tag:blogger.com,1999:blog-618615057955297502018-03-06T00:10:57.139-08:00FJHS MATH-8Anonymousnoreply@blogger.comBlogger21125tag:blogger.com,1999:blog-61861505795529750.post-51289701911224882032014-03-21T23:06:00.001-07:002014-03-31T11:15:40.965-07:00Modeling Irrational ApproximationsTo find rational approximations of irrational numbers students must first be able to differentiate between rational and irrational numbers (see the sorting activity highlighted in this previous <a href="http://fjhsmath-8.blogspot.com/2013/09/decimal-form-of-rational-numbers.html" target="_blank">Decimal Form of a Rational Number</a> post). The geometric approach to evaluating square roots of perfect squares can be extended to approximating irrational numbers. This modeling activity provides a visual proof that square roots of non-perfect squares are indeed irrational (see the concept builder highlighted in this previous <a href="http://fjhsmath-8.blogspot.com/2014/03/square-roots-and-cube-roots.html" target="_blank">Square Roots and Cube Roots</a> post). Consider scaffolding the geometric approach with this Stations Activity and record sheet based on square tiles.<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;"><a href="http://4.bp.blogspot.com/-OqoCnZ4lCXs/UzmwAqisVnI/AAAAAAAACCw/NoqKgjEFKbY/s1600/8.NS.A.2+Title+Pic.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="http://4.bp.blogspot.com/-OqoCnZ4lCXs/UzmwAqisVnI/AAAAAAAACCw/NoqKgjEFKbY/s1600/8.NS.A.2+Title+Pic.png" height="247" width="320" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://drive.google.com/folderview?id=0B5H2CSmfdlQEMHEtN0ZwSlByam8&usp=sharing" target="_blank">8.NS.A.2 Resources</a></td></tr></tbody></table><br />And then move students from the geometric model to a numeric approach with the number line (see this previous <a href="http://fjhsmath-8.blogspot.com/2013/09/irrational-approximations.html" target="_blank">Irrational Approximations</a> post). This will enable students to use rational approximations to compare the size of irrational numbers, locate them on a number line, and estimate the value of expressions.<br /><br /><br />This stations activity highlights Common Core State Standard 8.NS.A.2 included in MATH-8 and Accelerated MATH-7.Anonymousnoreply@blogger.com0tag:blogger.com,1999:blog-61861505795529750.post-89024413904451722062014-03-19T09:47:00.000-07:002014-03-19T09:47:09.557-07:00Grade 8 BenchmarkState testing is just around the corner! And all thoughts assessment can be found in the <a href="http://fjhsmath.blogspot.com/2014/03/tis-season.html" target="_blank">'Tis the Season</a> post. This Grade 8 activity set could be used with the Find Someone Who structure to conduct a general review of sample questions organized by Arkansas Frameworks strands. Each question is an adapted released item from Grade 8 Benchmark exams over the recent years. If you choose to use these in your classroom, remember to remind students to only pair with others who are not their teammates. This will allow students to return to their teams and wrap-up by using the RoundRobin structure to share solutions and discuss any questions that may arise.<br /><br /><div class="separator" style="clear: both; text-align: center;"></div><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;"><span style="margin-left: auto; margin-right: auto;"><a href="https://drive.google.com/folderview?id=0B5H2CSmfdlQEcWVxYU1SSlNQeXc&usp=sharing" target="_blank"><img border="0" src="http://1.bp.blogspot.com/-Kj3vDvaSswQ/UynHNhh_L-I/AAAAAAAACAw/91SB2UxKPPI/s1600/Benchmark+Practice+(Grade+8).jpg" height="320" width="247" /></a></span></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://drive.google.com/folderview?id=0B5H2CSmfdlQEcWVxYU1SSlNQeXc&usp=sharing" target="_blank">Grade 8 Benchmark Resources</a></td></tr></tbody></table><br />This structure requires students to coach each other as needed. Coach: Tip, Tip, Teach, Try again! Let me encourage you to use a coaching chart with these activities to strengthen the math vocabulary that is used during coaching. Perhaps let your students work with a classmate or two and then freeze the class to discuss a list of coaching tips. Review things they may say and things they may do while working collaboratively. For example, on the number and operations coaching chart you could list "Did you find the prime factorization?" or "GCF shows COMMON parts." under the say column. And then list these examples under the do column: "Draw a Venn diagram of prime factors." or "Make eye contact." or "Nod your head."<br /><br />You may choose to accompany each Find Someone Who activity with a coordinating sample open response question. Details are not included in this post because everything I know about setting kids up for success with open response questions was learned from Rhonda Kobylinski. Without a doubt, she is your resident expert.<br /><br />Happy testing to YOU!Anonymousnoreply@blogger.com2tag:blogger.com,1999:blog-61861505795529750.post-69028857673598127742014-03-19T08:53:00.002-07:002014-03-19T10:16:05.165-07:00Interactive Parallel Lines<div class="separator" style="clear: both; text-align: left;">Are your students struggling with the angle relationships formed when parallel lines are cut by a transversal? Check out this web-based interactive model. This prompts discovery of corresponding, alternate interior, and alternate exterior angles through measure and color coding. Angle notation is also supported in this model. Use for whole class demonstration or pair with a lab activity for 1:1 technology.<br /></div><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;"><span style="margin-left: auto; margin-right: auto;"><a href="http://www.mathwarehouse.com/geometry/angle/interactive-transveral-angles.php" target="_blank"><img border="0" src="http://1.bp.blogspot.com/-A0dvYMtQC5Q/Uym7YqtQUlI/AAAAAAAACAg/RN1g6gOwaaE/s1600/Interactive+Parallel+Lines.jpg" height="320" width="320" /></a></span></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="http://www.mathwarehouse.com/geometry/angle/interactive-transveral-angles.php" target="_blank">Interactive Discovery</a></td></tr></tbody></table><br />Perhaps combine this interactive model with a reference foldable to summarize the angle relationships investigated in the <a href="http://fjhsmath-8.blogspot.com/2014/02/angle-relationships.html" target="_blank">AngLegs discovery</a>.<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><span style="margin-left: auto; margin-right: auto;"><a href="https://drive.google.com/folderview?id=0B5H2CSmfdlQEb2NYMEJRZWZGWk0&usp=sharing" target="_blank"><img border="0" src="http://2.bp.blogspot.com/-_gEUFw5e5zs/UynOF3WPNkI/AAAAAAAACBE/m0Fuh1bWbhc/s1600/Angle+Relationships+Foldable+Title+Pic.jpg" height="320" width="247" /></a></span></td></tr><tr><td class="tr-caption" style="font-size: 13px;"><a href="https://drive.google.com/folderview?id=0B5H2CSmfdlQEb2NYMEJRZWZGWk0&usp=sharing" target="_blank">Angle Relationships Reference Foldable</a></td></tr></tbody></table>This activity set highlights Common Core Standard 8.G.A.5 included in MATH-8 and Accelerated MATH-7.Anonymousnoreply@blogger.com0tag:blogger.com,1999:blog-61861505795529750.post-43330362747833308772014-03-06T00:30:00.000-08:002014-03-06T00:30:03.258-08:00Volume of Cones, Cylinders, and SpheresHow do you address a standard that prompts students to "know" formulas? The word "know" is completely different from being prompted to "derive" formulas. 21st Century learning pushes us to ditch "know" being equated with "memorize" when a formula can quickly be obtained from Google. Perhaps a focus on the relationship within the structure of the formulas would best serve our students...thoughts?<br /><div class="separator" style="clear: both; text-align: center;"><br /></div>The emphasis of volume as layered base area starts with cylinders. And since cylinders are critical for understanding volume of cones and spheres, be sure students are firmly rooted in this concept. The Oreo lab activity can confirm the level of student understanding. Then consider the following activities that use <a href="http://www.learningresources.com/product/view-thru--174-+large+geometric+shapes+set.do?from=Search&cx=0" target="_blank">View-Thru Large Geometric Solids</a> from <a href="http://www.learningresources.com/" target="_blank">Learning Resources</a> for a hands-on investigation to determine the volume of cones and spheres from relational cylinders.