tag:blogger.com,1999:blog-86541923312934200792019-01-15T12:39:29.937-08:00Make Sense of MathMichelle Sigarannoreply@blogger.comBlogger31125tag:blogger.com,1999:blog-8654192331293420079.post-55355040009870278832019-01-07T19:20:00.000-08:002019-01-07T19:20:17.987-08:00Assessments: Conceptual Understanding vs. Procedural Fluency<div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-s7h2RGQGnGw/XDQViQ4IrtI/AAAAAAAAbDo/L4SjzvivQYAKsMWHNfn9FcithGw5eJI7QCLcBGAs/s1600/assessments%2Btop%2Bpic.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1539" data-original-width="1600" src="https://2.bp.blogspot.com/-s7h2RGQGnGw/XDQViQ4IrtI/AAAAAAAAbDo/L4SjzvivQYAKsMWHNfn9FcithGw5eJI7QCLcBGAs/s1600/assessments%2Btop%2Bpic.jpg" /></a></div><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;">I was at the beginning of my teaching career when the "turmoil" over the common core standards was in full force. My state had changed their standards to the "Utah Core Standards," but they were really the common core standards in disguise. They were trying to avoid the terminology "common core" and all the political problems it was causing, but the truth was that the state recognized that these were quality standards, and it would benefit the students in my state if they were implemented. </span><br /><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;">Before the 1960's arithmetic was the majority of what was taught in math class. Then the United States entered the space war with Russia...the USA was determined to become the best. As a result, the "new math" was introduced. The "new math" dove into matrices, trigonometry, geometry, and more all on a very conceptual level. The "new math" eventually received a lot of push back as many people thought it would be more beneficial for students to learn a little about a lot of math. The curriculum then changed to "a mile wide but an inch deep." At this point, math became less conceptual and more algorithm based. The students that naturally had good math reasoning were still pushed along and entered Calculus during high school, but every one else started to get left behind. This became evident when they entered college. The basic level math classes at the the Universities were full and many students were struggling. </span><br /><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;">It was clear that the standards were failing many students. Purely conceptual wasn't a solution, and purely procedural didn't work either. The new standards were created with the goal of valuing conceptual and procedural. With these new standards, the hope of many educators is to not lot students get left behind. To allow all students to succeed. First, teach at a conceptual level so students can reason through the mathematics and perhaps even discover an algorithm. Encourage procedural fluency, but only after they have mastered conceptual understanding. </span><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-8TiIFP7FW98/XDQV0NoUN9I/AAAAAAAAbDw/qWnfi4grLussgJ_VwCGZwwXyoHT8kPkewCLcBGAs/s1600/assessments%2Bpic.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="900" data-original-width="1408" height="127" src="https://3.bp.blogspot.com/-8TiIFP7FW98/XDQV0NoUN9I/AAAAAAAAbDw/qWnfi4grLussgJ_VwCGZwwXyoHT8kPkewCLcBGAs/s200/assessments%2Bpic.jpg" width="200" /></a></div><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;">With these ideas in mind is how I create all of my resources. Valuing both conceptual understanding and procedural fluency. If you are interested in some math assessments that assess both conceptual understanding and procedural fluency you can click on the links below. They are also editable for use year after year. </span><br /><br /><ul><li><a href="https://www.teacherspayteachers.com/Product/7th-Grade-Math-Assessments-Common-Core-Bundle-EDITABLE-3119055" style="font-family: Verdana, sans-serif;" target="_blank">7th Grade Math Assessments</a></li><li><span style="font-family: "verdana" , sans-serif;"><a href="https://www.teacherspayteachers.com/Product/8th-Grade-Math-Assessments-Common-Core-Bundle-EDITABLE-3185425" target="_blank">8th Grade Math Assessments</a></span></li></ul><div><span style="font-family: Verdana, sans-serif; font-size: large;"><br /></span></div><div><span style="font-family: Verdana, sans-serif; font-size: large;"><a href="https://mailchi.mp/638241b4d4e9/makesenseofmath" target="_blank">GRAB YOUR FREEBIES HERE!</a></span></div><div><br /></div><div class="separator" style="clear: both; text-align: center;"></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-oDHjLMpAFqA/XDQWexgRrFI/AAAAAAAAbD8/3_dFkHn2keYog79dSVfLEhahdyBxTDIkQCLcBGAs/s1600/assessments%2Bblog%2Bpin.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="1067" height="320" src="https://1.bp.blogspot.com/-oDHjLMpAFqA/XDQWexgRrFI/AAAAAAAAbD8/3_dFkHn2keYog79dSVfLEhahdyBxTDIkQCLcBGAs/s320/assessments%2Bblog%2Bpin.jpg" width="213" /></a></div><div><br /></div>Michelle Sigaranhttps://plus.google.com/109631622949404421728noreply@blogger.comtag:blogger.com,1999:blog-8654192331293420079.post-38678007263363515552018-12-03T20:35:00.000-08:002018-12-19T10:10:28.708-08:00How to Teach Percents So They Stick<div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-HYBwgJY9cyU/XAX9w9H3wJI/AAAAAAAAatQ/U_714byx5MUpMKSQWTG8fjZEknZwMLV2ACLcBGAs/s1600/percent%2Bblog%2Btop%2Bpic.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1539" data-original-width="1600" src="https://3.bp.blogspot.com/-HYBwgJY9cyU/XAX9w9H3wJI/AAAAAAAAatQ/U_714byx5MUpMKSQWTG8fjZEknZwMLV2ACLcBGAs/s1600/percent%2Bblog%2Btop%2Bpic.jpg" /></a></div><div class="separator" style="clear: both; text-align: center;"></div><br /><div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"></div><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;">Using bar models to teach percents of whole or to calculate the whole given the percent and part is a very effective way to teach percents conceptually. When introducing this way, I highly suggest starting off with percents that are divisible by 5. You can eventually do any percent with combinations of 5% and 1% as a tenth of 10%, but start off simple.</span><br /><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;">Let's look at percents of a whole.</span><br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Percents-and-Bar-Models-Task-Cards-2683738" target="_blank"><span style="font-family: "verdana" , sans-serif;"><img border="0" data-original-height="510" data-original-width="632" height="161" src="https://1.bp.blogspot.com/-8-Tf2PpBG6U/XAWqDp4AXAI/AAAAAAAAasM/Xy-d9CHz61wvtTtaJURcVJjjAVnXqGIbACLcBGAs/s200/blog%2Bpic%2B1.jpg" width="200" /></span></a></div><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;">An entire bar will represent the whole. Draw the bar and label the whole.</span><br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Percents-and-Bar-Models-Task-Cards-2683738" target="_blank"><span style="font-family: "verdana" , sans-serif;"><img border="0" data-original-height="492" data-original-width="639" height="153" src="https://1.bp.blogspot.com/-wGeQm3vClRM/XAWqDoSlADI/AAAAAAAAasQ/Lhy-85TxumIW1UEbSveAkUgyGtsy3tRCACEwYBhgL/s200/blog%2Bpic%2B2.jpg" width="200" /></span></a></div><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;">Then you need to divide up the bar based on the given percentage. 50% would be in half. 20% would be divided into fifths. 30% would be divided into tenths. Use guiding questions to help your students think of how to divide the bar. If they are stuck, always dividing it up into tenths or fifths should work, as long as you are using percentages that are divisible by 5. </span><br /><span style="font-family: "verdana" , sans-serif;"><br /></span><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Percents-and-Bar-Models-Task-Cards-2683738" target="_blank"><span style="font-family: "verdana" , sans-serif;"><img border="0" data-original-height="487" data-original-width="634" height="153" src="https://3.bp.blogspot.com/-0mRJNkjT5Nc/XAWqD3h85RI/AAAAAAAAasU/ZkojJsIIO_4lacBUsVMvrIHnclawMuYiQCEwYBhgL/s200/blog%2Bpic%2B3.png" width="200" /></span></a></div><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;">Next you need to divide the whole up into that many sections. Again, use guided questions to help your students figure out how to do this. They should come to the conclusion that the whole divided by the number of parts is the amount per section. Write that amount in each of the sections.</span><br /><span style="font-family: "verdana" , sans-serif;"><br /></span><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Percents-and-Bar-Models-Task-Cards-2683738" target="_blank"><span style="font-family: "verdana" , sans-serif;"><img border="0" data-original-height="515" data-original-width="664" height="155" src="https://3.bp.blogspot.com/-YaMJ6X94veM/XAWqEbE54AI/AAAAAAAAaso/NGO3euMdMx4PttB05Q37-YIlgwF_9dkPwCEwYBhgL/s200/blog%2Bpic%2B4.jpg" width="200" /></span></a></div><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;">Lastly, determine how many sections you need for the given percentage. The students should already know what percent is each section from the first step. After the number of sections is determined, I like to color the sections in on my bar so students can visually see the percentage of the whole. They can then determine the part by looking at the value of the total colored sections. </span><br /><span style="font-family: "verdana" , sans-serif;"><br /></span><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Percents-and-Bar-Models-Task-Cards-2683738" target="_blank"><span style="font-family: "verdana" , sans-serif;"><img border="0" data-original-height="489" data-original-width="637" height="153" src="https://1.bp.blogspot.com/-bu9WdCeL3sc/XAWqElu3aYI/AAAAAAAAass/OPKy9tB0x0484iJ-id8Wix6hNJBHyYnZQCEwYBhgL/s200/blog%2Bpic%2B5.jpg" width="200" /></span></a></div><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;">Bar models can also be used with finding the whole given a part and a percent as well as finding the percent given the part and whole. </span><br /><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;">Let me just put this disclaimer on this method: Doing percents with bar models may take a lot of work at first. Each problem will take longer than if you just gave your students an algorithm. This is how it is with most conceptual teaching. However, I know that as you teach conceptual at first, and take the time to have the math make sense to the students, they will retain the information, and in turn, you won't have to do all of the extra review at the end.</span><br /><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;">If you are interested in the task cards used in the photos you can get them <a href="https://www.teacherspayteachers.com/Product/Percents-and-Bar-Models-Task-Cards-2683738?aref=3ml3pyn0" target="_blank">HERE</a></span><br /><span style="font-family: Verdana, sans-serif; font-size: large;"><br /></span><a href="https://mailchi.mp/638241b4d4e9/makesenseofmath" target="_blank"><span style="font-family: Verdana, sans-serif; font-size: large;">GRAB YOUR FREEBIES HERE!</span></a><br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-NYqwU_9eMdc/XAX9xQYYp4I/AAAAAAAAatU/ImuzWDxikwwvpkP_Det-xSFp80obNoSnACLcBGAs/s1600/percent%2Bblog%2Bpin.jpg" imageanchor="1"><img border="0" data-original-height="1600" data-original-width="1067" height="320" src="https://2.bp.blogspot.com/-NYqwU_9eMdc/XAX9xQYYp4I/AAAAAAAAatU/ImuzWDxikwwvpkP_Det-xSFp80obNoSnACLcBGAs/s1600/percent%2Bblog%2Bpin.jpg" width="213" /></a></div><br />Michelle Sigaranhttps://plus.google.com/109631622949404421728noreply@blogger.comtag:blogger.com,1999:blog-8654192331293420079.post-33646597040859268342018-11-15T20:03:00.002-08:002018-12-19T11:01:34.754-08:00Using Writing to Make Sense of Math<div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-Acugd_9yuSc/W-5AbUmmz8I/AAAAAAAAafY/axVo5rBwy7QIeXAs4zxB7T61Bnveo_I5wCLcBGAs/s1600/writing%2Bblog%2Bcover.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1539" data-original-width="1600" height="614" src="https://4.bp.blogspot.com/-Acugd_9yuSc/W-5AbUmmz8I/AAAAAAAAafY/axVo5rBwy7QIeXAs4zxB7T61Bnveo_I5wCLcBGAs/s640/writing%2Bblog%2Bcover.jpg" width="640" /></a></div><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;">My first two years of teaching went ok. I was learning the ropes of running a classroom and honestly, just trying to survive. I didn't have my students write too much, because "Hey, I teach Math." The summer after my second year of teaching I took an intense master's class about math pedagogy...homework included. I noticed something that the professor always had us do on our homework, and that was to explain our reasoning. I suddenly had as much writing on my homework as I did actual math. I quickly learned the value of writing in a math classroom. To be able to actually explain in words <i>how</i> to do the math, takes the math to a deeper level. Students have to actually think about the <i>why</i> instead of just passing through meaningless algorithms. Also, as a teacher, have you ever tried grading a student's work, and you are just not quite sure if they understand the concept? Having students write their thinking can take your math in your classroom to a deeper level, and seriously, grading papers becomes an easier task. No more second guessing if the student really understands or not. If they can accurately explain their reasoning you know that they really understand the concept. </span><br /><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;">There are a few ways you can have your students write in the math classroom. One strategy is in a notebook.</span><br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-b8GV9tsbNR8/W-47PWu1xPI/AAAAAAAAafE/DoCSt9yIm3QdTrMjtfB2IafnpyDz4vWLQCLcBGAs/s1600/writing%2Bblog%2Bpic.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: "verdana" , sans-serif;"><img border="0" data-original-height="655" data-original-width="844" height="248" src="https://3.bp.blogspot.com/-b8GV9tsbNR8/W-47PWu1xPI/AAAAAAAAafE/DoCSt9yIm3QdTrMjtfB2IafnpyDz4vWLQCLcBGAs/s320/writing%2Bblog%2Bpic.jpg" width="320" /></span></a></div><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;">You can give writing prompts on the board, a classroom screen, or on task cards and have the students write in their notebooks. One suggestion that I enforced in my classroom was that they had to write in complete sentences. I also put a minimum of three sentences. Many students went beyond three sentences, but I learned I needed a minimum for some students in my classroom. Also, another strategy I often incorporated was to have them include an example of what they were explaining.</span><br /><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;">You can also had out slips of paper and use them as exit slips. </span><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-43u4LmrFcVQ/W-47PhebLRI/AAAAAAAAafQ/OjYp_kN469QhF-02vwN2sRwHAqi-51omwCEwYBhgL/s1600/writing%2Bblog%2Bpic2.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: "verdana" , sans-serif;"><img border="0" data-original-height="728" data-original-width="983" height="236" src="https://3.bp.blogspot.com/-43u4LmrFcVQ/W-47PhebLRI/AAAAAAAAafQ/OjYp_kN469QhF-02vwN2sRwHAqi-51omwCEwYBhgL/s320/writing%2Bblog%2Bpic2.jpg" width="320" /></span></a></div><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;">This is a great way to see how much your students understood the lesson. Hand out the slips of paper with the writing prompt and have them complete the writing and hand it to you as you walk out the door. Also, as a side note, if students know they have to complete these to leave class, they will be very engaged in the lesson ;). </span><br /><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;">You can also use these slips of paper as openers. Hand them to students as they walk in the classroom, and collect them when they are complete. This also helps students not be tardy, because they have an assignment write when class begins.</span><br /><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;">Writing in my math classroom, seriously took my class to a new level. If you have not yet tried writing, I highly suggest you do. </span><br /><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;">If you want 50 prompts for your 7th grade or 8th grade math classrooms, or the product in the photos you can click on the links below.</span><br /><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;"><a href="https://www.teacherspayteachers.com/Product/7th-Grade-Math-Writing-Prompts-3382724">CLICK HERE FOR 50 7TH GRADE PROMPTS, TASK CARDS AND WRITING SLIPS</a></span><br /><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;"><a href="https://www.teacherspayteachers.com/Product/8th-Grade-Math-Writing-Prompts-3455719">CLICK HERE FOR 50 8TH GRADE PROMPTS, TASK CARDS AND WRITING SLIPS</a></span><br /><br /><a href="https://mailchi.mp/638241b4d4e9/makesenseofmath" target="_blank"><span style="font-family: Verdana, sans-serif; font-size: large;">GRAB YOUR FREEBIES HERE!</span></a><br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-sp32hYS_4k4/W-5BhGgWclI/AAAAAAAAafg/akWAb2qPEn8_sUGavbhTOkdUeIaXjWeVQCLcBGAs/s1600/writing%2Bblog%2Bpin.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="1067" height="320" src="https://3.bp.blogspot.com/-sp32hYS_4k4/W-5BhGgWclI/AAAAAAAAafg/akWAb2qPEn8_sUGavbhTOkdUeIaXjWeVQCLcBGAs/s320/writing%2Bblog%2Bpin.jpg" width="213" /></a></div><br /><br />Michelle Sigaranhttps://plus.google.com/109631622949404421728noreply@blogger.comtag:blogger.com,1999:blog-8654192331293420079.post-82581698133040591252018-11-06T20:53:00.001-08:002018-12-19T11:02:39.348-08:004 Tips on Teaching the Distributive Property<div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-IZQYwxPhuPk/W-JpUnv90SI/AAAAAAAAaXw/zl0Kv4ISYn4rnaFqzPitEtRpPEZx4MBvgCLcBGAs/s1600/dp%2Bblog%2Btop.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1539" data-original-width="1600" height="307" src="https://4.bp.blogspot.com/-IZQYwxPhuPk/W-JpUnv90SI/AAAAAAAAaXw/zl0Kv4ISYn4rnaFqzPitEtRpPEZx4MBvgCLcBGAs/s320/dp%2Bblog%2Btop.jpg" width="320" /></a></div><div><span style="font-family: "verdana" , sans-serif; font-size: large;"><br /></span></div><span style="font-family: "verdana" , sans-serif; font-size: large;">1) Make Sense of Multiplication</span><br /><div><span style="font-family: "verdana" , sans-serif;">Students need to make sense of the meaning of multiplication in terms of groups. Students may have previously learned multiplication as repeated addition, though this is accurate, extend their understanding to multiplication as meaning <i>groups of</i>. For example, <i>2(x + 3) </i> means <i>2 groups of x plus 3</i>. Another example, <i>3(y - 1) </i>means <i>3 groups of y minus 1.</i></span></div><div><span style="font-family: "verdana" , sans-serif;"><br /></span></div><div><span style="font-family: "verdana" , sans-serif;"><span style="font-size: large;">2) Model the Expression with Manipulatives</span></span></div><div><span style="font-family: "verdana" , sans-serif;">Algebra tiles are great for modeling expressions, however, if you do not have Algebra tiles you can either make them with paper, or use objects to represent the variables and constants. Have your students model the expression. For example, they know that <i>2(x + 3)</i> means <i> 2 groups of x plus 3</i>. So now model the expression with manipulatives. See photo for example.</span></div><div><span style="font-family: "verdana" , sans-serif;"><br /></span></div><div class="separator" style="clear: both; text-align: center;"></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-sQmXV4JaHrc/W-Jjod4wuJI/AAAAAAAAaXE/R7jt6vXsm9Q2JZKRHbxiWDveLy2EBfz8wCLcBGAs/s1600/dp%2Bblog%2B1.