tag:blogger.com,1999:blog-19470428578212739422017-08-16T12:58:21.639-07:00The Math HatterChris Sielingnoreply@blogger.comBlogger57125tag:blogger.com,1999:blog-1947042857821273942.post-37724972447558131932017-08-16T12:57:00.001-07:002017-08-16T12:58:21.673-07:00Illustrative Math in MinnesotaThis year I am implementing a brand new curriculum,<a href="https://www.illustrativemathematics.org/" target="_blank"> Illustrative Mathematics</a>. I am really excited as they always have had great mathematical tasks on their site. This summer they released their full 6th-8th curriculum. Understandably so, it was based around the Common Core Math Standards. However, in Minnesota we do not use the Common Core. So my excitement was diminished when I realized that a complete re-organization of their units was needed to successfully do this in MN. <br /><br />So after many hours I have come up with a plan. It is briefly outlined below for 7th and 8th grade. I will hopefully blog a little about this as I go. I am sure changes will be needed, but right now, I am feeling pretty good about getting this done. <br /><br />While I am excited to be diving into a new curriculum, and excited about all the amazing problems my students will experience this year, I do have a couple concerns. <br /><br />1. I am trying to plan a curriculum I am only superficially familiar with. Some of the units are out of the order to help students group ideas and give the class a better flow. I am worried that some units will reference ideas we have not had a chance to go over yet. <br /><br />2. 7th grade math in MN is packed to the brim with math. It is hard to get in all the standards every year. (I usually fail at this.) Even with the IM units I have a planned 39 weeks of instruction. This is too much. I already know that. We will see how the timing works out. Since MN has packed so many standards into 7th grade, and those standards don't align perfectly with Common Core, I have had to grab some 6th grade units and some 8th grade units, while only getting to skip one 7th grade unit (7.7). So with some of these units I will have to cherry pick the lessons so they flow into the big learning target ideas. <br /><br />3. I will still have to supplement some higher end 8th grade material. In Minnesota, the 8th grade math standards are all the linear parts of algebra 1. So some things are not currently included in Illustrative Math. So I plan on using some of my old CMP curriculum to hit these learning targets. I hope when IM finished their HS curriculum, I can grab some units from there instead. <br /><br /><a href="https://4.bp.blogspot.com/-XbFFcuZ8UoE/WZShLSn-f6I/AAAAAAAAApY/9nEJq5berkQGhpPuny9y4vfXWf4cqefyQCLcBGAs/s1600/7th%2BIM%2BUnits%2BPlan.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" data-original-height="377" data-original-width="384" height="313" src="https://4.bp.blogspot.com/-XbFFcuZ8UoE/WZShLSn-f6I/AAAAAAAAApY/9nEJq5berkQGhpPuny9y4vfXWf4cqefyQCLcBGAs/s320/7th%2BIM%2BUnits%2BPlan.png" width="320" /></a><br /><br /><a href="https://4.bp.blogspot.com/-0ouRel5B-3g/WZShQWlh86I/AAAAAAAAApc/v0usaei33zoUNwmOWb9qoWkjHj0P_XzGQCLcBGAs/s1600/8th%2BIM%2BUnits%2BPlan.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img alt="" border="0" data-original-height="293" data-original-width="369" height="254" src="https://4.bp.blogspot.com/-0ouRel5B-3g/WZShQWlh86I/AAAAAAAAApc/v0usaei33zoUNwmOWb9qoWkjHj0P_XzGQCLcBGAs/s320/8th%2BIM%2BUnits%2BPlan.png" title="" width="320" /></a><br /><br /><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-tixJwphLmI8/WZShLeLn9dI/AAAAAAAAApU/sEZ3oJiYMdwUMU137yY0quX0sX5wzXPxACLcBGAs/s1600/7th%2BIM%2BLearning%2BTargets.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="294" data-original-width="915" height="126" src="https://3.bp.blogspot.com/-tixJwphLmI8/WZShLeLn9dI/AAAAAAAAApU/sEZ3oJiYMdwUMU137yY0quX0sX5wzXPxACLcBGAs/s400/7th%2BIM%2BLearning%2BTargets.png" width="400" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><br /></div><div style="text-align: center;"> <a href="https://4.bp.blogspot.com/-NGrBgpFF9L8/WZShLcOCy-I/AAAAAAAAApQ/8rkXpXQtyy8DIO0wHOc8WvYhrpzgu3AVwCLcBGAs/s1600/8th%2BIM%2BLearning%2BTargets.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" data-original-height="251" data-original-width="798" height="125" src="https://4.bp.blogspot.com/-NGrBgpFF9L8/WZShLcOCy-I/AAAAAAAAApQ/8rkXpXQtyy8DIO0wHOc8WvYhrpzgu3AVwCLcBGAs/s400/8th%2BIM%2BLearning%2BTargets.png" width="400" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><br /></div><br />Chris Sielinghttps://plus.google.com/116218190535784529711noreply@blogger.com0tag:blogger.com,1999:blog-1947042857821273942.post-70789324903640144392016-12-07T14:00:00.000-08:002016-12-08T06:51:10.801-08:00Bottle Flipping & ProbabilityLike most students, my 7th graders are obsessed with bottle-flipping. So I thought for a long time on how to use this to my advantage with the 7th grade standards. I came up with a probability lesson. The lesson combines experimental probability, writing odds from probabilities, and making predictions from probability. <br /><br />Lesson Plan<br />1. I lectured about how to turn odds to probability and back again. (5 min)<br /> I used examples from sports odds and various other examples. <br /><br />2. The class discussed bottle flipping. <br /> We started by discussing bottle flipping, and followed it up with a discussion of how full the bottle should be for optimal flipping. I handed a water bottle to each student. While we downloaded the PDF and discussed the instructions students drank some water to get their optimal level. <br /><br />3. The students flipped and flipped. <br /> I allowed 5-7 minutes for students to flip bottles and collect data. <br /><br />4. Students wrote probabilities and odds from the data. <br /> Students used their own data, and their groups total data (3-4 students) to write probabilities and odds. <br /><br />5. Students predicted how many successes from their next 10 flips, then tested their prediction.<br /><br />Overall a quick, hectic, and very loud day. However a great success for engagement. Now tomorrow, we will see if any students remember how to write odds and probability. <br /><br />The handout can be viewed <a href="https://goo.gl/WTxCvT" target="_blank">here</a>. <br /><br /><div class="separator" style="clear: both; text-align: center;"><br /><iframe allowFullScreen='true' webkitallowfullscreen='true' mozallowfullscreen='true' width='320' height='266' src='https://www.blogger.com/video.g?token=AD6v5dwB-CW-nbKyggsze8MeWQYMIgs57N9j4gEYoJR7PZ8QOrsVCjPVkzGKfY-asFoAa1WcSdj7SLgAHmEuvVGEXQ' class='b-hbp-video b-uploaded' FRAMEBORDER='0' /></div><br />Chris Sielinghttps://plus.google.com/116218190535784529711noreply@blogger.com0tag:blogger.com,1999:blog-1947042857821273942.post-53956879575193478942016-10-03T19:54:00.001-07:002016-10-03T19:54:56.685-07:00Support Math Class: UpdateIt has been a while since I got to post anything. It has been really busy. Math team has started (I coach JH and HS). Robotics is in full swing (I coach HS and JH). Add in lots of other family commitments and I have barely been able to keep up with teaching, much less blogging. <br /><br />So here are the updates on how the Junior High Support Math Class is going. <br /><br />Circle Talks<br />We now do circle talks on Monday, Wednesday, and Friday. We have some kids who go to band or choir during class so they are only in class 2-3 days a week. So by doing circle talks on these 3 days we guarantee that every kid has circle 3 times every two weeks. I do have some who are in class every day and they obviously get circle 3 times a week. <br /><br />On Mondays, we ask about their weekend. On Fridays, we ask about their week. I had a breakthrough last Friday as I asked about the "highs" and "lows" of their week. They suddenly were sharing a great deal about their week instead of just a one- or two-word answer. We also talk about what they are looking forward to for the upcoming weekend. <br /><br />We also continue to use the If book. The book is full of interesting questions to get the students talking. We give one student the book, another student picks a number from 5-129, and then the student with the book picks a question from that page. We try to get in a couple rounds of this every time we have circle. <br /><br />The kids have really begun to enjoy their circle time and ask for it when I am slow to get it going on Monday, Wednesday or Fridays. They also do ask for it on Tuesday and Thursday. <br /><br />Number Talks<br />We continued to use <a href="http://www.estimation180.com/" target="_blank">Estimation 180</a> for number talks for quite a while. At mid-term we switched to <a href="http://wodb.ca/" target="_blank">Which One Doesn't Belong</a>. Another number talk designed to get the students thinking and analyzing. The kids have really taken to this one and enjoy trying to come up with as many reasons as possible that each object doesn't belong. <br /><br />We will soon begin our number talks based on calculations. They will focus on Number Sense. I plan on using this <a href="https://www.amazon.com/Building-Powerful-Numeracy-Middle-Students/dp/0325026629" target="_blank">book by Pamela Weber Harris</a> as the basis for these talks. <br /><br /><br />DreamBox<br />We have also begun using the <a href="http://www.dreambox.com/" target="_blank">DreamBox</a> online system. Most of the students really love it. We are currently under a 3 month trial period. We can have unlimited students for $300. When the 3 months is up we are hoping to show growth and convince the district to invest in this program for the math support programs. Once the trial is over the pricing scheme will go back to a per student cost. <br /><br />The first week I let the students work on whatever standards they wanted to in a grade level band from 5th-8th. This week I narrowed their focus to the grade level standard we covered in normal math class this quarter. I got more questions today about the math, but they still seemed to really enjoy doing DreamBox. We usually try to get 10-15 minutes in per day. We are going to set a class goal for lessons completed per week, but we haven't gotten that done yet. <br /><br />Grade Level Standard Help:<br />During DreamBox time, I have started pulling small groups of students to work with on their work for their main math class. This has seemed pretty effective so far for some of the students. We will definitely continue this to help them achieve their grade level standards. <br /><br />Overall, things are going really well. I hope to put together some data to show growth. Just wondering what data to look at. I want something besides MCA scores. <br /><br /><br /><br /><br /><br /><br />Chris Sielinghttps://plus.google.com/116218190535784529711noreply@blogger.com0tag:blogger.com,1999:blog-1947042857821273942.post-53531695564596647382016-09-12T15:43:00.001-07:002016-09-12T15:43:12.414-07:00Support Math Class: Days 12-13Friday, Sept 9th<br />1. Circle Talk<br /> We just did a quick couple questions about reflecting on the week. These are their least favorite questions. I need to figure out how to phrase them differently. I am still getting mostly 1 word answers. I know I need to be patient. <br /><br />2. Number Talk<br /> As we do everyday, we did a number talk. This was the final bowl of cereal estimate from <a href="http://www.estimation180.com/day-213.html" target="_blank">estimation 180</a>. The students have really been explaining their thinking process well this week. We will continue to use these estimation 180 problems to continue to encourage their mathy communication.