Math Blog
http://www.nwaea.k12.ia.us/index.cfm?nodeid=19662&audienceID=1
en-usCopyright 2014 Northwest AEA All Rights Reserved.info@nwaea.org (Northwest AEA)support@globalreach.com (Global Reach Internet Productions)Sat, 19 Apr 2014 19:46:06 -0600Sat, 19 Apr 2014 19:46:06 -060060CP2 Classroom Practices (Mindset for the Math Classroom)
http://www.nwaea.k12.ia.us/index.cfm/19662-1/9711/cp2_classroom_practices_mindset_for_the_math_classroom
Fri, 21 Mar 2014 14:11:21 -0600Bloghttp://www.nwaea.k12.ia.us/index.cfm/19662-1/9711/cp2_classroom_practices_mindset_for_the_math_classroom<p>How many of you have read the book, <em>Mindset: The New Psychology of Success</em>, by Carol Dweck? If you have not, I would encourage you to take a look at it. Dweck explains that there are two distinct mindsets: fixed and growth.</p>
<p>According to Dweck, “in a fixed mindset, people believe their basic qualities, like their intelligence or talent, are simply fixed traits. They spend their time documenting their intelligence or talent instead of developing them. They also believe that talent alone creates success—without effort” (Dweck, 2010).</p>
<p>“In a growth mindset, people believe that their most basic abilities can be developed through dedication and hard work—brains and talent are just the starting point. This view creates a love of learning and a resilience that is essential for great accomplishment” (Dweck, 2010).</p>
<p>Carol Dweck and math education expert Jo Boaler, along with other researchers at Stanford University have developed the CP2 Classroom Practices program. This program is specifically designed to develop a growth mindset in your math students.</p>
<p>As we all know time is a precious commodity in the classroom, but if we can develop a growth mindset in our students we can unlock unlimited potential. The teacher program consists of five 20-minute sessions and can be done at a teachers’ convenience. The student program consists of one 45-minute session and one 15-minute session and should be completed on computers during school hours. Stanford is able to offer this program for <strong>free</strong> as part of a program evaluation. Some teachers and students who sign up will serve as a comparison group this year, but will gain full access to the program next year.</p>
<p align="left">A 45-minute survey is given at the beginning of the program, prior to any teacher PD, and assesses the students’ mindset. Once the survey is complete the teachers participate in online mini-trainings and implement the training received from the mini-trainings in the classroom. After the teacher has participated in all of the mini-trainings, the students will take a 15-minute follow-up survey. I spoke to some of the researchers on the phone and was able to preview some of the teacher trainings. The training videos are good and the activities that they encourage you to incorporate into the classroom are easy to manage and would be beneficial to any math classroom. </p>
<p align="left">An example of an activity that they would have you use in your classroom is:</p>
<p align="left"><em>Keep those mistakes - On the next assignment, ask students not to erase anything, but instead to put any mistakes they make in square brackets. Tell them that when you see their work, you want to see their whole process, including their mistakes along the way. For example, say “It's much more interesting to see that you've noticed a mistake and corrected it than to see a ‘perfect’ page with erase marks.”</em></p>
<p align="left">You can take a look at the CP2 Classroom Practices webpage by going to: <a href="http://www.perts.net/home/orientation/cp2.php">http://www.perts.net/home/orientation/cp2.php</a></p>
<p>If you are interested in participating in this program please let me know and I would be happy to help in any way that I can. The only issue is that the window to get started on the process closes on April 1st. I was also given some pamphlets for administrators if they are hesitant about the program, and I can share those with your principal if you would like. Participation does not require access to personal student information. </p>
<p>If you want further information about this please contact, Steve McHugh at smchugh@nwaea.org.</p>Northwest AEATeaching Mathematics Conceptually
http://www.nwaea.k12.ia.us/index.cfm/19662-1/9437/teaching_mathematics_conceptually
Thu, 20 Feb 2014 14:54:36 -0600Bloghttp://www.nwaea.k12.ia.us/index.cfm/19662-1/9437/teaching_mathematics_conceptually<p>"<a href="http://www.sedl.org/insights/1-4/">Teaching Mathematics Conceptually</a>" by Concepcion "Como" Molina, EdD was recently published in <em>SEDL Insights</em>. The article highlights four insights on teaching mathematics conceptually:</p>
<ol>
<li>Use instructional language with care</li>
<li>Emphasize concepts instead of algorithms and shortcuts</li>
<li>Avoid naked numbers</li>
<li>Help students make connections among concepts</li>
</ol>
<p>Each insight is explained in great detail with examples of "how" each insight can help teach mathematics conceptually. There are also several resources listed at the end of the article for further help.</p>Northwest AEAFormative Assessment Continued
http://www.nwaea.k12.ia.us/index.cfm/19662-1/9131/formative_assessment_continued
Fri, 10 Jan 2014 11:07:24 -0600Bloghttp://www.nwaea.k12.ia.us/index.cfm/19662-1/9131/formative_assessment_continued<p> Assessment for learning (formative assessment) “is any assessment for which the first priority in its design and practice is to serve the purpose of promoting pupils’ learning. It thus differs from assessment designed primarily to serve the purposes of accountability, or of ranking, or of certifying competence” (Hodgen & Wiliam, 2006).</p>
