tag:blogger.com,1999:blog-21424603914820143242024-03-13T22:37:45.447-07:00FactsWise: A Basic Facts Fluency Approach that Works!Building number sense and basic facts fluency for addition, subtraction, multiplication and division. Daily mini-lessons, games, and strategies based on properties of operations produce remarkable results.Unknownnoreply@blogger.comBlogger22125tag:blogger.com,1999:blog-2142460391482014324.post-17980040339836738992018-11-29T17:59:00.003-08:002018-11-29T18:34:02.504-08:00Timed Tests -- NOT the Way to Build Facts Fluency and NOT the Way to Assess Facts Fluency<br />
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If you'd like to learn more about FactsWise, you can freely preview a number of the FactsWise mini-lessons and games:<br />
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* <a href="http://factswise.thinkific.com/courses/free-preview-factswise-e-course-for-educators-addition-subtraction" target="_blank">Free Preview for FactsWise Add/Subtract Online Course</a><br />
* <a href="http://factswise.thinkific.com/courses/free-preview-factswise-multiplication-division-e-course-for-educators" target="_blank">Free Preview for FactsWise Multiply/Divide Online Course</a><br />
<br />Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-2142460391482014324.post-89438929743451627472018-08-01T16:15:00.000-07:002018-08-02T12:38:08.724-07:00<div style="margin: 0px; text-align: center;">
<b><span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif; font-size: large;">The Power of Fives and Tens </span></b></div>
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<span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;">by Valerie Henry, Ed.D.</span><br />
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<span style="font-family: "arial" , "helvetica" , sans-serif;"> <b style="text-align: center;"><u>The Power of 5s and 10s: Strategies for Making Facts Fluency Connections </u></b> </span><br />
<span style="background-color: white; color: #444444; font-family: "arial" , "helvetica" , sans-serif; font-size: 16px; white-space: pre-wrap;">I've been thinking a lot about this comment recently -- especially because the data I've collected over the years continues to demonstrate that a blend of all five FactsWise principles produces the most powerful results. In classrooms where only a few of the principles are implemented, students are less likely to make the amazing advances we see in classrooms where all five principles are fully implemented.</span><br />
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<b style="background-color: white; color: #444444; font-size: 16px; white-space: pre-wrap;"><u><span style="font-family: "arial" , "helvetica" , sans-serif;">Flexible Strategies support Mathematical Confidence</span></u></b><br />
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<span style="font-family: "arial" , "helvetica" , sans-serif;">The key reason I decided to prioritize 5s and 10s in both add/subtract and multiply/divide has everything to do with my experiences interacting with people who are mathematically confident. Almost without exception, these boys and girls, men and women use flexible mental math strategies with ease. And many of these strategies utilize 5 and 10 as benchmarks. </span><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;">When students can easily find sums and differences, products and quotients involving 5s and 10s, they have the tools they need to solve more complex problems. In the FactsWise mini-lesson video below, you'll see 4th grade dual-immersion students who are using 5s and 10s and other facts they know to reason about x8 facts they're still learning. </span><br />
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<span style="font-family: "arial" , "helvetica" , sans-serif;">The power of 5s and 10s starts showing up as early as Goal 5 in FactsWise Add/Subtract and continues all the way through Goal 9 and into the "secret" Goal 10 (two-digit mental math). The chart below illustrates several of the most common 5s and 10s strategies with problems from Goal 8 (With 9s).</span></div>
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<b><u><span style="font-family: "arial" , "helvetica" , sans-serif;">Focusing on each FactsWise Add/Subtract goal as a related group of facts</span></u></b><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;">"I just recently realized that I've been focusing on individual Goal 1 facts, and not really helping students see the connections -- that all of them add up to either 4 or 5. Now that I've started prioritizing the 5s connection, students are seeing the commonalities between the facts and are becoming much more fluent and confident!" (FactsWise kindergarten teacher).</span><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;">To help students make connections in the first four FactsWise addition/subtraction goals, consider calling the goals by their names rather than simply as Goal 1, Goal 2, etc. By naming them "Within 5", "With 5s", "Within 10" and "With 10s" (Goals 1 through 4 respectively), you and your students can continuously focus on the connections between the facts within each goal. </span><br />
<span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;"><b><u><span style="font-family: "arial" , "helvetica" , sans-serif;">Focusing on the connections between FactsWise Multiply/Divide goals</span></u></b></span><br />
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<span style="font-family: "arial" , "helvetica" , sans-serif;">FactsWise multiply/divide is designed to make it easy for teachers and students to make connections from one goal to the next. Goal 2 becomes much easier for students when they can make connections back to the x10s they learned in Goal 1. Goals 4 and 5 build off the fluency students develop in Goal 3. And the same holds true of Goals 6, 7 and 8.</span><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;">My next post will take a look at mini-lesson activities that help you and your students make connections and build fluency with the foundational 5s and 10s. </span></span><br />
<span style="font-family: "arial" , "helvetica" , sans-serif;"><span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;"><span style="color: black; font-size: 16px; white-space: normal;">If you'd like to learn more about FactsWise and how you can engage your students in powerful facts fluency learning experiences, you can preview and purchase FactsWise Resource Books and FactsWise Online Courses for Educators at </span><a href="http://www.factswise.com/" style="font-size: medium; white-space: normal;">www.factswise.com</a><span style="color: black; font-size: 16px; white-space: normal;">.</span></span></span></div>
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Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-2142460391482014324.post-86654520921217131262018-06-08T13:20:00.003-07:002018-06-08T13:24:35.761-07:00FactsWise: Students learn what you teach!I've been working to transform the teaching and learning of math basic facts fluency since 2004, and teachers keep telling me what a difference they see with students who have had daily mini-lessons that focus on conceptual understanding, patterns, and strategies as stepping stones to full fluency. I recently was talking with Myuriel, a 4th grade dual immersion teacher, who captured the power of FactsWise so well.<br />
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You're all invited to view the Introductory modules for both Addition/Subtraction and Multiplication/Division at any time at <a href="http://www.factswise.thinkific.com/">www.factswise.thinkific.com</a>. </div>
