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-8GkwzkaYgoY/UCga-bE9uxI/AAAAAAAAAEw/iJi8-Ja02WY/s1600/made4math.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://1.bp.blogspot.com/-8GkwzkaYgoY/UCga-bE9uxI/AAAAAAAAAEw/iJi8-Ja02WY/s1600/made4math.png" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;"><span style="text-align: -webkit-auto;">I like for students and parents to have websites and emails in a you-really-can't-lose-it place. I started printing the information on address labels and having the students stick them inside their planners. Once they lose their planner we will stick one on the inside of their math binder. Parents can pick one up at Open House to put in their planner. Next year I plan on making them much cuter. You'll have to check out @4mulafun's. Her's are super cute. </span></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"></div><br /><br /><br />Sarahhttp://www.blogger.com/profile/15836775412858228674noreply@blogger.com4tag:blogger.com,1999:blog-435790741888417218.post-26487649169832254052012-08-12T08:05:00.000-04:002012-08-12T08:05:10.342-04:00#MSSunFun - Notebooks<div class="separator" style="clear: both; text-align: center;"><a href="http://3.bp.blogspot.com/-u9-m4HFb5i4/UCaqbp7Im5I/AAAAAAAAAEY/_gARWY_eCZo/s1600/MSSunFun.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://3.bp.blogspot.com/-u9-m4HFb5i4/UCaqbp7Im5I/AAAAAAAAAEY/_gARWY_eCZo/s1600/MSSunFun.png" /></a></div><br /><br />I guess for this to make sense I need to describe a bit of my classroom structure. My class is made up of average to below average math students. I also have a large population of special education or other at risk students. We teach everything all the time. There are not traditional units and ideas are constantly coming back during instruction and learning. All quizzes and tests are cumulative. <br /><br /><br /><br />My students use a 3 ring binder with dividers for their math notebooks.<br /><br /><h4>Section 1 - Do Now</h4>This is the largest section of their notebook. Each day students come into the room and begin the Do Now (warm-up). It is usually a combination of old and new concepts. Sometimes it will take 5 minutes and other days it is the lesson. The idea is to have students engaged and working problems to develop understandings. <br /><br /><h4>Section 2 - Keep Forever Notes</h4>I don't expect my students to take notes everyday but they are expected to do mathematics. Once we have discussed and tossed around a concept enough I will provide a graphic organizer or formal notes page for my students. Each page is usually a different color so it is easier to reference and find.<br /><br /><h4>Section 3 - Quizzes/Tests</h4>All are cumulative. Last year I had 1 cumulative test and 3 quizzes each 9-weeks. <br /><br /><h4>Section 4 - Oldies But Goodies</h4>This is the homework section. Homework is also cumulative. Oldies but Goodies (OBGs) are given to students on Monday and due back on Friday. This is not a formal part of a students grade. Usually the quizzes mirror the feel of an Oldies but Goodies.<br /><br /><h4>Section 5 - Other</h4>Anything that doesn't fit anywhere else (practice worksheet, group activity, etc.)<br /><br /><br />Sarahhttp://www.blogger.com/profile/15836775412858228674noreply@blogger.com1tag:blogger.com,1999:blog-435790741888417218.post-91192934714012986332012-08-10T18:20:00.001-04:002012-08-10T18:20:47.337-04:00My Favorite Friday - Conversation Cards<div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-jaiw9OeeWQk/UCTuX51qM_I/AAAAAAAAADw/pxkVSLpoHPU/s1600/MFF.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="220" src="http://2.bp.blogspot.com/-jaiw9OeeWQk/UCTuX51qM_I/AAAAAAAAADw/pxkVSLpoHPU/s320/MFF.jpg" width="320" /></a></div><br /><br />I attended a workshop many, many years ago and they used photos to spark discussion at each group of teachers. It was fun and easy to open up. <br /><br />Have you ever seen the <a href="http://www.amazon.com/Blue-Book-Bradley-Trevor-Greive/dp/0740704818" target="_blank">Blue Day Book</a> by Bradley Trevor Greive? I can't help but love the photographs. I picked up a few of his other books and began cutting the pages apart. <br /><br />This is what I ended up with<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-pkOsRoYtFTo/UCWGh9d-sII/AAAAAAAAAEA/c5xsdT53Y-s/s1600/IMG_0590.