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="792" data-original-width="687" height="320" src="https://4.bp.blogspot.com/-sQmXV4JaHrc/W-Jjod4wuJI/AAAAAAAAaXE/R7jt6vXsm9Q2JZKRHbxiWDveLy2EBfz8wCLcBGAs/s320/dp%2Bblog%2B1.jpg" width="277" /></a></div><div><br /></div><div><span style="font-family: "verdana" , sans-serif;">Model with manipulatives for <i>3(y - 1)</i></span></div><div><span style="font-family: "verdana" , sans-serif;"><i><br /></i></span></div><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-LVJ-wlxIvy4/W-JjoU_nrPI/AAAAAAAAaXM/fjfr1S19zFUuf0cc54IrT_wdPSajBFAvwCEwYBhgL/s1600/dp%2Bblog%2B2.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="826" data-original-width="708" height="320" src="https://2.bp.blogspot.com/-LVJ-wlxIvy4/W-JjoU_nrPI/AAAAAAAAaXM/fjfr1S19zFUuf0cc54IrT_wdPSajBFAvwCEwYBhgL/s320/dp%2Bblog%2B2.jpg" width="274" /></a></div><div><span style="font-family: "verdana" , sans-serif;"><i><br /></i></span></div><div><span style="font-family: "verdana" , sans-serif;"><i><br /></i></span></div><div><span style="font-family: "verdana" , sans-serif;"><i><br /></i></span></div><div><span style="font-family: "verdana" , sans-serif;">After students model the expression have them write down what they see with combining like terms.</span></div><div><br /></div><div><span style="font-family: "verdana" , sans-serif;"><br /></span></div><div><span style="font-family: "verdana" , sans-serif;">If your students see the connection between the initial expression and the simplified expression at this point, that is great. If they don't, that is ok. Your goal for this step is that they conceptually understand multiplying expressions. </span></div><div><span style="font-family: "verdana" , sans-serif;"><br /></span></div><div><span style="font-family: "verdana" , sans-serif; font-size: large;">3) Model the Expression with Symbols</span></div><div><span style="font-family: "verdana" , sans-serif;">Now, instead of using manipulatives have your students write out the variables and the constants. In the photo the expression 2(x+3) is modeled by writing out the groups. </span></div><div><span style="font-family: "verdana" , sans-serif;"><br /></span></div><div><span style="font-family: "verdana" , sans-serif;"><br /></span></div><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-G69qDnTf7_0/W-Jjp0JJ0PI/AAAAAAAAaXY/TV3bTRYD2nofxiZxMt8sKa7OD-O7aHpqQCEwYBhgL/s1600/dp%2Bblog%2B6.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="794" data-original-width="692" height="320" src="https://2.bp.blogspot.com/-G69qDnTf7_0/W-Jjp0JJ0PI/AAAAAAAAaXY/TV3bTRYD2nofxiZxMt8sKa7OD-O7aHpqQCEwYBhgL/s320/dp%2Bblog%2B6.jpg" width="278" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;"><span style="font-family: "verdana" , sans-serif;">Here is the model for 3(y -1)</span></div><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-lHPYQltVYjk/W-Jjo2BW0OI/AAAAAAAAaXk/U5Is5-iCIRsSz3CLYoK63cwmnKwqPTHjQCEwYBhgL/s1600/dp%2Bblog%2B4.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="763" data-original-width="654" height="320" src="https://4.bp.blogspot.com/-lHPYQltVYjk/W-Jjo2BW0OI/AAAAAAAAaXk/U5Is5-iCIRsSz3CLYoK63cwmnKwqPTHjQCEwYBhgL/s320/dp%2Bblog%2B4.jpg" width="274" /></a></div><div><span style="font-family: "verdana" , sans-serif;"><br /></span></div><div><span style="font-family: "verdana" , sans-serif;"><br /></span></div><div><span style="font-family: "verdana" , sans-serif;">Again, have your students write the simplified version after modeling. At this point, if your students have not already noticed the "shortcut" guide them through questioning. Ideally you want your students to make the connection so they retain the information. </span></div><div><span style="font-family: "verdana" , sans-serif;"><br /></span></div><div><span style="font-family: "verdana" , sans-serif;"><br /></span></div><div><span style="font-family: "verdana" , sans-serif; font-size: large;">4) Multiply using the Distributive Property</span></div><div><span style="font-family: "verdana" , sans-serif;">Once your students have a strong conceptual understanding of the distributive property move on to actually using the property when multiplying. Students should understand that every term from one expression needs to be multiplied by every term of the other expression. Understanding this concept will greatly help them when multiplying binomials. One strategy I use with my students are circling the terms including the signs. This helps students not miss the negative signs. </span></div><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-uiKJT-LbfCo/W-JjoVx2AdI/AAAAAAAAaXg/CoglMP9JPBoCxqTdOcXLMmEwafSrESLxACEwYBhgL/s1600/dp%2Bblog%2B3.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="769" data-original-width="680" height="320" src="https://1.bp.blogspot.com/-uiKJT-LbfCo/W-JjoVx2AdI/AAAAAAAAaXg/CoglMP9JPBoCxqTdOcXLMmEwafSrESLxACEwYBhgL/s320/dp%2Bblog%2B3.jpg" width="282" /></a></div><div><span style="font-family: "verdana" , sans-serif;"><br /></span></div><div><span style="font-family: "verdana" , sans-serif;">Another strategy is drawing lines. Lines become extremely helpful when multiplying binomials and beyond. </span></div><div><span style="font-family: "verdana" , sans-serif;"><br /></span></div><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-vzurSTM5p64/W-JjpotWixI/AAAAAAAAaXk/WeuZ9eB42tcxq1VqSFJmqAUDyJVZZIhQwCEwYBhgL/s1600/dp%2Bblog%2B5.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="777" data-original-width="689" height="320" src="https://3.bp.blogspot.com/-vzurSTM5p64/W-JjpotWixI/AAAAAAAAaXk/WeuZ9eB42tcxq1VqSFJmqAUDyJVZZIhQwCEwYBhgL/s320/dp%2Bblog%2B5.jpg" width="283" /></a></div><div class="separator" style="clear: both; text-align: center;"><span style="font-family: "verdana" , sans-serif;"><br /></span></div><blockquote class="tr_bq" style="clear: both; text-align: left;"><span style="font-family: "verdana" , sans-serif;">If you don't have time to make your own notes about the distributive property, <a href="https://www.teacherspayteachers.com/Product/Distributive-Property-Stations-2920390" target="_blank">YOU CAN CLICK HERE TO USE MINE.</a> I've included two pages of notes to guide students in discovering the distributive property as well as FUN and ENGAGING stations so they can practice what they have learned. </span><br /><span style="font-family: "verdana" , sans-serif;"><br /></span></blockquote><span style="font-family: Verdana, sans-serif; font-size: large;"><a href="https://mailchi.mp/638241b4d4e9/makesenseofmath" target="_blank">GRAB YOUR FREEBIES HERE</a>!</span><br /><div><span style="font-family: "verdana" , sans-serif;"><br /></span></div><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-Yz4nsWA76R4/W-JvxjAxR3I/AAAAAAAAaX8/cNxNcydMofsvY-OkwU4LKQpBvqZ19pZMQCLcBGAs/s1600/dp%2Bblog%2Bpin.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="1067" height="320" src="https://1.bp.blogspot.com/-Yz4nsWA76R4/W-JvxjAxR3I/AAAAAAAAaX8/cNxNcydMofsvY-OkwU4LKQpBvqZ19pZMQCLcBGAs/s320/dp%2Bblog%2Bpin.jpg" width="213" /></a></div><div><span style="font-family: "verdana" , sans-serif;"><br /></span><br /><div> </div></div>Michelle Sigaranhttps://plus.google.com/109631622949404421728noreply@blogger.comtag:blogger.com,1999:blog-8654192331293420079.post-43019031337210275282018-10-24T20:36:00.001-07:002018-12-19T11:03:26.846-08:00Maximize your Teaching with Guided Notes<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-7obqKtmLMxY/W9E47in8ilI/AAAAAAAAaIk/sGEWtckRGV4P_Qq0_aj4XdJE9TgT8pyBQCLcBGAs/s1600/guided%2Bnotes%2Bblog%2Bfinal.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1240" data-original-width="1600" src="https://4.bp.blogspot.com/-7obqKtmLMxY/W9E47in8ilI/AAAAAAAAaIk/sGEWtckRGV4P_Qq0_aj4XdJE9TgT8pyBQCLcBGAs/s1600/guided%2Bnotes%2Bblog%2Bfinal.jpg" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"></div><div style="direction: ltr; language: en-US; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; mso-line-break-override: none; punctuation-wrap: hanging; text-align: left; unicode-bidi: embed; word-break: normal;"><span style="font-family: "verdana" , sans-serif;"><span style="color: black;"><br /></span></span></div><div style="direction: ltr; language: en-US; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; mso-line-break-override: none; punctuation-wrap: hanging; text-align: left; unicode-bidi: embed; word-break: normal;"><span style="font-family: "verdana" , sans-serif;"><span style="color: black;">Middle School is a time of transition for many students. As part of this </span><span style="color: black;">transition, </span><span style="color: black;">we as teachers expect them to start taking on more responsibility. Part of the problem, however, is that students change at different times and not all when we want them to.</span></span></div><div style="direction: ltr; language: en-US; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; mso-line-break-override: none; punctuation-wrap: hanging; text-align: left; unicode-bidi: embed; word-break: normal;"><span style="color: black;"><span style="font-family: "verdana" , sans-serif;"><br /></span></span></div><div style="direction: ltr; language: en-US; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; mso-line-break-override: none; punctuation-wrap: hanging; text-align: left; unicode-bidi: embed; word-break: normal;"><span style="font-family: "verdana" , sans-serif;"><span style="color: black;">My first year of teaching my idea was that every student would have a notebook and they </span><span style="color: black;">would </span><span style="color: black;">just listen to me and take down the notes from the </span><span style="color: black;">board. </span><span style="color: black;">My idea was to review their notebooks every so often to make sure they were getting down the notes. </span><span style="color: black;">After </span><span style="color: black;">reviewing their notebooks I </span><span style="color: black;">saw that </span><span style="color: black;">some students had great and fantastic notes just as I had wanted. However, others notebooks were empty, others had drawings, others had notes to friends, others were trying to take notes but they were very incomplete. I quickly learned that my idea was not very effective. Not because they didn't want </span><span style="color: black;">to, </span><span style="color: black;">but because they did not have the skills to do so. I didn't want to completely give up on my efforts to help them learn this life </span><span style="color: black;">skill</span><span style="color: black;">. However, I realized that having them take all the notes was not going to be effective and so I needed to find a balance between them taking notes and also them getting </span><span style="color: black;">all the </span><span style="color: black;">information.</span></span></div><div style="direction: ltr; language: en-US; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; mso-line-break-override: none; punctuation-wrap: hanging; text-align: left; unicode-bidi: embed; word-break: normal;"><span style="color: black;"><span style="font-family: "verdana" , sans-serif;"><br /></span></span></div><div style="direction: ltr; language: en-US; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; mso-line-break-override: none; punctuation-wrap: hanging; text-align: left; unicode-bidi: embed; word-break: normal;"><span style="font-family: "verdana" , sans-serif;"><span style="color: black;"> I decided to incorporate writing at the beginning of class through openers. Everyday I would have an opener on the board and they would have to write at least 3 complete sentences. I felt like I was supporting language arts in my classroom. What I started doing, was having guided notes for them. I found some online that were good enough. They were not exactly what I wanted, but they would work, as I knew I didn't have time to make them as thorough as I wanted them. I found this to be a very effective </span><span style="color: black;">method; </span><span style="color: black;">they were paying attention so they </span><span style="color: black;">could </span><span style="color: black;">complete their notes but it was they weren't so many notes that they were getting behind or lost.</span></span></div><div style="direction: ltr; language: en-US; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; mso-line-break-override: none; punctuation-wrap: hanging; text-align: left; unicode-bidi: embed; word-break: normal;"><span style="color: black;"><span style="font-family: "verdana" , sans-serif;"><br /></span></span></div><div style="direction: ltr; language: en-US; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; mso-line-break-override: none; punctuation-wrap: hanging; text-align: left; unicode-bidi: embed; word-break: normal;"><span style="font-family: "verdana" , sans-serif;"><span style="color: black;">After I took a break from the classroom and started making curriculum, I tried to<span style="mso-spacerun: yes;"> </span>think of materials that I wish I had but didn’t. </span><span style="color: black;">Of course, guided notes were at the top of my list. I knew this was something that I wanted to make. But I kept putting it off because I knew it was going to be a lot of work to get them as thorough as I </span><span style="color: black;">thought </span><span style="color: black;">that they should be. But I finally </span><span style="color: black;">dove </span><span style="color: black;">into </span><span style="color: black;">creating them and </span><span style="color: black;">I am so happy with the final product.</span></span></div><div style="direction: ltr; language: en-US; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; mso-line-break-override: none; punctuation-wrap: hanging; text-align: left; unicode-bidi: embed; word-break: normal;"><span style="color: black;"><span style="font-family: "verdana" , sans-serif;"><br /></span></span></div><div style="direction: ltr; language: en-US; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; mso-line-break-override: none; punctuation-wrap: hanging; text-align: left; unicode-bidi: embed; word-break: normal;"><span style="color: black;"><span style="font-family: "verdana" , sans-serif;">If you are interested in using some guided notes, check them out here. I currently have seventh grade completed, and will soon have eighth grade completed.</span></span></div><div style="direction: ltr; language: en-US; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; mso-line-break-override: none; punctuation-wrap: hanging; text-align: left; unicode-bidi: embed; word-break: normal;"><span style="color: black;"><span style="font-family: "verdana" , sans-serif;"><br /></span></span></div><div style="direction: ltr; language: en-US; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; mso-line-break-override: none; punctuation-wrap: hanging; text-align: left; unicode-bidi: embed; word-break: normal;"><span style="color: black;"><span style="font-family: "verdana" , sans-serif;">They are aligned to the common core. My goal is to have them as thorough and complete as possible. Feel free to email me at makesenseofmath@yahoo.com if you have comments or suggestions about them.</span></span></div><div style="direction: ltr; language: en-US; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; mso-line-break-override: none; punctuation-wrap: hanging; text-align: left; unicode-bidi: embed; word-break: normal;"><span style="font-family: "verdana" , sans-serif;"><span style="color: black;">Middle School is a time of transition for many students. As part of this </span><span style="color: black;">transition, </span><span style="color: black;">we as teachers expect them to start taking on more responsibility. Part of the problem, however, is that students change at different times and not all when we want them to.</span></span></div><div style="direction: ltr; language: en-US; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; mso-line-break-override: none; punctuation-wrap: hanging; text-align: left; unicode-bidi: embed; word-break: normal;"><span style="color: black;"><span style="font-family: "verdana" , sans-serif;"><br /></span></span></div><div style="direction: ltr; language: en-US; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; mso-line-break-override: none; punctuation-wrap: hanging; text-align: left; unicode-bidi: embed; word-break: normal;"><span style="font-family: "verdana" , sans-serif;"><span style="color: black;">My first year of teaching my idea was that every student would have a notebook and they </span><span style="color: black;">would </span><span style="color: black;">just listen to me and take down the notes from the </span><span style="color: black;">board. </span><span style="color: black;">My idea was to review their notebooks every so often to make sure they were getting down the notes. </span><span style="color: black;">After </span><span style="color: black;">reviewing their notebooks I </span><span style="color: black;">saw that </span><span style="color: black;">some students had great and fantastic notes just as I had wanted. However, others notebooks were empty, others had drawings, others had notes to friends, others were trying to take notes but they were very incomplete. I quickly learned that my idea was not very effective. Not because they didn't want </span><span style="color: black;">to, </span><span style="color: black;">but because they did not have the skills to do so. I didn't want to completely give up on my efforts to help them learn this life </span><span style="color: black;">skill</span><span style="color: black;">. However, I realized that having them take all the notes was not going to be effective and so I needed to find a balance between them taking notes and also them getting </span><span style="color: black;">all the </span><span style="color: black;">information.</span></span></div><div style="direction: ltr; language: en-US; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; mso-line-break-override: none; punctuation-wrap: hanging; text-align: left; unicode-bidi: embed; word-break: normal;"><div class="separator" style="clear: both; text-align: center;"></div><span style="color: black;"><span style="font-family: "verdana" , sans-serif;"><br /></span></span></div><div style="direction: ltr; language: en-US; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; mso-line-break-override: none; punctuation-wrap: hanging; text-align: left; unicode-bidi: embed; word-break: normal;"><span style="font-family: "verdana" , sans-serif;"><span style="color: black;">I decided to incorporate writing at the beginning of class through openers. Everyday I would have an opener on the board and they would have to write at least 3 complete sentences. I felt like I was supporting language arts in my classroom. What I started doing, was having guided notes for them. I found some online that were good enough. They were not exactly what I wanted, but they would work, as I knew I didn't have time to make them as thorough as I wanted them. I found this to be a very effective </span><span style="color: black;">method; </span><span style="color: black;">they were paying attention so they </span><span style="color: black;">could </span><span style="color: black;">complete their notes but it was they weren't so many notes that they were getting behind or lost.