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Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-2142460391482014324.post-65760152593714143952017-08-21T14:44:00.003-07:002018-08-02T12:48:15.223-07:00Announcing FactsWise E-Courses!<span style="font-family: "arial" , "helvetica" , sans-serif;">I'm delighted to announce that you can now learn all about FactsWise through online e-courses for both addition/subtraction and multiplication/division. These e-courses include all of the information from the two-day FactsWise workshops, as well as additional classroom videos and in-depth insights into the lessons and strategies that we just don't have time for in the workshops. (</span><a href="http://www.factswise.thinkific.com/" style="text-align: center;" target="_blank">FactsWise.thinkific.com</a>)<br />
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<span style="font-family: "arial" , "helvetica" , sans-serif;">If you're a teacher who wants to learn a bit more about FactsWise before you decide to enroll in the course, you'll be able to access the introductory chapter for free to see what it's all about. If you're a teacher who'd love to attend the two-day workshop but are a bit too far away from southern California to make it happen -- this online course is designed to help you transition to a simple approach to facts fluency development that time after time has had remarkable results. (</span><a href="http://www.factswise.thinkific.com/" style="text-align: center;" target="_blank">FactsWise.thinkific.com</a>)</div>
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<a href="https://1.bp.blogspot.com/-z5lhYYvXAsI/WZtVn64NdwI/AAAAAAAAEps/0a4VIcvr37g1n-iCZ8fZ1XYSd4QcdoZ3gCLcBGAs/s1600/Teacher%2Bcomment%2B1.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="318" data-original-width="1600" height="124" src="https://1.bp.blogspot.com/-z5lhYYvXAsI/WZtVn64NdwI/AAAAAAAAEps/0a4VIcvr37g1n-iCZ8fZ1XYSd4QcdoZ3gCLcBGAs/s640/Teacher%2Bcomment%2B1.JPG" width="640" /></a></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif;">If you're a teacher who's been introduced to FactsWise from a team member and you want to get a full understanding, this course is for you. Many teachers just like you have told me that they felt so much more confident about building their students' flexible number sense and facts fluency once they had a more in-depth understanding of the principles behind FactsWise. (</span><a href="http://www.factswise.thinkific.com/" style="text-align: center;" target="_blank">FactsWise.thinkific.com</a>)<br />
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<a href="https://3.bp.blogspot.com/-eW-Lr0_l9oM/WZtV_Lr4DVI/AAAAAAAAEpw/4_nDLZB5er05tfIXnqdVHscP_lI5kf07QCLcBGAs/s1600/Teacher%2Bcomment%2B2.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="542" data-original-width="1241" height="173" src="https://3.bp.blogspot.com/-eW-Lr0_l9oM/WZtV_Lr4DVI/AAAAAAAAEpw/4_nDLZB5er05tfIXnqdVHscP_lI5kf07QCLcBGAs/s400/Teacher%2Bcomment%2B2.JPG" width="400" /></a></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif;">And if you're a teacher who's been to a FactsWise workshop and you want to get a refresher or see it in action, this course is for you too! You'll be able to see many more video clips online than I could ever show during the workshops, and there are a number of bonus downloads you'll be able to access through the course. (</span><a href="http://www.factswise.thinkific.com/" style="text-align: center;" target="_blank">FactsWise.thinkific.com</a>)<br />
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<span style="font-family: "arial" , "helvetica" , sans-serif;">Of course, I'd be delighted to meet you in person at a two-day FactsWise workshop -- which are offered in the fall through both the Santa Barbara County Education Office as well as the Orange County (California) Department of Education. And if you attend one of these workshops, you'll get a special coupon to access the online course as well.</span><br />
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<iframe allowfullscreen='allowfullscreen' webkitallowfullscreen='webkitallowfullscreen' mozallowfullscreen='mozallowfullscreen' width='320' height='266' src='https://www.blogger.com/video.g?token=AD6v5dyxQWCf99EiOdG4QISysRbMV4IZpt2btwYfbntEVMHoKLwdY6USWcwCQVZnVlH42ElJAbAi9Q_Bk5s9z48rZQ' class='b-hbp-video b-uploaded' frameborder='0'></iframe></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif;">I'm happy to announce that both the FactsWise Addition/Subtraction and also the FactsWise Multiplication/Division courses are completed</span><span style="background-color: white;"><span style="font-family: "arial" , "helvetica" , sans-serif;">. The introductory module is completely free and will give you a strong overview of the approach and implementation research behind FactsWise. You can find them both at </span></span><span style="font-family: "arial" , "helvetica" , sans-serif;"><a href="http://www.factswise.thinkific.com/" style="text-align: center;" target="_blank">FactsWise.thinkific.com</a>.</span><br />
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<span style="background-color: white;"><span style="font-family: "arial" , "helvetica" , sans-serif;">Please feel free to share this with other teachers you think might be interested -- I'd love for you and your colleagues to be able to take advantage of these courses!</span></span></span><br />
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Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-2142460391482014324.post-20974478019564011132016-10-04T11:35:00.003-07:002016-10-04T11:47:42.104-07:00Subtracting from Teen NumbersWhen you are getting ready to begin Goal 8 Subtraction, you may be wondering how you can help your students move beyond counting back or counting up to solve these problems using strategies based on properties of operations. I've made a <a href="https://www.youtube.com/watch?v=rZlRAt2ZCQA" target="_blank">Subtracting from Teen Numbers screencast</a> that shares four different strategies that do just this. The screencast also includes a number talk approach that will provide students with time and tools to generate some or many of these strategies using logic and visuals. These four strategies will also be very relevant to Goal 9 subtraction.<br />
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You may also find you want to try this approach with Goal 5 subtraction. Relating subtraction to addition and Take from Ten may be particularly helpful for Goal 5.<br />
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I hope you and your students enjoy!<br />
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<br />Unknownnoreply@blogger.com1tag:blogger.com,1999:blog-2142460391482014324.post-81583146624011517122016-08-17T13:53:00.002-07:002016-08-17T15:45:42.034-07:00At your request ... Daily Activity Progressions<span style="font-family: "arial" , "helvetica" , sans-serif;">Many teachers have told me that they really want to focus on basic facts fluency for 5 to 10 minutes each day, but they have difficulty finding the time to plan those activities. So I've put together a set of sample activities for each of the goals for addition/subtraction and also for multiplication/division. </span><br />
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<span style="font-family: "arial" , "helvetica" , sans-serif;">The activities for each goal are numbered sequentially, working first on concept building with mostly concrete activities, then shifting to strategies and patterns using visual representations, and finally moving in the third column to abstract practice. You'll find the blackline masters referenced in the activities following each progression. </span><br />