<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-1xOSQN70v-g/V9csVJmB7qI/AAAAAAAAAjs/tcwgbYocW6ILaMBr7fkbvVdBjqCUuzqewCLcB/s1600/est%2B180%2Bcereal%2B3.jpeg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="240" src="https://4.bp.blogspot.com/-1xOSQN70v-g/V9csVJmB7qI/AAAAAAAAAjs/tcwgbYocW6ILaMBr7fkbvVdBjqCUuzqewCLcB/s320/est%2B180%2Bcereal%2B3.jpeg" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;">3. <a href="http://www.dr-mikes-math-games-for-kids.com/1-to-9-15-game.html" target="_blank">15 game</a><br /> We have been using Friday as fun math game day so far. This little adding game was a pretty big hit. They started off thinking this game was too elementary for them. Then they realized the strategies involved and were doing lots of number sense thinking. A big hit. </div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">Monday, Sept 12th</div><div class="separator" style="clear: both; text-align: left;">1. Circle Talk</div><div class="separator" style="clear: both; text-align: left;"> A check-in round from the weekend. A quick question about what they are looking forward to this week. (it always breaks my heart when they say nothing). Then a couple what-if questions. A good circle day with laughter and good stories. </div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">2. Number Talk 1</div><div class="separator" style="clear: both; text-align: left;"> <a href="http://www.estimation180.com/day-176.html" target="_blank">An estimation 180 problem</a>. Since I am picking the new problems I estimate answers as well with the class and do not know the answers before we go over them. Today, it was a "how fast will Mr. Stadel walk" and we all underestimated his walking speed. Only 1 groups minimum was low enough. Led to a good point about making good ranges. </div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">3. Number Talk 2</div><div class="separator" style="clear: both; text-align: left;"> We used this pattern and found out how many in figure 5 and 10, then went for a general rule. We used this as a springboard into their 1st learning target of SHOW WORK. We talked about examples of 4, 3, 2 and 1 on the Show Work rubric. Then we had each group write up their answer and then the class graded it together. </div><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-510wTGcWVMc/V9cvXCiyv3I/AAAAAAAAAj8/mnQi90cSnfU5juo9c_BFm6akFqksYUdxgCLcB/s1600/visualpatternsleaves.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="119" src="https://2.bp.blogspot.com/-510wTGcWVMc/V9cvXCiyv3I/AAAAAAAAAj8/mnQi90cSnfU5juo9c_BFm6akFqksYUdxgCLcB/s320/visualpatternsleaves.png" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;">Tomorrow we will go over learning target 2, asking for help. We will see how that one flies. </div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><br /></div><br /><br />Chris Sielinghttps://plus.google.com/116218190535784529711noreply@blogger.com0tag:blogger.com,1999:blog-1947042857821273942.post-59830520911170826292016-09-08T20:57:00.000-07:002016-09-08T20:57:08.375-07:00Support Math Class: Days 8-11Coming off Labor Day over the break, the class is going well. <br /><br /><u>Last Friday - Day 8</u><br />Circle Talk<br />We reflected on the week. The highlight for me was when I asked "what was your highlight of the week" and two students said the support math class. First major victory of the year! <br />Number Talk<br />The students are tiring of number talks. However, the thinking is so good for them. <br />Sprouts Game<br />I taught the class Sprouts and it was a really good time. They took to it and were engaged the whole time. <br /><br />Tuesday - Day 9<br />Circle Talk<br />Just questions about their weekend and prepping for the week. They requested some more would you rather questions as well. Those are always a good time. <br />Number Talk<br />Switched it up to some <a href="http://www.estimation180.com/" target="_blank">estimation 180 questions</a>. We did the first cereal estimation task. The students struggled trying to explain their reasoning for their estimations. Getting them beyond, "I don't know I just guessed" is hard. I made them write down 3 numbers. Too high, too low and their best guess. <br />Number Talk 2<br />We did another pattern to review their math from regular math class on linear relationships and proportional relationships. <br /><br />Wednesday - Day 10<br />Our football team won 66-12 the week before. So I took Dan Meyers 3-act problem "<a href="http://mrmeyer.com/threeacts/buckythebadger/" target="_blank">Bucky the Badger"</a> and used our stats instead. Our cheerleaders do jumping jacks after every score. So we estimated and calculated how many they did for the entire game. A good thinking problem on our early out day with 30-minute classes. <br /><br />Thursday - Day 11<br />Number Talk<br />We did the<a href="http://www.estimation180.com/day-212.html" target="_blank"> second cereal estimation</a> problem from Estimation 180. Today went better than Tuesday. The students, working in groups of 2, estimated the solution. Each group then explained their reasoning and did quite well. <br />Number Talk 2<br />Another <a href="http://www.visualpatterns.org/201-220.html" target="_blank">visual pattern</a> to help review linear patterns and writing equations. <br /><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-whbkA-LMLHU/V9IxwY-cR-I/AAAAAAAAAjQ/idiIYMam2uEMnlfJMWfefbPTQvbFeODIACLcB/s1600/starwarsnumbertalk.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="162" src="https://3.bp.blogspot.com/-whbkA-LMLHU/V9IxwY-cR-I/AAAAAAAAAjQ/idiIYMam2uEMnlfJMWfefbPTQvbFeODIACLcB/s320/starwarsnumbertalk.jpg" width="320" /></a></div><div class="separator" style="clear: both; text-align: left;">Practice Time</div><div class="separator" style="clear: both; text-align: left;">We have not set up our DreamBox accounts yet. I am still trying to recruit so we can have enough for the 40 minimum students required for a school account. So I sadly used the IXL program for practice. The 7th graders identified proportional relationships, and the 8th graders identified linear relationships. It went fine. Hopefully, it built some confidence for their upcoming quiz. </div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">All in all a good few days. Tomorrow will bring back some circle talk to help reflect on the week. Then we will review for the quiz. </div><br />Chris Sielinghttps://plus.google.com/116218190535784529711noreply@blogger.com0tag:blogger.com,1999:blog-1947042857821273942.post-18234347767193099132016-09-01T18:18:00.002-07:002016-09-01T18:18:13.250-07:00Support Math Class Day 7: Circle Talk, Number Talk and SproutsCircle talk again opened JH support math class today. First question was "what are two words that describe how you are doing today?" Sample answers:<br /> "Good, very good."<br /> "Good, great."<br /> "Fun, funions."<br />So I will have to try another strategy to get longer answers on that opening round. <br />Other questions from today:<br />1. What is your favorite junk food?<br />2. If you knew you could not fail, what would you do?<br /> (inspired from my amazing 6th grade teacher neighbors)<br />3. What does the best case scenario of school look like to you for this year?<br /><br /><a href="https://3.bp.blogspot.com/-o3omZpG0Shg/V8jR82nv2TI/AAAAAAAAAio/7hE4eI1EdPsDBUyhmwtRt29-36JLSMrJgCLcB/s1600/teach%2B180%2Bblog.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" height="240" src="https://3.bp.blogspot.com/-o3omZpG0Shg/V8jR82nv2TI/AAAAAAAAAio/7hE4eI1EdPsDBUyhmwtRt29-36JLSMrJgCLcB/s320/teach%2B180%2Bblog.JPG" width="320" /></a><br /><br />I also included a summary of the talking pieces I have used so far this week. Trying to change it up and see what sticks with the kids. These are all just things around my desk so far. <br /><br />The R2D2 thing is actually an eraser. Which allowed me to explain to the kids that I love Star Wars, and I love fixing mistakes. <br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-1NzEAckT83o/V8jR8mm9BVI/AAAAAAAAAik/0VgUl8F3ak85Lte8tSQ8NTj88uQYHhA6QCLcB/s1600/teach%2B180%2Bblog2.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://1.bp.blogspot.com/-1NzEAckT83o/V8jR8mm9BVI/AAAAAAAAAik/0VgUl8F3ak85Lte8tSQ8NTj88uQYHhA6QCLcB/s320/teach%2B180%2Bblog2.JPG" width="240" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;">The number talk went really well. They are getting closer and closer to coming up with rules for the patterns. Again the pattern came from <a href="http://www.visualpatterns.org/" target="_blank">Visual Patterns</a>. </div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-ZHLIkIU8tf8/V8jSodt357I/AAAAAAAAAiw/EyHAV6HgGhk4tTWZCkqAyaPKleQXNmh6ACLcB/s1600/trees.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="120" src="https://3.bp.blogspot.com/-ZHLIkIU8tf8/V8jSodt357I/AAAAAAAAAiw/EyHAV6HgGhk4tTWZCkqAyaPKleQXNmh6ACLcB/s320/trees.jpg" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><br />We finished up the pattern a little early, so inspired by Sarah Carter's great #teach180 tweets, we learned how to play the game sprouts. They were totally engaged and loving it. <br /><a href="https://www.youtube.com/watch?v=XXhS8PiUTvM" target="_blank">Here is a quick YouTube video explaining the game. </a><br /><br />A great week so far!<br /><br />Chris Sielinghttps://plus.google.com/116218190535784529711noreply@blogger.com0tag:blogger.com,1999:blog-1947042857821273942.post-12166256053522541752016-08-31T19:52:00.000-07:002016-08-31T19:52:12.581-07:00Support Math: Day 6 - Students bring Qs to Circle and Number Talks!Today was our third day of talking using the circle format. Yesterday I had a couple "Would You Rather" questions to get the discussion going. Today, trying to slowly share ownership of the circle, the students brought in the "Would You Rather" questions. I was scared about appropriate questions, and kids forgetting to come up with questions. Turns out I had nothing to worry about.<br /><br />We started with a quick check in round, again completed with one-word answers. Then each student got to ask one "Would You Rather" question to the circle. Everyone answered, and then the next student asked their question. It led to some great conversations. The answers were a little shorter than I would have predicted, but still fun. I tried to model giving longer answers, the kids just laughed at me for being weird. <br /><br />We then went into a number talk. The number talk was again from <a href="http://www.visualpatterns.org/" target="_blank">Visual Patterns</a>. <br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/--vipH4OREbQ/V8eVrnYZ5aI/AAAAAAAAAiI/ssEEFRzIMggzl1EgvN4KlSy1kF-RrI1GACLcB/s1600/trianglesquares.