</span></span></div><div style="direction: ltr; language: en-US; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; mso-line-break-override: none; punctuation-wrap: hanging; text-align: left; unicode-bidi: embed; word-break: normal;"><span style="color: black;"><span style="font-family: "verdana" , sans-serif;"><br /></span></span></div><div style="direction: ltr; language: en-US; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; mso-line-break-override: none; punctuation-wrap: hanging; text-align: left; unicode-bidi: embed; word-break: normal;"><span style="font-family: "verdana" , sans-serif;"><span style="color: black;">After I took a break from the classroom and started making curriculum, I tried to<span style="mso-spacerun: yes;"> </span>think of materials that I wish I had but didn’t. </span><span style="color: black;">Of course, guided notes were at the top of my list. I knew this was something that I wanted to make. But I kept putting it off because I knew it wa</span>s going to be a lot of work to get them as th</span><span style="font-family: "verdana" , sans-serif;">orough as I thought that they should be. But I finally dove into creating them and I am so happy with the final product.</span></div><div style="direction: ltr; language: en-US; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; mso-line-break-override: none; punctuation-wrap: hanging; text-align: left; unicode-bidi: embed; word-break: normal;"><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;">If you are interested in some guided notes for your classroom I have got you covered!</span><br /><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;"><a href="https://www.teacherspayteachers.com/Product/7th-Grade-Math-Guided-Notes-Bundle-Common-Core-Aligned-3754038" target="_blank">CLICK HERE FOR 7TH GRADE GUIDED NOTES</a></span><br /><a href="https://www.teacherspayteachers.com/Product/8th-Grade-Math-Guided-Notes-Bundle-Common-Core-Aligned-3958849" target="_blank"><span style="font-family: "verdana" , sans-serif;">CLICK HERE FOR 8TH GRADE GUIDED NOTES</span></a><br /><br /><div class="separator" style="clear: both; text-align: center;"><br /></div><span style="font-family: "verdana" , sans-serif;">As always, I am committed to quality products. Any questions or comments please feel free to email me at makesenseofmath@yahoo.com</span><br /><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;">Michelle</span><br /><span style="font-family: "verdana" , sans-serif;"><br /></span><a href="https://mailchi.mp/638241b4d4e9/makesenseofmath" target="_blank"><span style="font-family: Verdana, sans-serif; font-size: large;">GRAB YOUR FREEBIES HERE!</span></a></div><div style="direction: ltr; language: en-US; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; mso-line-break-override: none; punctuation-wrap: hanging; text-align: left; unicode-bidi: embed; word-break: normal;"><div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"><br /></div></div><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-DYZxYx4EjF4/W9E5FEJtGxI/AAAAAAAAaIo/bfNZehpioPgHrJJVDmPdo-zVmIiuWPYvwCEwYBhgL/s1600/guided%2Bnotes%2Bpin%2Bfrom%2Bblog.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img alt="Great post on the benefits of using guided notes in your middle school math classroom. Great for any 7th grade or 8th grade teacher who is looking for teaching ideas for math. #makesenseofmath" border="0" data-original-height="1600" data-original-width="1067" height="320" src="https://3.bp.blogspot.com/-DYZxYx4EjF4/W9E5FEJtGxI/AAAAAAAAaIo/bfNZehpioPgHrJJVDmPdo-zVmIiuWPYvwCEwYBhgL/s320/guided%2Bnotes%2Bpin%2Bfrom%2Bblog.jpg" title="Great post on the benefits of using guided notes in your middle school math classroom. Great for any 7th grade or 8th grade teacher who is looking for teaching ideas for math. #makesenseofmath" width="213" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div style="direction: ltr; language: en-US; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; mso-line-break-override: none; punctuation-wrap: hanging; text-align: left; unicode-bidi: embed; word-break: normal;"><br /></div>Michelle Sigaranhttps://plus.google.com/109631622949404421728noreply@blogger.comtag:blogger.com,1999:blog-8654192331293420079.post-16721453784730783222018-07-19T19:47:00.000-07:002018-12-19T11:05:50.548-08:00How to Stress your Students out the First Day of Math Class<div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-2k4tj7kxb9Q/W9EkgXUq9nI/AAAAAAAAaHo/KtaHLUS3-aAa45jxr9apA0wjQiHyS-UWgCLcBGAs/s1600/first%2Bday%2Bsquare%2Bblog%2Bfinal.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1240" data-original-width="1600" src="https://1.bp.blogspot.com/-2k4tj7kxb9Q/W9EkgXUq9nI/AAAAAAAAaHo/KtaHLUS3-aAa45jxr9apA0wjQiHyS-UWgCLcBGAs/s1600/first%2Bday%2Bsquare%2Bblog%2Bfinal.jpg" /></a></div><div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"></div><br /><span style="font-family: "verdana" , sans-serif;">1) <u>Give your students a TEST! </u> </span><br /><span style="font-family: "verdana" , sans-serif;">You want to know what your students know and what they don't know. What better way to assess their understanding than a test. Better yet, you can hand them a test right when they walk in the door. Tell them where to sit, and tell them to work on the test the entire period. This way you can look at the tests later and better plan what you need to review with your students.</span><br /><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;">2) <u>Be super strict and NEVER crack a smile</u></span><br /><span style="font-family: "verdana" , sans-serif;">You want your students to respect you, right? Well, you better let them know that you are in charge. If your students see any weakness in you, especially the first day, they will take advantage of you the rest of the year. Be stern, be strict, lay down the law, and most importantly NEVER crack a smile. </span><br /><br /><span style="font-family: "verdana" , sans-serif;">3) <u>Make your students feel like failures</u></span><br /><span style="font-family: "verdana" , sans-serif;">Give your students some really hard math problems the first day. Tell them that their understanding of these problems will go on their grade. Better yet, put them into groups and let them talk about these math problems. Those students who are afraid of math will feel so stressed out, they will feel like they failed on the very first day. </span><br /><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;">These are great tips to make sure your math students feel super stressed out on the first day.</span><br /><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;">I hope you caught my sarcasm in this post. Many students are afraid of their new math class before they even walk in the door. Love them, respect them, make them feel like winners and that they can be successful. Be careful with giving pre-tests the first day....or even the first week. Once the relationship between your students and you is more solid, and routines are in place, pre-tests can be given.</span><br /><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;">Thank you for having courage to teach math. May you have a great year!</span><br /><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;"><a href="https://mailchi.mp/638241b4d4e9/makesenseofmath" target="_blank"><span style="font-size: large;">GRAB YOUR FREEBIES HERE!</span></a></span><br /><span style="font-family: "verdana" , sans-serif;"><br /></span><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-hKM_wr1ThaI/W9Ek6GzOHMI/AAAAAAAAaHw/oqSm9FEH19cZu4rQiOYbY2uMGeFANh17QCLcBGAs/s1600/first%2Bday%2Bpin.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img alt="Great ideas to have a great start in your middle school math classroom. Things not to do on the first day so that your students are not stressed out. Great read for all teachers. #makesenseofmath" border="0" data-original-height="1600" data-original-width="1067" height="320" src="https://1.bp.blogspot.com/-hKM_wr1ThaI/W9Ek6GzOHMI/AAAAAAAAaHw/oqSm9FEH19cZu4rQiOYbY2uMGeFANh17QCLcBGAs/s320/first%2Bday%2Bpin.jpg" title="Great ideas to have a great start in your middle school math classroom. Things not to do on the first day so that your students are not stressed out. Great read for all teachers. #makesenseofmath" width="213" /></a></div><div class="separator" style="clear: both; text-align: center;"></div><span style="font-family: "verdana" , sans-serif;"><br /></span>Michelle Sigaranhttps://plus.google.com/109631622949404421728noreply@blogger.comtag:blogger.com,1999:blog-8654192331293420079.post-57335734189446495392018-06-08T20:29:00.001-07:002018-12-19T11:06:47.326-08:005 Keys to a Growth Mindset<div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-Va8V3me0w5M/W9EdcKT5tYI/AAAAAAAAaHM/ALPZaZpdzgUurUZu8iLz6lDdAuG9wXjIACLcBGAs/s1600/growth%2Bblog%2Bfinal.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1240" data-original-width="1600" src="https://3.bp.blogspot.com/-Va8V3me0w5M/W9EdcKT5tYI/AAAAAAAAaHM/ALPZaZpdzgUurUZu8iLz6lDdAuG9wXjIACLcBGAs/s1600/growth%2Bblog%2Bfinal.jpg" /></a></div><div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"></div><br /><span style="font-family: "verdana" , sans-serif;">A growth mindset is a powerful tool in a math classroom. Students need to learn that they are capable people who have control over their own learning. I created a mindset questionnaire to give to my students at the beginning to of the year to understand their mindset. You can download a FREE copy of the questionnaire <a href="https://www.teacherspayteachers.com/Product/Math-Mindset-Questionnaire-Back-to-School-3252471" target="_blank">HERE</a>. Here are 5 keys to a growth mindset that are very effective, especially in a math classroom.</span><br /><span style="font-family: "verdana" , sans-serif;"><br /></span><b><span style="font-family: "verdana" , sans-serif;">1. When I Struggle my Brain Grows</span></b><br /><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;">Growth comes through challenges. Often time students think that if a concept it not "easy" for them then they have a problem. Struggle should be important, encouraged, promoted and celebrated in your math classroom. Teach your students that when they are struggling that their brain is growing. This will help them view struggle as a positive rather than a negative. </span><br /><span style="font-family: "verdana" , sans-serif;"><br /></span><b><span style="font-family: "verdana" , sans-serif;">2. I CAN learn Math</span></b><br /><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;">A common misconception in society is that there are two types of people "Math People" and "Not Math People." If a student has labeled them self as as "Not a Math Person" or even worse, if a parent has labeled their child (which I have seen way too many times) as "Not a Math Person" then this student believes that they are not able to learn math. Teach your students that ALL people can learn math. Believe in them as a teacher, remind them often that they can learn math, and they will believe this too. </span><br /><span style="font-family: "verdana" , sans-serif;"><br /></span><b><span style="font-family: "verdana" , sans-serif;">3. I don't Understand YET!</span></b><br /><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;">Many students get down on themselves because they don't understand concepts quickly. This is especially a problem if their is that one student that constantly yells out that everything is "EASY!" In fact, the word "EASY" was banned in my classroom for the problems that it caused. Teach your students that it is OK if they don't understanding everything right now, but that they will eventually understand if they keep working on the concept. YET is a powerful word. Use it constantly in your classroom!</span><br /><span style="font-family: "verdana" , sans-serif;"><br /></span><b><span style="font-family: "verdana" , sans-serif;">4. Mistakes allow me to Learn</span></b><br /><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;">Mistakes are often viewed as negative. Who wants to make mistakes? This needs to change, mistakes need to be viewed as something positive, especially in a math classroom. Just think about your own life, how many times have we made a mistake, and learned to never do that again. Encourage students, especially on assessments, to analyze their mistakes. Rather than just having them do test corrections, consider having them analyze their errors and specifically writing about what mistake they made. Spend time talking about mistakes, don't ignore them and just talk about the right answer. Constantly talk about the power of learning from your mistakes. </span><br /><span style="font-family: "verdana" , sans-serif;"><br /></span><b><span style="font-family: "verdana" , sans-serif;">5. My Effort and Attitude determine my Success</span></b><br /><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;">This one goes along with #2. Many students believe that they cannot be successful in mathematics because they simply do not have the ability. They think of it as something you either have or do not have. Students need to be taught that they can control their success! They can control their effort and their attitude and this directly affects their level of success. Some students will need a constant reminder of this fact throughout the year. </span><br /><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;">To help my students remember these 5 keys, I made posters for my classroom. I also made coloring pages with these 5 keys on them so they can put them in their binders or lockers as a constant reminder. If you are interested in also using these in your classroom you can get your copy <a href="https://www.teacherspayteachers.com/Product/Growth-Mindset-Math-Coloring-Pages-and-Posters-3850176" target="_blank">HERE</a></span><br /><br /><span style="font-family: Verdana, sans-serif; font-size: large;"><a href="https://mailchi.mp/638241b4d4e9/makesenseofmath" target="_blank">GET YOUR FREEBIES HERE!</a></span><br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-xWv5Fbi3RAU/W8f67GultRI/AAAAAAAAaA8/mKOxnFfsfNU-xRNGxwbFdmwbFI2Q_t_lwCLcBGAs/s1600/growth%2Bmindset%2Bpin.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img alt="Great ideas to help your students develop a growth mindset in the classroom. Perfect for middle school students to become better students! #makesenseofmath" border="0" data-original-height="1600" data-original-width="1067" height="320" src="https://4.bp.blogspot.com/-xWv5Fbi3RAU/W8f67GultRI/AAAAAAAAaA8/mKOxnFfsfNU-xRNGxwbFdmwbFI2Q_t_lwCLcBGAs/s320/growth%2Bmindset%2Bpin.jpg" title="Great ideas to help your students develop a growth mindset in the classroom. Perfect for middle school students to become better students! #makesenseofmath" width="213" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-LIoZ2G-dYjg/WxtGANEj0pI/AAAAAAAAYrk/xXQ11iYpARU-vR-FmOSYx_0Gg135_CLpQCLcBGAs/s1600/growth%2Bposter%2Bpin.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: "verdana" , sans-serif;"></span></a></div><br />Michelle Sigaranhttps://plus.google.com/109631622949404421728noreply@blogger.comtag:blogger.com,1999:blog-8654192331293420079.post-47377679886699626092018-05-26T20:43:00.002-07:002018-12-19T11:07:28.000-08:0010 Ideas to keep Math Alive during Summer<div class="separator" style="clear: both; text-align: center;"></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/--E428PGsHsI/W9Erg6F8VGI/AAAAAAAAaIA/S1LFoZ7LaQ8gkxjWZXyhdqQApvr_je_1wCLcBGAs/s1600/summer%2Bblog%2Bfinal.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1240" data-original-width="1600" src="https://4.bp.blogspot.com/--E428PGsHsI/W9Erg6F8VGI/AAAAAAAAaIA/S1LFoZ7LaQ8gkxjWZXyhdqQApvr_je_1wCLcBGAs/s1600/summer%2Bblog%2Bfinal.jpg" /></a></div><div class="separator" style="clear: both; text-align: center;"></div><span style="font-family: "verdana" , sans-serif; font-size: x-small;"><br /></span><span style="font-family: "verdana" , sans-serif;">Doing math worksheets is likely not on the list of activities your students or child wants to do this summer. In fact, I read about a recent study from the Harvard Graduate School of Education that math worksheets during the summer do not actually improve a child's math performance. Instead, the Harvard Graduate School of Education suggests that by helping your child see and use math in every day life you can help prevent summer math loss. You can read more about this study <a href="https://www.gse.harvard.edu/news/uk/16/06/summer-math-loss" target="_blank">Here</a></span><br /><br /><span style="font-family: "verdana" , sans-serif;">Here are some great suggestions to keep math alive for your student during the summer. </span><br /><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;">1. Take a picture of three examples of people or companies using integers in the real-world. </span><br /><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;">2. Go to the grocery store and take three pictures of unit rates on the labels. Explain how you can use this information to save money. </span><br /><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;">3. Interview an adult who is a stay-at-home parent and how they use math in their life. Write a short report about what you learned. </span><br /><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;">4. Learn how to make a budget through research and/or by talking to an adult who uses a budget. Create a fake budget for a salary of $2,500/month. </span><br /><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;">5. Draw a scale drawing of your bedroom. Include a scale, and at least three items in your room. Use the scale drawing to discover different ways to re-arrange the furniture in your room.</span><br /><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;">6. Take a picture of three examples of people or companies using fractions in the real-world. </span><br /><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;">7. Calculate the surface area of your bedroom. How much paint will you need if</span><br /><span style="font-family: "verdana" , sans-serif;">you want to repaint the walls?</span><br /><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;">8. Interview a professional who uses math in their career. Write a short report on what you learned.</span><br /><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;">9. Search a grocery add and cut out three adds that advertise products as multiples/$, such as 2/$5. Figure out the unit cost of each product.</span><br /><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;">10. Learn about the Golden Ratio, and find examples of this ratio in nature. (I had my students do this once, and they loved it! The Golden Ratio is so fascinating!)</span><br /><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;">Adults often over look how often they use math in their lives: calculating distances, budgeting, area for gardens or decorating, cooking, etc... Talk with your child or students about how you use math every day and help them open their eyes to the math that lies at their fingertips.</span><br /><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;"><a href="https://mailchi.mp/638241b4d4e9/makesenseofmath" target="_blank"><span style="font-size: large;">GET YOUR FREEBIES HERE!</span></a></span><br /><span style="font-family: "verdana" , sans-serif;"> </span><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-7crhD6OtfJA/W9ErZMR3cjI/AAAAAAAAaIE/uediX4MwXh84y6Wmie56rz43aV1Dj4y7gCEwYBhgL/s1600/summer%2Bpin.