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<b><span style="font-family: "arial" , "helvetica" , sans-serif;"><a href="https://www.dropbox.com/s/v4s5awno3ul9vbh/FW%20AS%20Daily%20Activity%20Progressions%208.15.16.pdf?dl=0" target="_blank">FactsWise Addition/Subtraction Daily Activity Progressions (Goals 1 - 9)</a></span></b></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif;"> <a href="https://4.bp.blogspot.com/-A4Q2WNwzT6w/V7TJqBO_X4I/AAAAAAAAC6c/w-wtVWcdg8oW9k48fKpuM5M8a27uGfjFACLcB/s1600/AS%2BAct%2BProg%2B3.GIF" imageanchor="1" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" height="116" src="https://4.bp.blogspot.com/-A4Q2WNwzT6w/V7TJqBO_X4I/AAAAAAAAC6c/w-wtVWcdg8oW9k48fKpuM5M8a27uGfjFACLcB/s200/AS%2BAct%2BProg%2B3.GIF" width="200" /></a> <a href="https://2.bp.blogspot.com/-OERd2jHYZkY/V7TJqChjU9I/AAAAAAAAC6g/IhGEa_ltNrIcRiT8UnBgaD0NYJJgAjg2QCLcB/s1600/AS%2BAct%2BProg%2B2.GIF" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="105" src="https://2.bp.blogspot.com/-OERd2jHYZkY/V7TJqChjU9I/AAAAAAAAC6g/IhGEa_ltNrIcRiT8UnBgaD0NYJJgAjg2QCLcB/s200/AS%2BAct%2BProg%2B2.GIF" width="200" /></a></span></div>
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<b><span style="font-family: "arial" , "helvetica" , sans-serif;"><a href="https://www.dropbox.com/s/zu2x3o3jloui92n/FW%20MD%20Daily%20Activity%20Progressions%208.2016.pdf?dl=0" target="_blank">FactsWise Multiplication/Division Daily Activity Progressions (Goals 1 - 8)</a></span></b></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif;"><a href="https://4.bp.blogspot.com/-rYLsL0kjJd4/V7TMa5XIIII/AAAAAAAAC6w/5a8s7mmpHDklfaf72WJzVRjK747fV7OHQCEw/s1600/MD%2BAct%2BProg%2B2.GIF" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="200" src="https://4.bp.blogspot.com/-rYLsL0kjJd4/V7TMa5XIIII/AAAAAAAAC6w/5a8s7mmpHDklfaf72WJzVRjK747fV7OHQCEw/s200/MD%2BAct%2BProg%2B2.GIF" width="193" /></a> <a href="https://3.bp.blogspot.com/-b6gSbOzSIe4/V7TMa2PLKVI/AAAAAAAAC6s/odzR1aob2SsZtM3xTeV8xd7X5tkxVEEuACEw/s1600/MD%2BAct%2BProg%2B3.GIF" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="148" src="https://3.bp.blogspot.com/-b6gSbOzSIe4/V7TMa2PLKVI/AAAAAAAAC6s/odzR1aob2SsZtM3xTeV8xd7X5tkxVEEuACEw/s320/MD%2BAct%2BProg%2B3.GIF" width="320" /></a></span></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif;">I hope you find these resources helpful ... and please post here to share what you learn as you try them out with students! </span></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif;">Note: If you have attended a workshop in the past year, you probably recorded the password for the online FactsWise resources in your notebook. If you attended an earlier workshop, feel free to contact me at ellipsismath@gmail.com to get the password. </span><span style="font-family: "arial" , "helvetica" , sans-serif;">If you've not been able to attend a FactsWise workshop, you can purchase the activity progressions at Teachers Pay Teachers: </span><a href="https://www.teacherspayteachers.com/Product/Daily-Activity-Progressions-FactsWise-Addition-and-Subtraction-2736994" style="font-family: arial, helvetica, sans-serif;" target="_blank">Addition/Subtraction</a><span style="font-family: "arial" , "helvetica" , sans-serif;"> and </span><a href="https://www.teacherspayteachers.com/Product/Daily-Activity-Progressions-FactsWise-Multiplication-and-Division-2737027" style="font-family: arial, helvetica, sans-serif;" target="_blank">Multiplication/Division</a><span style="font-family: "arial" , "helvetica" , sans-serif;">. </span></div>
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<span style="font-family: "arial" , "helvetica" , sans-serif;">Also, if you'd like more more information about the entire FactsWise program, you can find the <i>2016 FactsWise Resource Books</i> at Teachers Pay Teachers: <a href="https://www.teacherspayteachers.com/Product/FactsWise-Add-Subtract-Basic-Facts-Resource-Book-1535531" target="_blank">Addition/Subtraction</a> and <a href="https://www.teacherspayteachers.com/Product/FactsWise-Multiply-Divide-Basic-Facts-Resource-Book-1541493" target="_blank">Multiplication/Division</a>.</span></div>
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Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-2142460391482014324.post-49580517391733332602016-06-06T07:21:00.000-07:002016-06-06T07:21:00.562-07:003 or 4 in a Row Game Directions - Multiplication/DivisionIf you've been looking for directions for the 3-in-a-Row games for each Multiplication/Division Goal, I've put together a video that explains them while showing a sample game being played. Following the 3-in-a-Row game, I've also included directions for the two different variations on the 4-in-a-Row games that are cumulative reviews after Goal 5 and Goal 8. I hope you and your students enjoy playing these games during the abstract practice phases of the different goals!<br />
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<br />Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-2142460391482014324.post-42595013358923310512015-07-23T10:02:00.000-07:002015-07-23T17:08:04.343-07:00Sample Planning Calendars<div class="separator" style="clear: both; text-align: center;">
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After talking with a number of teachers, I've put together some sample planning calendars for developing basic facts fluency across your school year. Hope they're helpful -- as samples!</div>
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<br />Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-2142460391482014324.post-57533527706763265552015-02-16T21:39:00.001-08:002015-02-16T21:39:33.782-08:00New Multiplication/Division Goal-by-Goal Resource File<pre style="background-color: white; padding: 0px; white-space: pre-wrap !important;"><span style="font-family: Arial, Helvetica, sans-serif;">At the request of a number of teachers, I have just put together a 353-page pdf file that organizes, for each goal, the directions for activities, blackline masters for activities and games, the pairs practice tents, flashcards, assessment pages, and other materials. I have designed this <a href="https://www.teacherspayteachers.com/Product/FactsWise-MultiplicationDivision-Goal-by-Goal-Resource-File-1711903" target="_blank">FactsWise Multiplication/Division Goal-by-Goal Resource File</a> to be used as a companion to the FactsWise Resource Book for Multiplication/Division.</span></pre>
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<a href="http://4.bp.blogspot.com/-dsgZi_7qdug/VNFdqM3K9II/AAAAAAAACm4/jPa07yjmE2Y/s1600/Goal-by-Goal%2BResource%2BFile%2Bimage.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://4.bp.blogspot.com/-dsgZi_7qdug/VNFdqM3K9II/AAAAAAAACm4/jPa07yjmE2Y/s1600/Goal-by-Goal%2BResource%2BFile%2Bimage.JPG" height="358" width="400" /></a></div>
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<pre style="background-color: white; padding: 0px; white-space: pre-wrap !important;"><span style="font-family: Arial, Helvetica, sans-serif;">I have posted this file on Teachers Pay Teachers for just $5.00 until the end of February. After that I'll place a more accurate price on it.</span></pre>
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<pre style="background-color: white; padding: 0px; white-space: pre-wrap !important;"><span style="font-family: Arial, Helvetica, sans-serif;">If you find this way of organizing all of the FactsWise multiplication and division resources helpful, I'd love to hear from you. Feel free to post your comments on this blog!</span></pre>