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="240" src="http://1.bp.blogspot.com/-pkOsRoYtFTo/UCWGh9d-sII/AAAAAAAAAEA/c5xsdT53Y-s/s320/IMG_0590.JPG" width="320" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://3.bp.blogspot.com/-EYupEsqSC50/UCWGn7BvGHI/AAAAAAAAAEI/0Y8Z-PtLkAQ/s1600/IMG_0591.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="240" src="http://3.bp.blogspot.com/-EYupEsqSC50/UCWGn7BvGHI/AAAAAAAAAEI/0Y8Z-PtLkAQ/s320/IMG_0591.JPG" width="320" /></a></div><br /><br /><br /><br /><br />I will ask students to choose the photo that best represents how they feel about ___________ (test, math, next year, etc.). Sometimes they will share out with the group or I will have them write about it. This has worked well with groups who have been more hesitant to share or open up. <br /><br /><br /><br /><br />Sarahhttp://www.blogger.com/profile/15836775412858228674noreply@blogger.com5tag:blogger.com,1999:blog-435790741888417218.post-58902330712500045442012-08-05T13:50:00.001-04:002012-08-05T13:50:11.605-04:00#MSMath First Day ActivitiesI love starting with math the very first day of school. <br /><div><br /></div><div>As 6th graders students do the <a href="http://connectedmath.msu.edu/CD/Grade6/Locker/index.html">Locker Problem</a>. Well, an extended version of it. We try as much as we can to find problems where we can integrate multiple skills and connections. </div><div><br /></div><div>I have 8th graders so we will be revisiting the Locker Problem. It will be interesting to see how much the students remember and how they will react when we connect new ideas to it. </div><div><div><br /></div><div>The outline of how I will do it is <a href="http://msmathwiki.pbworks.com/w/page/55399779/Rich%20Tasks%20in%20Middle%20School">here</a>. I <b>quickly</b> presented it at TMC12. The document is still in draft form and not complete. </div><div><br /></div><div>We'll get to the get-to-know-you stuff later and organize the binders next week. Let's jump in and do some math!!!</div><div><br /></div><div><br /></div><div><br /></div><div><br /></div></div>Sarahhttp://www.blogger.com/profile/15836775412858228674noreply@blogger.com2tag:blogger.com,1999:blog-435790741888417218.post-54556799909651328282012-08-01T22:38:00.000-04:002012-08-01T22:38:09.908-04:00#TMC12 and My Irrational FearMy first steps into the Twitterblogosphere started with finding a few wonderful blogs. I read and read and read some more. Then I noticed the bloggers were also on twitter. I lurked for an obnoxious amount of time and jumped in a few times but not enough for anyone to really get to know me. At TMC I wasn't at all surprised that people didn't really know me that well. I just hadn't really put myself out there. <br /><br />I started my blog a few years ago to help me sort out some of the ideas I had for the class I had to pick up. For 6 years I was an Instructional Coach for my Middle School. That position was eventually cut and I found myself back in the classroom. The problem with the blog is that I have a completely irrational fear of writing. The thought of a 1 page reflection paper sends me over the edge. College was a nightmare. Tears, tears and more tears. I'm still not sure how I made it through. Fast forward to Math Bratt. It died. I know I have stuff to share. Stuff I really want to share but the words always escape me. Those of you who meet me in person know I have stuff to share and you are allowed to tell me to shut up once in a while. <br /><br />Everyone has already written so much of how I feel about TMC12. I never could have put all of my emotions in words as well as everyone else. Thank you for writing what I could not. But most of all, <b>thank you for believing in me</b> and encouraging me to write. Even if it is difficult. I have the strength to do it because of all of you. How could anyone not be inspired by each and every one of you?<br /><br />Please forgive me when my posts are less than eloquently written. I hope you read them anyway.Sarahhttp://www.blogger.com/profile/15836775412858228674noreply@blogger.com7tag:blogger.com,1999:blog-435790741888417218.post-56346999460800324802012-07-24T20:37:00.001-04:002012-07-24T20:37:49.947-04:00Subtracting IntegersIn one of the middle school sessions at TMC12 we were talking about integers and how students struggle especially with subtraction. We were brainstorming different strategies (chips, number lines, rules, etc.) This is the distance strategy I shared with the group.