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="125" src="https://1.bp.blogspot.com/--vipH4OREbQ/V8eVrnYZ5aI/AAAAAAAAAiI/ssEEFRzIMggzl1EgvN4KlSy1kF-RrI1GACLcB/s320/trianglesquares.png" width="320" /></a></div><div class="separator" style="clear: both; text-align: left;">The students focused on the number of triangles. I found it very surprising how easy it was for students to miss the triangles with the point down. For example, they kept counting three triangles in figure 2. Which is fine. It leads to a nice triangular number pattern. However, the pattern is easier to generalize if you count all the triangles. The students picked up on the pattern quickly, but struggled to reach a formula. We did get there, but it took awhile. </div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">I cannot overstate how these number talks based on patterns has helped the students in their 8th grade math class this week. In their regular math class we have started studying linear relationships. I always do this by starting with patterns. The students who are in support math have developed a comfort with patterns that is letting them engage in the linear patterns with more confidence. </div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">Preteaching some skills using support math is a highly valuable practice I will try to use more this year.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><br /></div><br />Chris Sielinghttps://plus.google.com/116218190535784529711noreply@blogger.com0tag:blogger.com,1999:blog-1947042857821273942.post-26954118396116280422016-08-30T19:48:00.001-07:002016-08-30T19:48:10.513-07:00Support Math Day 5: Circle Talk Day 2 and More Number TalksToday we started class with our second circle talk. We did a quick check-in round to see how everyone was doing. To no surprise, it was mostly 1 word answers by everyone. We will have to come up with something to work on that.<br /><br />Then we played about 4 rounds of Would You Rather. I found this excellent set of w<a href="http://www.themeasuredmom.com/wp-content/uploads/2014/05/WYRCrds.pdf" target="_blank">ould you rather</a> questions online. It is from the Measured Mom blog. It is aimed at younger kids, but by selecting the right questions and aging up some others, it will be a great resource. The kids had a great time and they got homework. They were each asked to create a "would you rather" question for circle time tomorrow. Hopefully the questions are appropriate and lead to some good answers. <br /><br />Circle today created some fun moments with the kids and I can already start to see the sense of community starting to build among these students. It might all be based on the fact that they are "getting out of doing normal math" but I will take that for right now.<br /><br />The number talk we did today was a step up in difficulty from yesterday. We took 20-25 minutes breaking it down. Most students really dug into it and wouldn't give up. We eventually arrived at a nice formula for triangular numbers. Are they going to remember that, probably not. Right now though it is about not giving up and sticking with hard problems. <br /><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-3mCIng6Ei6I/V8ZEpHcbzBI/AAAAAAAAAhs/HpBMfvM4dq4NyVsRp50cdEQxmT9ukMW3wCLcB/s1600/7685089_orig.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="106" src="https://4.bp.blogspot.com/-3mCIng6Ei6I/V8ZEpHcbzBI/AAAAAAAAAhs/HpBMfvM4dq4NyVsRp50cdEQxmT9ukMW3wCLcB/s320/7685089_orig.png" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;">In 8th grade math today, we tackled some tough patterns to talk about linear patterns. The students in TIP math did really well. I hope that the foundation for that was partly laid down in TIP math by working with difficult patterns the last couple days of class. </div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">So things are off to a great start so far. We are building a good foundation for a couple of my 4 pillars of support math. </div><br />Chris Sielinghttps://plus.google.com/116218190535784529711noreply@blogger.com0tag:blogger.com,1999:blog-1947042857821273942.post-44441091917975249952016-08-29T14:45:00.002-07:002016-08-29T14:58:18.940-07:00Support Math Day 4: First Circle Talk and a Number Talk<b><u>Day 4:</u></b><br />Today in support math class was our first day talking using the circle format. We started by writing down 1 word on a note card that represents how we like to be treated. We then used that as a springboard into creating guidelines we will use for our circle time and class time. Our guidelines we agreed to are:<br /><br />1. Respect talking piece<br />2. What's said in circle stays in circle<br />3. No fighting<br />4. Listen to each other<br />5. Can pass the talking piece without answering<br />6. Eye contact with speaker<br />7. Don't talk while others talk<br />8. Have fun, get work done<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-opoV4_3xs6g/V8Sv9lQbHxI/AAAAAAAAAhQ/J_N1mVe_hJcFYxiyaP6EunNvH1FW1DUbgCLcB/s1600/teach180%2Bday4%2BTIP.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="200" src="https://1.bp.blogspot.com/-opoV4_3xs6g/V8Sv9lQbHxI/AAAAAAAAAhQ/J_N1mVe_hJcFYxiyaP6EunNvH1FW1DUbgCLcB/s320/teach180%2Bday4%2BTIP.jpg" width="320" /></a></div><br /><br />We then did a couple rounds of questions to help build people's confidence and the community of the circle. Those questions were:<br />1. If you could be any superhero, who would you be and why?<br />2. What was the highlight of the first four days of school?<br /><br />There might have been another question, but I can't recall it right now. <br /><br /><br />The second part of class was a number talk. <br />We used this image and asked<br />1. What do you notice?<br />2. What do you wonder?<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-SwonN19sn3I/V8SsdpYhDEI/AAAAAAAAAg8/OGz1pMEqWGAqHfqDC6QCoLl0bzFhec95wCLcB/s1600/visual%2Bpatterns%2B2.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="127" src="https://3.bp.blogspot.com/-SwonN19sn3I/V8SsdpYhDEI/AAAAAAAAAg8/OGz1pMEqWGAqHfqDC6QCoLl0bzFhec95wCLcB/s320/visual%2Bpatterns%2B2.jpg" width="320" /></a></div><br /><br />We talked about what we noticed. They still didn't wonder to much, but that is really okay at this point. They noticed how it grew and immediately latched onto the rate of change of 2. (although not in those words)<br /><br />I then asked groups of 2-3 to answer the following questions<br />1. How many cubes in figure 5?<br />2. How many cubes in figure 10?<br /><br />After discussing the classes solutions, we then asked about figure 20. <br /><br />These questions brought out some great misconceptions and things for us to work on the rest of the week. <br /><br />This week will be about creating the foundation for a good circle community and talking through number talks. <br /><br /><br /><br />Chris Sielinghttps://plus.google.com/116218190535784529711noreply@blogger.com0tag:blogger.com,1999:blog-1947042857821273942.post-68035489772721807142016-08-28T10:21:00.001-07:002016-08-28T10:21:37.326-07:00First Week of Support Math ClassMy initial goal is to continually blog about how my support math class for 7th and 8th graders is going this year. This is the first year in a long time I have taught a support math class for junior high and I am pretty excited about it. I wrote about my 4 pillars for the class last time. <br /><br />My first week goal, was to get the kids over the dread of having a second math class. The typical students in support math are not excited to even have 1 math class, much less 2. <br /><br /><b>Day 1</b>: <a href="http://www.tomwujec.com/design-projects/marshmallow-challenge/" target="_blank">Marshmallow Challenge</a><br /><br />The students walked in on day 1 and we quickly went over why we were in the class. Then we quickly went over the 4 class expectations. <br /> 1. No Meanness<br /> 2. Make Mistakes<br /> 3. ...Yet<br /> 4. Ask for Help<br /><br />I then handed out materials for the marshmallow challenge. The students were totally engaged. This is a great problem with a great ending that allows me to again repeat expectation #2 about making mistakes. It was a great day 1. <br /><br /><br /><b>Day 2:</b> Bridge Challenge<br />The second day we reviewed that class goals and expectations then quickly got to another building challenge. This one involved the following materials for each group:<br /> 12 marshmallows<br /> 20 straws<br /> 1 small cup<br /> 50 pennies<br /><br />the goal was to build the longest bridge that could hold at least 50 pennies that were sitting in a cup. <br /><br />Overall the kids were just as engaged as day 1. We did have small mishap as one group decided to smash up 5 marshmallows to create a paste to stick the straws to the desk. (Had to leave 10 minutes at the end of the period for cleanup) I encouraged creativity, and then taking responsibility for clean up for those decisions as well. <br /><br /><br /><b>Day 3: Number Talk 1 and Build Challenge 3</b><br />On the third day, I threw in our first of many number talks. I grabbed the first pattern of <a href="http://visualpatterns.org/">visualpatterns.org</a>. (seen below) I just asked the students 2 questions,<br /> 1) What do you notice?<br /> 2) What do you wonder?<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-x4Jf0JBdURU/V8MbBwqMd6I/AAAAAAAAAgg/-E6eq-NygTQlfgdRTRMYUxHoXwTlaAevgCLcB/s1600/pattern1.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="106" src="https://2.bp.blogspot.com/-x4Jf0JBdURU/V8MbBwqMd6I/AAAAAAAAAgg/-E6eq-NygTQlfgdRTRMYUxHoXwTlaAevgCLcB/s320/pattern1.jpg" width="320" /></a></div><div class="separator" style="clear: both; text-align: left;">For their first time, they handled this pretty well. They focused more on the noticing, and less on the wondering, but that was expected. They focused on the number of small squares. So after some questions about how it is growing, and how many would be in pattern 4, I then asked them to think about how many small squares would be in pattern 10? They got time to think, and then discuss in small groups. We then discussed as a class and it went incredibly well for the first number talk. </div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">We then spent 20 minutes on our third building challenge of the week. They got spaghetti, straws, tape and string and their job was to build out from the desk as long as possible. To pick a winner I measured from the edge of the desk out to where there structure stopped horizontal to the floor. </div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">It was a creative and fun week! </div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">Next week will see more number talks, and the introduction of circle time. </div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><br /></div><br /><br />Chris Sielinghttps://plus.google.com/116218190535784529711noreply@blogger.com0tag:blogger.com,1999:blog-1947042857821273942.post-32374298723965821562016-08-25T18:50:00.000-07:002016-08-25T18:50:37.112-07:00My 4 Pillars of Support Math ClassSupport Math Class for Junior High Students<br /><br />This year I get to have a support math class for 7th and 8th graders for the first time in years. I have learned a lot of different things since the last time I taught this class. I am trying an entirely new approach this time around. I am going to build the class around 4 pillars. <br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-JxaEhrptsaI/V7-Y1fCb6HI/AAAAAAAAAfg/zQeOn7lZEq8ZisNfO6Og6eM5QAM3WdasgCLcB/s1600/dreambox-logo.