<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><span style="margin-left: auto; margin-right: auto;"><a href="https://drive.google.com/folderview?id=0B5H2CSmfdlQEaHpGYVNmMTMzSjQ&usp=sharing" target="_blank"><img border="0" src="http://4.bp.blogspot.com/-laDvQRHacV0/UxdtRcUciwI/AAAAAAAAB_0/NRNxddhV1Pc/s1600/8.G.C.9+Title+Pic.png" height="320" width="301" /></a></span></td></tr><tr><td class="tr-caption" style="font-size: 13px;"><a href="https://drive.google.com/folderview?id=0B5H2CSmfdlQEaHpGYVNmMTMzSjQ&usp=sharing" target="_blank">8.G.C.9 Resources</a></td></tr></tbody></table><br />Short on time from the recent ice days? This animation is quick but powerful in showing the 3:1 volume ratio of cone to cylinder.<br /><br /><iframe allowfullscreen="" frameborder="0" height="315" src="//www.youtube.com/embed/f1Kpa2YR08g" width="420"></iframe><br /><br />Similar extensions can be made to investigate the volume of a square pyramid from a relational cube. Note: Pyramids are included in Grade 7 standards (7.G.A.3) with respect to cross sections and High School Geometry standards (HSG-GMD.A.1 and HSG-GMD.A.3) with respect to volume.<br /><br />These investigations highlight Common Core State Standard 8.G.C.9 included in MATH-8 and Accelerated MATH-7. Anonymousnoreply@blogger.com0tag:blogger.com,1999:blog-61861505795529750.post-197975842586846062014-03-05T00:30:00.000-08:002014-03-05T00:30:01.394-08:00Square Roots and Cube RootsHow do you teach students to evaluate square roots of small perfect squares and cube roots of small perfect cubes? The foundational concept behind evaluating roots is the connection between side length of a square and its area or edge length of a cube and its volume. Do you stop there? No need. Start with the geometric connection and then extend to a visual proof that the square root of 2 is irrational. This investigation will pave the road to move <a href="http://fjhsmath-8.blogspot.com/2013/09/irrational-approximations.html" target="_blank">approximating irrational numbers</a> from concrete to abstract understanding...which is a natural prerequisite to the Pythagorean theorem.<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><span style="margin-left: auto; margin-right: auto;"><a href="https://drive.google.com/folderview?id=0B5H2CSmfdlQEcnNpbkM2SGhSamM&usp=sharing" target="_blank"><img border="0" src="http://2.bp.blogspot.com/-XOCMtRrvxvw/UxZt_aazu_I/AAAAAAAAB_k/LomxZiV67Gw/s1600/Concept+Builder+Title+Pic.jpg" height="320" width="247" /></a></span></td></tr><tr><td class="tr-caption" style="font-size: 13px;"><a href="https://drive.google.com/folderview?id=0B5H2CSmfdlQEcnNpbkM2SGhSamM&usp=sharing" target="_blank">8.EE.A.2 Resources</a></td></tr></tbody></table><br />This investigation highlights Common Core State Standard 8.EE.A.2 included in MATH-8 and Accelerated MATH-7.Anonymousnoreply@blogger.com0tag:blogger.com,1999:blog-61861505795529750.post-48623843445117210882014-02-24T12:19:00.003-08:002014-02-24T13:42:01.931-08:00Transformations ContinuedDo you have a classroom theme? A motto of sorts...something that drives everything that you and your students do in your classroom...and hopefully beyond those walls as well?!?<br /><br />Do you see the same idea within your course curriculum? With the implementation of the CCSS, there has been speculation as to the theme (or emphasis) for each grade level. Educators present arguments for a particular theme that acts as the ongoing thread in that grade level of math. For Grade 8, educators seem to fall into different camps as two threads have risen to the top of discussions in the past few years. Some say transformations. Some say functions. What are your thoughts? Would you say that transformations or functions drive everything you do in MATH-8? Is it a difference between results and relationships?<br /><br />That's a big discussion.<br />And it's a discussion that needs to occur sooner rather than later.<br />Because it really is different to spy all standards with a lens of transformations versus a lens of functions.<br /><br />As for the MATH-8 standards that involve developing the concept of transformations, what seems to be the most difficult for students to grasp? Historically, my students have struggled with coordinate notation and the process of rotations. Review a previous post on <a href="http://fjhsmath-8.blogspot.com/2013/08/thinking-transformations.html" target="_blank">Thinking Transformations</a> that discusses the transformations standards that are expected for students in MATH-8 and Accelerated MATH-7.<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><span style="margin-left: auto; margin-right: auto;"><a href="https://drive.google.com/folderview?id=0B5H2CSmfdlQEck5IekJKUC1fOVU&usp=sharing" target="_blank"><img border="0" src="http://1.bp.blogspot.com/-SGGVEP71yDQ/UwulYQNiRmI/AAAAAAAAB7Q/MF_pUd2k7EQ/s1600/Transformations+Bundle+Title+Pic.png" height="320" width="320" /></a></span></td></tr><tr><td class="tr-caption" style="font-size: 13px;"><a href="https://drive.google.com/folderview?id=0B5H2CSmfdlQEck5IekJKUC1fOVU&usp=sharing" target="_blank">Transformations Resources</a></td></tr></tbody></table><br />The following resource includes record sheets to coordinate with the transformations activities adapted from the Hands-On Standards Grades 7-8 book. Create four stations, one per transformation, for students to rotate through as a team. Consider duplicating to set two stations for each transformation in an effort to manage manipulatives setup.<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><span style="margin-left: auto; margin-right: auto;"><a href="https://drive.google.com/folderview?id=0B5H2CSmfdlQENmdGNlVEdWtIV1E&usp=sharing" target="_blank"><img border="0" src="http://2.bp.blogspot.com/-iRCX18GiiuI/UwumI-giCvI/AAAAAAAAB7c/a-yOfHApfSo/s1600/Transformations+Stations+Activity+Title+Pic.png" height="320" width="320" /></a></span></td></tr><tr><td class="tr-caption" style="font-size: 13px;"><a href="https://drive.google.com/folderview?id=0B5H2CSmfdlQENmdGNlVEdWtIV1E&usp=sharing" target="_blank">Transformations Stations Activity Record Sheets</a></td></tr></tbody></table><br />These activities highlight Common Core State Standards 8.G.A.1, 8.G.A.2, 8.G.A.3, and 8.G.A.4 included in MATH-8 and Accelerated MATH-7.Anonymousnoreply@blogger.com0tag:blogger.com,1999:blog-61861505795529750.post-27911781068665451952014-02-19T12:25:00.003-08:002014-02-26T09:19:29.327-08:00Similarity<div class="separator" style="clear: both; text-align: left;">There are four types of transformations or changes that can be made to the position of a geometric figure. When a geometric figure undergoes a transformation, the line segments still result in line segments and angles still result in angles. Translations, reflections, and rotations produce congruent figures meaning the shape is identical in that the corresponding line segments maintain their same length and the corresponding angles maintain their same measure...the exact figure is simply in a new position. (CPCTC=corresponding parts of congruent triangles are congruent!) The location changes, and sometimes the orientation changes as well. Dilations produce similar figures meaning the figure is the same shape and the corresponding angles maintain their same measure but the corresponding line segments are proportional in length. (<a href="http://fjhsmath-8.blogspot.com/2014/02/transformations-continued.html" target="_blank">CCSS 8.G.A.4</a>)</div><br />In CCSS 8.G.A.5 students investigate angle-angle criterion for similarity of triangles. What happened to the unmentioned third angle? Why not angle-angle-angle criterion for similarity? Ask your students. Prompt them to realize that the third angle is implied by interior angle sum of a triangle. In the lab activity below, students discover that two angle measures in a triangle do not yield congruence between the figures. This sets the stage to discuss the definition of similarity. The AngLegs Simultaneous RoundTable puts the definition to work and makes connections to dilation and percent increase. This is prerequisite knowledge for CCSS 8.EE.B.6 standard that connects slope and similar triangles including the derivation of y=mx+b.<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><span style="margin-left: auto; margin-right: auto;"><a href="https://drive.google.com/folderview?id=0B5H2CSmfdlQEVVZ5MmE1MWVZSnc&usp=sharing" target="_blank"><img border="0" src="http://1.bp.blogspot.com/-i-CuPyAdDLw/Uw4hIOpOR2I/AAAAAAAAB7w/gtUaNZe4SKs/s1600/8.G.A.5+AA+Similarity+Title+Pic.png" height="320" width="301" /></a></span></td></tr><tr><td class="tr-caption" style="font-size: 13px;"><a href="https://drive.google.com/folderview?id=0B5H2CSmfdlQEVVZ5MmE1MWVZSnc&usp=sharing" target="_blank">8.G.A.5 Similarity Resources</a></td></tr></tbody></table><br />These discovery activities highlight Common Core State Standards 8.G.A.5 and 8.EE.B.6 included in MATH-8 and Accelerated MATH-7.Anonymousnoreply@blogger.com0tag:blogger.com,1999:blog-61861505795529750.post-20827133548704667912014-02-19T12:23:00.004-08:002014-03-04T12:05:17.399-08:00Angle RelationshipsPrior to Common Core implementation, angle measure was a frequently repeated topic. Now, basic angle rules begin in Grade 7 and extend to angle relationships in Grade 8. These geometry standards prompt visual investigations with the use of manipulatives. The standards call students to "use informal arguments to establish facts..." about angle relationships. Grab your AngLegs and patty paper to accompany the activities outlined below.