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img alt="Great blog to give your students ideas of how to keep math alive for them during the summer. Great ideas for teachers to assign during summer or parents to have kids complete to keep their minds thinking about math during summer. #makesenseofmath" border="0" data-original-height="1600" data-original-width="1067" height="320" src="https://2.bp.blogspot.com/-7crhD6OtfJA/W9ErZMR3cjI/AAAAAAAAaIE/uediX4MwXh84y6Wmie56rz43aV1Dj4y7gCEwYBhgL/s320/summer%2Bpin.jpg" title="Great blog to give your students ideas of how to keep math alive for them during the summer. Great ideas for teachers to assign during summer or parents to have kids complete to keep their minds thinking about math during summer. #makesenseofmath" width="213" /></a></div><span style="font-family: "verdana" , sans-serif;"><br /></span><br /><div style="direction: ltr; language: en-US; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; mso-line-break-override: none; punctuation-wrap: hanging; text-align: left; unicode-bidi: embed; word-break: normal;"><br /></div>Michelle Sigaranhttps://plus.google.com/109631622949404421728noreply@blogger.comtag:blogger.com,1999:blog-8654192331293420079.post-29233802625593154472018-05-16T19:56:00.001-07:002018-12-19T11:08:13.056-08:00Make Sense of Exponent Properties<div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-eStPD1pA5VA/W9EdbfceOII/AAAAAAAAaHc/Eqi_ZtbeGJsCmezmASTVl3OBu6aCh65LACEwYBhgL/s1600/exponent%2Bproperties%2Bblog%2Bfinal.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1240" data-original-width="1600" src="https://1.bp.blogspot.com/-eStPD1pA5VA/W9EdbfceOII/AAAAAAAAaHc/Eqi_ZtbeGJsCmezmASTVl3OBu6aCh65LACEwYBhgL/s1600/exponent%2Bproperties%2Bblog%2Bfinal.jpg" /></a></div><br />T<span style="font-family: "verdana" , sans-serif;">he exponent properties can be super confusing for students if they do not make sense of them. For example, when looking at the expression: <span style="font-style: italic; text-align: center;">x</span><span style="font-style: italic; text-align: center; vertical-align: super;">5</span><span style="font-style: italic; text-align: center;">x</span><span style="font-style: italic; text-align: center; vertical-align: super;">3 </span>no where in the expression is their an addition sign, but if you know the property, addition is used to simplify the expression. I want to share some tried and true tips for successfully teaching exponent properties. </span><br /><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;">First off, I want to discuss what is NOT effective: I highly suggest not just telling your students the rules. Having them simply copy down the rules then practice them will be ineffective, especially for students who struggle with memorization.</span><br /><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;">What IS effective: I want to present a four-step process for helping students discover and make sense of the exponent properties. This process includes: helping students make sense of the expression, modeling the expression, simplifying the expression from the model, and noticing the pattern.</span><br /><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;">Let's look at the expression: <span style="font-style: italic; text-align: center;">x</span><span style="font-style: italic; text-align: center; vertical-align: super;">5</span><span style="font-style: italic; text-align: center;">x</span><span style="font-style: italic; text-align: center; vertical-align: super;">3 </span></span><br /><span style="font-family: "verdana" , sans-serif;">1. Make sense of the expression: </span><br /><span style="font-family: "verdana" , sans-serif;">I would start by asking my students, "What does this expression mean?" Hopefully they could make sense that it is the product of x multiplied by itself 5 times and x multiplied by itself 3 times.</span><br /><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;">2. Modeling the expression: </span><br /><span style="font-family: "verdana" , sans-serif;">I would then have them write out the meaning of what they explained in the first step. (x.x.x.x.x)(x.x.x).</span><br /><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;">3. Simplifying the expression:</span><br /><span style="font-family: "verdana" , sans-serif;">We would then talk about how (x.x.x.x.x)(x.x.x) is the same as <span style="font-style: italic; text-align: center;">x</span><span style="font-style: italic; text-align: center; vertical-align: super;">8</span></span><br /><div style="text-align: left;"><span style="font-family: "verdana" , sans-serif;"><br /></span></div><div style="text-align: left;"><span style="font-family: "verdana" , sans-serif;">4.Noticing patterns: </span><br /><span style="font-family: "verdana" , sans-serif;">After doing a couple of the same types of problems following this method I would then ask the students to look for a pattern. Hopefully they would notice that the exponent in the simplified expression is the sum of the exponents with the same bases.</span><br /><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;">Lets look at another expression </span><span style="font-family: "verdana" , sans-serif; font-style: italic; text-align: center;">x</span><span style="font-family: "verdana" , sans-serif; font-style: italic; text-align: center; vertical-align: super;">5</span><span style="font-family: "verdana" , sans-serif; font-style: italic; text-align: center;">/x</span><span style="font-family: "verdana" , sans-serif; font-style: italic; text-align: center; vertical-align: super;">3 </span></div><div style="text-align: left;"><span style="font-family: "verdana" , sans-serif;">1. Make sense of the expression: </span><br /><span style="font-family: "verdana" , sans-serif;">Ask your students the meaning of the expression</span></div><div style="text-align: left;"><span style="font-family: "verdana" , sans-serif;"><br /></span></div><div style="text-align: left;"><span style="font-family: "verdana" , sans-serif;">2.. Modeling the expression: </span><br /><span style="font-family: "verdana" , sans-serif;">Write out in symbols what they said in words from the first step. (x.x.x.x.x)/(x.x.x). </span></div><div style="text-align: left;"><span style="font-family: "verdana" , sans-serif;"><br /></span></div><div style="text-align: left;"><span style="font-family: "verdana" , sans-serif;">3. Simplifying the expression: </span><br /><span style="font-family: "verdana" , sans-serif;">You may need to review with your students that x/x=1, just as 2/2 = 1 or 5/5=1. After canceling out, this will simplify to x.x = </span><span style="font-family: "verdana" , sans-serif; font-style: italic; text-align: center;">x</span><span style="font-family: "verdana" , sans-serif; font-style: italic; text-align: center; vertical-align: super;">2</span><span style="font-family: "verdana" , sans-serif; font-style: italic; text-align: center; vertical-align: super;"> </span><br /><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;">4. Noticing patterns:</span><br /><span style="font-family: "verdana" , sans-serif;">Again, do the process a couple more times with similar problems. Ask the students if they notice a pattern or a "shortcut" They should notice that the power in the simplified expression is the difference of the exponents in the original expression. </span><br /><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;">I follow this method with every exponent rule. With the negative exponents, I create a table with the positive exponents, and have them notice a pattern and continue the pattern to discover negative exponents. </span><br /><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;">By following this method your students will make sense of the exponent properties. The best part about using this method is that if a student doesn't memorize this property they can always go through the process of modeling and simplifying. Memorization is not required. If their is an expression such as <span style="font-style: italic; text-align: center;">x</span><span style="font-style: italic; text-align: center; vertical-align: super;">50</span><span style="font-style: italic; text-align: center;">x</span><span style="font-style: italic; text-align: center; vertical-align: super;">30</span>, and your student cannot remember the rule, they probably don't want to model the expression either...that would be a lot of x's. Instead of telling them the rule, I often write a simpler expression, have them go through the process of simplifying, modeling, and noticing the pattern, then apply their pattern to the larger expression. </span><br /><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;">If you are looking for some guided notes on exponent properties I have taken then time to create some. Students will discover all the rules through this method and apply their learning on expressions. You can <a href="https://www.teacherspayteachers.com/Product/8th-Grade-Math-Exponent-Properties-Guided-Notes-3802957" target="_blank">Click Here</a> to check out these exponent properties notes.</span><br /><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;">In the mean time,</span><br /><span style="font-family: "verdana" , sans-serif;">Happy Teaching!</span><br /><span style="font-family: "verdana" , sans-serif;"><br /></span><br /><span style="font-family: "verdana" , sans-serif;"><a href="https://mailchi.mp/638241b4d4e9/makesenseofmath" target="_blank"><span style="font-size: large;">GET YOUR FREEBIES HERE!</span></a></span><br /><span style="font-family: "verdana" , sans-serif;"><br /></span><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-kHtAlI6gEpw/W8f5FBaQ80I/AAAAAAAAaAw/XEHu0QjvZrsPsPsEP0MIFmu6_eDnVCvEACLcBGAs/s1600/teaching%2Bexponents%2Bpin.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img alt="Looking for ideas to teach exponent properties and exponent rules? These are great ideas so that your 8th grade math and Algebra students understand the rules to simplify exponents. Read on for my ideas! #makesenseofmath" border="0" data-original-height="1600" data-original-width="1067" height="320" src="https://2.bp.blogspot.com/-kHtAlI6gEpw/W8f5FBaQ80I/AAAAAAAAaAw/XEHu0QjvZrsPsPsEP0MIFmu6_eDnVCvEACLcBGAs/s320/teaching%2Bexponents%2Bpin.jpg" title="Looking for ideas to teach exponent properties and exponent rules? These are great ideas so that your 8th grade math and Algebra students understand the rules to simplify exponents. Read on for my ideas! #makesenseofmath" width="213" /></a></div><span style="font-family: "verdana" , sans-serif;"><br /></span></div>Michelle Sigaranhttps://plus.google.com/109631622949404421728noreply@blogger.comtag:blogger.com,1999:blog-8654192331293420079.post-79826587543357695662018-04-24T20:43:00.002-07:002018-12-19T11:09:14.910-08:00How to Survive the Last Day of Class<div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-xqc0PQWrrl0/Wt_5YDSDhwI/AAAAAAAAYA8/ocxYNo0ugN4fGM2qjUFlunhEabX5iKx6QCLcBGAs/s1600/laptop-3087585_960_720.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="640" data-original-width="960" height="133" src="https://3.bp.blogspot.com/-xqc0PQWrrl0/Wt_5YDSDhwI/AAAAAAAAYA8/ocxYNo0ugN4fGM2qjUFlunhEabX5iKx6QCLcBGAs/s200/laptop-3087585_960_720.jpg" width="200" /></a></div><div><br /></div><div>I<span style="font-family: "verdana" , sans-serif;">n my previous post I talked about ways to survive the last weeks of school, especially when state testing is over. But now let's talk about how to survive the last day of class. Before I share some ideas I want to share some ideas of what NOT to do. These may or may not be from experience.</span></div><div><span style="font-family: "verdana" , sans-serif;"><br /></span></div><div><span style="font-family: "verdana" , sans-serif;">Don't just try to "wing it", meaning, trying to get through the class period without a plan. I'll admit there were days during each school year that I had to "wing it" because my original plans fell through, and I actually got through the day pretty well. However, doing this on the last day of school does not work. Your students, especially if they are middle school students or beyond, will already be full of energy, and if the teacher doesn't have a plan, the students will take over. 😨</span></div><div><span style="font-family: "verdana" , sans-serif;"><br /></span></div><div><span style="font-family: "verdana" , sans-serif;">The other activity that I do NOT recommend is a bunch of work that you are going to have to grade. Big tests and loads of worksheets may keep them busy and quiet, but what teacher wants to be stuck with a handful of papers to grade on the very last day of school? I would recommend doing these items on the last week of school, but not on the last day. Give yourself some time to grade the work before the last day. That way you can still give feedback to your students and you are not left with a stack of work. </span></div><div><span style="font-family: "verdana" , sans-serif;"><br /></span></div><div><span style="font-family: "verdana" , sans-serif;">Now I would like to share two activities that I started doing on the last day. The students have loved these and they are low-stress for both students and teacher. The first activity is a letter. I have my students write a letter to my future students. I have them write what they think the students should know so they can be successful in my class. These are fun to read, and they are actually really helpful for my next year's students. I always proofread them first, but at the beginning of the next school year I hand them out to students to read. They love reading them, and they tend trust their peers more doing their teenage years, so it works out great.</span></div><div><span style="font-family: "verdana" , sans-serif;"><br /></span></div><div><span style="font-family: "verdana" , sans-serif;">The second activity I do is a fun review game. I have always done this in groups of 3-4 students, thought it certainly could be doing in pairs or individually. I hand out the following paper. </span></div><div><div class="separator" style="clear: both; text-align: center;"><span style="font-family: "verdana" , sans-serif;"><img border="0" data-original-height="1067" data-original-width="1600" height="133" src="https://3.bp.blogspot.com/-EDtKUExR5-8/Wt_230XUUwI/AAAAAAAAYAw/rgYokx0Vwy8ptw11_hq4dA4TsCOsrFelACLcBGAs/s200/last%2Bday%2Breview%2Bgame%2Bblog%2Bphoto.jpg" width="200" /></span></div><div class="separator" style="clear: both; text-align: left;"><span style="font-family: "verdana" , sans-serif;">I then give the students 5 minutes to fill in each box with a term or concept that they have learned this year. Each word must start with the letter in the box. After 5 minutes, the students take turns sharing their answers and scoring their grid. They receive one point for each box they filled if and only if nobody else had their same word. The students have really enjoyed this activity, and it's a great way for them to review concepts that we have learned throughout the year. I have attached a link to the pdf document so you can download and use in your classroom.</span></div></div><div><span style="font-family: "verdana" , sans-serif;"><a href="https://www.dropbox.com/s/fcf74zf6gmk517j/Last%20Day%20Review%20Game.pdf?dl=0" target="_blank">Last Day Review Game Document</a></span></div><div><span style="font-family: "verdana" , sans-serif;"><br /></span></div><div><span style="font-family: "verdana" , sans-serif;">Congratulations on another successful year of teaching!</span><br /><span style="font-family: "verdana" , sans-serif;"><br /></span><a href="https://mailchi.mp/638241b4d4e9/makesenseofmath" target="_blank"><span style="font-family: Verdana, sans-serif; font-size: large;">GRAB YOUR FREEBIES HERE!</span></a></div>Michelle Sigaranhttps://plus.google.com/109631622949404421728noreply@blogger.comtag:blogger.com,1999:blog-8654192331293420079.post-28308545785966173102018-04-10T21:04:00.001-07:002018-12-19T11:10:03.160-08:00State Test is Over...Now What? A Teacher's Survival Guide<div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-QAYcFRrNMkE/Ws2MgTFECYI/AAAAAAAAX_s/uT4t81wrGrAd8v31t8fZ3jfcid0z8e2CgCLcBGAs/s1600/homework-2521144_960_720.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="640" data-original-width="960" height="133" src="https://4.bp.blogspot.com/-QAYcFRrNMkE/Ws2MgTFECYI/AAAAAAAAX_s/uT4t81wrGrAd8v31t8fZ3jfcid0z8e2CgCLcBGAs/s200/homework-2521144_960_720.jpg" width="200" /></a></div><span style="font-family: "verdana" , sans-serif;"><br /></span><br /><div class="separator" style="clear: both; text-align: center;"></div><span style="font-family: "verdana" , sans-serif;">You did it...almost.😖. You taught everything outlined in the curriculum for the end of year test...and your students nailed it. Problem is, however, there are three weeks of school left, now what? I stressed about this every single year. I tried different things every single year. Here are some strategies and ideas to keep you sane. </span><br /><span style="font-family: "verdana" , sans-serif;"><br /></span><u><span style="font-family: "verdana" , sans-serif;">Strategies</span></u><br /><span style="font-family: "verdana" , sans-serif;">1) Routines. This is probably the most important. The last thing you want to do is make the class feel different to the students. Not sticking to the routines you have established will result in students not knowing what to do, therefore they start acting out. Treat every day like another day at school. </span><br /><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;">2) Expectations. This goes along with number one. Don't let your expectations slide, students will pick up on it and take advantage. Expect that they continue to try their best. Expect them to complete their work. Expect quality work from them every single time. </span><br /><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;">3) Keep your students thinking. I know you're tired, and I know your students are tired...but it's not over yet. Do not assign busy work to your students. Busy work is work that doesn't require much thought. Your students will get bored and may perceive the work as unimportant. Once the kids do not see the work as important...you're toast. 😲</span><br /><span style="font-family: "verdana" , sans-serif;"><br /></span><u><span style="font-family: "verdana" , sans-serif;">Ideas</span></u><br /><span style="font-family: "verdana" , sans-serif;">1) Just keep on teaching. Some years I created my own end of year test that was given not three weeks before school was out, but with only a few days left. I continued teaching, connecting, and reviewing their math up until MY end of year test, not the state test. Giving it just a few days before school was out was just enough time to correct it, and review it with the students. </span><br /><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;">2) Cumulative project. A cumulative project in math would be a large project that ties in many concepts that your students learned during the year. The great thing about cumulative projects is that students will be able to see how many of the math concepts intertwine and are used in the real-world. May I suggest, however, that the project is planned out very well. Know what your students will be doing every single day for the project. When I did this, I feel like that is where I failed. I had a cumulative project planned, and I gave specific dates for when they needed to have certain parts of the project completed, however, it was not planned daily. The problem I encountered is that students were "enjoying" the end of the year, and then procrastinated the work time. So it was like a handful of days where they weren't working much, and a few days where it was like chaos, because they were all trying to get done on time. So if you go this route, just make sure that every day has a specific task that needs to be complete.