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<a href="http://4.bp.blogspot.com/-Eytc9ag1rik/VNFcN_DLLxI/AAAAAAAACms/WxYxZXySqW4/s1600/FW%2BMMM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://4.bp.blogspot.com/-Eytc9ag1rik/VNFcN_DLLxI/AAAAAAAACms/WxYxZXySqW4/s1600/FW%2BMMM.png" height="116" style="cursor: move;" width="320" /></a></div>
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<br />Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-2142460391482014324.post-415838662349213732015-02-03T15:46:00.001-08:002015-02-03T15:46:15.195-08:00New FactsWise Goal-by-Goal Resource File Available<pre style="background-color: white; padding: 0px; white-space: pre-wrap !important;"><span style="font-family: Arial, Helvetica, sans-serif;">At the request of a number of teachers, I have just put together a 338-page pdf file that organizes for each goal the directions for activities, blackline masters for activities and games, the pairs practice tents, flashcards, assessment pages, and other materials. I have designed this <a href="https://draft.blogger.com/It%20turns%20out%20that%20Teachers%20Pay%20Teachers%20expects%20this%20large%20a%20file%20(338%20pages)%20to%20generate%20some%20income,%20so%20I%20set%20it%20at%20$5.00%20until%20the%20end%20of%20February.%20After%20that%20I'll%20place%20a%20more%20accurate%20price%20on%20it.%20%20https://www.teacherspayteachers.com/Product/FactsWise-Goal-by-Goal-Resource-File-Addition-and-Subtraction-1686374" target="_blank">FactsWise Goal-by-Goal Resource File</a> to be used as a companion to the FactsWise Resource Book.</span></pre>
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<pre style="background-color: white; padding: 0px; white-space: pre-wrap !important;"><span style="font-family: Arial, Helvetica, sans-serif;">I have posted this file on Teachers Pay Teachers for just $5.00 until the end of February. After that I'll place a more accurate price on it.</span></pre>
<pre style="background-color: white; padding: 0px; white-space: pre-wrap !important;"><span style="font-family: Arial, Helvetica, sans-serif;">
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<pre style="background-color: white; padding: 0px; white-space: pre-wrap !important;"><span style="background-color: transparent; font-family: Arial, Helvetica, sans-serif;">If you find this way of organizing all of the FactsWise addition and subtraction resources helpful, I'd love to hear from you. Feel free to post your comments on this blog!</span></pre>
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Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-2142460391482014324.post-73304757675049949152014-10-28T21:45:00.001-07:002014-10-28T21:45:42.945-07:00Counting Comes First!Before students can develop part-whole thinking, they need to understand how our numbers work and become confident counters. Here are a series of activities that can help students develop their understanding and fluency with counting.<div>
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<a href="http://3.bp.blogspot.com/-JDft_E1h-hU/VFBvOvNykFI/AAAAAAAACNU/jr5lAf5INMY/s1600/Counting%2B1.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://3.bp.blogspot.com/-JDft_E1h-hU/VFBvOvNykFI/AAAAAAAACNU/jr5lAf5INMY/s1600/Counting%2B1.JPG" height="540" width="640" /></a></div>
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<a href="http://4.bp.blogspot.com/-DaITxK64Dq8/VFBvOoBPGQI/AAAAAAAACNA/m9cqtPXGy2o/s1600/Counting%2B2.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://4.bp.blogspot.com/-DaITxK64Dq8/VFBvOoBPGQI/AAAAAAAACNA/m9cqtPXGy2o/s1600/Counting%2B2.JPG" height="314" width="640" /></a></div>
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<a href="http://2.bp.blogspot.com/-vZM6_pDvzDA/VFBvPGjFKFI/AAAAAAAACNE/JubrVkuM-O0/s1600/Counting%2B4.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" src="http://2.bp.blogspot.com/-vZM6_pDvzDA/VFBvPGjFKFI/AAAAAAAACNE/JubrVkuM-O0/s1600/Counting%2B4.JPG" height="372" width="640" /></a><br />
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The key idea behind all of these activities is the connection between concrete objects and/or representations and counting. I hope you and any of your students that need support with counting will enjoy these interactive activities!</div>
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<a href="http://4.bp.blogspot.com/-nfEOtGguePc/VFBw5kTz8sI/AAAAAAAACNg/veIg2Hu9rkE/s1600/Thanks%2BMMM.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://4.bp.blogspot.com/-nfEOtGguePc/VFBw5kTz8sI/AAAAAAAACNg/veIg2Hu9rkE/s1600/Thanks%2BMMM.jpg" height="142" width="320" /></a></div>
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Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-2142460391482014324.post-27005123300062711672014-06-20T12:26:00.003-07:002014-06-20T12:26:43.587-07:00A FactsWise Friendly Online Multiplication GameI haven't found many online games that align well with the principles we talk about in FactsWise. Here's one game, though, that might prove helpful when students are ready for abstract work on a particular goal: <a href="http://www.multiplication.com/games/play/quick-flash-ii" target="_blank">Quick Flash II</a>.<br />
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<a href="http://4.bp.blogspot.com/-E3RMdpQCdoE/U6SGwdPsuWI/AAAAAAAABnI/tZ8N5t2WYKs/s1600/Online+Mult+2.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://4.bp.blogspot.com/-E3RMdpQCdoE/U6SGwdPsuWI/AAAAAAAABnI/tZ8N5t2WYKs/s1600/Online+Mult+2.jpg" height="184" width="320" /></a></div>
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<a href="http://1.bp.blogspot.com/-swbPcWIw9Ag/U6SGwUMc1KI/AAAAAAAABnQ/K36SpAM3KCE/s1600/Mult+Online+1.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://1.bp.blogspot.com/-swbPcWIw9Ag/U6SGwUMc1KI/AAAAAAAABnQ/K36SpAM3KCE/s1600/Mult+Online+1.jpg" height="230" width="320" /></a></div>
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Even though this game starts out with little graphic interest, students get to earn their way to more interesting backgrounds.</div>
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<a href="http://2.bp.blogspot.com/-w-86xHAlZQs/U6SHxHrWJxI/AAAAAAAABnU/a9HkQLo-IMU/s1600/Mult+Online+3.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://2.bp.blogspot.com/-w-86xHAlZQs/U6SHxHrWJxI/AAAAAAAABnU/a9HkQLo-IMU/s1600/Mult+Online+3.jpg" /></a></div>
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Some of the features of this game that make it a good learning experience (in contrast to a good review experience), are:</div>
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1) Students can concentrate on the facts from one goal;</div>
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2) Students get immediate feedback;</div>
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3) Students get multiple opportunities to rehearse the same facts;</div>
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4) Students, teachers, and parents can see which facts are less fluent. Although there isn't a built-in feature for this, if you have your student press the "print screen" key on their computer as they finish the last problem on the third round, the game will pause (at least on my computer) and you can record the problems that aren't all green, or take a screen shot and then paste it into a word document. </div>
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<a href="http://4.bp.blogspot.com/-h3UnLy9ipNo/U6SB7fWCyhI/AAAAAAAABm4/Jh4gsdmIsWU/s1600/Thanks+MMM.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://4.bp.blogspot.com/-h3UnLy9ipNo/U6SB7fWCyhI/AAAAAAAABm4/Jh4gsdmIsWU/s1600/Thanks+MMM.jpg" height="142" width="320" /></a></div>
Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-2142460391482014324.post-70110292998133158362014-06-20T11:49:00.001-07:002014-06-20T11:49:15.682-07:00At Your Request - Multiplication/Division Flower RepresentationsI hope you're all enjoying the start of summer! I just finished working with a great group of teachers who tried out a new idea -- <a href="https://www.dropbox.com/s/55z19qzvlrza2ht/Flowers%20in%20Rows%20of%2010%20-%20Goals%203%2C%204%2C%205.doc" target="_blank">flower representations for Goals 3, 4, and 5</a>. <div>
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Goal 3 (x 2s)</div>
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<a href="http://1.bp.blogspot.com/-AmHEntjGOHI/U6RwWKIgSqI/AAAAAAAABlk/niqs3EJRGhQ/s1600/Flowers+G3+(x+2s).jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://1.bp.blogspot.com/-AmHEntjGOHI/U6RwWKIgSqI/AAAAAAAABlk/niqs3EJRGhQ/s1600/Flowers+G3+(x+2s).jpg" height="80" width="320" /></a></div>
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Goal 4 (x 4s)</div>
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<a href="http://1.bp.blogspot.com/-yjj_pA8Fcr8/U6RwZb7kCFI/AAAAAAAABlw/R3n4mgl7Nf8/s1600/Flowers+G4+(x+4s).jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://1.bp.blogspot.com/-yjj_pA8Fcr8/U6RwZb7kCFI/AAAAAAAABlw/R3n4mgl7Nf8/s1600/Flowers+G4+(x+4s).jpg" height="158" width="320" /></a></div>
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Goal 5 (x 8s)</div>
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<a href="http://3.bp.blogspot.com/-o51x5xVcgYQ/U6RwZROjo4I/AAAAAAAABls/N8kIRDIYIys/s1600/Flowers+G5+(x+8s).jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://3.bp.blogspot.com/-o51x5xVcgYQ/U6RwZROjo4I/AAAAAAAABls/N8kIRDIYIys/s1600/Flowers+G5+(x+8s).jpg" /></a></div>
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Students can share copies of these flowers, and can work together to answer questions such as: "What do you notice?" and "How can the patterns you're noticing help you remember your facts for this goal?". </div>
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After students have found many of the patterns, you may want to organize the numeric patterns in two rows so that students can see the distributive property in action. For instance, with Goal 5, it could look like this:</div>
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<a href="http://3.bp.blogspot.com/-o51x5xVcgYQ/U6RwZROjo4I/AAAAAAAABls/N8kIRDIYIys/s1600/Flowers+G5+(x+8s).jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" src="http://3.bp.blogspot.com/-o51x5xVcgYQ/U6RwZROjo4I/AAAAAAAABls/N8kIRDIYIys/s1600/Flowers+G5+(x+8s).jpg" height="198" width="200" /></a> <a href="http://3.bp.blogspot.com/-GYgHpJSFs3U/U6R0j5HaUBI/AAAAAAAABmA/zk6opt_Yxj4/s1600/Goal+5+Pattern+Grid.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" src="http://3.bp.blogspot.com/-GYgHpJSFs3U/U6R0j5HaUBI/AAAAAAAABmA/zk6opt_Yxj4/s1600/Goal+5+Pattern+Grid.jpg" height="57" width="320" /></a></div>
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Students will be able to notice the patterns, that 48 is 40 more than 8, 56 is 40 more than 16, and so on. With your help, they can figure out that this pattern happens because of the distributive property, and because 5 x 8 makes 40. Since 40 is a "friendly 10", the ones place repeats. For instance:</div>
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8 x 1 = 8</div>
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+ <u>8 x 5 = 40</u></div>
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8 x 6 = 48 or, more traditionally 8 x 6 = 8 x (1 + 5) = (8 x 1) + (8 x 5) = 8 + 40 = 48</div>
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8 x 2 = 16</div>
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+ <u>8 x 5 = 40</u></div>
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8 x 7 = 56 or, more traditionally 8 x 7 = 8 x (2 + 5) = (8 x 2) + (8 x 5) = 16 + 40 = 56</div>
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The distributive property helps explain similar patterns for Goal 3, Goal 4, and Goal 7 as well.</div>
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<a href="http://4.bp.blogspot.com/-pXz4PGzMaxg/U6R3OH9UFfI/AAAAAAAABmM/RL-55lJaats/s1600/Goal+3+Pattern+Grid.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://4.bp.blogspot.com/-pXz4PGzMaxg/U6R3OH9UFfI/AAAAAAAABmM/RL-55lJaats/s1600/Goal+3+Pattern+Grid.jpg" height="60" width="320" /></a> </div>
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2 x 4 = 8</div>
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+ <u>2 x 5 = 10</u></div>
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2 x 9 = 18 or, more traditionally 2 x 9 = 2 x (4 + 5) = (2 x 4) + (2 x 5) = 8 + 10 = 18</div>
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This "friendly ten" pattern shows up in all of the even factor goals (e.g., x2, x4, x6, and x8).</div>
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<a href="http://4.bp.blogspot.com/-RCNk3cWjI0k/U6R4WIq95VI/AAAAAAAABmc/W41Fdj7HzZQ/s1600/Goal+4+Pattern+Grid.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://4.bp.blogspot.com/-RCNk3cWjI0k/U6R4WIq95VI/AAAAAAAABmc/W41Fdj7HzZQ/s1600/Goal+4+Pattern+Grid.jpg" height="60" width="320" /></a></div>
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<a href="http://4.bp.blogspot.com/-OPS0ng8r-Xg/U6R4WD1StBI/AAAAAAAABmg/xstyfLHzC2E/s1600/Goal+7+Pattern+Grid.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://4.bp.blogspot.com/-OPS0ng8r-Xg/U6R4WD1StBI/AAAAAAAABmg/xstyfLHzC2E/s1600/Goal+7+Pattern+Grid.jpg" height="60" width="320" /></a></div>
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And, since Goal 7 is part of the 3s, 6s, 9s sequence, I decided to change the image from flowers to apples. It's also on the "flowers" file linked at the top of this post.</div>
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<a href="http://4.bp.blogspot.com/-PG_r4aPhjF0/U6SBMbuSg4I/AAAAAAAABms/H9HG6fEeX_0/s1600/Goal+7+Pattern+Grid+Apples.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://4.bp.blogspot.com/-PG_r4aPhjF0/U6SBMbuSg4I/AAAAAAAABms/H9HG6fEeX_0/s1600/Goal+7+Pattern+Grid+Apples.jpg" height="210" width="320" /></a></div>
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If you decide to use these with students, it would be great if you could share what you and your students learned. I hope you all enjoy looking for patterns and making connections to algebraic thinking!</div>
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Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-2142460391482014324.post-87793629800509137882014-05-20T16:25:00.001-07:002014-05-20T16:27:06.673-07:00Multiplication/Division Chart Planning - SamplesI've been thinking about charting each of the different multiplication/division goals -- how to build in a concrete experience, at least one or two representations, a connection to properties and/or patterns, and a connection between multiplication and division. Here are my initial ideas -- I'd love to see what you wind up charting in your classrooms!<br />
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<a href="http://4.bp.blogspot.com/-88CYzG9cZs8/U3vjb8tE-KI/AAAAAAAABRA/XEic81yu8oI/s1600/G4+Multiply+Chart+Planner.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://4.bp.blogspot.com/-88CYzG9cZs8/U3vjb8tE-KI/AAAAAAAABRA/XEic81yu8oI/s1600/G4+Multiply+Chart+Planner.jpg" height="320" width="240" /></a> <a href="http://1.bp.blogspot.com/-BL458SAmj_g/U3vjbpb8k6I/AAAAAAAABRE/3-WYrjVfU5Q/s1600/G4+Divide+Chart+Planner.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://1.bp.blogspot.com/-BL458SAmj_g/U3vjbpb8k6I/AAAAAAAABRE/3-WYrjVfU5Q/s1600/G4+Divide+Chart+Planner.jpg" height="320" width="240" /></a></div>