<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;"><span style="margin-left: auto; margin-right: auto;"><a href="https://drive.google.com/folderview?id=0B5H2CSmfdlQEM3RIdVRaNWQ4eU0&usp=sharing" target="_blank"><img border="0" src="http://2.bp.blogspot.com/-JArEuqRQZRc/UxYr44VgkLI/AAAAAAAAB_U/xhcyfpSitvs/s1600/Angles+Title+Pic.png" height="320" width="303" /></a></span></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://drive.google.com/folderview?id=0B5H2CSmfdlQEM3RIdVRaNWQ4eU0&usp=sharing" target="_blank">8.G.A.5 Resources</a></td></tr></tbody></table><br />Are your students struggling with basic angle rules and angle relationships formed by parallel lines cut by a transversal? This game focuses on these angle relationships and as the levels increase the content extends to angle relationships with polygons and circles for enrichment.<br /><br />Game Description:<br />Help Itzi the spider climb the clock to rescue his family! Solving cunning angle puzzles to reveal a path through each level's maze of tangled webs and reach the goal. It's sure to make your head spin!<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;"><div style="text-align: left;"><span style="margin-left: auto; margin-right: auto;"><a href="http://www.mangahigh.com/en-us/games" target="_blank"><img border="0" src="http://4.bp.blogspot.com/-LdDegnmY7vI/UxYpazN91hI/AAAAAAAAB_I/PViohxRGMxE/s1600/Tangle+Web.png" height="160" width="320" /></a></span></div></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="http://www.mangahigh.com/en-us/games" target="_blank">Manga High Math Games</a></td></tr></tbody></table><br />These concept builders highlight Common Core State Standard 8.G.A.5 included in MATH-8 and Accelerated MATH-7.<br />Anonymousnoreply@blogger.com0tag:blogger.com,1999:blog-61861505795529750.post-80001632821713077872014-02-07T10:34:00.001-08:002014-02-07T10:37:00.735-08:00Formative and Summative AssessmentWith the implementation of Common Core State Standards, it is no surprise that assessment has been a topic of discussion from the beginning. There are proponents for almost every possibility who claim a particular assessment option is required for CCSS. And the terms are certainly flying...rigor, depth of knowledge, task, inquiry learning, PBL (does that mean project-based learning, problem-based learning, or performance-based learning?!?). Perhaps if everyone had a common meaning for each "buzz" word then significant analysis could occur.<br /><br />Meanwhile, let's not get overwhelmed by one right way. Each student is different; fair isn't always equal...and equal isn't always fair. Focus on the big picture first. Categorize the types of assessment used in a classroom as formative or summative. Confused by those terms? Consider the road test that is required to receive a driver's license as an analogy...<br /><blockquote class="tr_bq"><span style="font-family: inherit;"><span style="background-color: white; color: #484848; font-size: 14px; line-height: 22px;">What if, before getting your driver's license, you received a grade every time you sat behind the wheel to practice driving? What if your final grade for the driving test was the average of all of the grades you received while practicing? Because of the initial low grades you received during the process of learning to drive, your final grade would not accurately reflect your ability to drive a car. In the beginning of learning to drive, how confident or motivated to learn would you feel? Would any of the grades you received provide you with guidance on what you needed to do next to improve your driving skills? Your final driving test, or summative assessment, would be the accountability measure that establishes whether or not you have the driving skills necessary for a driver's license</span><span style="background-color: white; border: 0px; color: #484848; font-size: 14px; line-height: 22px;">—</span><span style="background-color: white; color: #484848; font-size: 14px; line-height: 22px;">not a reflection of all the driving practice that leads to it. --Catherine Garrison and Michael Ehringhaus in <a href="http://www.amle.org/BrowsebyTopic/Assessment/AsDet/TabId/180/ArtMID/780/ArticleID/286/Formative-and-Summative-Assessments-in-the-Classroom.aspx" target="_blank">Formative and Summative Assessments in the Classroom</a></span></span> </blockquote>Students need the driving practice [formative assessment]. And the detailed feedback provided before, during, and after those practice sessions is critical to (1) influence the design of the next practice session and (2) enable the student to realize the key skills they are using effectively and the ones that need refining for continued growth. The final driving test [summative assessment] definitely paints a picture of how well students combine a variety of skills. Caution: Do you know anyone who has a driver's license and cannot parallel park? Students can understand a concept, make connections between concepts, and still lack depth in skill. Find a balanced approach to assessment in the classroom that checks both skills and connections.<br /><div class="separator" style="clear: both; text-align: center;"><br /></div>With that being said, there is a difference between students demonstrating their mathematical understanding via tasks that have one correct solution and tasks in which multiple solutions can be accurately justified. When using tasks with one correct solution, let's strive for multiple paths to arrive at that solution. For example, review the following fundraiser problem. There is only one correct answer; however, students are not required to follow a particular path to reach the solution. A student could begin problem solving by using a graph while another student could generate data to initially solve the problem. Furthermore, the detail with which they communicate their reasoning will also reflect comprehension.<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><span style="margin-left: auto; margin-right: auto;"><a href="https://drive.google.com/folderview?id=0B5H2CSmfdlQEUkRLLWtJS3JvZHc&usp=sharing" target="_blank"><img border="0" src="http://4.bp.blogspot.com/-Cyl2sRfg1pE/UvUlZWHbyDI/AAAAAAAAB1o/9Jgk0ZIayjU/s1600/Solving+Systems+Assessment+Title+Pic.png" height="320" width="318" /></a></span></td></tr><tr><td class="tr-caption" style="font-size: 13px;"><a href="https://drive.google.com/folderview?id=0B5H2CSmfdlQEUkRLLWtJS3JvZHc&usp=sharing" target="_blank">Sample Assessment Resource</a></td></tr></tbody></table><br />Thoughts? What do you find most effective in gauging student understanding? Try the sample assessment above and provide feedback. What adjustments needed to be made for your students?<br /><br />This assessment document highlights Common Core State Standard 8.EE.C.8 included in MATH-8 and Accelerated Algebra 1.Anonymousnoreply@blogger.com0tag:blogger.com,1999:blog-61861505795529750.post-59334045158660763672014-01-29T23:30:00.000-08:002014-03-19T11:41:52.716-07:00Scientific NotationThink back to your days in geometry. Do you remember the two-column proofs and the joy that would come with writing "by definition" as the reason to support a statement? There are just some things in mathematics that exist by declaration. By definition, the square root of negative one is represented with i. Why? Because the Italian mathematician Rafael Bombelli said so.<br /><br />There is no "But why?" behind scientific notation either. It is a definition created to ease the cumbersome nature of incredibly large or microscopically small numbers. Scientific notation is a method of writing a number as a decimal multiplied by a power of ten. The definition restricts the decimal to a number greater than or equal to 1 and less than 10. It's still the same number...just written in a specified format.<br /><br />Have you used place value and powers of ten to rewrite numbers according to the scientific notation format? Base ten blocks can model the decomposition of a number and serve as a beneficial launching pad for writing large numbers in scientific notation.<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;"><a href="http://3.bp.blogspot.com/-Gl4NhwWBaa4/UuqYGgDLQbI/AAAAAAAABzQ/5QnvYBUjgLk/s1600/Scientific+Notation+Pic.