<br /><br />When working with students it is important for them to understand that subtraction is more than just "take away". Yes, we can figure 25 - 3 as "You have 25 candies in your hand and you eat 3. What do you have left?" but that limits us when we expand to include integers. <br /><br />Using a number line students can also recognize that the distance between 25 and 3 is also 22. Continue building on what students know.<br /><br />13 - 4 = 13 take away 4 but also the distance between 13 and 4<br /><br />So what happens when you switch it?<br /><br />4 - 13<br /><br />Many students will intuitively notice the result would have to be negative. What is the distance between 4 and 13? It is the same as 13 and 4 only it is negative because the smaller number is first.<br /><br />*Students have to understand the above to be able to move forward.<br /><br />9 - (-2) = the distance between 9 and -2, notice 9 is larger than -2 = 11<br />-2 - 9 = the distance between -2 and 9, notice the -2 is smaller than 9 = -11<br />-3 - (-8) = the distance between -3 and -8, notice the -3 is larger than -8 = 5<br /><br />If students have trouble determining the distance, provide a number line. Counting on to determine how far apart numbers are is another strategy that some students might need practice with.<br /><br />-135 - 124 =<br />(the distance from -135 to 0 is 135, the distance from 0 to 124 is 124 so the distance from -135 to 124 is 135 + 124)<br /><br /><br /><br /><br />Sarahhttp://www.blogger.com/profile/15836775412858228674noreply@blogger.com8tag:blogger.com,1999:blog-435790741888417218.post-7770117718373462792011-06-30T22:40:00.004-04:002011-06-30T23:01:50.804-04:00Sierpinski's Triangle - 8th gradeHere I go brainstorming ideas for next year. One of my goals was to use the blog to more formally reflect on my year. I have been reflecting but I find those reflections morph into new plans very quickly. This is hopefully going to be a place to brainstorm, get feedback and develop a plan for next year. I will be teaching 8th grade pre-algebra and Algebra I. <div><br /></div><div>I wanted to start the year with something that would allow me the flexibility to review previous ideas and introduce some of the big ideas for 8th grade. I'm looking at Sierpinski's Triangle to be that "kick-off" to the year.</div><div><br /></div><div>This is a rough list but here are the ideas that connect to Sierpinski's Triangle </div><div><ul><li>Midpoint/midpoint formula</li><li>Similar Figures </li><li>Fraction/Percent Representation and Operation</li><li>Probability</li><li>Rate of Change</li><li>Representation (graph, table, equation)</li><li>Exponents</li><li>Triangular Numbers (other special numbers)</li><li>Area of triangles (other shapes - how related to triangles)</li><li>Parallel lines/Transversal/special angles</li><li>Pythagorean Theorem and Distance Formula</li><li>Other triangle patterns</li><li>Slope triangles (similarity)</li><li>Other recursive relationships/Fractals</li></ul><div>The kick off is Sierpinski's Triangle but the focus widens to include multiple triangle connections. I'm still working on the details of what connections students need to make first and a loose timeline but I am interested in your feedback.</div><div><br /></div><div>Thanks! </div></div>Sarahhttp://www.blogger.com/profile/15836775412858228674noreply@blogger.com1tag:blogger.com,1999:blog-435790741888417218.post-22586716547225823982011-04-19T21:51:00.005-04:002011-04-19T22:01:17.978-04:00NCTM - More day 1<div style="text-align: left;">I feel like I should confess that I am a session hopper. I have a very hard time sitting in a session for the entire time. So many times there are multiple sessions at the same time I want to see. So yeah... I left early on this one...</div><div style="text-align: left;"><br /></div><div style="text-align: center;">Connecting and Communicating in Math Class Using Graphic Organizers</div><div style="text-align: center;">Carol A. Hynes</div><div style="text-align: center;"><br /></div><div style="text-align: left;"><br /></div><div style="text-align: left;">Better utilizing graphic organizers is something I'd like to work on next year so I thought this session might give me some ideas. As part of the introduction, Carol talked about the power of using graphic organizers when adopted school-wide or district-wide. </div><div style="text-align: left;"><br /></div><div style="text-align: left;">Some of the graphic organizers she shared were</div><div style="text-align: left;">Links (rule of 4)</div><div style="text-align: left;">Webs</div><div style="text-align: left;">Sorts</div><div style="text-align: left;">Splashes</div><div style="text-align: left;"><br /></div><div style="text-align: left;">You can find numerous examples <a href="http://www.umassmed.edu/MathGraphicOrganizers.aspx">here</a>. You can download the zip file at the bottom of the page.