</span><br /><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;">3) Smaller real-life tasks. This is where I have felt the most successful with the end of year. Real-life tasks also combine concepts that students have learned throughout the year. However, they are not as large as the cumulative project. They are real-life tasks that can be completed in one or two class periods. Tasks such as budgeting, planning a trip, designing a scale model, etc... They are engaging, yet not overwhelming. If you need help coming up with some end of year tasks <a href="https://www.teacherspayteachers.com/Product/End-Of-Year-Middle-School-Math-Activities-2948890?utm_source=MSOM%20Blog&utm_campaign=End%20of%20Year%20Activities" target="_blank">Click Here</a> for some that I have created, and my students have loved.</span><br /><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;">You've made it this far....just keep swimming! 💜</span><br /><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;"><a href="https://mailchi.mp/638241b4d4e9/makesenseofmath" target="_blank"><span style="font-size: large;">GRAB YOUR FREEBIES HERE!</span></a></span>Michelle Sigaranhttps://plus.google.com/109631622949404421728noreply@blogger.comtag:blogger.com,1999:blog-8654192331293420079.post-84496891661640789442018-03-14T20:41:00.003-07:002018-12-19T11:11:03.366-08:00How Changing my Questioning Changed Everything<div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-RgRSqeupThc/W9EdcBEcJCI/AAAAAAAAaHg/mIpMMw7Dc9A3egmR_xcCc-8QW-P9ejOmACEwYBhgL/s1600/reverse%2Bblog%2Bfinal.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1240" data-original-width="1600" src="https://2.bp.blogspot.com/-RgRSqeupThc/W9EdcBEcJCI/AAAAAAAAaHg/mIpMMw7Dc9A3egmR_xcCc-8QW-P9ejOmACEwYBhgL/s1600/reverse%2Bblog%2Bfinal.jpg" /></a></div><div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"></div><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;">After my second year of teaching my state switched to using the Common Core State Standards. While the standards weren't too different from the standards we were already using, how they wanted us to teach math switched drastically. No more feeding students algorithms, they wanted students to discover, apply and connect. I was totally on board with this switch, but the problem was ALL of our textbooks were now considered old. I suddenly had no resources for my students to use. However, that summer before school started I went to various classes that taught about how we would now be teaching math. They also addressed the issue of our lack of resources. They taught us how we could actually use our old resources but we just needed to reverse the questions. This idea was brilliant! Let me give an example, a math question may have said something like, "Find the volume of this rectangular prism with a height of 3 inches, a width of 2 inches and a length of 10 inches." Instead, reverse the question, "Create a rectangular prism that has a volume of 60 cubic inches. Justify your answer." So much more reasoning goes into the second question. </span><br /><div><span style="font-family: "verdana" , sans-serif;"><br /></span></div><div><span style="font-family: "verdana" , sans-serif;">I used this idea of reverse questioning and created an activity called "What's the Question?" Essentially, I give students the answer to the question, and they have to come up with the question. Many times there is more than one answer, but as long as students can justify their reasoning it works for me. </span></div><div><span style="font-family: "verdana" , sans-serif;"><br /></span></div><div><span style="font-family: "verdana" , sans-serif;">I am giving away a sample page so you can get an idea of this activity, and use it with your students. You will see deep-thinking increase in your classroom!</span><br /><span style="font-family: Verdana, sans-serif;"><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;"><a href="https://www.dropbox.com/s/8whcc9542ulxquu/Surface%20Area%20and%20Volume%20Whats%20the%20questions%20Blog.pdf?dl=0" target="_blank">CLICK HERE for "What's the Question?" sample page</a></span></span></div><div><span style="font-family: Verdana, sans-serif;"><br /></span></div><div><a href="https://www.teacherspayteachers.com/Product/7th-Grade-Math-Higher-Order-Thinking-Skills-Activity-Whats-the-Question-3425429" target="_blank"><span style="font-family: Verdana, sans-serif;">CLICK HERE for more 7th grade "What's the Question?"</span></a></div><div><a href="https://www.teacherspayteachers.com/Product/8th-Grade-Math-Higher-Order-Thinking-Skills-Activity-Whats-the-Question-3414002" target="_blank"><span style="font-family: Verdana, sans-serif;">CLICK HERE for more 8th grade "What's the Question?"</span></a><br /><br /><a href="https://mailchi.mp/638241b4d4e9/makesenseofmath" target="_blank"><span style="font-family: Verdana, sans-serif; font-size: large;">GRAB YOUR FREEBIES HERE!</span></a><br /><br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-8ewINVf3XMQ/W1FVJQYrZqI/AAAAAAAAY8U/DMskaG6G7IUgd8LliEey4wFwiP14Y-0_wCLcBGAs/s1600/reverse%2Bquestioning%2Bblog.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img alt="Great ideas to engage your middle school math students on a higher-level thinking. Change your questioning and help your algebra students delve deeper into the content." border="0" data-original-height="1600" data-original-width="1067" height="320" src="https://2.bp.blogspot.com/-8ewINVf3XMQ/W1FVJQYrZqI/AAAAAAAAY8U/DMskaG6G7IUgd8LliEey4wFwiP14Y-0_wCLcBGAs/s320/reverse%2Bquestioning%2Bblog.jpg" title="Great ideas to engage your middle school math students on a higher-level thinking. Change your questioning and help your algebra students delve deeper into the content." width="213" /></a></div><br /></div>Michelle Sigaranhttps://plus.google.com/109631622949404421728noreply@blogger.comtag:blogger.com,1999:blog-8654192331293420079.post-57050624046661772272018-02-26T20:45:00.001-08:002018-12-19T11:11:45.834-08:00Thoughts about Teaching Statistics<div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-o3q29oM9tA4/WpTiKONhuaI/AAAAAAAAXig/SyrZfQI29EURk-tAChaiCaN58iIT8-kIwCLcBGAs/s1600/hand-982058_960_720.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="460" data-original-width="960" height="95" src="https://1.bp.blogspot.com/-o3q29oM9tA4/WpTiKONhuaI/AAAAAAAAXig/SyrZfQI29EURk-tAChaiCaN58iIT8-kIwCLcBGAs/s200/hand-982058_960_720.jpg" width="200" /></a></div><div><span style="font-family: "verdana" , sans-serif;"><br /></span></div><span style="font-family: "verdana" , sans-serif;">I've been thinking a lot lately about statistics. I have no stats on my thought, but I was thinking that statistics has to be the most versatile major. If you majored in statistics you could probably look for a job in virtually any company. Statistics is so vital and so useful for companies. Also, on that thought, I recently read an article how statistics would be better taught in the social studies classroom. While I don't 100% agree with this idea, the author makes a good point. Social studies is statistics in action. </span><br /><div><span style="font-family: "verdana" , sans-serif;"><br /></span></div><div><span style="font-family: "verdana" , sans-serif;">However, I think a better argument would be that math educators need to do a better job of applying statistics to the real world. I have not had the opportunity to be in math classes around the country, although I would love to, but my overall feel is that statistics is being taught on a very superficial level. I feel this because that's how I was taught, until my AP statistics class as a senior in high school, but up until that point statistics was very superficial. Yes, I could find the mean, median, and mode, I could make a histogram, and even a box-and-whisker plot, but I had no idea why I would want to do those things. I had no idea how much information I could pull from data. I had no idea how truly useful statistics can be. </span><br /><div><span style="font-family: "verdana" , sans-serif;"><br /></span></div><div><span style="font-family: "verdana" , sans-serif;">The Millennial Generation is the generation of entrepreneurs. As business owners, using statistics correctly can make your business flourish. Ignoring the statistics of your company can cause your business to fail. We can give our students a strong advantage for their futures if we delve into statistics with them more effectively. </span></div><div><span style="font-family: "verdana" , sans-serif;"><br /></span></div><div><span style="font-family: "verdana" , sans-serif;">I'm interested in other people's opinions on my thoughts. Feel free to comment!</span><br /><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;"><a href="https://mailchi.mp/638241b4d4e9/makesenseofmath" target="_blank"><span style="font-size: large;">GRAB YOUR FREEBIES HERE!</span></a></span></div></div>Michelle Sigaranhttps://plus.google.com/109631622949404421728noreply@blogger.comtag:blogger.com,1999:blog-8654192331293420079.post-76680287310552481372018-01-22T19:55:00.001-08:002018-12-19T11:12:32.201-08:00How to Effectively Teach Solving Equations<div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-N8ptvgTAaSI/W9Dr0G_VWRI/AAAAAAAAaGk/krEJ4Ey-iEAPN77Q_C9Kc_igTiYwMXIHQCLcBGAs/s1600/combined%2Bequations%2Bblog.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1240" data-original-width="1600" src="https://3.bp.blogspot.com/-N8ptvgTAaSI/W9Dr0G_VWRI/AAAAAAAAaGk/krEJ4Ey-iEAPN77Q_C9Kc_igTiYwMXIHQCLcBGAs/s1600/combined%2Bequations%2Bblog.jpg" /></a></div><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;">Do you feel like you are constantly teaching and re-teaching how to solve equations? Try this process and watch your students' eyes light up with understanding. </span><br /><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;">Teaching mathematics should take the form of concrete -> symbolic -> abstract. If you just jump right into teaching abstractly you will not reach all of your students. In this post I will review how you can take solving equations through these 3 steps. I have used this process in my classroom, and it has proved to be<i> </i>very effective.</span><br /><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;">I will go through this process with the equation x - 3 = 10</span><br /><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;">Before going through the process emphasize the meaning of the equal sign. Many students will think that the equal sign means "the answer is". Teach that the equal signs means that both sides are the same. Many teachers relate this to a scale, which is a great visual. The scale will become unbalanced if you only add or subtract from one side of the equal sign.</span><br /><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;">CONCRETE</span><br /><span style="font-family: "verdana" , sans-serif;">To concretely solve this equation have students use Algebra tiles. Tip: Have students circle the terms separately, this will help them to not be confused with the signs. Hopefully you have already talked about the additive inverse when teaching integers, if not, teach this property. Tell students they can add or subtract anything from both sides until the variable is alone. </span><br /><span style="font-family: "verdana" , sans-serif;"><br /></span><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-WwOXag-4FIs/Wmax7Qe78VI/AAAAAAAAXM0/ULuZ0ZVLH0E63f6OfBclBPzlPtdtSlQMACLcBGAs/s1600/tiles%2Bequations.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="367" data-original-width="1600" height="146" src="https://2.bp.blogspot.com/-WwOXag-4FIs/Wmax7Qe78VI/AAAAAAAAXM0/ULuZ0ZVLH0E63f6OfBclBPzlPtdtSlQMACLcBGAs/s640/tiles%2Bequations.jpg" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"></div><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;">SYMBOLIC</span><br /><span style="font-family: "verdana" , sans-serif;">Now you will move to drawing symbols for the tiles. I often still let students use the tiles if they need it to guide them in their thinking. I will have them draw a symbol for each tile. Many students start by actually drawing the blocks, but they soon change to just writing the "1" or "-1". </span><br /><span style="font-family: "verdana" , sans-serif;"><br /></span><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-sEB7Yzkv7vI/Wmat_DLCIbI/AAAAAAAAXMg/BhlvHgS6RrAjhsHl1Nkb2sjTnlIaXW22wCLcBGAs/s1600/symbolic%2Bequations.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="426" data-original-width="1551" height="172" src="https://1.bp.blogspot.com/-sEB7Yzkv7vI/Wmat_DLCIbI/AAAAAAAAXMg/BhlvHgS6RrAjhsHl1Nkb2sjTnlIaXW22wCLcBGAs/s640/symbolic%2Bequations.jpg" width="640" /></a></div><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;">ABSTRACT</span><br /><span style="font-family: "verdana" , sans-serif;">Next you will move to abstract. Instead of writing "1 1 1" students will write "+3".</span><br /><span style="font-family: "verdana" , sans-serif;"><br /></span><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-4IgWq5ogMEI/WmavF0YzMQI/AAAAAAAAXMo/7ci-YOMrqfI6RV71q4dwkX96htohgyi5wCLcBGAs/s1600/abstract%2Bequations.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: "verdana" , sans-serif;"><img border="0" data-original-height="456" data-original-width="523" height="278" src="https://2.bp.blogspot.com/-4IgWq5ogMEI/WmavF0YzMQI/AAAAAAAAXMo/7ci-YOMrqfI6RV71q4dwkX96htohgyi5wCLcBGAs/s320/abstract%2Bequations.jpg" width="320" /></span></a></div><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;">One more tip: ALL students should start at the concrete level. Allow students to move through the progression of concrete, symbolic, abstract at their own pace. Allowing students to take they time they need at each level will help students to develop a deep understanding of the mathematics. </span><br /><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;"><b>This post is also featured on the <a href="https://blog.teacherspayteachers.com/make-equations-make-sense-students/" target="_blank">TpT Blog</a></b></span><br /><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;"><a href="https://mailchi.mp/638241b4d4e9/makesenseofmath" target="_blank"><span style="font-size: large;">GRAB YOUR FREEBIES HERE!</span></a></span>Michelle Sigaranhttps://plus.google.com/109631622949404421728noreply@blogger.comtag:blogger.com,1999:blog-8654192331293420079.post-20615243180934764962017-12-22T20:27:00.000-08:002018-12-19T12:19:58.370-08:003 Keys to Become a Better Math Teacher<div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-RihfLyqS9rQ/Wj3a7zti7EI/AAAAAAAAWiE/7rHqZE0GvnUtIoTKKF1sC9FCNyOPW7zwgCLcBGAs/s1600/Blog%2BPictures.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1200" data-original-width="1600" height="150" src="https://3.bp.blogspot.com/-RihfLyqS9rQ/Wj3a7zti7EI/AAAAAAAAWiE/7rHqZE0GvnUtIoTKKF1sC9FCNyOPW7zwgCLcBGAs/s200/Blog%2BPictures.jpg" width="200" /></a></div><br /><span style="font-family: Verdana, sans-serif;">1) Help students make connections between different math topics, especially Algebra and Geometry. Many people think of mathematics as discrete topics, this is detrimental to students' learning. As you study mathematics you will learn that math is intricately connected. Helping students make connections will help them make sense of math and retain the material.</span><br /><span style="font-family: Verdana, sans-serif;"><br /></span><span style="font-family: Verdana, sans-serif;">2) Beware of giving your students algorithms. Students may be able to memorize a few lists of step-by-step algorithms that you give them, but do you expect them to be able to remember ALL the steps for every algorithm? What about the students that have difficulty memorizing? I'm not against algorithms, I'm just against giving step-by-step algorithms to your students. Instead, give them a problem and let them figure it out, then have a discussion with them about what they noticed in their process. Guide them to discover the algorithm. Doing this will help them make sense of the mathematics, and internalize the algorithm.</span><br /><span style="font-family: Verdana, sans-serif;"><br /></span><span style="font-family: Verdana, sans-serif;">3) Get writing. Have your students explain their thinking as much as possible. Teach them to use mathematical vocabulary as they explain. Students will often resist writing in math class at first, but be consistent and show good and bad examples so they know what you expect of them. If you continually require written explanations of their math then your students will internalize the mathematics better.</span><br /><span style="font-family: Verdana, sans-serif;"><br /></span><span style="font-family: Verdana, sans-serif;">If you are looking for some resources to get your students writing check out these writing prompts.</span><br /><span style="font-family: Verdana, sans-serif;"><br /></span><a href="https://www.teacherspayteachers.com/Product/7th-Grade-Math-Writing-Prompts-3382724?utm_source=Blog%20MSOM&utm_campaign=7th%20Grade%20Writing%20Prompts" target="_blank"><span style="font-family: Verdana, sans-serif;">Click Here for 7th Grade Writing Prompts</span></a><br /><span style="font-family: Verdana, sans-serif;"><a href="https://www.teacherspayteachers.com/Product/8th-Grade-Math-Writing-Prompts-3455719?utm_source=Blog%20MSOM&utm_campaign=8th%20Grade%20Writing%20Prompts" target="_blank">Click Here for 8th Grade Writing Prompts</a></span><br /><br /><a href="https://mailchi.mp/638241b4d4e9/makesenseofmath" target="_blank"><span style="font-family: Verdana, sans-serif; font-size: large;">GET YOUR FREEBIES HERE!</span></a>Michelle Sigaranhttps://plus.google.com/109631622949404421728noreply@blogger.comtag:blogger.com,1999:blog-8654192331293420079.post-29028719185293307582017-11-06T19:29:00.000-08:002018-12-19T12:20:54.259-08:00Are you Making the Same Mistake I Made? (Free Resource Included)<span style="font-family: "arial" , "helvetica" , sans-serif;"> </span><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-q49GlZ1dcHc/WgEqBVHAXJI/AAAAAAAAWUo/1hRkuaE6CwoTfQaHXN10WrdSnfKxssWqwCLcBGAs/s1600/low-poly-2767146_640.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="400" data-original-width="640" height="125" src="https://4.bp.blogspot.com/-q49GlZ1dcHc/WgEqBVHAXJI/AAAAAAAAWUo/1hRkuaE6CwoTfQaHXN10WrdSnfKxssWqwCLcBGAs/s200/low-poly-2767146_640.png" width="200" /></a></div><span style="font-family: "arial" , "helvetica" , sans-serif;"><br /></span><span style="font-family: "arial" , "helvetica" , sans-serif;"> About two years into teaching middle school math, I realized a HUGE mistake I had been making. I wasn't teaching something that was very important. I never thought to teach this topic, it wasn't explicitly written in the curriculum. However, I noticed this was a problem by the questions I started receiving from students while teaching. I realized I needed to take a day or two and explicitly teach this. To me, it was just something I knew and picked up, but I realized not everyone picks it up the same way. This topic is parentheses notation. Yes, I explained that parentheses also meant multiplication, but that's about as far as I went. </span><br /><span style="font-family: "arial" , "helvetica" , sans-serif;"><br /></span><span style="font-family: "arial" , "helvetica" , sans-serif;"> Parentheses notation can actually be very complex, and many math teachers likely don't realize the confusion this can cause for students. For example, comparing the two equations 6(-2) and (6)-2. SO many similarities between the two expressions, yet so different in meaning. Or are they different? What exactly am I trying to say in the second expression? Six take away two, or the product of 6 and -2, and what does it depend on? This can be SO CONFUSING for some students. Other students will just know, and they may not even know how they know, but they will just get it, others need parentheses notation taught explicitly. Take the time to teach parentheses notation, you do not need to spend a whole unit on it, but at least spend a day. This will help students in the long run. I made a "Preventing Parentheses Pitfalls" resource to teach this very subject. I have decided to make it FREE to all fellow math teachers in hopes that they will take the time to teach this topic. Click below to download yours now.