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="153" src="https://4.bp.blogspot.com/-JxaEhrptsaI/V7-Y1fCb6HI/AAAAAAAAAfg/zQeOn7lZEq8ZisNfO6Og6eM5QAM3WdasgCLcB/s200/dreambox-logo.png" width="200" /></a></div><br />1. Computer Program - DreamBox Learning<br /> This pillar is pretty typical in a support math class. I choose DreamBox over other computer based programs because it does a pretty good job of focusing on concepts and big ideas over skills. My own children (7, 11, and 13) used the program over the summer and liked it. I plan on not even introducing this part of the class for quite a while. <br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-B2WPuw1B3Os/V7-ZIXAXKmI/AAAAAAAAAfk/EelX80Y0ED0EwSgwLBLItKnYhYf3-OZQACLcB/s1600/numbertalks.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="169" src="https://1.bp.blogspot.com/-B2WPuw1B3Os/V7-ZIXAXKmI/AAAAAAAAAfk/EelX80Y0ED0EwSgwLBLItKnYhYf3-OZQACLcB/s320/numbertalks.png" width="320" /></a></div><br />2. Number Talks<br /> I think this pillar could really be a whole support math class by itself. I love number talks. I use them in every class, just not often enough. I plan to use Chris Danielson's "<a href="http://wodb.ca/" target="_blank">Which One Doesn't Belong</a>" to start with. It has a low enough entry point that most students should be comfortable talking about these problems. I will then shift <a href="http://www.mathtalks.net/" target="_blank">math talks</a>, <a href="http://www.visualpatterns.org/" target="_blank">visual patterns</a>, <a href="http://www.estimation180.com/" target="_blank">estimation 180</a> and activities from <a href="https://www.amazon.com/Building-Powerful-Numeracy-Middle-Students/dp/0325026629/ref=sr_1_3?s=books&ie=UTF8&qid=1472174729&sr=1-3&keywords=pamela+weber+harris" target="_blank">Pamela Weber Harris' great book</a>. I envision this as the main pillar of the four. <br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/--Wl_NGmwrF4/V7-bGSvewJI/AAAAAAAAAf0/xICSvVNfi4EchWyfJUdwYkOkgQO5kEgxgCLcB/s1600/genius%2Bhour.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="146" src="https://1.bp.blogspot.com/--Wl_NGmwrF4/V7-bGSvewJI/AAAAAAAAAf0/xICSvVNfi4EchWyfJUdwYkOkgQO5kEgxgCLcB/s200/genius%2Bhour.png" width="200" /></a></div><br />3. MakerSpace/Hands-on/Genius Hour<br /> This pillar is kind of a mish-mash approach to getting the students moving and trying to ignite their passion. I started the first couple days on this pillar. I envision creating, making and igniting curiosity. I am worried about resources for this pillar, especially in the MakerSpace part. Trying to find the right kind of things the students will be curious about seems daunting, especially with no funds. <br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-Ba0nuNV4cX0/V7-b7HgmDoI/AAAAAAAAAf8/H7ZhMmi7SawJJAIi0IyAdopZisug7dejwCLcB/s1600/rjcircles.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://3.bp.blogspot.com/-Ba0nuNV4cX0/V7-b7HgmDoI/AAAAAAAAAf8/H7ZhMmi7SawJJAIi0IyAdopZisug7dejwCLcB/s1600/rjcircles.jpg" /></a></div><br />4. Restorative Justice/Circle Practices<br /> This portion will be used to create a community feeling in the classroom. I was a circle volunteer for years in my county in the RJ program. It was a great way to help and connect with youth and connect youth to the community. I say in a 4-day training on using RJ in schools this summer. It got me completely excited about bringing this tradition to my classroom. <a href="http://www.centerforrestorativeprocess.com/teaching-restorative-practices-with-classroom-circles.html" target="_blank">This article</a> is a nice summary of using the circle process in schools. Here is also a nice edutopia video about circles.<br /><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="YOUTUBE-iframe-video" data-thumbnail-src="https://i.ytimg.com/vi/qTr4v0eYigM/0.jpg" frameborder="0" height="266" src="https://www.youtube.com/embed/qTr4v0eYigM?feature=player_embedded" width="320"></iframe></div><br />Trying to get all this together in a cohesive fashion is going to be a challenge. It is a challenge I look forward to in the upcoming year. I look forward to the mistakes, the victories and all the in-between. <br /><br /><br /><br /><br />Chris Sielinghttps://plus.google.com/116218190535784529711noreply@blogger.com1tag:blogger.com,1999:blog-1947042857821273942.post-9052874474929671182015-09-18T20:58:00.001-07:002015-09-18T20:58:13.579-07:00SBG using 2 Types of QuizzesFor over 5 years I have used a SBG (standards-based grading) system in my room. It starts with listing out the learning targets and only using assessments on those learning targets for the grade. No homework, no behaviors, etc... I have always liked this setup, but I have noticed it shifted my class to a more skill based class. Math became a series of skills, that though they were connected, it seemed the students were less able to apply them in other situations. <br /><br />My homework reflected this as well. I don't give a lot of HW, but for the last couple years I have exclusively used websites like <a href="http://ixl.com/">IXL.com</a> and <a href="http://buzzmath.com/">Buzzmath.com</a> for homework. <br /><br />So I decided something needed to change this year. Here is my plan. In both homework and quizzes there will be two categories: Skills and ACE. Skills HW is from websites and Skill Quizzes are the same as they have been. They are pretty bare bones and focus on whether or not the student can do the math skill or not. What I have added is the ACE HW and quizzes. I took the ACE HW name from my old CMP2 curriculum. It stands for Applications, Connections and Extensions. I could think of no better name for what I am trying to get at with this new HW and quizzes. So I am currently alternating between IXL skills HW and ACE HW. <br /><br />In both cases I am still allowing student choice. The Skill IXL homework comes with 3 choices, Level 4, Level 3 and Level 2 HW. The ACE HW comes with the directions to answer 2 of the questions. The questions have multiple parts and often involve multiple steps and critical thinking to be properly solved. I have a variety of Level 4 and Level 3 problems on the ACE HW. The last ACE HW for 8th grade can be seen<a href="https://www.dropbox.com/s/xxwpq8ulzz9r90w/8th%20ACE%20Linear%20Relationships.pdf?dl=0" target="_blank"> here</a>. <br /><br />The 7th graders just had their <a href="https://www.dropbox.com/s/8iec1i69txfw9dk/7th%20ACE%20Quiz%201.pdf?dl=0" target="_blank">first ACE quiz</a>. It went pretty well. Most students perfectly applied their knowledge to the problem. The average score on the Skills quiz was 3.6, while on the ACE quiz it was 3.2. The 3.6 included retakes by numerous students. The 8th graders will have their first ACE quiz next week. <br /><br />Grading has stayed mostly the same. Their grade was always based on their most recent two quizzes. Now their grade for each learning target is based on their most recent Skills quiz and their most recent ACE quiz. So parents will get a report listing each learning target, their 2 quiz scores and the resulting grade. A summary of how I go from 2 1-4 scores to a percentage grade can be found <a href="http://cjsieling.blogspot.com/2014/02/standards-based-grading-levels.html" target="_blank">HERE</a>.<br /><br />So far, I am very happy with how this is going. I hope it will lead to more problem solving, critical thinking, and applying math in various contexts. <br /><br /><br /><br />Chris Sielinghttps://plus.google.com/116218190535784529711noreply@blogger.com0tag:blogger.com,1999:blog-1947042857821273942.post-38203101663606356612015-08-20T15:08:00.002-07:002015-08-20T15:08:54.411-07:00Starting My Interactive Notebook JourneyI have decided to do Interactive Notebooks this year for 7th and 8th grade math. So I have been reading many blogs and posts about INB. The amazing blogs <a href="http://mathequalslove.blogspot.com/p/inb-resources.html" target="_blank">Math Equals Love</a> and <a href="http://everybodyisageniusblog.blogspot.com/" target="_blank">Everybody is a Genius</a> have been my main reading although there have been many more. Also my great teaching friend Becky over at <a href="https://summathmadness.wordpress.com/" target="_blank">Sum Math Madness</a> has been amazingly helpful as I start this adventure. <br /><br />I have been really excited about this adventure, but there have been a couple major sources of stress. First, the process in class of getting these things made in an efficient manner. Second, what goes in the first couple pages? <br /><br />For the first concern, I created little baskets of materials for each group. They contain things they may need each day as we create materials for the INB. Scissors, tape, glue sticks, markers, colored pencils, and calculators. I found these super cute little baskets at Target for really cheap. I am also going to spray paint some ice cream buckets to use as trash baskets for each group. <br /><div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-NjZcXOlVDFI/VdZL9u0gs2I/AAAAAAAAAZs/aCOhjmY6Nuc/s1600/math%2Bgroup%2Bbasket.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="240" src="http://1.bp.blogspot.com/-NjZcXOlVDFI/VdZL9u0gs2I/AAAAAAAAAZs/aCOhjmY6Nuc/s320/math%2Bgroup%2Bbasket.JPG" width="320" /></a></div><br /><br /><br />For my second concern, I finally got it hammered out last night and created some templates in word to create some basic INB pages. I decided to start with a table of contents, then small individual version of this <a href="http://mathequalslove.blogspot.com/2014/08/growth-mindset-and-sbg-bulletin-board.html" target="_blank">amazing bulletin board</a>, and finally classroom information. <br /><br /><br /><br />I have been a big standards-based grader for years now. This has led to my creating a 1-4 rubric for each of the learning targets of the class. This year I cut them down to 24 for each 7th and 8th grade math. So I wanted to figure out a way to include the rubrics in the INB. I am pretty sure I figured out a format to do this pretty efficiently. We will see how it works out. I will probably have to adjust multiple times as I go. I just have to remember that I will not get everything perfect this year. <br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://3.bp.blogspot.com/-ywrR0LArxIw/VdZP0uxtXxI/AAAAAAAAAZ8/VkcXQsfYJvs/s1600/blog%2B1.