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<a href="http://3.bp.blogspot.com/-JIFK8TYVJP0/U3vjbkBWsrI/AAAAAAAABQ8/AS5COEESpik/s1600/Goal+5+Divide+Chart+Planner.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><br /></a><a href="http://3.bp.blogspot.com/-JIFK8TYVJP0/U3vjbkBWsrI/AAAAAAAABQ8/AS5COEESpik/s1600/Goal+5+Divide+Chart+Planner.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><br /></a><a href="http://1.bp.blogspot.com/-Q9c1vv-yPG0/U3vjdbIsUHI/AAAAAAAABRQ/SWm7Yydmvxs/s1600/Goal+5+Multiply+Chart+Planner.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://1.bp.blogspot.com/-Q9c1vv-yPG0/U3vjdbIsUHI/AAAAAAAABRQ/SWm7Yydmvxs/s1600/Goal+5+Multiply+Chart+Planner.jpg" height="320" width="240" /></a><a href="http://3.bp.blogspot.com/-JIFK8TYVJP0/U3vjbkBWsrI/AAAAAAAABQ8/AS5COEESpik/s1600/Goal+5+Divide+Chart+Planner.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://3.bp.blogspot.com/-JIFK8TYVJP0/U3vjbkBWsrI/AAAAAAAABQ8/AS5COEESpik/s1600/Goal+5+Divide+Chart+Planner.jpg" height="320" width="240" /></a></div>
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Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-2142460391482014324.post-75776618588007262672014-05-20T15:41:00.002-07:002014-05-20T15:41:44.750-07:00At Your Request: C-R-A OverviewIn order to clarify what may be considered concrete, representational, and abstract activities, I've made a chart that I hope will help. Let me know what you think!<div>
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<a href="http://2.bp.blogspot.com/-9YGsj-iXNfc/U3vZ5iF6fSI/AAAAAAAABQo/WAhJc3ZAaXk/s1600/CRA+Concept+Chart.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://2.bp.blogspot.com/-9YGsj-iXNfc/U3vZ5iF6fSI/AAAAAAAABQo/WAhJc3ZAaXk/s1600/CRA+Concept+Chart.JPG" height="305" width="640" /></a></div>
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Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-2142460391482014324.post-20593634824908485112014-03-13T20:17:00.001-07:002014-03-13T20:17:35.809-07:00Hands Cards for Games Focusing on 5s and 10sI enjoyed visiting with a group of teachers this afternoon, where I shared <a href="https://www.dropbox.com/s/lacpbcs8a2qjlv8/FW%20Game%20makeit%20takeit.doc" target="_blank">a set of hand cards</a> that can be used to play Addition War with any of the numbers facing up as the addend. For instance:<br />
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<a href="http://1.bp.blogspot.com/-pST-9JEY8C8/UyJy1RHagLI/AAAAAAAAA-0/X5Vxv5VaNMs/s1600/Hand+Card+Games+Chart.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://1.bp.blogspot.com/-pST-9JEY8C8/UyJy1RHagLI/AAAAAAAAA-0/X5Vxv5VaNMs/s1600/Hand+Card+Games+Chart.jpg" height="114" width="320" /></a></div>
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Sample Goal 5 Game Set-Up<br />
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<a href="http://4.bp.blogspot.com/-K1QMwiHR3z8/UyJzFs30X1I/AAAAAAAAA_E/Oc_GUUI0Ezc/s1600/5+hand+card.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://4.bp.blogspot.com/-K1QMwiHR3z8/UyJzFs30X1I/AAAAAAAAA_E/Oc_GUUI0Ezc/s1600/5+hand+card.jpg" height="154" width="200" /></a></div>
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Face-Up Card</div>
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Val's Card Calvyn's Card<br />
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In this round, Val turns up the top card of her stack and says "5 + 6 makes 11". Then Calvyn turns up his top card and says "5 + 8 makes 13". Since Calvyn has the larger sum, he gets both the 6 and 8 cards and puts them at the bottom of his stack. The 5 stays face up, so that every time they take turns they are practicing adding 5 to another addend. <br />
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You can download the <a href="https://www.dropbox.com/s/lacpbcs8a2qjlv8/FW%20Game%20makeit%20takeit.doc" target="_blank">Hand Game Cards here</a>. If you think you'll have more than two students playing together, you may want to print and cut out more than one set of the cards for each deck.<br />
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As always, I encourage you to have students share, in writing or through a whole-class discussion, strategies they found helpful and facts they were learning as a result of playing the game.<br />
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<br />Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-2142460391482014324.post-32496564039377633722014-02-18T20:57:00.000-08:002014-02-18T20:57:01.991-08:00Sharing Recent Add/Subtract PowerpointI've done some major updates on the FactsWise Addition/Subtraction powerpoint over the past couple of months, and have been exploring different options for sharing it. It looks like my Dropbox account should do the trick. If you want to view or download the file, here's the<a href="https://www.dropbox.com/s/flk7mdz87mnlwwy/FW%20AS%20Day%201%202.2014%20Blog%20Ready.pdf" target="_blank"> link</a>.<div>
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And here are a couple of slides that folks specifically asked for:</div>
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Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-2142460391482014324.post-9977839727590309682014-01-05T12:57:00.000-08:002014-01-05T12:57:12.479-08:00At Your Request - Goal 2 Animal Strips Handout (Snails)When introducing Goal 2 (x 5s), it can be helpful to have students focus first on the even factors of 5. Students can use an animal strips handout that helps them see the multiples of 10 patterns.<div class="separator" style="clear: both; text-align: center;">
<a href="http://2.bp.blogspot.com/-svJSfB43KfU/UsnC-NcneDI/AAAAAAAAAsE/ToSmN-6eMLM/s1600/Goal+2+Chart+with+Snails.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://2.bp.blogspot.com/-svJSfB43KfU/UsnC-NcneDI/AAAAAAAAAsE/ToSmN-6eMLM/s1600/Goal+2+Chart+with+Snails.jpg" height="320" width="301" /></a></div>
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<a href="https://docs.google.com/document/d/1cfCSmx1AtqY0LZy6CJeidEye6RuxRqdAtNaTRb8e9Wc/edit?usp=sharing" target="_blank">Goal 2 Animal Strips Handout - Snails</a></div>
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Once students are fluent with products of the even factors of 5, then they can work on the odd factors of 5. Students will be able to use the distributive property frequently with this approach. For instance:</div>
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7 x 5 = (6 x 5) + (1 x 5) = 30 + 5 = 35</div>
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You can also use the snails handout as students begin working on Goal 2 division. "How many groups of 5 snails are in 30 snails?" </div>
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Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-2142460391482014324.post-55216187032478526332014-01-05T11:28:00.002-08:002014-01-05T11:54:09.823-08:00At Your Request - New Multiplication/Division FlashcardsAfter hearing from teachers how well the factor-factor-product grids have been helping students make connections between multiplication and division, I spent some of the winter holiday making flashcards with these grids. <br />
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You have a couple of different options to choose from if you want to use these with your students. If you want to save paper, option 1 below is the way to go. If you want to have each goal start on a new page, and have a set that includes both multiplication facts (e.g., 2x3 and 3x2), then you'll want to use option 2. And if you have students who are ready for the Top 21 facts, use option 3.<span style="text-align: center;"> </span><br />