</span><br /><span style="font-family: "arial" , "helvetica" , sans-serif;"><br /></span><br /><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="https://2.bp.blogspot.com/-OO7cd1J6UEs/WgEnwlYMJzI/AAAAAAAAWUc/UGA74fix_sA1PAir2HHza8-iyVqmsahHwCLcBGAs/s1600/Preventing%2BParentheses%2BPItfalls%2BTitle%2BPage-min%2B%25281%2529.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1600" data-original-width="1600" height="200" src="https://2.bp.blogspot.com/-OO7cd1J6UEs/WgEnwlYMJzI/AAAAAAAAWUc/UGA74fix_sA1PAir2HHza8-iyVqmsahHwCLcBGAs/s200/Preventing%2BParentheses%2BPItfalls%2BTitle%2BPage-min%2B%25281%2529.png" width="200" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Preventing-Parentheses-Pitfalls-3475080?utm_source=Blog%20MSOM&utm_campaign=Parentheses%20Post" target="_blank">CLICK HERE</a> TO DOWNLOAD YOURS NOW</td></tr></tbody></table><span style="font-family: Verdana, sans-serif; font-size: large;"><br /><a href="https://mailchi.mp/638241b4d4e9/makesenseofmath" target="_blank">GET YOUR FREEBIES HERE</a></span><br /><span style="font-family: "arial" , "helvetica" , sans-serif;"><br /></span>Michelle Sigaranhttps://plus.google.com/109631622949404421728noreply@blogger.comtag:blogger.com,1999:blog-8654192331293420079.post-24187355623392548982017-10-27T20:21:00.003-07:002018-12-19T12:21:44.380-08:007 Steps to Master Mathematics with FREE Bookmarks<div align="center" class="MsoListParagraphCxSpFirst" style="text-align: center;"><span style="font-size: 16.0pt; line-height: 115%;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><br /></span></span><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-RtqFcy5o9DI/WfP5VMhEH_I/AAAAAAAAWGY/Ydgk0fxb9XwtwdQ6Du_hmSy7i3A39C16wCLcBGAs/s1600/teacher-953427_1920.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1068" data-original-width="1600" height="133" src="https://1.bp.blogspot.com/-RtqFcy5o9DI/WfP5VMhEH_I/AAAAAAAAWGY/Ydgk0fxb9XwtwdQ6Du_hmSy7i3A39C16wCLcBGAs/s200/teacher-953427_1920.jpg" width="200" /></a></div><div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Bookmarks-7-Steps-to-Master-Mathematics-2188737?utm_source=Makesenseofmath.com&utm_campaign=Bookmark%20Blog%20Post" target="_blank">**********CLICK HERE FOR YOUR FREE BOOKMARKS**********</a></div><br /></div><div class="MsoListParagraphCxSpFirst" style="text-align: left;"><span style="font-family: "arial" , "helvetica" , sans-serif;"> As a math teacher, I can't even tell you how many times a student would excuse their poor math work with the comment, "Well, I'm just not a math person." What was even more horrifying, is when a PARENT would excuse the poor math work of the student with the comment, "Well, I'm not a math person, so he/she is not a math person." There does not exist two categories of math people or not math people. However, I do believe that there exists two categories of people who know how to learn math and people who do not know how to learn math. The great thing is that these categories are flexible and you can easily teach your students to belong to the "I know how to learn math" category. Here are 7 steps to help your students be successful in the math classroom. </span></div><div class="MsoListParagraphCxSpFirst" style="text-align: left;"><br /></div><div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;"><!--[if !supportLists]--><span style="font-family: "arial" , "helvetica" , sans-serif;">1 1)<span style="font-size: 7pt; font-stretch: normal; font-variant-numeric: normal; line-height: normal;"> </span><!--[endif]-->Daily engagement</span></div><div class="MsoListParagraphCxSpMiddle" style="margin-left: 1.0in; mso-add-space: auto;"><span style="font-family: "arial" , "helvetica" , sans-serif;">Stress the difference between engagement and participation. Participating students may simply be copying notes. Engaging students may be copying notes and trying to internalize the notes by making connections. Engagement encourages the use of higher-order thinking skills. In order for students to engage daily, your classroom instruction needs to promote critical thinking skills.</span></div><div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;"><span style="font-family: "arial" , "helvetica" , sans-serif;"> 2)<span style="font-size: 7pt; font-stretch: normal; font-variant-numeric: normal; line-height: normal;"> </span><!--[endif]-->Learn from mistakes</span></div><div class="MsoListParagraphCxSpMiddle" style="margin-left: 1.0in; mso-add-space: auto;"><span style="font-family: "arial" , "helvetica" , sans-serif;">Encourage students to never erase mistakes. Instead have them leave their mistakes, and with a different color they can mark and explain their mistakes. Continually model this to students by marking your mistakes on the board. A safe environment is required for students to feel safe to do this step. Celebrate mistakes as a step in learning.</span></div><div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-stretch: normal; font-variant-numeric: normal; line-height: normal;"> 3) </span><span style="font-size: 7pt; font-stretch: normal; font-variant-numeric: normal; line-height: normal;"> </span><!--[endif]-->Ask critical questions </span></div><div class="MsoListParagraphCxSpMiddle" style="margin-left: 1.0in; mso-add-space: auto;"><span style="font-family: "arial" , "helvetica" , sans-serif;">An example of a non-critical question is, “What’s the next step?” An example of a critical question is, “How do ratios connect with the circumference of a circle?” Make a poster of words that help create critical questions. You could teach them Bloom’s taxonomy, and classify different questions for each level. Consistently point out and praise critical questions in the classroom.</span></div><div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;"><!--[if !supportLists]--><span style="font-family: "arial" , "helvetica" , sans-serif;"> 4) Show all your thinking</span></div><div class="MsoListParagraphCxSpMiddle" style="margin-left: 1.0in; mso-add-space: auto;"><span style="font-family: "arial" , "helvetica" , sans-serif;">Teach students different ways to show their thinking. This can include in writing, with models, diagrams, equations, expressions, etc... Showing calculations depends on the level of the student. Teach students to write in complete sentences. Students should label their models and diagrams. Do not accept low quality with this step. Consistently push the students to do more and more. Have them redo the assignment over and over until they are showing quality work. </span></div><div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;"><!--[if !supportLists]--><span style="font-family: "arial" , "helvetica" , sans-serif;"> 5) <span style="font-size: 7pt; font-stretch: normal; font-variant-numeric: normal; line-height: normal;"> </span><!--[endif]-->Don’t cut corners</span></div><div class="MsoListParagraphCxSpMiddle" style="margin-left: 1.0in; mso-add-space: auto;"><span style="font-family: "arial" , "helvetica" , sans-serif;">Students often just want to “be done” with the problem. To help students to not cut corners, assign fewer problems, but require quality. Cutting corners causes students to make mistakes and not critically think through the problem.</span></div><div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-stretch: normal; font-variant-numeric: normal; line-height: normal;"> 6) </span>Make connections</span></div><div class="MsoListParagraphCxSpMiddle" style="margin-left: 1.0in; mso-add-space: auto;"><span style="font-family: "arial" , "helvetica" , sans-serif;">When students make connections they will retain the information more easily. Many times connections are not obvious and you will need to guide them to discover different connections. Connections between algebra and geometry are critical to understanding higher-level mathematics. Consistently push them to find connections.</span></div><div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-stretch: normal; font-variant-numeric: normal; line-height: normal;"> 7) </span><span style="font-size: 7pt; font-stretch: normal; font-variant-numeric: normal; line-height: normal; text-indent: -0.25in;"> </span><span style="text-indent: -0.25in;">Be humble</span></span></div><div class="MsoListParagraphCxSpLast" style="margin-left: 1.0in; mso-add-space: auto;"><span style="font-family: "arial" , "helvetica" , sans-serif;">Humility is essential for students to learn mathematics. The students that think they are “bright” are often those students who learn very quickly, mostly because they can memorize. These students often don’t think they need to explain their thinking, because they already have the correct answer. Don’t let these students cut corners. Push these students to ask higher-order thinking skills. The students who struggle often don’t want you to know that they will struggle, so they will erase mistakes and try to cover up their weaknesses. Having a positive environment that values mistakes will help these student</span><span style="font-family: "arial" , "helvetica" , sans-serif;">s.</span><br /><span style="font-family: "arial" , "helvetica" , sans-serif;"><br /></span><br /><div style="text-align: center;"><span style="font-family: "arial" , "helvetica" , sans-serif;"><a href="https://www.teacherspayteachers.com/Product/Bookmarks-7-Steps-to-Master-Mathematics-2188737?utm_source=Makesenseofmath.com&utm_campaign=Bookmark%20Blog%20Post" target="_blank">CLICK HERE FOR YOUR FREE BOOKMARKS</a></span><br /><br /><div style="text-align: left;"><span style="font-family: Verdana, sans-serif; font-size: large;"><a href="https://mailchi.mp/638241b4d4e9/makesenseofmath" target="_blank">GRAB YOUR FREEBIES HERE!</a></span></div></div></div><br /><div class="MsoListParagraphCxSpLast" style="margin-left: 1.0in; mso-add-space: auto;"><br /></div>Michelle Sigaranhttps://plus.google.com/109631622949404421728noreply@blogger.comtag:blogger.com,1999:blog-8654192331293420079.post-45523202915808367452017-10-03T12:22:00.000-07:002018-12-19T19:18:41.333-08:00Implementing Mathematical Practices in your Classroom<div class="separator" style="clear: both; text-align: center;"></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-6OJ2geBW0mQ/WTdfNip1O-I/AAAAAAAAT2M/gM-6j1aVu08awTGJLO47O46DRURonA98wCLcB/s1600/abacus-1866497__340.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="340" data-original-width="510" height="133" src="https://1.bp.blogspot.com/-6OJ2geBW0mQ/WTdfNip1O-I/AAAAAAAAT2M/gM-6j1aVu08awTGJLO47O46DRURonA98wCLcB/s200/abacus-1866497__340.jpg" width="200" /></a></div><br /><span style="font-family: "verdana" , sans-serif;">When the new core was implemented in my state I was heading into my third year teaching. I attended an intense 80 hour course on the new material as well as the new strategies to teach math. I fell in love with the new strategies that I learned and I was excited to implement them in my classroom. However, I was caught off guard when I was told that the <a href="http://www.corestandards.org/Math/Practice/" target="_blank">8 Mathematical Practices</a> would be tested. I had never actually explicitly <i>taught</i> mathematical practices, but I knew now was the time to start. Through my years of teaching, I have done a few things in my classroom that have greatly impacted their learning of these practices. Technically, these practices are supposed to be taught since early elementary grades, but even as a middle school math teacher, I always took the time to explicitly teach them.</span><br /><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;">Here are three ideas that have worked in my classroom.</span><br /><span style="font-family: "verdana" , sans-serif;"><br /></span><u><span style="font-family: "verdana" , sans-serif;">Assign a Reading Assignment</span></u><br /><span style="font-family: "verdana" , sans-serif;">That's right, I printed out the mathematical practices and their explanations and I assigned my students to read them. I had them mark up the text, as though they might do in their Language Arts class. I had them highlight the text, annotate the text, and write questions about the text. I had them collaborate in small groups about the text and then we had a large group discussion. Taking the time to do this, truly made the world of difference. </span><br /><span style="font-family: "verdana" , sans-serif;"><br /></span><u><span style="font-family: "verdana" , sans-serif;">Practice the Mathematical Practices</span></u><br /><span style="font-family: "verdana" , sans-serif;">An excellent time to explicitly teach these skills is the first week or two of school. I used logic problems to practice these skills. For example, I would give a logic problem to the students, I often did this in small groups, and have them work on it together. Then I would have the small groups present their "viable argument"to the class. The students would then focus on "critiquing their reasoning." The purpose of the class was not the answer to the logic problem, rather teaching the mathematical practice of, "<span style="color: #202020; font-size: 16.8px;">Construct viable arguments and critique the reasoning of others." This is just one example, but can easily be applied to other mathematical practices. </span></span><br /><span style="font-family: "verdana" , sans-serif;"><u><br /></u><u>Post and Refer</u></span><br /><span style="font-family: "verdana" , sans-serif;">I made posters for the mathematical practices and hung them at the front of my room. I kept them there then entire year. I included them in my teaching on a daily basis. I would tell the students what skill we were practicing along with the new material. I would also have my students tell me what skill they were practicing, and have them write about what mathematical practice skill they were practicing on the assignment. The key for this to be successful is to refer to them and talk about them on a daily basis. Let them become part of your vocabulary and the students' vocabulary. </span><br /><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;"><a href="https://mailchi.mp/638241b4d4e9/makesenseofmath" target="_blank"><span style="font-size: large;">GRAB YOUR FREEBIES HERE!</span></a></span>Michelle Sigaranhttps://plus.google.com/109631622949404421728noreply@blogger.comtag:blogger.com,1999:blog-8654192331293420079.post-16056438476740044792017-04-12T20:02:00.004-07:002018-12-19T12:23:23.642-08:00How to Create Higher-Order Thinking Questions for your Math Classroom<div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-qdOMAeJVHps/WTDMo-NzqVI/AAAAAAAATz0/ZRd6f9kKD1AtiW8tE2OPHjhO6BhIR7s0wCLcB/s1600/kids-girl-pencil-drawing-159823%2B%25281%2529.jpeg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1067" data-original-width="1600" height="133" src="https://3.bp.blogspot.com/-qdOMAeJVHps/WTDMo-NzqVI/AAAAAAAATz0/ZRd6f9kKD1AtiW8tE2OPHjhO6BhIR7s0wCLcB/s200/kids-girl-pencil-drawing-159823%2B%25281%2529.jpeg" width="200" /></a></div><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;">Many math teachers know they need to step up the quality of math problems in their classroom, but are not sure how to do it. I was taught a great strategy and would like to share it with my fellow math teachers. </span><br /><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;">Teachers are often given math textbooks to teach from, and sadly, open-ended questions are not apart of the majority of math textbooks. However, changing common math problems into open-ended questions is very doable. Here is an idea that I have been taught that has helped to step up the rigor in my math classroom. Take a common math problem and flip the question and the answer. </span><span style="font-family: "verdana" , sans-serif;">Students can create questions with the given answer. Take the problem one step further by having them justify their answer either through writing or modeling (or both.)</span><br /><div><span style="font-family: "verdana" , sans-serif;"><br /></span></div><span style="font-family: "verdana" , sans-serif;">For example, a common math question might be the following: </span><span style="font-family: "verdana" , sans-serif;">"Find the volume of a box with height 3 inches, width 5 inches and length 10 inches." If you are familiar with Bloom's Taxonomy, I would suggest this falls into the "knowledge" category. Students simply recall the algorithm and calculate the answer. While I do believe these questions have their place in a math classroom, they should be in the minority. </span><span style="font-family: "verdana" , sans-serif;"> What if you instead changed the question to this, "Create a box that has a volume of 150 cubic inches." Suddenly this question now falls into the "synthesis" category, which is considered a higher-order thinking skill. </span><br /><div><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;">Here is another example: Instead of, "Solve the following equation 3x + 2 = 11," flip around the question and say, "Create a two-step equation where the variable equals 3. Write your equation in two different ways."</span></div><div><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;">Another example: "Find the mean of 12, 15, 18, 20 and 30." Flip around the question and answer and ask, "What five numbers have a mean of 19 and a range of 18? Justify your reasoning." </span><br /><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;">Last example: "Simplify the expressions 2(x + 1) + 4." Change this problem to "Write three expressions that simplify to 2x + 6. Prove that your expressions are all equivalent."</span><br /><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;">Flipping questions does take time, and sometimes it is "easier" to assign the basic problems. Remember, however, that having students problem-solve and make sense of math will require less review and better retention. I can assure you that doing so will definitely be worth your time. </span><br /><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;">If you want a head start on using open-ended questions in your math classroom, here are some great tasks to get started with. They work great at the end of the year to keep your students engaged, or any time of the year to help your students make sense of math. </span><br /><span style="font-family: "verdana" , sans-serif;"><br /></span><br /><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="https://2.bp.blogspot.com/-bwW3akCc2yQ/WO7oFRNgQJI/AAAAAAAAThs/Jp5cJ8nTaCcOX1ZY3dLR0-qbNo2W2ky6gCLcB/s1600/End%2Bof%2BYear%2BActivities%2BTitle%2BPage.