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="291" src="http://3.bp.blogspot.com/-ywrR0LArxIw/VdZP0uxtXxI/AAAAAAAAAZ8/VkcXQsfYJvs/s320/blog%2B1.jpg" width="320" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-NnyMf0BnnD4/VdZP0oyEMCI/AAAAAAAAAaA/bn_rZ5wvHEA/s1600/blog%2B2.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="248" src="http://2.bp.blogspot.com/-NnyMf0BnnD4/VdZP0oyEMCI/AAAAAAAAAaA/bn_rZ5wvHEA/s320/blog%2B2.jpg" width="320" /></a></div><br /><br />Chris Sielinghttps://plus.google.com/116218190535784529711noreply@blogger.com1tag:blogger.com,1999:blog-1947042857821273942.post-4446741649456317132015-08-16T15:57:00.001-07:002015-08-16T15:57:57.478-07:00Getting students to think about Brain Function in MathAs we get ready to start another school year, I am really thinking about my first week of school. My first week has couple major goals:<div><ul><li>Get to know students' names</li><li>Convince students they can do math</li><li>Discuss Multiple Intelligences</li><li>Discuss how a teenagers brain works</li><li>Discuss Growth Mindset and Fixed Mindset</li></ul></div><div>I usually don't start any of my official "learning targets" until the second week. I have used numerous approaches for this each year. This year I am going to try to use the youcubed material for "<a href="https://www.youcubed.org/week-of-inspirational-math/" target="_blank">A Week of Inspirational Math.</a>" I am pretty excited about this approach this year. It seems to cover most of my major goals while simultaneously getting into some interesting math. </div><div><br /></div><div>During the week I am going to slowly go through my first week <a href="http://prezi.com/8ygtm_y9yvxr/?utm_campaign=share&utm_medium=copy&rc=ex0share" target="_blank">Prezi presentation</a> about the goals as well. I am going to use this instead of the youcubed videos on various days. </div><div><br /></div><div>When talking about how the brain can get better at math by "doing math" I have used a road analogy in the past. This year I am going to add some visuals to this analogy to hopefully help it sink in. </div><div><br /></div><div>Image 1: Grassy Field</div><div>The road to math starts as a grassy field that is slow and hard to cross. It takes a lot of effort to do math but it can be done. </div><div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-x75aqeUYjZc/VdES5j-NA7I/AAAAAAAAAY4/LNCnYe7fON8/s1600/mindset%2Broads%2B1.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="243" src="http://1.bp.blogspot.com/-x75aqeUYjZc/VdES5j-NA7I/AAAAAAAAAY4/LNCnYe7fON8/s320/mindset%2Broads%2B1.jpg" width="320" /></a></div><br />Image 2: Small Dirt Path<br />As you do more math, the brain upgrades the path a little bit to do math. Now when a student does math the thinking goes a little better because of the repetitive use of that part of the brain. <br /><div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/-RtwLvgql-QI/VdES5f9vsbI/AAAAAAAAAY0/ZHdOp9rMAQk/s1600/mindset%2Broads%2B2.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="http://4.bp.blogspot.com/-RtwLvgql-QI/VdES5f9vsbI/AAAAAAAAAY0/ZHdOp9rMAQk/s320/mindset%2Broads%2B2.jpg" width="269" /></a></div><br />Image 3: Dirt Road<br />The brain upgrades again to you can do harder math and it comes a little faster. <br /><div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/-n30TbUR0uwQ/VdES5p0KufI/AAAAAAAAAY8/bfGxAp0sgh4/s1600/mindset%2Broads%2B3.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="180" src="http://4.bp.blogspot.com/-n30TbUR0uwQ/VdES5p0KufI/AAAAAAAAAY8/bfGxAp0sgh4/s320/mindset%2Broads%2B3.jpg" width="320" /></a></div><br />Image 4: Tarred Road<br />The brain keeps upgrading those connections to math knowledge. The more often you work on math, the better the pathway to math gets so you can learn more complicated math.<br /><div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/-nBm7Alcunm4/VdES5xh86kI/AAAAAAAAAZA/-fQirM7Aeko/s1600/mindset%2Broads%2B4.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="176" src="http://4.bp.blogspot.com/-nBm7Alcunm4/VdES5xh86kI/AAAAAAAAAZA/-fQirM7Aeko/s320/mindset%2Broads%2B4.jpg" width="320" /></a></div><br />Image 5: Interstate Highway<br />The brain keeps upgrading the connections for harder math problems. <br /><div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-e__bUmEtD1g/VdES5294ryI/AAAAAAAAAZE/nokXZE0ZV7o/s1600/mindset%2Broads%2B5.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="224" src="http://2.bp.blogspot.com/-e__bUmEtD1g/VdES5294ryI/AAAAAAAAAZE/nokXZE0ZV7o/s320/mindset%2Broads%2B5.jpg" width="320" /></a></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">Hopefully these images combined with the messages from YouCubed will help convince students that if they keep on trying in math, they will improve their math skills. </div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div><br /></div>Chris Sielinghttps://plus.google.com/116218190535784529711noreply@blogger.com0tag:blogger.com,1999:blog-1947042857821273942.post-14263498258294852572015-02-06T20:48:00.001-08:002015-02-06T20:48:05.905-08:00We're Going on a Square Hunt: Simplifying RadicalsThe class spent a week exploring the Pythagorean Theorem. After creating a need with the students to handle square roots, on Friay we went over how to simplify them. This topic has always been a bit dry and never quite landed with the students. I have always talked about trying to find perfect squares and use those to break down the number. <br /><br />The previous night was parent-teacher conferences. I had some free time and the other math teacher and I started talking about the very topic of simplifying radicals. He said he just went over it with one of his HS classes. He used a factor tree approach and was very successful. So this ignited a crazy idea for the lesson.... <br /><br />So as the class entered today I played this <a href="https://www.youtube.com/watch?v=0gyI6ykDwds" target="_blank">video</a> of Michael Rosen acting out the book We're Going on a Bear Hunt. The kids looked at me and screen like I was crazy. They stared in a silent weirdness at the board for the first minute. Then a crazier thing happened...they started singing along. They all remember this book. They started laughing and getting really into it. It was really fun. <br /><br />After the video, I showed them a couple slides. I used images from the book but changed the words.<br /><div style="text-align: center;"><i>We're going on a square hunt. </i></div><div style="text-align: center;"><i>We're gonna catch a big one.</i></div><div style="text-align: center;"><i>What a beautiful day.</i></div><div style="text-align: center;"><i>Were not scared.</i></div><div style="text-align: center;"><i><br /></i></div><br /><div style="text-align: center;"><i>Oh no, a radical. </i></div><div style="text-align: center;"><i>A big, scary radical.</i></div><br /><div style="text-align: center;"><i>We can't square root it.</i></div><div style="text-align: center;"><i>We can't go around it.</i></div><div style="text-align: center;"><i>We have to go through it.</i></div><br />My mini-version of the story ended with a picture and the square root of 28.<br />We then broke down 28 by using a factor tree. We ended up with Sqrt(2x2x7).<br /><br />I then talked about how we are now starting the "square hunt." We went looking for a length and a width that would make a square. We found the 2x2 to make a square. However, the 7 had no pair to make a square so we left it in the cave. Then we rewrote it as....2 Sqrt(7). <br /><br />We went through another example or too like this. The students really caught on to the method. I am hoping that at some point some students find the shortcut during the method. Even if they don't, this method easily gets exapnded to variables, cube roots, and higher. <br /><br />Anyway it was a really fun day and the students learned something. All in all a great day!<br /><br /><br /><br /><br /><br />Chris Sielinghttps://plus.google.com/116218190535784529711noreply@blogger.com0tag:blogger.com,1999:blog-1947042857821273942.post-31920300053692975052015-02-04T05:13:00.001-08:002015-02-04T05:13:27.639-08:00Conceptual vs Skills (The Pendulum Ever Swings)When I first started teaching, I really didnt know what I was doing. I do what most teachers do, I taught how I was taught math. My second year of teacher the school adopted the Connected Math Project curriculum (CMP). We were trained to teach the curriculum and it was fully implemented the next year. I believe I learned more about middle school math teaching with this curriculum than I did when I was actually in middle school. I continued to use CMP, and then CMP2 almost exclusively for almost 10 years. <br /><br />I found that although the students lacked a couple skills here and there, they could really think through problems. They were great at math reasoning and understanding the big concepts. <br /><br />With more and more emphasis on standards, and with my master's research being about standards based grading, I have slowly drifted away from CMP and more and more towards a traditional looking math classroom. I currently do not use any textbook. I gather materials from various textbooks and sources. While the overall plan was to stick with my favorite parts of CMP, its use has slowly diminished over the past couple years.<br /><br />I didn't reallly realize how far I had drifted away from my CMP roots until about 3 weeks ago when I attended a local math conference. There was a keynote address about Conceptual Understanding vs Skills Proficiency. One of the tools used in this presentation was the "How Old is Your Shepard Problem." (<a href="https://www.youtube.com/watch?v=kibaFBgaPx4" target="_blank">view video here</a>) It was pretty funny and convincing of the need for conceptual understanding. I thought to myself that there is no way my students would do this terrible at the problem. National average is that 25% of students see the problem for what it is, unsolvable. When I polled my own students, only about one-third of them successfully recognized the problem as unsolvable. <br /><br />Some of my student's responses to How Old is the Shepard:<br />"62, because in the Bible, shepdards look old and 62 is old."<br />"37 because he must be living by himself and you probably have to be so old to own sheep."<br />"There is no shepard."<br />"60, it seems like the shepard would have to be older if they have so many animals. Unless there were a lot of shepards then there a bunch of middle aged guys."<br />"70 because shepards have grey beards"<br />"There isn't even such a thing as a flock of dogs."