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="http://3.bp.blogspot.com/-Gl4NhwWBaa4/UuqYGgDLQbI/AAAAAAAABzQ/5QnvYBUjgLk/s1600/Scientific+Notation+Pic.png" height="247" width="320" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Scientific Notation with Base Ten Blocks</td></tr></tbody></table><br />Once students grasp the definition, continue with the "Sort This!" activity to rewrite numbers from different forms including standard notation, product or quotient form, as a power of ten, or scientific notation. The "I have... Who has..." activity provides a quick informal assessment of converting numbers. Also the "RallyCoach" and "Stations" activities require students to solve problems involving numbers written in scientific notation.<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;"><span style="margin-left: auto; margin-right: auto;"><a href="https://drive.google.com/folderview?id=0B5H2CSmfdlQEcGxRTjVUWmV2ZkE&usp=sharing" target="_blank"><img border="0" src="http://4.bp.blogspot.com/-cCxgvkDa9r0/UuqmHQUPd7I/AAAAAAAABzg/Z_W9SBCj4Dw/s1600/Scientific+Notation+Resources+Title+Pic.png" height="320" width="302" /></a></span></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://drive.google.com/folderview?id=0B5H2CSmfdlQEcGxRTjVUWmV2ZkE&usp=sharing" target="_blank">Scientific Notation Resources</a></td></tr></tbody></table><br />This activity set highlights Common Core State Standards 8.EE.A.3 and 8.EE.A.4 included in MATH-8 and Accelerated MATH-7.Anonymousnoreply@blogger.com0tag:blogger.com,1999:blog-61861505795529750.post-28185030947062711442014-01-28T14:00:00.000-08:002014-01-28T14:00:05.360-08:00The Distributive Property<div class="separator" style="clear: both;">How do you teach the distributive property? When planning lessons, be sure you are maintaining perspective. Ask: What have your students already experienced with the content? This is particularly critical when students have gaps and require support to bridge that gap. You will need to have the perspective of how the related content has developed over the years/courses so that you can replicate that progression for struggling students via individualized learning. Ask: What leaps will your students make in upcoming courses that stem from what you do with the content now? It is important to identify future learning so that you can ensure adequate depth in your course. Let's review the progression of the distributive property...<br /></div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td><a href="http://1.bp.blogspot.com/-7OgIED8PZHE/Uuf2ALgUE-I/AAAAAAAABxo/SSFQuzwircw/s1600/3.OA.B.5.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="http://1.bp.blogspot.com/-7OgIED8PZHE/Uuf2ALgUE-I/AAAAAAAABxo/SSFQuzwircw/s1600/3.OA.B.5.png" height="237" width="320" /></a></td></tr><tr><td class="tr-caption" style="font-size: 13px;">3.OA.B.5</td></tr></tbody></table>In Grade 3, students use the distributive property as a strategy for multiplying. This is the concept builder for the distributive property. If students were unsuccessful when working strictly with numbers, then their efforts in applications with variables will be a stretch at best. Or worse yet...what if students memorized multiplication facts and never made sense of the concept through the distributive property?!?<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><a href="http://3.bp.blogspot.com/-ohOWIM32hoY/Uuf2AZn2p0I/AAAAAAAABxg/Y8X6J_OVEg8/s1600/6.EE.A.3.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="http://3.bp.blogspot.com/-ohOWIM32hoY/Uuf2AZn2p0I/AAAAAAAABxg/Y8X6J_OVEg8/s1600/6.EE.A.3.png" height="208" width="320" /></a></td></tr><tr><td class="tr-caption" style="font-size: 13px;">6.EE.B.5</td></tr></tbody></table><br />In Grade 6, students use the distributive property to produce equivalent expressions. Notice the example includes using the distributive property to toggle between factored form (the result from division) and expanded form (the result from multiplication).<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><a href="http://4.bp.blogspot.com/-91v6RF87_nM/Uuf2AMJK_JI/AAAAAAAABxc/_FiyQfysQBI/s1600/7.EE.A.1.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="http://4.bp.blogspot.com/-91v6RF87_nM/Uuf2AMJK_JI/AAAAAAAABxc/_FiyQfysQBI/s1600/7.EE.A.1.png" height="160" width="320" /></a></td></tr><tr><td class="tr-caption" style="font-size: 13px;">7.EE.A.1</td></tr></tbody></table><br />In Grade 7, students continue with the same concepts learned in Grade 6 with an extension to using rational numbers. Should 7th graders be solving equations that require using the distributive property? Continue reading.<br /><br /><div class="separator" style="clear: both; text-align: center;"></div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td><a href="http://4.bp.blogspot.com/-QGJbNM-Hu1Y/Uuf44bJnW0I/AAAAAAAAByA/HA1zQzu-Ofc/s1600/8.EE.C.7.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="http://4.bp.blogspot.com/-QGJbNM-Hu1Y/Uuf44bJnW0I/AAAAAAAAByA/HA1zQzu-Ofc/s1600/8.EE.C.7.png" height="258" width="320" /></a></td></tr><tr><td class="tr-caption" style="font-size: 13px;">8.EE.C.7b</td></tr></tbody></table><div class="separator" style="clear: both; text-align: center;"><br /></div>In Grade 8 (and Accelerated MATH-7), students will use the distributive property to solve linear equations with rational coefficients. Notice the standard says "whose solutions <b>REQUIRE</b> expanding expressions using the distributive property..." in order to solve the linear equation.<br /><br /><div class="separator" style="clear: both; text-align: center;"></div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td><a href="http://1.bp.blogspot.com/-m0hMakbEHQM/UughugjQDMI/AAAAAAAAByg/rupgmVqN2mE/s1600/Distributive+Property+Sample+(8.EE.C.7b).png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="http://1.bp.blogspot.com/-m0hMakbEHQM/UughugjQDMI/AAAAAAAAByg/rupgmVqN2mE/s1600/Distributive+Property+Sample+(8.EE.C.7b).png" height="289" width="320" /></a></td></tr><tr><td class="tr-caption" style="font-size: 13px;">Differentiate the necessity of the distributive property.</td></tr></tbody></table><br />Perhaps MATH-7 students should be asked to solve equations that are similar to the equation in the left column above; however, this begs the question "How do we hope students solve that type of equation?". We also hope MATH-8 students recognize the need for the distributive property before they start the process of solving equations that are similar to the equation in the right column above.<br /><br />This discussion highlights the Common Core State Standards 7.EE.A.1 and 8.EE.C.7b included in MATH-7, MATH-8 and Accelerated MATH-7.Anonymousnoreply@blogger.com0tag:blogger.com,1999:blog-61861505795529750.post-25867705852528380282014-01-24T15:39:00.003-08:002014-01-24T15:39:51.069-08:00Solving Systems of Equations<div class="separator" style="clear: both; text-align: left;">If MATH-8 teachers ever doubted that they teach algebra, diving into the Common Core State Standard 8.EE.C.8 would certainly end the debate. Students are required to solve and analyze pairs of simultaneous linear equations. The depth of this standard involves understanding the meaning of solution(s) of a system, solving a system graphically and algebraically, and using this knowledge to solve real-world problems that lead to a system of two linear equations.</div><br />The prerequisite for this content includes solving one-variable equations in Grade 7 and previously in Grade 8 as outlined in this <a href="http://fjhsmath-8.blogspot.com/2013/09/solutions-of-linear-equations.html" target="_blank">Solutions of Linear Equations</a> post. The tiling activity towards the end of the post would be a great review of types of solutions to set the stage for systems.<br /><br />In a recent Genius Hour, we focused on how to teach 8th grade students to solve a system of linear equations algebraically. While it may be common to ask student to solve each equation for the variable "y" and set the two resulting expressions equal to solve for the variable "x", this process begs the question "Why?". Are we helping our students make connections so that they understand the origin of the algebraic method and know this process is valid? Do they understand the concept behind solving algebraically?<br /><br />We looked at an introduction activity that extends from the "Balance This!" Activity in the <a href="http://fjhsmath-8.blogspot.com/2013/09/solutions-of-linear-equations.html" target="_blank">Solutions of Linear Equations</a> post. The visual of the balanced scale was used to discuss solutions and the adjustments necessary if the conditions are represented with two different scales. In this activity, students reason with a balance of shapes and a given value to determine the value of each shape.