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<li><a href="https://drive.google.com/file/d/0Bz42do61UbEjQU1vTDdSR19CU0k/edit?usp=sharing" target="_blank">FactsWise Multiplication/Division Flashcards - Factor-Factor-Product Grids - Paper Saver</a></li>
<li><a href="https://drive.google.com/file/d/0Bz42do61UbEjNXg0SnBZY1JwdGc/edit?usp=sharing" target="_blank">FactsWise Multiplication/Division Flashcards - Factor-Factor-Product Grids - Complete</a></li>
<li style="text-align: left;"><a href="https://drive.google.com/file/d/0Bz42do61UbEjRXJYTnpEb2JpV2M/edit?usp=sharing" target="_blank">FactsWise MD Top 21 Flashcards - Factor-Factor-Product Grids</a></li>
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It's also important to teach students how to use flashcards effectively:</div>
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<li>Focus on just one goal at a time to start. (Later on you can put two or more goals together when reviewing.)</li>
<li>Look at the front of each flashcard. If you think you know the answer, check the back of the flashcard. If correct, then decide whether you knew it "fluently" -- within 2 seconds, without having to count to figure it out. If you knew the fact fluently, place the flashcard in a pile with other "fluent" facts. If you had to count, take more than 2 seconds, or didn't know the correct answer, place the flashcard in a "Still Working On It" pile. </li>
<li>Once you've gone through all of the facts for the goal you're working on, now concentrate on the "Still Working On It" flashcards. Practice those facts several times. When you notice that you are developing fluency with a fact, you can move it to your "Fluent" pile.</li>
<li>When you have moved all of the facts to your "Fluent" pile, then go back through the entire set of flashcards and decide if they are really fluent or whether you need to move some back to the "Still Working On It" pile again.</li>
<li>Be sure and work on these same facts several days in a row, until you can put every fact in the "Fluent" pile in your first run through the cards. Make sure you shuffle the cards frequently so that you are truly learning the facts, and not just the order you're used to.</li>
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Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-2142460391482014324.post-54362673094371579292011-11-04T10:11:00.000-07:002011-11-04T10:11:37.226-07:00Basic Facts Every Day!<span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;">When we look at all the different topics that need to be covered every day, it's easy to see how basic facts can slip through the cracks. In an effort to avoid this, some teachers block out 20 or 30 minutes one day a week to work on facts. This seems like a good idea, but for too many students it misses the critical window of rehearsal effectiveness.</span><div>
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<span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;">We know from psychology research that memorization is much more likely to happen if the <span class="Apple-style-span" style="color: #3d85c6;"><b>facts are rehearsed every 24 to 48 hours</b></span>. In fact, it turns out that shorter, more frequent rehearsal sessions are significantly more effective than longer, less frequent practice activities.</span></div>
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<span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;">So the question is, how can teachers ensure that their students are getting daily basic facts practice? </span></div>
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<li><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;">The daily practice has to happen in the classroom. It's a given that only some students will have the consistency and parent involvement at home to ensure daily practice. </span></li>
<li><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;">Build in 5 to 10 minutes as a daily routine. If you do a daily calendar or rug time, you've already got a daily routine system. Including basic facts practice during this routine could be very powerful -- although you might have to let go of some other part(s) of your rug time. It's all a matter of priorities -- and basic facts fluency and part-whole thinking need to be at the top of the math priority list!</span></li>
<li><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;">Incorporate basic fact choral response activities into transition times, such as lining up for recess or refocusing students as they are waiting to walk back into the classroom after lunch. If you notice your students are finding a few facts particularly troublesome, you can do quick comparisons and choral responses for those few facts several times a day during small breaks in the action.</span></li>
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<span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;">The second important insight from psychology research is that the daily memorization practice needs to be</span><b style="font-family: 'Trebuchet MS', sans-serif;"> <span class="Apple-style-span" style="color: #3d85c6;">focused consistently on a small number of facts</span></b><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"> until they are mastered. So if you are working with your class on Goal 2 facts, then you want your daily practice time to focus primarily on this chunk of facts. </span></div>
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<span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;">The third factor in making facts memorization time effective is that students need </span><span class="Apple-style-span" style="color: #3d85c6; font-family: 'Trebuchet MS', sans-serif;"><b>immediate feedback -- within a second or two</b></span><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"> -- each time they practice a fact. Choral responses provide immediate feedback, although they don't guarantee that every student is actually engaged in the rehearsal process. </span></div>
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<span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;">Another rehearsal strategy that provides immediate feedback is what many students like to call "tents" ... pairs practice tents. The idea with these tents is that two students can work together with the folded tent, one saying the number bond ("2 + 5 makes 7") while the other looks on the reverse side to verify the correct answer. That person can nod or say "yes" if the answer is correct, or say "try again" if the answer is incorrect. Teachers say that students really enjoy this form of practice, and it turns out that both students are learning at the same time! (Click here for <a href="http://www.mediafire.com/file/jthmdy4onf4/Pairs%20Practice%20-%20Goals%201%20to%209%20Add%20Subtract.pdf" target="_blank">addition/subtraction tents</a> and here for <a href="http://www.mediafire.com/file/mwy0mt3ghqk/MD%20Pairs%20Practice%20EM.pdf" target="_blank">multiplication/division tents</a>.)</span></div>
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<span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"> </span></div>Unknownnoreply@blogger.com1tag:blogger.com,1999:blog-2142460391482014324.post-73511676653034903332011-10-14T13:46:00.000-07:002011-10-19T15:33:26.192-07:00Recording and Posting Key Ideas<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://1.bp.blogspot.com/-kUVz-W39AJo/TpiTPZRV0QI/AAAAAAAAAUM/rP_fHxuRH2o/s1600/Goal+1.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="400" src="http://1.bp.blogspot.com/-kUVz-W39AJo/TpiTPZRV0QI/AAAAAAAAAUM/rP_fHxuRH2o/s400/Goal+1.JPG" width="300" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><b>Goal 1 - Ways to Make 5 with Part-Part-Whole Grids</b></span></td></tr>