</div><div style="text-align: left;"><br /></div><div style="text-align: left;"><br /></div>Sarahhttp://www.blogger.com/profile/15836775412858228674noreply@blogger.com1tag:blogger.com,1999:blog-435790741888417218.post-60960430299645964682011-04-18T17:58:00.003-04:002011-04-18T18:09:25.920-04:00NCTM Day 1 - Do you see what I see?<div style="text-align: center;">Do You See What I See?</div><div style="text-align: center;">3-D Reasoning, 2-D Students</div><div style="text-align: center;">Peg Cagle</div><div style="text-align: center;"><br /></div><div style="text-align: left;">This session focused on how students today are different. Peg Cagle spent the majority of the session demonstrating the differences in play for students today.</div><div style="text-align: left;"><br /></div><div style="text-align: left;">Play was different</div><div style="text-align: left;"><span class="Apple-tab-span" style="white-space:pre"> </span>mechanical vs. electronic</div><div style="text-align: left;"><span class="Apple-tab-span" style="white-space:pre"> </span>do-it-yourself vs. pre-made</div><div style="text-align: left;"><span class="Apple-tab-span" style="white-space:pre"> </span>nature of public playgrounds</div><div style="text-align: left;"><br /></div><div style="text-align: left;">She talked about each of these in more detail.</div><div style="text-align: left;"><br /></div><div style="text-align: left;">I was hoping to walk away with the so what do I do to help students and toward the end of the session she gave these suggestions:</div><div style="text-align: left;"><br /></div><div style="text-align: left;"><ul><li>encourage physical activity (team sports to tree climbing)</li><li>introduce 2-d and 3-d dissection puzzles</li><li>full, pour, estimate, measure as much as you can (figure it out - which holds more?)</li><li>play with string (make knots, shapes, loops)</li><li>build stuff</li></ul><div>At one point she had us look at paper folding and all the questions you could ask students.</div><div><br /></div><div>She wonders if memory is stored in a geometric construct how students lack of experience with spatial reasoning might influence memory access. </div><div><br /></div><div><br /></div></div><div style="text-align: left;"><br /></div><div style="text-align: left;"><br /></div><div style="text-align: left;"><br /></div><div style="text-align: left;"><br /></div><div style="text-align: left;"><br /></div><div style="text-align: left;"><br /></div>Sarahhttp://www.blogger.com/profile/15836775412858228674noreply@blogger.com0tag:blogger.com,1999:blog-435790741888417218.post-52962485696660235402010-07-13T07:48:00.006-04:002010-07-13T08:04:50.053-04:00Problem SolvingI started working on the problem solving rubric. I want it to work for any problem I give students and I want to use it every time I assess their <a href="http://mathbratt.blogspot.com/2010/07/what-do-good-mathematicians-do.html">problem solving</a>. Problem solving, in my opinion, has to be non-routine and out of context. They are not application problems of current material. <div><br /></div><div>I have a 4 point scale listed for each item in my rubric. I did not include a description because I'm not sure what it would say. Like my learning targets, much of the determination will be my professional opinion backed by evidence. I tried to include what evidence I would be looking for and I'm hoping to better define the levels through class discussion. <!--EndFragment--> </div><div><br /></div><div>Go <a href="https://docs.google.com/document/edit?id=1mmzJWrNqQ77k0MuL9mvMBK2etVlD2uSOXx2Vy6W4EU4&hl=en&authkey=CKGp6NYF">here</a> to see the rubric.