<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><span style="margin-left: auto; margin-right: auto;"><a href="https://drive.google.com/folderview?id=0B5H2CSmfdlQEeWoxSEtEUHFTZWM&usp=sharing" target="_blank"><img border="0" src="http://1.bp.blogspot.com/-qGv8xn6yf9U/UuLvGeQWo8I/AAAAAAAABwA/qnyJJoQcj94/s1600/Systems+Title+Pic.png" height="320" width="320" /></a></span></td></tr><tr><td class="tr-caption"><a href="https://drive.google.com/folderview?id=0B5H2CSmfdlQEeWoxSEtEUHFTZWM&usp=sharing" target="_blank">Solving Systems of Linear Equations</a></td></tr></tbody></table><br />We started with a school store scenario in which two different "store specials" were offered. One special involved a purchase of three items from the top shelf and two items from the bottom shelf for a total of $16. The second special involved a purchase of two items from the top shelf and three items from the bottom shelf for a total of $14.<br /><br /><blockquote class="tr_bq"><ul><li>What are some possible values that keep the firsts scale balanced? How many different combinations can you find? How many combinations are possible?</li></ul><ul><li>What about the second scale? How many total combinations are possible?</li></ul><ul><li>What if you consider both scales simultaneously...meaning the possible values that keep the first scale balanced must also be the same values that keep the second scale balance? How many different combinations can you find? How many combinations are possible?</li></ul></blockquote>How much do the items on each shelf cost? Which shelf has the more expensive items? Justify your reasoning. Many students will use trial and error to begin solving the puzzle, but beware of students who verbalize a strategy that is actually substitution! The activity opens several paths, one of which is solving numerically and then making sense of how that cumbersome numeric approach connects to a systematic algebraic approach. The activity extends to all types of solutions and coordinates with several support activities that were reviewed.<br /><br /><br />These activities highlight the Common Core State Standard 8.EE.C.8 that is included in MATH-8 and Accelerated Algebra 1.Anonymousnoreply@blogger.com0tag:blogger.com,1999:blog-61861505795529750.post-57398755773956800192013-11-08T12:58:00.000-08:002013-11-08T12:58:24.949-08:00Modeling FunctionsDuring the November 6th Genius Hour, we reviewed a variety of instructional practices that help build conceptual understanding. The following samples aligned to linear functions were provided.<br /><br />The "Build This!" activity is the brilliant work of Nat Banting from his <a href="http://www.musingmathematically.blogspot.ca/2013/02/relation-stations.html" target="_blank">Relation Stations</a> post over on his <a href="http://www.musingmathematically.blogspot.ca/" target="_blank">{Musing Mathematically}</a> blog. The link was shared by Kathryn Freed during a recent #alg1chat on Twitter. Students view three patterns and determine what all three patterns have in common...a starting point and a constant change. Then students are asked to create a pattern of their own. Finally students rotated stations to investigate the models created by their classmates and build a table of values to model the pattern. The extension outlined in the blog post involves students using their record sheet to write equations for each pattern the following day. Starting with a concrete model of color tiles and eventually expanding to the abstract algebraic equation is powerful.<br /><br />Nat mentioned in the #alg1chat that he has reversed the activity to provide students an equation and ask for the model. The possibilities are endless! You could have each team build two patterns with the same starting point...one with a constant change and one with a varying change to emphasize linear and nonlinear patterns. You could also add graphing to the table of values record sheet to make further connections.<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><span style="margin-left: auto; margin-right: auto;"><a href="https://drive.google.com/file/d/0B5H2CSmfdlQETS0tcGxucWdZdnM/edit?usp=sharing" target="_blank"><img border="0" height="248" src="http://2.bp.blogspot.com/-22C11svxpQk/Un1Banydq7I/AAAAAAAABf8/p4NJ12KQjvg/s320/Build+This+Pic.png" width="320" /></a></span></td></tr><tr><td class="tr-caption" style="font-size: 12.727272033691406px;"><a href="https://drive.google.com/file/d/0B5H2CSmfdlQETS0tcGxucWdZdnM/edit?usp=sharing" target="_blank">Create a Model</a></td></tr></tbody></table><br />The next activity is adapted from the <a href="http://www.illustrativemathematics.org/illustrations/417" target="_blank">Modeling with a Linear Function</a> task on the <a href="http://www.illustrativemathematics.org/" target="_blank">Illustrative Mathematics</a> website. (On a complete side note...we simply must chat about the word "task" and its use in today's math classroom. Care to define that one for me?) The activity poses a linear function and proceeds to outline a variety of models...some describe the linear function while others do not. However, the descriptions that do not match the linear function are common misconceptions. When structured as a Takeoff... Touchdown..., this activity is an engaging way to get students to differentiate between concept and misconceptions.<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><span style="margin-left: auto; margin-right: auto;"><a href="https://drive.google.com/file/d/0B5H2CSmfdlQEd1NadEh3YjhmaEU/edit?usp=sharing" target="_blank"><img border="0" height="248" src="http://3.bp.blogspot.com/-ap4njd-5UlY/Un1BRCrNwsI/AAAAAAAABfo/Q8sbcxqQWrk/s320/Takeoff+Touchdown+Pic.png" width="320" /></a></span></td></tr><tr><td class="tr-caption" style="font-size: 12.727272033691406px;"><a href="https://drive.google.com/file/d/0B5H2CSmfdlQEd1NadEh3YjhmaEU/edit?usp=sharing" target="_blank">Differentiate Common Misconceptions</a><div style="text-align: left;"><a href="https://drive.google.com/file/d/0B5H2CSmfdlQEd1NadEh3YjhmaEU/edit?usp=sharing" target="_blank"><br /></a></div></td></tr></tbody></table>The following prompt (which would be a fabulous RoundTable...or, better yet, use three additional functions to create a Simultaneous RoundTable) is an adaptation of a <a href="http://www.arkansased.org/public/userfiles/Learning_Services/Student%20Assessment/2013/EOC/eoc_algebra/Released_Item_Booklet.pdf" target="_blank">released open response item</a> from the <a href="http://www.arkansased.org/divisions/learning-services/student-assessment/end-of-course-exams/algebra%20I" target="_blank">Arkansas Department of Education</a>. The original function was quadratic and the table didn't contain the same rational values. This prompt integrates prior knowledge of transformations and operations with rational numbers with the current knowledge of linear functions.<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><span style="margin-left: auto; margin-right: auto;"><a href="https://drive.google.com/file/d/0B5H2CSmfdlQEbS1lOENCMW5VQVE/edit?usp=sharing" target="_blank"><img border="0" height="320" src="http://2.bp.blogspot.com/-ke1hH7bm7l4/Un1BQ6pKRRI/AAAAAAAABfk/G6JA7EFJJco/s320/Functions+Open+Response+Pic.png" width="248" /></a></span></td></tr><tr><td class="tr-caption" style="font-size: 12.727272033691406px;"><a href="https://drive.google.com/file/d/0B5H2CSmfdlQEbS1lOENCMW5VQVE/edit?usp=sharing" target="_blank">Integrate Prior Knowledge</a></td></tr></tbody></table>All of these instructional practices help students build conceptual understanding and/or make connections between content. And that is the key to success in math...whether that's today, the next unit, the standardized test, or next year's math class.<br /><br />These activities highlight Common Core State Standards 8.F.A.3 and 8.F.B.4 that are included in MATH-8 and Accelerated Algebra 1.Anonymousnoreply@blogger.com0tag:blogger.com,1999:blog-61861505795529750.post-4800338595392894592013-10-31T10:48:00.002-07:002013-10-31T10:48:31.959-07:00Definition of Function<div class="separator" style="clear: both; text-align: left;">Vocabulary development becomes essential in a mathematics classroom that focuses on the Common Core Standards for Mathematical Practice of attending to precision (SMP.6). In order for math students to communicate precisely to others, they must use clear definitions in their discussion and reasoning. And then subsequently, students can use their vocabulary in constructing arguments (SMP.3).<br /><br />One strategy for vocabulary development involves the teacher telling a story that involves the new term. Use the Vending Machine Saga to help students determine if the machine is functioning properly for each transaction. (We are working under the assumption that if a product type is unavailable then the machine returns your dollar in exact change; therefore, no transaction has occurred for our review.)