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<span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif; font-size: large;">Recording and Posting Key Ideas</span></div>
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<span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;">As you and your students are sharing math ideas and strategies, it can be really helpful to create a permanent record of the key concepts, relationships, and strategies. With these records posted on your walls, your students can reference them as often as needed until they become permanent memories.</span></div>
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<span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><b><u>Addition/Subtraction Focus:</u></b></span></div>
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<span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;">As you're working on Goals 1 and 3 (Ways to make 4/5 and Ways to make 10), one concrete way to engage students is to have them stand in groups and move! </span><br />
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<span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span style="font-family: 'Helvetica Neue', Arial, Helvetica, sans-serif; font-size: x-small;">[If the video clip below is blocked by your district's web filter, </span></span><br />
<span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><span style="font-family: 'Helvetica Neue', Arial, Helvetica, sans-serif; font-size: x-small;">a more district-friendly version is available at </span><a href="http://www.mediafire.com/?f813ye3mz3wkd"><span style="font-family: 'Helvetica Neue', Arial, Helvetica, sans-serif; font-size: x-small;">TPR Ways to Make Five</span></a><span style="font-family: 'Helvetica Neue', Arial, Helvetica, sans-serif; font-size: x-small;">.]</span> </span><br />
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<span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;">This TPR activity can help students organize their thinking. When you make charts to record the facts, you and your students can talk about the patterns. </span></div>
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<a href="http://2.bp.blogspot.com/-hlFW40IsOSI/TpiXGG9UM6I/AAAAAAAAAUU/XsV2DJ1wNMI/s1600/Ways+to+Make+5+Chart.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="52" src="http://2.bp.blogspot.com/-hlFW40IsOSI/TpiXGG9UM6I/AAAAAAAAAUU/XsV2DJ1wNMI/s400/Ways+to+Make+5+Chart.jpg" width="400" /></a></div>
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<span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;">Once you have developed the chart with your students, you can incorporate it into your daily routine with a choral chant. You can hide the bottom row and have the students say together "5 equals 0 + 5, 5 equals 1 + 4, ...".</span></div>
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<span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;">You can also invite pairs of students to practice together in their spare time if you give them post-its to hide the bottom row.</span></div>
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<span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;"><b><u>Multiplication/Division Focus:</u></b></span></div>
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<span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;">Even though students may already know and believe the Commutative Property for addition, it's important to focus on this idea when you start working with multiplication. To make it really relevant to students, you can use word problems such as the ones below.</span></div>
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<span class="Apple-style-span" style="font-family: 'Trebuchet MS', sans-serif;">In this example, students can see that 4 groups of 10 (4 children each making 10 cards) generates the same product as 10 groups of 4 (10 children each making 4 cards). You can record this in multiplication factor-factor-product grids too.</span></div>
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<span class="Apple-style-span" style="font-family: Verdana, sans-serif; font-size: large;">... and a special thanks to the</span></div>
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<br /></div>Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-2142460391482014324.post-30646932859106406772011-09-30T20:59:00.001-07:002011-10-18T22:50:16.817-07:00Welcome and Introduction<a href="http://4.bp.blogspot.com/-71Um-c7N39I/ToaWlc5ancI/AAAAAAAAARk/-BpMUagPILs/s1600/Goal%2B1.jpg"><br /></a><br />
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<span class="Apple-style-span" style="color: #0b5394; font-family: "Trebuchet MS", sans-serif; font-size: x-large;">Welcome to a New FactsWise Resource!</span></div>
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<span class="Apple-style-span" style="font-family: "Trebuchet MS", sans-serif;">Welcome to our brand new FactsWise Blog -- designed to share strategies for building number sense and basic facts fluency for both addition/subtraction and multiplication/division!</span></div>
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<span class="Apple-style-span" style="font-family: "Trebuchet MS", sans-serif;">You'll have access to a variety of resources here, including:</span></div>
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<span class="Apple-style-span" style="font-family: "Trebuchet MS", sans-serif;"> 1) Weekly posts that will include images, video clips, games, and strategies to help you build a dynamic and engaging basic facts program</span></div>
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<span class="Apple-style-span" style="font-family: "Trebuchet MS", sans-serif;"> 2) Pages that you can reference at any time for every FactsWise goal that will give you immediate access to the concrete-representation-abstract whole-class activities, as well as games and practice activities for small group and individual use.</span></div>
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<span class="Apple-style-span" style="font-family: "Trebuchet MS", sans-serif;">I'm also looking forward to hearing from you -- what's working well, what you've developed to share with other teachers, and what challenges you'd like help with. </span><br />
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<span style="font-family: Trebuchet MS;">If you'd like to know whenever I write a new FactsWise post, you can enter your e-mail address at the bottom of this screen.</span> </div>
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<span class="Apple-style-span" style="font-family: "Trebuchet MS", sans-serif;">And finally, if you are looking for a FactsWise resource, I've posted the most current version of most <a href="http://www.mediafire.com/factswiseresources">FactsWise resources</a> online. When you get to this site, you should be able to download individual files or entire folders without charge -- you can just say no to any request to subscribe. <a href="http://draft.blogger.com/"></a></span></div>
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<span class="Apple-style-span" style="font-family: Verdana, sans-serif;"><b><span style="font-family: "Comic Sans MS"; font-size: 18pt; mso-bidi-font-size: 11.0pt;">Thanks for all that you do for students!</span></b></span></div>
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