<br /><br />The Conceptual vs Skills debate has been the eternal argument since I have started my math teaching career. I got really sick of having this argument with parents and other teachers. Things got really ugly form both sides for awhile. It was the main cause of some "parent's nights" in math we had at our school where our program and myself were attacked in public. It was not a fun time for anyone. I always vowed to avoid that type of fighting in the future. I now find I am having those same exact arguments but inside my own head. I have come a realization that my own pendulum has swung too far to the skills side. I need to try to find my center again. <br /><br />The timing is kind of perfect, as in the 8th grade we are just starting our Pythagorean Theorem unit. This was always my favorite when using CMP. So this week we tried our first couple days using more materials based from CMP. It got off to a rocky start. Partly because I was a little rusty teaching in the "inquiry" style and partly because the students have not had a lot of practice at it. However, when I saw the looks on the students' faces that discovered the Pythagorean Theorem all on their own, and could not wait to share with the class their marvelous discovery, it reminded me how powerful this can be. <br /><br />I am sure at some point my pendulum will swing too far back the other way and I will need another course correction, but that worry can hold off for another time...Chris Sielinghttps://plus.google.com/116218190535784529711noreply@blogger.com0tag:blogger.com,1999:blog-1947042857821273942.post-4419641632022043222015-01-29T19:20:00.002-08:002015-01-29T19:20:35.710-08:00Something funny and kind of scary happened....So on Monday this week, I woke up really sick at about 3 am. Now it so happened that I had planned on getting most of my lessons ready to go during my period 2 prep that day. So I knew that I had not much ready for a sub to work with if I just stayed home. Throw in another fact that I was supposed to be running a junior high math league meet 45 minutes before school started. So I ended up pulling myself together enough to get through the math league meet. Then I would use 30 minutes to get lesson plans together for the day. I would then head home and let the sub run the rest of the day for periods 3-9. <br /><br />So after no sub signed up for my gig, I told the secretary that we only needed someone for periods 3-9 because I would be there for the first two periods because of math league. She said okay, I ran my math league meet, created some activities and headed home. <br /><br />My usual routine when I am going to be gone for the day is to email lesson plans not only to our secretary, but all the students as well. I find it usually helps the sub out and helps the students know what is going ot happen that day even though I am not in the room. On this Monday I did send an email to all my students giving a quick outline to the plan for class and I attached the necessary materials. <br /><br />So when I get to school on Tuesday, and interesting thing happened. I immediately had 3 students run up to me and say "We had no teacher Mr. Sieling!" I said "What?" They told me "all from the same class, that no teacher ever showed up to run class on Monday. It happened in just 1 class period, but still I was a little worried about what had happened. <br /><br />So I believe they came into class on Monday, realized there was no teacher. At some point looked for the normal Monday game, realized there was no game, no teacher and then started working on their assignment. Now, these are 7th grade students. I doubt it was quiet. In fact, a group of girls moved to work in the hallway because "the boys were loud." However, they all got their work done without the teacher even being there. I was pretty proud of them for that. <br /><br />Chris Sielinghttps://plus.google.com/116218190535784529711noreply@blogger.com0tag:blogger.com,1999:blog-1947042857821273942.post-614201623496273002015-01-25T06:07:00.003-08:002015-01-25T06:09:42.304-08:00Quizzing to Promote MasteryIts been a long time since the last post. I have been pretty busy lately, even more than usual. From coaching junior high and high school math league to coaching the inaugural year of our junior high robotics league to presenting at various conferences, it has been a crazy winter so far. I thought I would try to get a quick post out while I have a moment. <br /><br />In 8th grade we have been studying solving equaitons and inequalities that past 2-3 weeks. The students took a paper/pencil quiz on equations in December. So I tried a different way to quiz last week. I got the foundation of this idea from a book, don't remember which one, I will try to find that title later.<br /><br />The basic gist is that students answer 1 question at a time on their own. We switch, correct that problem in class and go over how to do it. Then we try another question (or set of questions) and repeat. We do this over and over again so students can be remediated during their quiz. I like the idea of this "quiz to mastery." <br /><br />I took this to the next level by adding my differentiated rubric to the idea. It went like this, the first round of the quiz everyone tried to solve 1 Level 2 question. (<a href="http://cjsieling.blogspot.com/2014/02/standards-based-grading-levels.html" target="_blank">leveled grading blog</a>) When people were done we switched and corrected that question. If the student got it right they earned at least a score of a 2 on that quiz. If they got it wrong they got some help about their mistakes. When we were ready (about 3-5 minutes later) round 2 began. <br /><br />Round 2 now had two questions on the board. The slide had two questions on it: level 2 question that was similar in difficulty to the first question, as well as a level 3 question for those who got the first one question correct. After about 3-5 minutes we switched and corrected those two questions. We again spent some time helping each other out and figuring out mistakes. <br /><br />Round 3 had three questions on the board: Level 2, Level 3 and Level 4. We continued this way until the end of class. We got in about 5 rounds of this style quiz. The score the student earned on the quiz was the highest level of question they got correct. <br /><br />Overall the students seemed to like this style quiz. There were some who did not like it. The biggest reasons seemed to be that it was different or they did not ge the score they wanted. This type of quiz works particularly well for skills like solving equations. I may use it again for solving inequalities, I will probably leave that choice up to the students. <br /><br />Here is my google slide presentation for giving this quiz to mastery.<br /><br /><iframe allowfullscreen="true" frameborder="0" height="299" mozallowfullscreen="true" src="https://docs.google.com/presentation/d/1ZpP-RKFuXGLxiQx8mO1ykd2imEiNWsADjCsgPjSHwCc/embed?start=false&loop=true&delayms=5000" webkitallowfullscreen="true" width="480"></iframe>Chris Sielinghttps://plus.google.com/116218190535784529711noreply@blogger.com0tag:blogger.com,1999:blog-1947042857821273942.post-68253846100231472502014-11-16T14:46:00.000-08:002014-11-16T14:46:44.514-08:00Parallel & Perpendicular SlopeI have always struggled getting students to really understand how to use slope to create parallel and perpendicular lines. I have tried many things and many different activities over the years. <br /><br />This year I did the typical investigation about parallel and perpendicular slopes. It works pretty well for setting up 3 sets of parallel lines and 3 sets of perpendicular lines and asking students to analyze the equations for patterns. This took 2 days and went pretty well. <br /><br />Now on the third day I wanted them to put this new found knowledge to use. So I created the following <a href="http://www.lakeview2167.com/cms/lib02/MN01001909/Centricity/Domain/123/Desmos%20Graphing%20Challenge.pdf" target="_blank">DESMOS graphing challenge</a> for them. (feel free to use and change for your use)<br /><br />The challenge started pretty basic to make sure they correctly recalled the patterns for parallel and perpendicular slopes.<br /><div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-27ePg9As4YU/VGkm4NPn7SI/AAAAAAAAAS0/fo_RFyqxV-E/s1600/blog1.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://2.bp.blogspot.com/-27ePg9As4YU/VGkm4NPn7SI/AAAAAAAAAS0/fo_RFyqxV-E/s1600/blog1.jpg" height="246" width="400" /></a></div><br /><br />The next couple asked the students to start creating shapes using their patterns.<br /><div class="separator" style="clear: both; text-align: center;"><a href="http://3.bp.blogspot.com/-snAAoGuAWBU/VGknLz4BJwI/AAAAAAAAAS8/cygvXuAuGto/s1600/blog2.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://3.bp.blogspot.com/-snAAoGuAWBU/VGknLz4BJwI/AAAAAAAAAS8/cygvXuAuGto/s1600/blog2.jpg" height="302" width="400" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;">There were a couple more like this and students overall handled it pretty well. There were a couple questions about what a parallelogram was, which I totally expected. </div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">A few students got off to a slow start because they did not recall anything about parallel and perpendicular slopes. This did allow me to find them quickly and re-teach the concept. Once they could visualize the graph on DESMOS with the slopes they seemed to do much better. </div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">A few student got off to a slow start because they did not understand what they were being asked to do. This was partially because my projector lamp blew up and I had no way to project anything. It was also because I threw this together quickly and I don't think it was as clear as it should have been. I will have to tackle that next year.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">Overall it worked pretty well. We will see if this is the year where I can get students to remember perpendicular slopes!</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">Chris</div><br />Chris Sielinghttps://plus.google.com/116218190535784529711noreply@blogger.com0tag:blogger.com,1999:blog-1947042857821273942.post-89483934564451657882014-11-05T13:37:00.001-08:002014-11-05T13:37:21.894-08:00Class Debates in Math Continued...So yesterday we had a debate about math totally go off the rails. Students kept arguing without really basing anything on logic or facts or even good common sense. It sometimes sounded like a 24 hour news network where people yell "I''m right because I feel I am right!" and then someone else yells "No, I'm Right, because I'M LOUDER!" Only 1 section had this, but still I couldn't stop thinking about how badly this went. <br /><br />So today we started <a href="http://www.mathtalks.net/teachers.html" target="_blank">number talks</a>. Number talks are just a format for discussing interesting math questions that stress reasoning and estimation skills. Fawn Nguyen is the amazing teacher behind this website. Her <a href="http://fawnnguyen.com/" target="_blank">blog</a> is awesome of course. <br /><br />We started with the first question on the site. <br /><br /><b><i>"Are there more seconds in a day, or inches in a mile?"