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="200" src="https://2.bp.blogspot.com/-bwW3akCc2yQ/WO7oFRNgQJI/AAAAAAAAThs/Jp5cJ8nTaCcOX1ZY3dLR0-qbNo2W2ky6gCLcB/s200/End%2Bof%2BYear%2BActivities%2BTitle%2BPage.png" width="200" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><br /></td></tr></tbody></table><span style="font-family: "verdana" , sans-serif;"> <a href="https://www.teacherspayteachers.com/Product/End-Of-Year-Middle-School-Math-Activities-2948890" target="_blank">Math Tasks for your Middle School Math Classroom</a></span><br /><br /><a href="https://mailchi.mp/638241b4d4e9/makesenseofmath" target="_blank"><span style="font-family: Verdana, sans-serif; font-size: large;">GRAB YOUR FREEBIES HERE!</span></a></div><div><br /></div><div><div><br /></div><div><br /></div></div>Michelle Sigaranhttps://plus.google.com/109631622949404421728noreply@blogger.comtag:blogger.com,1999:blog-8654192331293420079.post-28927773962244922882017-03-07T20:47:00.001-08:002018-12-19T12:24:00.780-08:00How to Step Up the Rigor in your Math Classroom<div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-c7SmURE-Rpc/W9EdbTp3VlI/AAAAAAAAaHU/dtr7aQhI8FEYUJdY3ea9okNkBcMBn1BCwCEwYBhgL/s1600/blog%2Brigor%2Bfinal.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1240" data-original-width="1600" src="https://4.bp.blogspot.com/-c7SmURE-Rpc/W9EdbTp3VlI/AAAAAAAAaHU/dtr7aQhI8FEYUJdY3ea9okNkBcMBn1BCwCEwYBhgL/s1600/blog%2Brigor%2Bfinal.jpg" /></a></div><div class="separator" style="clear: both; text-align: center;"></div><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;"><br /></span><br /><span style="font-family: "verdana" , sans-serif;">Starting my third year of teaching I realized it was time to step up my game as a teacher. I finally felt that I had the basics down enough to run my class smoothly, now I wanted to become a better teacher as far as teaching my content. That summer before my third year, I took a week long middle-school math teaching course. My eyes were opened to <i>everything</i> that I was doing wrong. However, I didn't feel upset, I felt excited. I felt so excited that I finally knew <i>how </i>to become a better teacher. My BIGGEST mistake was that I was teaching to my low students. I thought in my head, well if my low students can understand then that will mean that all my students will understand. This thinking is not necessarily wrong, it's just not very effective. You see, for my low students to understand the content I had to significantly decrease the rigor of my classroom teaching, and the rest of the students suffered and were not reaching their potential. I needed to step up the rigor of my classroom. Here are 4 ways that I stepped up the rigor in my math classroom.</span><br /><div><span style="font-family: "verdana" , sans-serif;"><br /></span></div><div><span style="font-family: "verdana" , sans-serif;">1- Believe in your Students: I didn't believe in my lower students. I didn't believe that they would understand if I didn't teach to their level. Wow, was I wrong! Our school director consistently taught us as teachers that if we believe in our students then they will believe in themselves. I finally took this teaching to heart that year. Instead of seeing them as "low" students, I started seeing them as students with lots of potential who could achieve and understand this content. This mental shift was not a one moment occurrence. There were various times throughout the year where I questioned whether or not I should simplify the content. I had to <i>consistently</i> remind myself that they could achieve. </span></div><div><span style="font-family: "verdana" , sans-serif;"><br /></span></div><div><span style="font-family: "verdana" , sans-serif;">2- Target your high middle-achievers: Instead of targeting my low achievers, I started targeting my high middle-achievers. I gave extensions to my high achievers so they were still being challenged, but I didn't feel comfortable making my high achievers my target audience. I taught at a higher level, and do you know what happened? The lower achievers rose to the challenge.</span></div><div><span style="font-family: "verdana" , sans-serif;"><br /></span></div><div><span style="font-family: "verdana" , sans-serif;">3- Vocabulary: Using correct vocabulary may seem as though it is not as important in a math classroom, I highly disagree. From day 1, I started pushing correct vocabulary. I banned the words "it" and "thing" or any other vague word. I forced myself to use correct vocabulary and I forced my students to use correct vocabulary. I did not simplify my math language into non-math terms. If needed, I spoke "above" their math level, because I wanted them to learn math correctly. My students actually enjoyed this change, I believe they felt more intelligent as they started speaking more intelligently. </span></div><div><span style="font-family: "verdana" , sans-serif;"><br /></span></div><div><span style="font-family: "verdana" , sans-serif;">4- Open-ended Tasks: This was a game changer in my classroom. If you do not know what open-ended tasks are let me briefly describe them. Next week I will write about how to write and incorporate open-ended tasks more specifically into your classroom. Open-ended tasks are story problems that contain all/most of the following criteria: have more than one correct answer, students may need to make some assumptions to finish the problem, there is more than one way to solve the problem, students prove their work, real-world application. </span></div><div><span style="font-family: "verdana" , sans-serif;">I believe that there is a place for fluency practice in your classroom. There is still a need to practice procedures, but DO NOT ignore the need to do extreme reasoning and problem-solving. This practice is where students truly will make sense of math and stretch their brains. </span><br /><span style="font-family: "verdana" , sans-serif;"><br /></span><span style="font-family: "verdana" , sans-serif;"><a href="https://mailchi.mp/638241b4d4e9/makesenseofmath" target="_blank"><span style="font-size: large;">GRAB YOUR FREEBIES HERE!</span></a></span><br /><span style="font-family: "verdana" , sans-serif;"><br /></span><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-_V3EX8V_E2k/W8ikqPjskpI/AAAAAAAAaBc/IrCSQJtIhpAC9K-LnxG-cg62L7miXKUJACLcBGAs/s1600/rigor%2Bpin.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img alt="Looking to step up the rigor in your math classroom? This post is for you! Great ideas to delve into mathematics and get your students thinking! #makesenseofmath #middleschoolmath" border="0" data-original-height="1600" data-original-width="1067" height="320" src="https://4.bp.blogspot.com/-_V3EX8V_E2k/W8ikqPjskpI/AAAAAAAAaBc/IrCSQJtIhpAC9K-LnxG-cg62L7miXKUJACLcBGAs/s320/rigor%2Bpin.jpg" title="Looking to step up the rigor in your math classroom? This post is for you! Great ideas to delve into mathematics and get your students thinking! #makesenseofmath #middleschoolmath" width="213" /></a></div><span style="font-family: "verdana" , sans-serif;"><br /></span></div>Michelle Sigaranhttps://plus.google.com/109631622949404421728noreply@blogger.comtag:blogger.com,1999:blog-8654192331293420079.post-62841287294290515312017-01-06T20:58:00.001-08:002018-12-19T12:24:38.047-08:00How to Teach for Retention in your Math Classroom<br /><div style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-wtHnXxsWJa0/WHRyvpr3KyI/AAAAAAAAS1Q/_rLFv4w9FRcb0A4oNbuhVUF69W0F4x61gCLcB/s1600/classroom-1300761_640.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="144" src="https://1.bp.blogspot.com/-wtHnXxsWJa0/WHRyvpr3KyI/AAAAAAAAS1Q/_rLFv4w9FRcb0A4oNbuhVUF69W0F4x61gCLcB/s200/classroom-1300761_640.jpg" width="200" /></a></div><br /><br />I was two years into my teaching when the new core curriculum was rolled out. I was excited about the rigor of the new curriculum, but stressed out about how I was going to teach all of it. I had mapped out the year various different ways to try and fit all the curriculum in the time allowed, including a few weeks for review at the beginning of the year. I just couldn't make it work. I talked to my director about my concern, and she very wisely asked me, "Why do you have to review at the beginning of the year?" Her question caused me to do some deep reflection. Why <i>do</i> I have to review at the beginning of the year? Are we as teachers teaching so poorly that the students need <i>so</i> much review. She suggested that I review small concepts as they come up during the teaching of other topics, but that I didn't need to devote so much time to review as I had originally planned. Also, she helped me to realize that I needed to teach smarter. I read and implemented lots of strategies and I learned some key strategies to teach for retention.<br /><br />1- Connect your Concepts: Connect both across topic and connect linearly. For example, connect Algebra with Geometry. Connect Algebra with Arithmetic. The more we as teachers help students to see the connections they will make sense of the math. As students make sense of the math their retention increases. Also, as you connect the mathematics there will be a natural constant review of concepts. <br /><br />2- Teach Deeper: Instead of assigning 20 algebraic equations to solve, assign 4 in-depth questions that really cause the students to critically think and analyze. If you are familiar with Bloom's Taxonomy aim for the higher levels. I like <a href="https://teachingcommons.stanford.edu/resources/course-preparation-resources/course-design-aids/bloom%E2%80%99s-taxonomy-educational-objectives" target="_blank">this diagram</a> as the words help me to create questions that use higher-order thinking skills.<br /><br />3- Believe in Your Students: Step up the rigor in your classroom and BELIEVE that they can achieve. If you believe in your students then they will believe in themselves. If you see success in your students, they see success in themselves, as you act like they can succeed then they act like they can succeed. <br /><br />Implementing the above strategies will help your students retain mathematics. This may feel scary at first implementing these strategies, but I have seen success in my own classroom as I connected the concepts, taught deeper and believed in my students, and I know that your students can succeed too.<br /><br />Below are some links to tasks that implement higher-order thinking skills and connect concepts. Perfect to help your students retain mathematics.<br /><br /><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><img alt="Math 7 Task-Based Assessment Prisms Taxes and Inequalities" height="200" src="https://ecdn.teacherspayteachers.com/thumbitem/Math-7-Task-Based-Formative-Assessment-Pacific-Pools-2364776-1483762395/original-2364776-1.jpg" style="margin-left: auto; margin-right: auto;" width="200" /></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Math-7-Task-Based-Assessment-Prisms-Taxes-and-Inequalities-2364776" target="_blank">Click Here</a></td></tr></tbody></table><br /><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><img alt="Math 7 Task-Based Assessment Rational Numbers Tables Graph" height="200" src="https://ecdn1.teacherspayteachers.com/thumbitem/Math-7-Task-Based-Assessment-Rational-Numbers-Tables-Graphs-Percents-2378525-1483762418/original-2378525-1.jpg" style="margin-left: auto; margin-right: auto;" width="200" /></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://www.teacherspayteachers.com/Product/Math-7-Task-Based-Assessment-Rational-Numbers-Tables-Graphs-and-Percents-2378525" target="_blank">Click Here</a></td></tr></tbody></table><span style="font-family: Verdana, sans-serif; font-size: large;"><a href="https://mailchi.mp/638241b4d4e9/makesenseofmath" target="_blank">GRAB YOUR FREEBIES HERE</a>!</span><br /><br /><br />Michelle Sigaranhttps://plus.google.com/109631622949404421728noreply@blogger.comtag:blogger.com,1999:blog-8654192331293420079.post-20773059329062033362016-12-14T19:28:00.001-08:002018-12-19T12:25:10.814-08:00Why I Will Never Tell my Students it is Easy<br /><div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-WZ-qAsbdYY8/WFIPTook6LI/AAAAAAAAScQ/FCoJY1XMN2cYSB9pt3DBECAjdoJXWYNWQCEw/s1600/Slide5.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="205" src="https://4.bp.blogspot.com/-WZ-qAsbdYY8/WFIPTook6LI/AAAAAAAAScQ/FCoJY1XMN2cYSB9pt3DBECAjdoJXWYNWQCEw/s320/Slide5.PNG" width="320" /></a></div><span style="font-family: "arial" , "helvetica" , sans-serif;"><br /></span><span style="font-family: "arial" , "helvetica" , sans-serif;"><br /> </span><br /><span style="font-family: "arial" , "helvetica" , sans-serif;">When I started teaching math, I encountered a problem that I didn't realize I would encounter. I had many students who just didn't want to try. They would just sit there and do NOTHING. I thought that they maybe felt defeated, or that they thought it was too hard for them. So I did what I've heard many teachers do. I said, "It's EASY, you can do it." I thought I was giving them encouragement to try, motivating them, inspiring them to pick up their pencil and at least try. It wasn't until about three years later, that I realized I perhaps was doing the very opposite that I was hoping to do. You see, the problem is that it's NOT EASY for them, and by me telling them that it is easy, they feel so much more defeated. Now they feel like that can't do something that is labeled EASY. Now they <i>definitely </i>weren't going to try, because it's one thing to not be able to do something that is hard, but to not be able to do something that is easy, is completely different. </span><br /><span style="font-family: "arial" , "helvetica" , sans-serif;"><br /></span><span style="font-family: "arial" , "helvetica" , sans-serif;">I teach students who are 12-14 years old. Looking stupid, is the absolute last impression they want to give to their peers. They will choose lazy over looking stupid. So, after this realization, I started changing my words. When they aren't working, I let them know that it IS hard. That I am asking them to do something very difficult, but I believe in them. I believe that they can try, I believe that they can fail, and I believe that they can learn from their mistakes. I believe that they can do hard things and it may not be today, or tomorrow, or this week or month, but I believe that they will eventually get it. And it's OK if it takes them longer than their friend. It's OK if they are faster than their friend. </span><br /><span style="font-family: "arial" , "helvetica" , sans-serif;"><br /></span><span style="font-family: "arial" , "helvetica" , sans-serif;">It's wonderful, because if they try and fail, they don't feel stupid, because they failed doing something difficult. Also, they don't just try and fail, they try and fail and try and fail and eventually try and succeed. And when they succeed they feel so proud, because they succeeded at doing something difficult. This motivates them to keep trying other hard things. It is a cycle that keeps on giving...to them. </span><br /><span style="font-family: "arial" , "helvetica" , sans-serif;"><br /></span><span style="font-family: "arial" , "helvetica" , sans-serif;">Also, this is something that you need to teach your students. Teach them that even if they feel that something is easy, it is not easy for everyone. So they better not be saying in class that it is easy. I do not allow the word EASY in my class, and my students know that. </span><br /><span style="font-family: "arial" , "helvetica" , sans-serif;"><br /></span><span style="font-family: "arial" , "helvetica" , sans-serif;">I challenge you , that if are using words like I was using, to change your mindset. Tell your students that it is hard, but you believe in them. Tell them that you expect them to fail, but you also expect them to learn from their mistakes. You will be surprised how they change their work ethic. </span><br /><span style="font-family: "arial" , "helvetica" , sans-serif;"><br /></span><span style="font-family: "arial" , "helvetica" , sans-serif;"><a href="https://mailchi.mp/638241b4d4e9/makesenseofmath" target="_blank"><span style="font-size: large;">GRAB YOUR FREEBIES HERE!</span></a></span>Michelle Sigaranhttps://plus.google.com/109631622949404421728noreply@blogger.comtag:blogger.com,1999:blog-8654192331293420079.post-55776451838735912002016-12-06T19:24:00.002-08:002018-12-19T12:25:46.732-08:00FREE Transformation Task cards<div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-nr0ZdYXZb8M/WEeA-OUNIcI/AAAAAAAASUM/kUidQzZHdzkgNVQoGp56OyxpVqKHQ746wCLcB/s1600/Slide4.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="408" src="https://4.bp.blogspot.com/-nr0ZdYXZb8M/WEeA-OUNIcI/AAAAAAAASUM/kUidQzZHdzkgNVQoGp56OyxpVqKHQ746wCLcB/s640/Slide4.PNG" width="640" /></a></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"><br /></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"><br /></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"><span style="font-family: "calibri"; font-size: 10pt;"><a href="https://www.teacherspayteachers.com/Product/Free-Transformations-Task-Cards-2860886" target="_blank">CLICK HERE TO DOWNLOAD YOUR FREE SET OF TRANSFORMATION TASK CARDS</a></span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"><span style="font-family: "calibri"; font-size: 10pt;"><br /></span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"><span style="font-family: "calibri"; font-size: 10pt;">These 36 transformation task cards are perfect to make sense of and reinforce transformations and coordinate rules. There are 12 matching sets covering rotations, reflections, dilations and translations. Each set includes a visual of the transformation, the corresponding coordinate rule, and a written explanation of the transformation. These are perfect to make sense of transformations as well as to reinforce the concepts. </span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"><span style="font-family: "calibri"; font-size: 10pt;"></span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"><u><span style="font-family: "calibri"; font-size: 10pt;">Uses in your Classroom</span></u><span style="font-family: "calibri"; font-size: 10pt;"></span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"><span style="font-size: 10.0pt;"><span style="font-family: "arial"; mso-special-format: bullet;">•</span></span><span style="font-family: "calibri"; font-size: 10pt;"> Games: Matching, Go Fish, Spoons, etc, …</span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"><span style="font-size: 10.0pt;"><span style="font-family: "arial"; mso-special-format: bullet;">•</span></span><span style="font-family: "calibri"; font-size: 10pt;"> Exit slips </span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"><span style="font-size: 10.0pt;"><span style="font-family: "arial"; mso-special-format: bullet;">•</span></span><span style="font-family: "calibri"; font-size: 10pt;"> Openers</span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"><span style="font-size: 10.0pt;"><span style="font-family: "arial"; mso-special-format: bullet;">•</span></span><span style="font-family: "calibri"; font-size: 10pt;"> Math Stations</span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"><span style="font-size: 10.0pt;"><span style="font-family: "arial"; mso-special-format: bullet;">•</span></span><span style="font-family: "calibri"; font-size: 10pt;"> Quick formative assessments</span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"><span style="font-size: 10.0pt;"><span style="font-family: "arial"; mso-special-format: bullet;">•</span></span><span style="font-family: "calibri"; font-size: 10pt;"> Putting groups together</span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"><span style="font-size: 10.0pt;"><span style="font-family: "arial"; mso-special-format: bullet;">•</span></span><span style="font-family: "calibri"; font-size: 10pt;"> Pair work or individual work</span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"><br /></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"><u><span style="font-family: "calibri"; font-size: 10pt;">Possible Questions to Accompany Task Cards</span></u><span style="font-family: "calibri"; font-size: 10pt;">:</span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"><span style="font-size: 10.0pt;"><span style="font-family: "arial"; mso-special-format: bullet;">•</span></span><span style="font-family: "calibri"; font-size: 10pt;"> Given the visual transformation write a coordinate rule</span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"><span style="font-size: 10.0pt;"><span style="font-family: "arial"; mso-special-format: bullet;">•</span></span><span style="font-family: "calibri"; font-size: 10pt;"> Given the visual transformation explain in words what is happening in the transformation</span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"><span style="font-size: 10.0pt;"><span style="font-family: "arial"; mso-special-format: bullet;">• </span></span><span style="font-family: "calibri"; font-size: 10pt;">Given a coordinate rule draw a visual transformation that follows the rule</span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"><span style="font-size: 10.0pt;"><span style="font-family: "arial"; mso-special-format: bullet;">•</span></span><span style="font-family: "calibri"; font-size: 10pt;"> Given a coordinate rule explain whether the new figure will be congruent and/or similar to the original figure</span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"><span style="font-size: 10.0pt;"><span style="font-family: "arial"; mso-special-format: bullet;">•</span></span><span style="font-family: "calibri"; font-size: 10pt;"> Given a coordinate rule explain in words what is happening with the transformation</span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"><span style="font-size: 10.0pt;"><span style="font-family: "arial"; mso-special-format: bullet;">•</span></span><span style="font-family: "calibri"; font-size: 10pt;"> Given the written description write a coordinate rule</span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"><span style="font-size: 10.0pt;"><span style="font-family: "arial"; mso-special-format: bullet;">•</span></span><span style="font-family: "calibri"; font-size: 10pt;"> Given the written description draw a graph that follow the rules</span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"><span style="font-family: "calibri"; font-size: 10pt;"></span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"><u><span style="font-family: "calibri"; font-size: 10pt;">Make Sense of Transformations</span></u><span style="font-family: "calibri"; font-size: 10pt;">:</span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"><span style="font-family: "calibri"; font-size: 10pt;"> *Higher-order thinking ideas to help students make sense of transformations.