<br /></div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td><span style="margin-left: auto; margin-right: auto;"><a href="https://drive.google.com/file/d/0B5H2CSmfdlQEUGF4bXFVVW5tdTA/edit?usp=sharing" target="_blank"><img border="0" height="248" src="http://1.bp.blogspot.com/-A5baqQYFgMI/UnKQpmqYhpI/AAAAAAAABd8/jeRIEJL1U6E/s320/Vending+Machine+Saga+Title+Pic.png" width="320" /></a></span></td></tr><tr><td class="tr-caption" style="font-size: 12.727272033691406px;"><a href="https://drive.google.com/file/d/0B5H2CSmfdlQEUGF4bXFVVW5tdTA/edit?usp=sharing" target="_blank">Concrete Function Story Expands to Abstract</a></td></tr></tbody></table><div class="separator" style="clear: both; text-align: left;">Another effective vocabulary strategy is engaging students in an activity that helps students add to their knowledge of the term. Present students with a two-column example/counterexample description. Provide think time for each student to generate facts or characteristics consistent with the term. Have students use the RoundRobin structure to share their pieces of a definition. With each rotation the team forms and refines a definition to present to the class. Once the teams reach consensus, the teacher and class discuss samples to develop a class definition. The final definition, examples, and counterexamples can be recorded in a Frayer Model template. Or the examples and counterexamples can be used as a card sort in an interactive student notebook.<br /></div><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;"><span style="margin-left: auto; margin-right: auto;"><a href="https://drive.google.com/file/d/0B5H2CSmfdlQEemptZ1BoNWhJSXM/edit?usp=sharing" target="_blank"><img border="0" height="248" src="http://2.bp.blogspot.com/-mhOxWfZsETs/UnH7MN0ek7I/AAAAAAAABdk/OuDqItdxReU/s320/Function+Definition+Title+Pic.png" width="320" /></a></span></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://drive.google.com/file/d/0B5H2CSmfdlQEemptZ1BoNWhJSXM/edit?usp=sharing" target="_blank">Definition of Function</a></td></tr></tbody></table><br />Although students investigate linear functions in MATH-8, the conceptual definition of a function is most critical for success with using function notation and finding an inverse function in Algebra 1. This investigation highlights Common Core State Standard 8.F.A.1 that is included in MATH-8 and Accelerated Algebra 1.Anonymousnoreply@blogger.com2tag:blogger.com,1999:blog-61861505795529750.post-2261821395924207542013-09-28T13:52:00.002-07:002013-09-28T13:52:06.685-07:00Integer Exponents<div class="separator" style="clear: both; text-align: left;">Middle school students generally enjoy working with patterns and find much success with number patterns. So discovering patterns with positive and negative exponents is a great way to conceptually teach integer exponents.</div><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;"><span style="margin-left: auto; margin-right: auto;"><a href="https://docs.google.com/file/d/0B5H2CSmfdlQEcXJCTGtocTltclk/edit?usp=sharing" target="_blank"><img border="0" height="320" src="http://1.bp.blogspot.com/-pYWg3cZ_gb8/Ukc_xZiIo3I/AAAAAAAABZQ/Nl6Rp3mtU8E/s320/RoundRobin+Pic.png" width="248" /></a></span></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://docs.google.com/file/d/0B5H2CSmfdlQEcXJCTGtocTltclk/edit?usp=sharing" target="_blank">Integer Exponents Discovery Activity</a></td></tr></tbody></table><br />The general laws of exponents can be developed from the number patterns discovered in the Integer Exponents RoundRobin activity and record sheet. And the discussion of base 10 will set the stage for scientific notation.<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;"><span style="margin-left: auto; margin-right: auto;"><a href="https://docs.google.com/file/d/0B5H2CSmfdlQEdUFlSjVPdHdOMUU/edit?usp=sharing" target="_blank"><img border="0" height="320" src="http://3.bp.blogspot.com/-S-mmHBIJbVU/Ukc_wgWwiSI/AAAAAAAABZI/jZLvKMWc-Qo/s320/Expo+Rules+%2528Part+1%2529+Pic.png" width="248" /></a></span></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://docs.google.com/file/d/0B5H2CSmfdlQEdUFlSjVPdHdOMUU/edit?usp=sharing" target="_blank">Integer Exponents Quiz-Quiz-Trade</a></td></tr></tbody></table><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;"><span style="margin-left: auto; margin-right: auto;"><a href="https://docs.google.com/file/d/0B5H2CSmfdlQEQldpVnI3aXhJZWM/edit?usp=sharing" target="_blank"><img border="0" height="248" src="http://2.bp.blogspot.com/-fIJaDQJWZKo/Ukc_wqik7rI/AAAAAAAABZE/uHTz1igrPac/s320/Expo+Rules+%2528Part+2%2529+Pic.png" width="320" /></a></span></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://docs.google.com/file/d/0B5H2CSmfdlQEQldpVnI3aXhJZWM/edit?usp=sharing" target="_blank">Integer Exponents Quiz-Quiz-Trade</a></td></tr></tbody></table><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;"><span style="margin-left: auto; margin-right: auto;"><a href="https://docs.google.com/file/d/0B5H2CSmfdlQEZ1RiQjg3UFZnY1E/edit?usp=sharing" target="_blank"><img border="0" height="248" src="http://2.bp.blogspot.com/-DeAUc6kZwZo/Ukc_w1m37PI/AAAAAAAABZM/2WQsaU_H8KY/s320/Expo+Rules+Fan+N+Pick+Pic.png" width="320" /></a></span></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://docs.google.com/file/d/0B5H2CSmfdlQEZ1RiQjg3UFZnY1E/edit?usp=sharing" target="_blank">Integer Exponents Fan-N-Pick</a></td></tr></tbody></table><br />This standard (CCSS 8.EE.A.1) will also bridge understanding to Algebra 1 as students explore geometric sequences and exponential functions.Anonymousnoreply@blogger.com2tag:blogger.com,1999:blog-61861505795529750.post-22557489810614528492013-09-18T13:45:00.000-07:002014-01-24T13:31:40.037-08:00Solutions of Linear Equations<div class="separator" style="clear: both; text-align: left;">Once students are fluent with the order of operations, they are ready to solve linear equations. When teaching the order of operations, I emphasize that we are simplifying numerical expressions. So when I provide the total value of a numerical expression BUT make one of the values in your expression a mystery, then my students have an equation to solve. And the process of solving for the mystery value requires students to use the order of operations in reverse.</div><br /><h3 style="text-align: center;">2x + 5 = 17</h3><br />What happened to the mystery value? It was doubled (or multiplied by 2) and then 5 was added for a total of 17. What happened last? The 5 was added to result in a total of 17. So take away (or subtract) 5. Now the total is 12...which is the result when I double the mystery value. So divide the total by 2 and you have revealed the mystery value of 6.<br /><br />In middle school, students are moving from concrete thinking to abstract thinking...some a little more quickly than others. But our goal is to help all students find success dealing with abstract concepts. Solving linear equations may require the use of manipulatives to support concrete thinkers as they conceptualize this abstract concept.<br /><br />And then when you add the possibility of multiple mysteries value that would reveal the same total result or no mystery value at all that would yield the total, the abstract becomes more abstract. Sarah over at <a href="http://everybodyisageniusblog.blogspot.com/" target="_blank">Everybody is a Genius</a> posted an excellent approach to <a href="http://everybodyisageniusblog.blogspot.com/2012/07/solving-special-case-equations.html" target="_blank">Solving Special Case Equations</a>. I love the introductory "puzzle" approach with balanced scales. I altered the format to a Showdown activity to provide structure for the discussion with the record sheet.<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;"><span style="margin-left: auto; margin-right: auto;"><a href="https://docs.google.com/file/d/0B5H2CSmfdlQEZE1mZHNDNDVKNGs/edit?usp=sharing" target="_blank"><img border="0" src="http://2.bp.blogspot.com/-mqsHfR32ur4/UjoNN6jZPyI/AAAAAAAABYQ/duYGzgm5Ie0/s320/Balance+This+Showdown+Pic.png" height="248" width="320" /></a></span></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://docs.google.com/file/d/0B5H2CSmfdlQEZE1mZHNDNDVKNGs/edit?usp=sharing" target="_blank">Balance This! Showdown Activity</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;"><span style="margin-left: auto; margin-right: auto;"><a href="https://docs.google.com/file/d/0B5H2CSmfdlQEc3NxRjJoQTd0UEU/edit?usp=sharing" target="_blank"><img border="0" src="http://2.bp.blogspot.com/-Iqd1pAiVjOc/UjoNNFl-SZI/AAAAAAAABYY/Opg1oWtxQtQ/s320/Balance+This+Record+Sheet+Pic.png" height="320" width="248" /></a></span></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://docs.google.com/file/d/0B5H2CSmfdlQEc3NxRjJoQTd0UEU/edit?usp=sharing" target="_blank">Balance This! Record Sheet</a></td></tr></tbody></table><br />Sarah also shared the notes her students created for their Interactive Notebooks to summarize their learning. I created the foldable in PowerPoint so it could be sent to the print shop if you prefer.