</i></b><br /><br />Before we started, I wasn't sure what to expect. I wasn't sure the students would be engaged, participate in quiet thinking time or be able to explain their thoughts. I was worried that students wouldn't even know where to start and give up right away. <br /><br />So I put together this smartnotebook slide to help keep the class focused. <br /><div class="separator" style="clear: both; text-align: center;"><a href="http://3.bp.blogspot.com/-EFS_l_WUeFw/VFqXFkqyQJI/AAAAAAAAASk/66FNMLUn-pQ/s1600/number%2Btalks.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://3.bp.blogspot.com/-EFS_l_WUeFw/VFqXFkqyQJI/AAAAAAAAASk/66FNMLUn-pQ/s1600/number%2Btalks.jpg" height="281" width="400" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;">The timer is clearly displayed as well as the steps. Also the blue box is a random name generator. I like having the first name displayed because it gives fair warning to that student that they are going to be expected to speak about this question. (you can also see I type to fast and have a typo in the question!)</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">So every section today went extremely well! Students respected the 2 minutes of initial thinking time. I could see some students racking their brain for an answer, a way to approach the problem, or just an idea. Some students looked around like "He is crazy if he thinks I can do this in my head!"</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">The discussion time was the best. All students were engaged. I mean 100% engagement. Students either could not wait to share their ideas or they could not wait to hear someone give them a clue about the answer. I heard great discussion all day long about this problem and different and fantastic ways to approach it. </div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">The sharing part was a little rough in most classes, but all reasons for picking a side were grounded in math and common sense. There were no 24-hour news channel type arguments, just reasonable debate. </div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">I told them I plan to do a problem like this 1-2 times a week. Most were excited. Some groaned. However when I asked them why they groaned, they almost all responded about "having to think to hard" That is just what a math teacher loves to hear!</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><br /></div><br />Chris Sielinghttps://plus.google.com/116218190535784529711noreply@blogger.com0tag:blogger.com,1999:blog-1947042857821273942.post-32283884862367407232014-11-04T17:50:00.001-08:002014-11-04T17:50:49.046-08:00Classroom Debates about Math...Today the 7th graders were studying integers. We are getting ready to add and subtract them. Yesterday we represented adding and simple subtracting on a number line. Today we went with a chip board, with black chips representing positive numbers, and red chips representing negative numbers. <br /><br />I told them that we are going over multiple representations of adding and subtracting to get to the best understanding we could about the operations. I emphasized we are not going to depend on memorized rules, we must strive to understand adding and subtracting. This was of course met with some blank stares and confusion. During their previous year in 6th grade the teachers quickly skimmed the service of arithmetic with negative numbers. Of course they talked about rules like adding two negatives is always negative, multiplying two negatives is always positive and so forth. <br /><br />Everything was going quite well with the chip board lesson for the first 30 minutes. Then with 14 minutes left I asked them to solve -4 - -3 and represent the solution on a chip board. This was the first negative subtracted by a negative problem of the day. The previous section and last section of the day handled this fine. They used the methods we had talked about and it resulted in a short discussion. <br /><br />However in my middle section of 7th graders, most of the students had ended up with -7 as an answer. The seating arrangement of the class has 6 groups of 4-5 students in each group. Four of the groups had come to a -7 conclusion. One of the groups came to a -1 conclusion. The last group knew the answer was either -7 or -1 but they couldn't decide which way to go. <br /><br />So we set up a little debate on the topic. A very loud and confident 7th grader proudly proclaimed a misstated rule from 6th grade and proclaimed -7 to be the answer. I held back any judgement and most of the students nodded in agreement. I then called on a student to present their argument for -1. They went to the smartboard and explained in a perfectly correct way that -4 - -3 was -1. No mention of rules they remembered they just used the chip board. When they finished 2 students loudly and confidently recited different rules incorrectly proclaiming -7 to be the answer. <br /><br />At this point I reminded them how using rules can be confusing and we have to focus on what adding and subtracting means. This fell on completely deaf ears. At this point the 4 groups held fast to their wrong -7 answer, but there were now 2 groups solidly in the -1 camp. We were also down to about 4 minutes left of class. <br /><br />Now I love student debate, I love discussions in math, I love to hear the thought processes of students, and I whole heartedly believe that mistakes push learning forward. However, I just couldn't bring myself to let the class leave thinking that -4 - -3 was -7. So I asked for anybody to argue for the -1 answer, because there were several students still shouting out arguments for -7. When nobody stepped up I felt I had to make an argument for -1. <br /><br />So I asked them the questions that I thought would end the debate:<br />"If you have 4 red things, and you take away 3 red things, how many red things do you have left?" <br />They all correctly answered 1 red thing. The 2 groups beamed with delight that -1 was correct. Most of the other students looked a little confused, and 3 students starting misquoting rules to me about negative numbers to continue arguing for -7. At this point I told them that -1 was the answer. I showed them in a similar way to the first student using the chip board that -4 - -3 was -1. Some students still did not believe me. <br /><br />At this point there is about 1 minute left of class and I am desperate to make sure students know that -4 - -3 is -1. So I made a last ditch effort and pulled up my smartboard calculator. I typed in the problem, asked them if it was entered correctly and hit enter. When -1 popped up as the answer, I actually think there were still students who thought -7 was the answer. <br /><br />There is no great ending to this story yet. I have to tackle all the misconceptions tomorrow. I am pretty sure I completely messed up this lesson and students thinking about integers. I am not sure what I should have done differently after the debate started. I made sure in my next 7th grade section to take the subtraction slower and emphasize that subttracting is 'taking away.' Now I just have to figure out how to right the ship for a group of stubborn 7th graders. Chris Sielinghttps://plus.google.com/116218190535784529711noreply@blogger.com0tag:blogger.com,1999:blog-1947042857821273942.post-60915354971435588462014-11-01T09:38:00.000-07:002014-11-01T09:38:51.444-07:00PLCs, sharing ideas, creating lessons and StatisticsI just want to share how much I love my PLC group. In our school we do PLCs by content area. We are a small school so we have 2 math teachers, 2 science teachers, 1 STEM teacher, and a special education teacher. We meet about every other week for 1.5 hours. It is always an amazing experience. <br /><br />2 meetings ago, I went in to develop a lesson on mean and median. I mentioned how I always struggle with students realizing how an outlier can effect mean much more than median. Through discussion and brainstorming we came up with a great idea using blocks, a meter stick, and a balance point. This lesson would have never come together the way it did without my PLC group. <br /><br />The lesson involved creating sets of data with a mean of 50. A meter stick was then balanced and blocks were placed at the data points to create a balance. Students were asked to put on an "outlier" block and recalculate the mean and median. <br /><br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/-YfabAbTfgok/VFPS9QgOjJI/AAAAAAAAASM/QaTylDiVB74/s1600/blogpic1.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://4.bp.blogspot.com/-YfabAbTfgok/VFPS9QgOjJI/AAAAAAAAASM/QaTylDiVB74/s1600/blogpic1.jpg" height="205" width="400" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><br />This activity was also used to visualize missing data point problems with a given mean. Students placed blocks on the meter stick and saw how it didn't balance. Then they were asked to place a block so the meter stick would balance at 50 (have a mean of 50). <br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-HxhKHdCSB58/VFPS9fyUNhI/AAAAAAAAASQ/0NzmvFRHqQ8/s1600/blogpic2.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://2.bp.blogspot.com/-HxhKHdCSB58/VFPS9fyUNhI/AAAAAAAAASQ/0NzmvFRHqQ8/s1600/blogpic2.jpg" height="246" width="400" /></a></div><br />A quick bare-bones handout can be found <a href="https://drive.google.com/file/d/0B3wXpTi1HaDUdmFPMXc3X09wQVk/view?usp=sharing" target="_blank">here</a>. <br /><br /><br />Chris Sielinghttps://plus.google.com/116218190535784529711noreply@blogger.com0tag:blogger.com,1999:blog-1947042857821273942.post-20350428997968061792014-10-22T17:26:00.000-07:002014-10-22T17:26:17.170-07:00Estimation 180 & Statistics I am late to the party here, but the website estimation180.com is amazing. <br />I have just this year finally started using it during class. <br /><br />For those not familiar with the site, math teacher Andrew Stadal created some great problems and hooks that require students to use estimation and reasoning skills. Some very important skills that are getting lost in the standards driven era of school. <br /><br />For example, this is the first and second problem I had my students think about. <br /><br /><div class="separator" style="clear: both; text-align: center;"><b>#1) How many almonds in the 1/4 cup?</b></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://3.bp.blogspot.com/-dh1eOsnGdZs/VEhEugC2AXI/AAAAAAAAARg/q4HZGVR7-bw/s1600/almonds%2B1.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://3.bp.blogspot.com/-dh1eOsnGdZs/VEhEugC2AXI/AAAAAAAAARg/q4HZGVR7-bw/s1600/almonds%2B1.jpg" height="240" 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;"><b>#2) How many almonds in the large container?</b></div><div class="separator" style="clear: both; text-align: center;"><b><br /></b></div><div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/-gMOLcfOX6R4/VEhEuswiWAI/AAAAAAAAARk/p1OofJM-ydM/s1600/almonds2.