</span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"><span style="font-family: "calibri"; font-size: 10pt;"> Laminate cards (or place in plastic sleeves) so that students can write on the cards with a dry erase marker. </span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"><u><span style="font-family: "calibri"; font-size: 10pt;">Reflections</span></u><span style="font-family: "calibri"; font-size: 10pt;">:</span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"><span style="font-family: "calibri"; font-size: 10pt;"> Have students connect corresponding points and notice that the lines are parallel but not the same length. Ask them if this will always be the case. Have them justify their reasoning. They can draw additional reflections and continue to analyze. Have them practice reflecting over lines that are not the axes. Challenge them to write a coordinate rule for their new reflection. Again, have them analyze lines connecting corresponding points, are they still parallel? How do the lines compare to the line of reflection? They should notice that the lines are perpendicular.</span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"><span style="font-family: "calibri"; font-size: 10pt;"></span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"><u><span style="font-family: "calibri"; font-size: 10pt;">Rotations</span></u><span style="font-family: "calibri"; font-size: 10pt;">:</span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"><span style="font-family: "calibri"; font-size: 10pt;"> Have students connect only one set of corresponding points to the center of rotation and measure the created angle with a protractor. Students should be able to verify that this is the degree of rotation. Also, guide the students to notice that the length of their lines are also the same length. You can move deeper into this idea by using compasses. Ask the students if corresponding points will always be the same distance from the center of rotation. Have students justify their reasoning. Students can practice rotating the figure varying amount of degrees. </span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"><span style="font-family: "calibri"; font-size: 10pt;"></span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"><u><span style="font-family: "calibri"; font-size: 10pt;">Translation</span></u><span style="font-family: "calibri"; font-size: 10pt;">:</span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"><span style="font-family: "calibri"; font-size: 10pt;"> Have students connect corresponding points and notice that the lines are parallel, and the same magnitude (length) Will this always be the case? Will the lines always be parallel and the same length? Have them justify their reasoning. Have them draw more translations and continue to analyze and justify their reasoning. </span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"><span style="font-family: "calibri"; font-size: 10pt;"></span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"><u><span style="font-family: "calibri"; font-size: 10pt;">Dilations</span></u><span style="font-family: "calibri"; font-size: 10pt;">:</span></div><br /><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; unicode-bidi: embed; word-break: normal;"><span style="font-family: "calibri"; font-size: 10pt;"> Have students connect corresponding points and extend the lines until they intersect. Students should notice that these lines intersect at the center of dilation. Challenge them to draw a new dilation with a different center of dilation and check their thinking. </span><br /><span style="font-family: "calibri"; font-size: 10pt;"><br /></span><a href="https://mailchi.mp/638241b4d4e9/makesenseofmath" target="_blank"><span style="font-family: Verdana, sans-serif; font-size: large;">GRAB YOUR FREEBIES HERE!</span></a></div>Michelle Sigaranhttps://plus.google.com/109631622949404421728noreply@blogger.comtag:blogger.com,1999:blog-8654192331293420079.post-59102088835099325882016-11-10T21:32:00.000-08:002017-10-27T20:26:24.917-07:00Why I will Never Teach F.O.I.L.<div class="separator" style="clear: both; text-align: center;"></div><br /><div class="separator" style="clear: both; text-align: center;"></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-s8xUYykSMss/WD2Z8iSy_6I/AAAAAAAASJA/Al4hyn-YmGIPMY8If-ilwgKcIBxzFIJmACLcB/s1600/Slide2.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="205" src="https://1.bp.blogspot.com/-s8xUYykSMss/WD2Z8iSy_6I/AAAAAAAASJA/Al4hyn-YmGIPMY8If-ilwgKcIBxzFIJmACLcB/s320/Slide2.PNG" width="320" /></a></div><br />Tell me if this scenario sounds familiar. You are planning your classes for next week and you notice that your students will need to learn to multiply binomials. You are so excited, because you have a great trick to teach your students, and it's SO easy, right? If your kids can just remember the acronym F.O.I.L.,then they'll have the concept learned in no time. This may have been the way you learned to multiply binomials, you know your students will catch on in no time. Many teachers use F.O.I.L. to teach multiplying binomials such as (x + 3)(x + 4). The F. represents FIRST, multiply first terms. x(x) = x<sup style="background-color: white; font-family: inherit;">2 </sup> Next comes O. = outside terms x(4) = 4x, then I.= inside terms 3(x) = 3x then L. = last terms 3(4) = 12. Combining the terms we have x<sup style="background-color: white; font-family: inherit;">2 </sup>+ 4x + 3x + 12 = x<sup style="background-color: white; font-family: inherit;">2 </sup>+ 7x + 12. Voila...you can multiply binomials. O.K. I hope I'm not convincing you to use F.O.I.L. I'll give you some credit, F.O.I.L., is usually easy for the kids to learn and memorize (if they can memorize), however teaching F.O.I.L. has many, many downfalls. Let me explain why I NEVER will teach my kids F.O.I.L.<br /><div><br /></div><div>1) F.O.I.L., has no mathematical basis. Your quick memorizers may attach quickly to F.O.I.L. and zoom through their 20 practice problems that you have assigned them. However, ask them to explain why F.O.I.L. works and they will stare at you blankly. Generally, if students do not understand why an algorithm works they will not be able to retain the concept, or they will not be able to apply the concept to new skills. Also, if you are just teaching a shortcut, are you really teaching pure mathematics? <br /><br /></div><div></div><div>2) What about the students who can't memorize? F.O.I.L., is based on the assumption that all students can memorize the acronym, what each letters stands for, and when to apply it. If you haven't learned already, you soon will, all kids are not great memorizers. The ability to memorize should not be a requisite for being a mathematician, rather the ability to reason and problem-solve. As a teacher you should work to develop reasoning and problem-solving skills in your students at every opportunity. Teaching F.O.I.L. does not to do this. </div><div><br /></div><div>3) The MOST important reason I will never teach F.O.I.L. is that students suddenly get stumped when in their next math class they have to multiply polynomials like the following : (x + 2)(x<sup style="background-color: white; font-family: inherit;">2</sup> + 3x + 4) or even a little more complicated (x<sup style="background-color: white; font-family: inherit;">2</sup> + 2x + 1)(x<sup style="background-color: white; font-family: inherit;">2</sup> + 3x + 4). In fact, many students who learn the F.O.I.L. method try and apply this to these polynomials, and the result is disastrous. <br /><br />So, if you should not teach F.O.I.L. what should you use? The answer is simple, you should teach mathematics, not tricks. If a students happens to discover the F.O.I.L. method you applaud them and let them explain to you why it works. If they understand why, they will have no problem with advanced polynomial multiplication, because they discovered it and understand it. <br /><br />I teach the multiplication of polynomials using two methods, sometimes simultaneously, sometimes consecutively. I use algebra tiles so students can see the geometric connection, and I teach the distributive property. If you have not used algebra tiles in your classroom before, the time to start is NOW. Using algebra tiles is a hands-on method that reaches all students, and can easily challenge the top-learners as well in your classroom. You can purchase algebra tiles; however, they are kind of pricey. You can download some FREE algebra tiles here for your students. They are available in color and as black-line versions to print on colored paper. <a href="https://www.teacherspayteachers.com/Product/Free-Algebra-Tiles-2421344" target="_blank">FREE ALGEBRA TILES</a><br /><br />In a different post I will cover how to teach with Algebra Tiles, but if you would like to get started today <a href="https://www.teacherspayteachers.com/Product/Factors-and-Models-with-Algebra-Tiles-Task-Cards-2406492" target="_blank">THESE TASK CARDS</a> are a great addition to your classroom. <br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-CwnbgBFUfe0/WCELuVmX6JI/AAAAAAAARzo/2gKMR08dsH054qldpDlm7wE0wMO3HHcRQCLcB/s1600/Slide3.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="150" src="https://1.bp.blogspot.com/-CwnbgBFUfe0/WCELuVmX6JI/AAAAAAAARzo/2gKMR08dsH054qldpDlm7wE0wMO3HHcRQCLcB/s200/Slide3.PNG" width="200" /></a></div><br />Teaching the distributive method is also VERY effective. Students who understand the distributive property can apply this concept to multiplying polynomials with various terms.<br /><br />Set your students up for success, not just in your class, but for their future math classes. Say adios to F.O.I.L. and starting working with algebra tiles. Your students will thank you.<br /><br /><br /><br /><span style="font-family: inherit;"><sup style="background-color: white;"></sup></span></div>Michelle Sigaranhttps://plus.google.com/109631622949404421728noreply@blogger.comtag:blogger.com,1999:blog-8654192331293420079.post-6307983282935573452016-09-21T22:18:00.001-07:002018-12-19T12:26:29.032-08:00Why I Don't Grade Papers at Home<div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-wMvFLoP5oqU/W9EdbWTmLEI/AAAAAAAAaHY/AX8idpOrAgcaktDd0Dvp_JNinUz6MYgBACEwYBhgL/s1600/grade%2Bpapers%2Bblog%2Bfinal.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1240" data-original-width="1600" src="https://2.bp.blogspot.com/-wMvFLoP5oqU/W9EdbWTmLEI/AAAAAAAAaHY/AX8idpOrAgcaktDd0Dvp_JNinUz6MYgBACEwYBhgL/s1600/grade%2Bpapers%2Bblog%2Bfinal.jpg" /></a></div><div class="separator" style="clear: both; text-align: center;"></div><span style="font-family: "arial" , "helvetica" , sans-serif;"><br /></span><span style="font-family: "arial" , "helvetica" , sans-serif;"><br /></span><br /><span style="font-family: "arial" , "helvetica" , sans-serif;">I was in my third year of teaching and we had a new technology teacher. This teacher has a fantastic personality for teaching. All students love him from day one, and he has an ability to connect with them immediately. He had just left a job at a bank, and this was his first year teaching. He did what many first year teachers do. He worked, and worked, and worked. He came early, he left way late and he was very, very tired. He came to me one day after a few months and mentioned to me that the school director wanted to meet with him. He was a little nervous, and didn't know what she was going to say. I gave him some assurance and let him know that our director was fantastic, and I'm sure anything that she had to say was just to help him. The next day I asked him what the meeting was about, and he told me that she was worried about him. She was worried that he was working way too hard. She gave him some ideas to grade more efficiently and not have to work so hard. You see, our very experienced educator knew something that only the best teachers know. Let me explain further, because I made the same mistake. </span><br /><span style="font-family: "arial" , "helvetica" , sans-serif;"><br /></span><span style="font-family: "arial" , "helvetica" , sans-serif;"> Years ago I attended a commencement ceremony, and something was spoken that made a huge impact on me, though not the exact words, the message was along these lines. "Congratulations to all those who have graduated with A's, you have worked really hard, studied countless nights and you deserve those grades, but I would like to congratulate even more those who graduated with B's. Getting B's because you have made your family a priority, B's because you also are a parent, spouse, friend, and neighbor." I thought, Yes, that is what is important. </span><br /><span style="font-family: "arial" , "helvetica" , sans-serif;"><br /></span><span style="font-family: "arial" , "helvetica" , sans-serif;">I started out teaching trying to be the "straight A" teacher, and as a result everything else suffered....even my students. I stayed late hours at school....then I would go home, eat....and continue working. I worked, worked and worked. Interestingly enough this often backfires on teachers. I was so stressed, wasn't sleeping, and my patience in the classroom greatly diminished. </span><br /><span style="font-family: "arial" , "helvetica" , sans-serif;"><br /></span><span style="font-family: "arial" , "helvetica" , sans-serif;">As the years went on, I realized that what I was doing wasn't working. So, instead of planning curriculum over the summer, I spent time reading, studying and planning systems so that my classroom could run more efficiently, and I told myself that I would leave school everyday at 4:00, and I would not work at home. I didn't stick to my plan 100% at first, but I did better. Each year, I perfected my systems and stuck better to my plan. I noticed something interesting......I actually became a better teacher. I had more patience for my students, and I noticed that I began to value every minute while at work. I learned to use my time wisely. I then began applying this with my students. I began to value my time with them even more, and when my students were in my class, they thought and problem-solved until they walked out the door. I took it as a compliment when they said their head hurts from thinking so much.</span><br /><span style="font-family: "arial" , "helvetica" , sans-serif;"><br /></span><span style="font-family: "arial" , "helvetica" , sans-serif;">I'm not necessarily saying that you need to work less and you will be a better teacher, rather, the point I am trying to make is that you need to work smarter. You need to work very efficiently and effectively while at school. While at home, you need to work hard at not working :) It's tough to relax and spend time on other things when you feel like you have a long to-do-list. However, you need to trust that doing so will truly make you a better teacher.</span><br /><span style="font-family: "arial" , "helvetica" , sans-serif;"><br /></span><span style="font-family: "arial" , "helvetica" , sans-serif;">I have learned that what we do at school is important, very important, but what we do at home is more important. When teachers set their priorities straight, your teaching and classroom will improve because you will be happier and less stressed. Set a goal and try to change something today to act according to your priorities. </span><br /><span style="font-family: "arial" , "helvetica" , sans-serif;"><br /></span><span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: Verdana, sans-serif; font-size: large;"><a href="https://mailchi.mp/638241b4d4e9/makesenseofmath" target="_blank">GRAB YOUR FREEBIES HERE!</a></span></span><br /><span style="font-family: "arial" , "helvetica" , sans-serif;"><br /></span><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-MXuIqvwJcV0/W8f7i8cKwdI/AAAAAAAAaBI/fpxuYFQhshkjA9w8Scn4ybp0Vt_2qnLHgCLcBGAs/s1600/no%2Bgrade%2Bat%2Bhome%2Bpin.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img alt="Great blog post to encourage teachers not to grade papers at home. Teaching middle school math can be stressful, but here are some great ideas to keep your priorities straight! #makesenseofmath" border="0" data-original-height="1600" data-original-width="1067" height="320" src="https://2.bp.blogspot.com/-MXuIqvwJcV0/W8f7i8cKwdI/AAAAAAAAaBI/fpxuYFQhshkjA9w8Scn4ybp0Vt_2qnLHgCLcBGAs/s320/no%2Bgrade%2Bat%2Bhome%2Bpin.jpg" title="Great blog post to encourage teachers not to grade papers at home. Teaching middle school math can be stressful, but here are some great ideas to keep your priorities straight! #makesenseofmath" width="213" /></a></div><span style="font-family: "arial" , "helvetica" , sans-serif;"><br /></span>Michelle Sigaranhttps://plus.google.com/109631622949404421728noreply@blogger.com