<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;"><span style="margin-left: auto; margin-right: auto;"><a href="https://docs.google.com/file/d/0B5H2CSmfdlQEVFhKNlRsUFBQRjQ/edit?usp=sharing" target="_blank"><img border="0" src="http://4.bp.blogspot.com/-J7ZwQd-0lDI/UjoNNZWZT-I/AAAAAAAABYU/TxSkFPvCvEQ/s320/Types+of+Solution+Foldable+Pic.png" height="248" width="320" /></a></span></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://docs.google.com/file/d/0B5H2CSmfdlQEVFhKNlRsUFBQRjQ/edit?usp=sharing" target="_blank">Types of Solutions Foldable (Student)</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;"><span style="margin-left: auto; margin-right: auto;"><a href="https://docs.google.com/file/d/0B5H2CSmfdlQEZXB0amZBeWRwSFk/edit?usp=sharing" target="_blank"><img border="0" src="http://1.bp.blogspot.com/-ALJBxYsVAXw/UjoOdMz8MgI/AAAAAAAABYo/0E4I-8KAFG0/s320/Types+of+Solution+Foldable+(Teacher)+Pic.png" height="248" width="320" /></a></span></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://docs.google.com/file/d/0B5H2CSmfdlQEZXB0amZBeWRwSFk/edit?usp=sharing" target="_blank">Types of Solutions Foldable (Teacher)</a></td></tr></tbody></table><br /><div class="separator" style="clear: both; text-align: center;"><br /></div>And this tiling activity is a great activity to informally assess student understanding of solution types.<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><span style="margin-left: auto; margin-right: auto;"><a href="https://drive.google.com/file/d/0B5H2CSmfdlQEUldWMnM1eWxYTEE/edit?usp=sharing" target="_blank"><img border="0" src="http://4.bp.blogspot.com/-2IFJyuyCbKo/UuLbFjbcE4I/AAAAAAAABvw/Z2NamM3bMjo/s1600/Tiling+Activity+Pic.png" height="320" width="320" /></a></span></td></tr><tr><td class="tr-caption" style="font-size: 13px;"><a href="https://drive.google.com/file/d/0B5H2CSmfdlQEUldWMnM1eWxYTEE/edit?usp=sharing" target="_blank">Types of Solutions Tiling Activity</a></td></tr></tbody></table>These activities highlight the Common Core State Standard 8.EE.C.7a included in MATH-8 and Accelerated MATH-7.Anonymousnoreply@blogger.com0tag:blogger.com,1999:blog-61861505795529750.post-16525961447820317032013-09-18T09:08:00.005-07:002013-09-18T09:10:14.764-07:00Decimal Form of a Rational NumberThe progression of understanding rational numbers bridges between MATH-7 and MATH-8. (Note: This content is merged in Accelerated MATH-7.) And in the midst of discussing process teaching and concept teaching, we have highlighted the following standards.<br /><br /><blockquote class="tr_bq">7.NS.A.2d<br />Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.</blockquote><blockquote class="tr_bq">8.NS.A.1<br />Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.</blockquote>Hop over to the MATH-7 tab to see the <a href="http://fjhsmath-7.blogspot.com/2013/09/decimal-form-of-rational-number.html" target="_blank">Decimal Form of Rational Numbers</a> post to jump start the conceptual understanding of these standards.<br /><br />First ensure that students understand the classification of rational and irrational numbers. You could engage students in a sorting activity based on a few provided examples and counterexamples. (If you use all cards in the set, this activity will set the stage for Algebra 1 teachers to discuss the results of rational and irrational number operations.)<br /><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><span style="margin-left: auto; margin-right: auto;"><a href="https://docs.google.com/file/d/0B5H2CSmfdlQEQlJRRWowY1dBYlE/edit?usp=sharing" target="_blank"><img border="0" height="248" src="http://4.bp.blogspot.com/-2P2hOjK0wYE/UjnNu3FZr0I/AAAAAAAABYA/Vlt7fE5Ip7w/s320/Rational+Number+Frayer+Model+Pic.jpg" width="320" /></a></span></td></tr><tr><td class="tr-caption" style="font-size: 12.727272033691406px;"><a href="https://docs.google.com/file/d/0B5H2CSmfdlQEQlJRRWowY1dBYlE/edit?usp=sharing" target="_blank">Sorting Activity</a></td></tr></tbody></table><br /><br />And then you could spin off of the MATH-7 activity of why some rational numbers terminate and others repeat to continue towards the concept of rewriting a repeating decimal as its equivalent fraction.<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><span style="margin-left: auto; margin-right: auto;"><a href="https://docs.google.com/file/d/0B5H2CSmfdlQESzMteGY1aWJWVGs/edit?usp=sharing" target="_blank"><img border="0" height="320" src="http://4.bp.blogspot.com/-Z4pvxUi08Pk/UjnNunHbdAI/AAAAAAAABX8/fXAPHaRH7xQ/s320/Algebraic+Discovery+for+Rational+Numbers+Pic.jpg" width="248" /></a></span></td></tr><tr><td class="tr-caption" style="font-size: 12.727272033691406px;"><a href="https://docs.google.com/file/d/0B5H2CSmfdlQESzMteGY1aWJWVGs/edit?usp=sharing" target="_blank">Algebraic Discovery</a></td></tr></tbody></table><br />Would it be easier to teach the process for converting a repeating decimal to its equivalent fraction? Which benefits the students today, next month, next year? Process teaching or concept teaching?<br /><br />Be sure to reflect on other related posts:<br /><br /><a href="http://fjhsmath.blogspot.com/2013/09/ccss-call-for-rigor.html" target="_blank">CCSS Call for Rigor</a><br /><br /><a href="http://fjhsmath.blogspot.com/2013/09/process-vs-concept-teaching.html" target="_blank">Process vs. Concept Teaching</a>Anonymousnoreply@blogger.com1tag:blogger.com,1999:blog-61861505795529750.post-61807538885428097942013-09-06T13:47:00.002-07:002013-09-06T13:47:30.395-07:00Irrational ApproximationsThe Common Core State Standards are filled with number sense. Students engaged in the Common Core aligned curriculum will have a deep understanding of rational and irrational numbers...including a rational approximation of an irrational number (CCSS 8.NS.A.2).<br /><br />How would you find the rational approximation of this number?<br /><a href="http://1.bp.blogspot.com/-eKBHFdupCM4/T2whkSGSdPI/AAAAAAAAAbU/gDL6MvuWO6Y/s1600/Radical.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="120" src="http://1.bp.blogspot.com/-eKBHFdupCM4/T2whkSGSdPI/AAAAAAAAAbU/gDL6MvuWO6Y/s200/Radical.jpg" width="200" /></a><br />Ummm...without a calculator. ;)<br /><br />Here's how we approach this one in my classroom...Well. Let's start with square roots that are rational. We know the square root of 20 is somewhere between the square root of 16 and the square root of 25...so something between 4 and 5. Can you be more specific? Hmmm...the list begins to form...<br />root 16 = 4<br />root 17 = ?<br />root 18 = ?<br />root 19 = ?<br />root 20 = ?<br />......................about 4.5<br />root 21 = ?<br />root 22 = ?<br />root 23 = ?<br />root 24 = ?<br />root 25 = 5<br /><br />Since we have 9 numbers to cover an increase of 1 unit, each increase will be a little more than 0.1. Why? Because 1/9 > 1/10. So we can approximate that root 20 is approximately 4.4. {Ish! At this point we discuss if the "little more" is "enough more" to justify rounding.}<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;"><span style="margin-left: auto; margin-right: auto;"><a href="https://docs.google.com/file/d/0B5H2CSmfdlQEcHh6ZnNXTkJMQnc/edit?usp=sharing" target="_blank"><img border="0" height="320" src="http://4.bp.blogspot.com/-ezyxtgVLCS0/Uio9fKargsI/AAAAAAAABUo/cPz6b0oRIdU/s320/Find+Someone+Who+Pic.PNG" width="247" /></a></span></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://docs.google.com/file/d/0B5H2CSmfdlQEcHh6ZnNXTkJMQnc/edit?usp=sharing" target="_blank">Find Someone Who</a></td></tr></tbody></table>But what about simplest radical form?!? We've searched high and low. No sign of "simplest radical form" in our copy of the CCSS document. (If you find it...please put me out of my misery!)<br /><br />Could we teach our students to simplify radicals and then in turn use that to find the rational approximation of an irrational number? In simplest radical form, the square root of 20 is exactly 2 times the square root of 5. Hmmm...the square root of 5 is some number between the square root of 4 and the square root of 9...between 2 and 3.<br /><br />root 4 = 2<br />root 5 = ?<br />root 6 = ?<br />..................about 2.5<br />root 7 = ?<br />root 8 = ?<br />root 9 = 3<br /><br />Since we have 5 numbers to cover an increase of 1 unit, each increase will be more than 0.1. Why? Because 1/5 > 1/10 (some students will automatically go to the fact that 1/5 = 0.2). So we can approximate that root 5 is approximately 2.2 and therefore 2(2.2) = 4.4.