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://4.bp.blogspot.com/-gMOLcfOX6R4/VEhEuswiWAI/AAAAAAAAARk/p1OofJM-ydM/s1600/almonds2.jpg" height="240" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;">The website is called estimation 180 because they recommend one of these problems a day. I do not use it that way. I do two problems at a time, once a week. I use these problems a lot with 7th graders. In MN many of the standards in 7th grade deal with proportional reasoning. </div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">So I have them do the first question shown above and ask the students for 3 numbers. </div><div class="separator" style="clear: both; text-align: left;">1. What number is too high?</div><div class="separator" style="clear: both; text-align: left;">2. What number is too low?</div><div class="separator" style="clear: both; text-align: left;">3 What is your best estimation? (your "bestimation")</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">Then I when they have those three numbers, I reveal the answer, drawing the moment out until they are begging for the answer. After I reveal the answer I immediately throw up the second image as well. Now I add a question to the mix...</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both;">1. What number is too high?</div><div class="separator" style="clear: both;">2. What number is too low?</div><div class="separator" style="clear: both;">3 What is your best estimation? (your "bestimation")</div><div class="separator" style="clear: both;">4. Explain your reasoning (more than "I guessed")</div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;">The more we do these the better the students are getting at thinking with proportionality. If they know how many almonds are in the 1/4 cup, they use that number to make a good estimation for the large container. </div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;">We are on about our 5th week of this. The answers I am getting are starting to get better and the reasoning more sound. When I give them feedback on their answers, I focus solely on the reasoning aspect. </div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;">We started our statistics learning target about a week ago. This entails measures of center and measures of variability. So when we did our weekly estimation problem last week, I had them submit their answers and reasoning using a google form. </div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;">The estimation problem was about the large pumpkin below. </div><div class="separator" style="clear: both;">Knowing the weight of the small pumpkin, they had to estimate the large pumpkin's weight. </div><div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/-STUN-hfeouk/VEhKGzsaJAI/AAAAAAAAAR8/ql403iMqT0Y/s1600/pumpkin1.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://4.bp.blogspot.com/-STUN-hfeouk/VEhKGzsaJAI/AAAAAAAAAR8/ql403iMqT0Y/s1600/pumpkin1.jpg" height="239" width="320" /></a></div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;">Then this week I created a quick PDF with their best estimations sorted by class. Today their job was to analyze the data (find the mean, median, mode, range quartiles and IQR) for each class. </div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;">Then after they worked to find the answers to those, they took 5-10 minutes to discuss which class had the "best estimations." I left this vague on purpose. This led to some great conversations among the students. It also let me reteach where the meaning of the numbers was missing. For example some students tried to argue that a class's IQR was close to 14 (weight of large pumpkin), so they were the best. So it was good to catch those misconceptions early. </div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;">It was really nice that it worked out that one class had the closest mean, another had the closest median, and the other class had the closest mode. That was a little magical bonus I got with no planning whatsoever. </div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;">The 3 data sets are here if you would like to look at them. </div><div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-i2z7CRETwoc/VEhJb--eIqI/AAAAAAAAAR0/7UsIs3kcIEc/s1600/qrcode.25437788.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://2.bp.blogspot.com/-i2z7CRETwoc/VEhJb--eIqI/AAAAAAAAAR0/7UsIs3kcIEc/s1600/qrcode.25437788.png" height="200" width="200" /></a></div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;">All in all it was a great day of talking and analyzing statistics. </div><div><br /></div><div>thanks!</div><div>Chris</div><br /><br />Chris Sielinghttps://plus.google.com/116218190535784529711noreply@blogger.com1tag:blogger.com,1999:blog-1947042857821273942.post-83852902865134136302014-09-10T20:04:00.002-07:002014-09-10T20:04:47.069-07:00Algebra & MathemagicThe 7th graders recently started studying algebraic expressions. We started with combining like terms with a heavy emphasis on algebra tiles. This really helps the 7th graders make it visual. So we spent a couple days playing around with the algebra tiles and combining like terms. All this sets the stage for<br /><br />MATHEMAGIC<br /><br />So we started today's class with a little "<a href="https://www.teachingchannel.org/videos/class-warm-up-routine" target="_blank">my favorite mistake</a>" to review expressions. <br />The students then we told "we are going to have a little contest." <br /><br /><ul><li>Students were asked to pick a number from 0-50. </li><li>I told the students they would be asked to perform 5 steps with the number.</li><li>At the end of the steps, whichever student was closest to the "magic number" would win.</li><li>The students were instructed to keep their numbers a secret. </li><li>The students then performed the following steps.</li><ul><li>Add 5 to your number</li><li>Double the result</li><li>Subtract 4 from the result</li><li>Divide the result by 2</li><li>Subtract the number you originally chose</li></ul><li>The instructions were given slowly, deliberately, and in a way that increases the drama</li><li>(really the slowness is to make sure students are doing their arithmetic correctly)</li><li>After the final step, students are instructed to keep their final number a secret</li><li>The magic number is then revealed by playing <a href="https://www.youtube.com/watch?v=LVfe6rdHRKI" target="_blank">this video</a></li></ul>Watching the joy cross the faces of the students as they realize their number is the magic number, and then the subsequent confusion is priceless. They are completely hooked by these magical results. Every student (no matter what number they picked) ends up with an answer of 3. <br /><br />I then challenge students to think of a number that will break this trick. Students vary in their suggestions but the fun ones include super large numbers, decimals, and negative numbers. Today I had 1,000,000,001 suggested along with -2.51515. By allowing the students to chose the numbers they are more invested in the process and it really hits home that "any number" ends up with an answer of 3. <br />After the students realize they can not "break the trick" we break down the trick with algebra tiles. We walk through each step and perform the operation with algebra tiles. <br /><br />This is pretty much the end of day 1. <br /><br />The next couple days are spent practicing number tricks with algebra tiles and eventually being able to seamlessly manipulate algebraic expressions without algebra tiles. <br /><br />The lesson is loosely based off of a CPM lesson. <br /><br />Chris<br />Chris Sielinghttps://plus.google.com/116218190535784529711noreply@blogger.com0tag:blogger.com,1999:blog-1947042857821273942.post-5313535300991957562014-09-07T06:43:00.000-07:002014-09-07T06:43:50.643-07:00No Grades for Homework...We just finished up our third week of school on Friday. I recently wrote about my first week of school where we talked about the brain, mindset, and multiple intelligences. During that week I mentioned several times that homework this year will not be a part of the grade. The first week of school is always a tidal wave of information for students. Our school is rolling out a 1:1 program this year, so that kind of doubles the first week information. <br /><div><br /></div><div>So I was helping some 8th grade students with their homework this week, which was tough, and a student asked me "what grade do I get for this?" I said "what do you mean?" They responded "you know how many points do I get?" I reminded him that homework does not actually count towards their quarter grade. Homework is for practice. I had about 10-15 kids in the room at that time. About half said "Oh yeah, I remember that." About a quarter of them said "Really?!" Then the last group said "What?!?! Then why am I doing this?!?!?" One girl even marched out of the room in a hissy fit. </div><div><br /></div><div>I noticed that the majority of my 7th graders knew, and my 8th graders had forgotten or never heard that in the first place. So that day I talked about it again with the 8th grade students. During 8th grade math I reminded all the students that HW does not count towards your final grade. Some asked "So do we have to do all of it?" I fell back on the practice vs game analogy as that is probably the easiest way to explain to students the point that homework is for practice to make yourself better. The game is what decides the level of our success. I asked them if they would look at their coach and say "do we have to do this?" or even walk out of practice when it was half done. They agreed that that would be silly. </div><div><br /></div><div>I give one weekly homework assignment. It is based around basic applications of the ideas we are doing in class. I always give two choices of problems to do as well, an "A-level" and a 'B-level." I use class time for the upper end of Bloom's. I am tracking their scores on HW so I can report to parents. The scores do show up in their online gradebook with a weight of zero (which probably caused some of the confusion). </div><div><br /></div><div>I am wondering what will happen to their scores now that they think "homework doesnt count." Just how successful will I be in trying to instill an intrinsic motivation to get homework done. Will some of them ever see that they are doing homework to help make them better? </div><div><br /></div><div>Also I am just waiting for the parent wave of questions, comments and complaining. I do send out a weekly newsletter via email. I did address it in the newsletter. I also made a video explaining how grading works in my room and why homework is not counted in the grade. However after sending out the email to over 100 sets of parents, I got exactly 2 views. So I need to rethink that strategy. I did put the video on the front page of my website. </div>Chris Sielinghttps://plus.google.com/116218190535784529711noreply@blogger.com0