</div><div><br /></div><div><br /></div><div><br /></div>Sarahhttp://www.blogger.com/profile/15836775412858228674noreply@blogger.com1tag:blogger.com,1999:blog-435790741888417218.post-4626448351599198432010-07-01T06:57:00.004-04:002010-07-01T07:46:41.308-04:00What do good mathematicians do?In my role as an instructional coach we (the other coaches and I) spend time reading, discussing for our own professional growth. Each elementary school has a literacy/math coach. At the middle school, each building has a 1/2 time literacy coach and a 1/2 time math coach. I'm the math coach at my building. The first few years we spent a lot of time building the coaches' understanding of how students learn math. Much of the focus was on developing number sense. It was a great time in my personal professional learning. This year the focus shifted to literacy. I'm 7-12 math certified and have no to very little literacy background. I definitely believe that all teachers have to also be reading teachers. I'm just not sure how to do that... Now back to the main point of the blog...<div><br /></div><div>One of the literacy resources we looked at was all about creating a workshop structure. (I can't remember the book or author. I'll have to get back to you on that one.) The chapter I had to read was about a teacher who focused her workshop time on What do good readers do? That got me thinking about the math connection. What do good mathematicians do? How can I use that to create/drive a workshop culture in my math class?</div><div><br /></div><div>This is what I've come up with...</div><div><ul><li>Good Mathematicians work on solving problems.</li><li>Good Mathematicians play games and work on puzzles.</li><li>Good Mathematicians ask questions and explore ideas.</li><li>Good mathematicians practice their skills.</li></ul><div>*Disclaimer: I did not come up with this all by myself. Some of the other coaches and I have been talking about what this would look like for math. We are great sounding boards for each other. Some of the other coaches have also included vocabulary to connected it to the <a href="http://www.thedailycafe.com/">Daily Cafe</a>. For my first attempt at this I'm sticking with my four listed above.</div></div><div><br /></div><div><b>What it will look like (I hope) </b></div><div><br /></div><div>Problem Solving - Students will have a non-routine problem to solve. In the past I've used problems from <a href="nctm.org">Mathematics Teaching in the Middle School</a> or <a href="nctm.org">Mathematics Teacher</a>. I also love <a href="http://nrich.maths.org/public/">this place</a>. I hope to have a rubric in place where I can give feedback on the students' ability to understand the problem, devise a strategy, and follow it through (adapting when necessary). Required for all students - At least twice a grading period?</div><div><br /></div><div>Games and Puzzles - I'm hoping to have a collection of games that connect to the content or a specific outcome. The first grading period I'm focusing on these games with the hope to add more as the year progresses. <a href="http://illuminations.nctm.org/LessonDetail.aspx?id=L270">Polygon Capture</a>, <a href="http://www.nctm.org/eresources/article_summary.asp?URI=MT2010-05-656a&from=B">Docfish</a>, <a href="http://http://mathbratt.blogspot.com/2010/06/number-subset-game.html">Number Subset Game</a></div><div><br /></div><div>Inquiry and Exploration - I think this is open for students but I'm probably going to provide some ideas to start with. Networks, fractals, history of math, mathematicians, math careers, math in animation, computer programming, etc. I'm not sure how I'll assess but I'd like students to have a product to summarize their learning. I don't think this will be required of all students.</div><div><br /></div><div>Practice - State testing anyone? This is built in time for practicing the skills for the state test and for Algebra I. My students are required to take the 8th grade state test but they learned most of the material in 6th and 7th grade. This is a way to keep it fresh. For Algebra I this is time for those students who want to/need to practice a particular learning target. This practice will be graded only for feedback purposes not as a part of their grade.</div><div><br /></div><div>During the workshop time students will need to working on one of the above areas. My hope is to have my students well trained to be self-sufficient during that time so that I can work with small groups of students re-teaching concepts.</div><div><br /></div><div><br /></div>Sarahhttp://www.blogger.com/profile/15836775412858228674noreply@blogger.com4tag:blogger.com,1999:blog-435790741888417218.post-85738723855406083742010-06-27T07:52:00.022-04:002010-06-27T10:32:53.564-04:00GradingThe past few days there have been numerous conversations on twitter discussing SBG and how individuals make it work. I feel so blessed to be a part of those conversations. My realization last night was to try to formalize and describe in detail how I'm going to approach grading next year. Big ideas are great but I need to get to the nitty gritty. Here are some of my initial thoughts. Nothing is finalized and I'm writing more to get my ideas organized. I would appreciate feedback and other thoughtful questions.