<br /><br />Bottom line. We reach a valid approximation either way. I think it's important for our students to discover both paths...and even more important for them to critique which approach they prefer and under what circumstances they would select that particular method. I'm ready for a viable argument. How about you?!?<br /><br />Cooperative practice would be crucial for students to have perspective to support their argument.<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;"><span style="margin-left: auto; margin-right: auto;"><a href="https://docs.google.com/file/d/0B5H2CSmfdlQEcWMyMkhhd2RkQkE/edit?usp=sharing" target="_blank"><img border="0" height="247" src="http://1.bp.blogspot.com/-dXgmJxI7uks/T2woZq5DDeI/AAAAAAAAAbk/9g3VAc-hvvc/s320/Simplifying+Radicals+(preview).jpg" style="margin-left: auto; margin-right: auto;" width="320" /></a></span></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://docs.google.com/file/d/0B5H2CSmfdlQEcWMyMkhhd2RkQkE/edit?usp=sharing" target="_blank">Quiz-Quiz-Trade or Inside-Outside Circle</a></td></tr></tbody></table>This topic has a natural connection to Pythagorean Theorem application (CCSS 8.G.B.7). When students are determining the length of an unknown side in a right triangle, they should be able to state their solution as both an exact and approximate number. And how do we teach students to solve using the Pythagorean Theorem when they don't know the first thing about a quadratic equation? That will be for another post...after we finish investigating rational and irrational numbers...stay tuned!<br /><br />Anonymousnoreply@blogger.com0tag:blogger.com,1999:blog-61861505795529750.post-6892823863558985782013-08-14T21:32:00.000-07:002013-08-14T21:32:10.042-07:00Frayer Model SampleThe Frayer Model was developed by Dorothy Frayer and her colleagues at the University of Wisconsin. This graphic organizer will lead students to a thorough understanding of new words. The corners generally include definition, facts or characteristics, examples and non-examples.<br /><br />This is the modified template used in my math classroom. Based on the content, the example corner may include non-examples as well.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-VqtHY4NtUVo/UgxXuAPkWoI/AAAAAAAABRo/lXqSP3R6xoQ/s1600/Frayer+Geometry+(template).jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="247" src="http://1.bp.blogspot.com/-VqtHY4NtUVo/UgxXuAPkWoI/AAAAAAAABRo/lXqSP3R6xoQ/s320/Frayer+Geometry+(template).jpg" width="320" /></a></div><div style="text-align: center;"><br /></div>In order for students to communicate mathematically, they need a deep understanding of the content. Summarizing critical vocabulary via the Frayer Model can jumpstart this process.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://3.bp.blogspot.com/-q6E7VGCuRG0/UgxZW7ZfeHI/AAAAAAAABR4/hm-wWP43G0w/s1600/Frayer+Math8.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="247" src="http://3.bp.blogspot.com/-q6E7VGCuRG0/UgxZW7ZfeHI/AAAAAAAABR4/hm-wWP43G0w/s320/Frayer+Math8.jpg" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div>This vocabulary graphic organizer highlights the Common Core State Standard 8.G.A.3 that is included in MATH-8 and Accelerated MATH-7.Anonymousnoreply@blogger.com0tag:blogger.com,1999:blog-61861505795529750.post-18738326665456817392013-08-06T15:24:00.001-07:002014-02-24T13:45:02.797-08:00Thinking TransformationsIn grade 4, Common Core standards include lines of symmetry based on folding two-dimensional figures...not reflections. In grade 7, Common Core standards include scale drawings based on proportional relationships...not dilations. So unless our 8th grade students remember slide, flip, and turn from their elementary days or they were in a 7th grade classroom that reviewed transformations for the Benchmark last Spring, the knowledge bank will likely appear significantly different than in the past years.<br /><br />Let's begin with the end in mind. Our students must describe a sequence of transformations in a set of congruent two-dimensional figures. This implies that students need to<br /><ul><li>perform each type of transformation on a coordinate plane</li><li>recognize when conditions prove congruence vs. similarity</li><li>know the structure of coordinate notation to describe the sequence</li></ul><br />Perhaps we can still draw from the elementary experiences with real-life images that display transformations and provide the backdrop for building vocabulary. Next we can transfer that knowledge to the coordinate plane; beginning with one point and then extending to polygons. In the past, students seem to struggle most with rotations. A set of question cards (with answers) can be used with the Kagan structures Inside-Outside Circle or Quiz-Quiz-Trade. Or perhaps 1-2 pages could be copied and used with the Kagan structure RallyCoach. This set is versatile to provide you with individual transformation practice or the freedom to create a mixed set of question cards. The set you create could be used strategically for small group meetings or Seminar study sessions.<br /><br /><div style="text-align: center;"><div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"><a href="https://drive.google.com/file/d/0B5H2CSmfdlQEWlNUbWJ0LTVZUTg/edit?usp=sharing" target="_blank"><img border="0" src="http://3.bp.blogspot.com/-j_eQTnvTPRI/UgFN77nVUiI/AAAAAAAABPc/Y76iyN_lrWU/s320/Transformations+Title+Pic.jpg" height="247" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div style="text-align: left;">When extending to polygons, let's work towards building the concept of congruence and similarity. The following lab activity uses color tiles and a work mat. Students build a figure and perform a variety of transformations to observe the properties. The record sheet is included and can be completed in pairs with the Kagan structure RallyCoach.</div></div><br /><div style="text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://docs.google.com/file/d/0B5H2CSmfdlQESkxDOXFVZGpVMHc/edit?usp=sharing" imageanchor="1" style="margin-left: 1em; margin-right: 1em;" target="_blank"><img border="0" src="http://4.bp.blogspot.com/-r7oSnVpIJjk/UgFN7qAfIGI/AAAAAAAABPM/crzWPE_Eh1s/s320/Properties+of+Transformations+Title+Pic.jpg" height="247" width="320" /></a></div><br /><br /><div style="text-align: left;">The key to every activity is the questioning that helps students gain conceptual understanding. The Properties of Transformations activity builds the conditions for congruence vs. similarity as summarized in the following mind map.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://docs.google.com/file/d/0B5H2CSmfdlQEem9ZRDBWYkxvVHc/edit?usp=sharing" target="_blank"><img border="0" src="http://4.bp.blogspot.com/-rXZ8WVBjqNE/UgFgQ6bT09I/AAAAAAAABPo/lUwMrcExm6c/s320/Mind+Map+Title+Pic.jpg" height="247" width="320" /></a></div><div style="text-align: center;"><br /></div>While building the mind map together, we can discuss rigid transformations...definitions of congruence and similarity...review proportional relationships within similarity...the possibilities are endless! And the understanding of these properties enable students to be successful in identifying a sequence of transformations from a pre-image to the subsequent image. A variety of approaches are included in the following set of questions and can be used with the Kagan structure Showdown.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://docs.google.com/file/d/0B5H2CSmfdlQESkZWcjU1Ym4wOUE/edit?usp=sharing" target="_blank"><img border="0" src="http://1.bp.blogspot.com/-xelVvoKHBJQ/UgFN7alBxCI/AAAAAAAABPU/EthkzFjqHJE/s320/Sequence+of+Transformations+Title+Pic.jpg" height="247" width="320" /></a></div><div style="text-align: center;"><br /></div>These activities highlight the Common Core State Standards 8.G.A.1, 8.G.A.2, and 8.G.A.3 that are included in Accelerated MATH-7, MATH-8, and 7th Grade Accelerated Algebra 1.<br /><br />Does that help? What else do you need? Chat with each other...some of our teachers tackled these standards last year...tap into their expertise. Remember to adjust your filter! And be sure to share your thoughts in the comments below. {All thoughts invited...the good, the bad, and the ugly!}</div></div><br /><br /><br /><br /><br /><br />Anonymousnoreply@blogger.com0tag:blogger.com,1999:blog-61861505795529750.post-26509928586926051552013-07-24T11:35:00.000-07:002013-07-24T11:35:30.845-07:00Coming soon...<br /><span style="background-color: rgba(255, 255, 255, 0);">UNDER CONSTRUCTION</span><br /><span style="background-color: rgba(255, 255, 255, 0);"><br /></span><span style="background-color: rgba(255, 255, 255, 0);">This page will host content specific to the MATH-8 standards.</span>Anonymousnoreply@blogger.com0