<div><br /></div><div><b>Some background</b></div><div><ul><li>My district has an online grade program. Parents are able to access their child's current grade and scores at any time.</li><li>I have been out of the classroom for the past four years working as an instructional coach. I have not used this grade program at all so I'm making some assumptions on what it can do.</li><li>The middle school and high school Algebra I teachers created a common list of learning targets and a common semester exam.</li></ul><div><br /></div><div><b>Learning Target Score</b> (skills list)</div><div><br /></div><div>I'm fortunate to already have a list of learning targets. Unfortunately, there are so many of them. I still need to condense them to the list that I will be reporting out. I was drawn to @mctownsley at<span class="Apple-style-span" style=" color: rgb(51, 51, 51); line-height: 16px; font-family:'Lucida Grande', sans-serif;font-size:14px;"> </span><a href="http://mctownsley.blogspot.com/2010/02/making-sense-of-standards-based-grading.html">Meta Musings</a> 4 point scale. I've modified it and a lot of it will depend on my professional discretion of what students understand or are able to do.</div><div><ul><li>4 points - You can work through all examples successfully.</li><li>3 points - You can do basic examples.</li><li>2 points - You are able to start the problem but unable to see it through.</li><li>1 point - You can describe what the problem is asking but unable to find a starting point.</li><li>0 points - You do not understand what the problem is asking.</li></ul></div><div>These learning targets will spiral throughout the year so students will have multiple opportunities to demonstrate understanding. I will have skills quizzes but I also like the idea of giving an assessment at a Do Now or whenever I see evidence of that understanding. My hope is to collect all the evidence and at the end of the grading period have a score (0-4) for each learning target.</div><div><br /></div><div><b>Summative Exams</b></div><div><br /></div><div>In Algebra I we already have a semester and final exam scheduled. I'm going to add a summative 9-weeks exam for the 1st quarter and the 3rd quarter. I don't know what this is going to look like. I'd like to include a mix of skills and application problems. This will be reported separately from the learning targets score although some of the questions might influence them.</div><div><br /></div><div><b>Problem-Solving</b></div><div><br /></div><div>I am passionate about developing my students' problem solving abilities. The challenging part is making sure that the problems are out of context and non-routine. If they aren't then they become application problems versus problem solving. David at <a href="http://coxmath.blogspot.com/2010/06/problem-solving-rubric.html">Questions?</a> has developed a rubric for problem solving in his class. I need to do the same thing (look for that in the future). </div><div><br /></div><div><b>Big Questions</b></div><div><br /></div><div>In an earlier <a href="http://mathbratt.blogspot.com/2010/06/my-vision-for-algebra-i-part-1.html">post</a> I wrote about the big ideas I really want my students to walk away with. I feel like I have to have a way of reporting this to students and parents. Perhaps a 4 point scale similar to the learning targets would work. </div><div><br /></div><div><b>The Grade Book</b></div><div><br /></div><div>This is what my <a href="http://spreadsheets.google.com/ccc?key=0As_nOiBhNEL7dDhOV2R0WHR0U3RyMjk1LUxvYWhrcnc&hl=en">grade book</a> might look like. I think I'll have to keep a spreadsheet of my own and the online one that reports to parents. For the Parent version I'd like to report only the most current understanding of each topic, learning target, etc. When it comes to calculating the final grade I want to consider all evidence when determining the score. I'm sure someone is wondering how I'm going to weight everything and I have absolutely no idea right now :) </div><div><br /></div><div><b>Other thoughts</b></div><div><br /></div><div>There are some other things that I want students to do but I'm not sure how or where it would fit in with their grade. Projects? Blogging? Maybe the other process standard focus will be communication or maybe they won't be a part of their grades at all.</div></div><div><br /></div><div><br /></div><div><br /></div><div><br /></div>Sarahhttp://www.blogger.com/profile/15836775412858228674noreply@blogger.com3tag:blogger.com,1999:blog-435790741888417218.post-88882091307195824162010-06-25T07:31:00.002-04:002010-06-25T07:40:33.195-04:00Number Subset GameI'm working on finding/collecting games to use during my workshop days (more explanation to come). ODE had a lesson where students would assign points to certain number subsets. I've adapted it so that 2 or more students could play as a game. <div><br /></div><div><b>Supplies</b>: a number cube, set of subset cards, paper, writing utensil</div><div><br /></div><div>Each player writes 5 numbers. Player 1 draws a card and rolls the number cube. If the card is written in red letters, subtract the number rolled for each number that falls in that subset. If the card is written in black letters, add the number rolled for each number in that subset. Keep a running total of your score. Player 2 takes a turn.</div><div><br /></div><div><b>Example</b></div><div><br /></div><div>Player 1: 3, -10, 2/3, 0, 100</div><div><br /></div><div>Player 2: 3/4, 4.5, 1, -72, -2.3</div><div><br /></div><div>Player 1 draws a red integer card and rolls a 4. He will need to subtract 4 four times (3, -10, 0, and 100). His score is -16.</div><div><br /></div><div>Player 2 draws a black whole number card and rolls a 1. She will need to add 1 once (1). Her score is 1. </div><div><br /></div><div>Repeat this process. The student with the highest score is the winner.</div><div><br /></div><div><br /></div><div>I'm hoping this a way to keep this vocabulary alive throughout the year. </div>Sarahhttp://www.blogger.com/profile/15836775412858228674noreply@blogger.com5tag:blogger.com,1999:blog-435790741888417218.post-86171675439411151142010-06-24T07:04:00.004-04:002010-06-24T07:14:24.922-04:00My vision for Algebra I (part 1)What are the big ideas in Algebra I? I'm not 100% sure of my sequencing but I know I want to weave the following questions into each unit. <div><br /></div><div>Big Questions:</div><div>1. What is a solution? How do you find them?</div><div>2. What is rate?</div><div>3. What does it mean to be a function?</div><div>4. Why is equivalency important? (this one bothers me - not sure how to word it)</div><div><br /></div><div>I'm hoping to keep record of students' understanding of these big ideas along with their algebra skills. </div><div><br /></div><div><br /></div><div><br /></div>Sarahhttp://www.blogger.com/profile/15836775412858228674noreply@blogger.com4tag:blogger.com,1999:blog-435790741888417218.post-62955844139292870222010-06-14T21:54:00.004-04:002010-06-14T22:39:43.185-04:00Ian Jukes came to townMy school district invited <a href="http://committedsardine.com">Ian Jukes</a> to speak at our summer academy this year about learning and teaching in the 21st century. In the morning, he set the stage on why we need to be aware of quickly changing technology. That afternoon he spoke about the Digital Learner's profile and summarized what the research says. Much of the information presented was not completely new but I still find it an important and motivating message. Here are some of the ideas that resonated with me:<div><ul><li>Finding balance - We want DLs to respect "school". We must respect where they are coming from too.</li><li>Problem based learning<br /></li><li>Progressive Withdrawl - getting kids to think on their own</li></ul><div>I definitely have a lot to think about this summer as I decide the structures and routines that will define my time with kids. </div></div>Sarahhttp://www.blogger.com/profile/15836775412858228674noreply@blogger.com0tag:blogger.com,1999:blog-435790741888417218.post-2012686321182324512010-06-13T12:09:00.000-04:002010-06-13T12:13:45.814-04:00It has to begin somewhereSo here we go! I'm incredibly nervous to start this journey of blogging. My hope is that I am better able to document and reflect on my journey next year. I've spent the last four years working as a math instructional coach. That is still my role but I have the opportunity to teach one section of Algebra I next year. The thought of having my own classroom of kids to experiment with is exciting.Sarahhttp://www.blogger.com/profile/15836775412858228674noreply@blogger.com5