<div> </div>
<div>We will continue our look at formative assessment practices for the math classroom.</div>
<div>Provided below are some formative assessment practices that teachers can integrate into the classroom so teachers and students can gauge their progress towards the intended learning goals. </div>
<div> </div>
<div><b>These practices are only formative if the results inform both teachers and students of progress and lead to necessary adjustments to instruction.</b></div>
<div><b> </b></div>
<div><b> </b></div>
<div><a href="/documents/filelibrary/blogs/blogs/3_2_1_summarizer_with_template_0D5D708C7EE8C.doc">3 – 2 – 1 Summarizer</a></div>
<div> </div>
<div><a href="/documents/filelibrary/blogs/blogs/CCC_Collaborative_Clued_Corrections_8334C08DCB801.docx">Collaborative Clued Corrections (CCC)</a></div>
<div> </div>
<div>
<div><a href="/documents/filelibrary/blogs/blogs/Directed_Paraphrasing_6BBC6B77192CD.docx">Directed Paraphrasing</a></div>
</div>
<div> </div>
<div>
<div><a href="/documents/filelibrary/blogs/blogs/Guided_Reciprocal_Peer_Questioning__C00751EA388AC.docx">Guided Reciprocal Peer Questioning</a></div>
</div>
<div> </div>
<div>
<div><a href="/documents/filelibrary/blogs/blogs/I_ThinkWe_Think_Formative_Assessmen_847D1E9342DE3.docx">I Think – We Think</a></div>
</div>
<div> </div>
<div><a href="/documents/filelibrary/blogs/blogs/Parking_Lot_D3E886E09C518.docx">Parking Lot</a></div>
<div> </div>
<div><b> </b></div>
<div align="center" style="text-align:center"><b>Sources</b></div>
<div><b> </b></div>
<div>Hodgen, J., & Wiliam, D. (2006). <i>Mathematics inside the black box: Assessment for learning in the mathematics classroom.</i> London: NFER/Nelson.</div>
<div><b> </b></div>
<div>Keeley, P., & Tobey, C. R. (2011). <i>Mathematics formative assessment: 75 practical strategies for linking assessment, instruction, and learning</i>. Thousand Oaks, Calif: Corwin Press.</div>
<p> </p>Northwest AEAHelping Your Child Learn Mathematics
http://www.nwaea.k12.ia.us/index.cfm/19662-1/9022/helping_your_child_learn_mathematics
Fri, 20 Dec 2013 22:08:12 -0600Bloghttp://www.nwaea.k12.ia.us/index.cfm/19662-1/9022/helping_your_child_learn_mathematics<p><em>Helping Your Child Learn Mathematics</em> published by US Department of Education</p>
<p>We know from research that children are more likely to be successful learners of any subject when<br />
parents actively support their learning. Today, helping children to make the effort to learn, appreciate<br />
and master mathematics is more important than ever. Our increasingly technological world demands<br />
strong skills in mathematics, not only in the workforce but also in everyday life, and these demands<br />
will only increase over the lifetimes of our children. <br />
</p>
<p>To ensure that our children are ready for high school and on track for success in college and the<br />
workforce, parents must become involved early—and stay involved over the school years—to reinforce<br />
children’s skills in and positive attitudes toward mathematics. <br />
</p>
<p>Starting in elementary school, children should be learning beginning concepts in algebra, geometry,<br />
measurement, statistics and logic. In addition, they should be learning how to solve problems by<br />
applying knowledge of math to new situations. They should be learning to think of themselves as<br />
mathematicians—able to reason mathematically and to communicate mathematical ideas by talking <br />
and writing. <br />
</p>
<p>Through the No Child Left Behind Act of 2001, President George W. Bush has made clear his commitment<br />
to the goals of raising standards of achievement for all children and providing all children with highly<br />
qualified teachers and instruction that is based on scientific research. Helping Your Child Learn<br />
Mathematics is part of the president’s efforts to provide parents with the latest research and practical<br />
information that can help them both to support children’s learning at home and to understand what<br />
they should expect from their children’s schools.<br />
</p>
<p>This <a href="http://www2.ed.gov/parents/academic/help/math/math.pdf">booklet</a> includes a range of activities for families with children from preschool age through grade 5.<br />
These activities use materials found inside your home and also make learning experiences out of<br />
everyday routines, such as grocery shopping and doing laundry. The activities are designed for you to<br />
have fun with your child while developing and reinforcing mathematical skills. We hope you and your<br />
child will enjoy the activities suggested in this booklet and develop many more of your own. </p>
<p> </p>Northwest AEAMath Networking Day: Jan. 24
http://www.nwaea.k12.ia.us/index.cfm/19662-1/8970/math_networking_day_jan_24
Wed, 11 Dec 2013 13:09:46 -0600Bloghttp://www.nwaea.k12.ia.us/index.cfm/19662-1/8970/math_networking_day_jan_24<p>Please join your peers at a Math Networking Day to be held at Northwest AEA in Sioux City on Jan. 24 from 9 a.m. to 3 p.m. for grades 6-12. Please see the <a href="/documents/news/MathNetworking_4493203AECB2E.pdf">attached flyer </a>for more information.</p>Northwest AEAFormative Assessment
http://www.nwaea.k12.ia.us/index.cfm/19662-1/8795/formative_assessment
Tue, 19 Nov 2013 10:25:59 -0600Bloghttp://www.nwaea.k12.ia.us/index.cfm/19662-1/8795/formative_assessment<div>First, what is formative assessment?</div>
<div> </div>
<div>To answer this, let’s take a look at a few definitions…</div>
<div> </div>
<div style="margin-left:.5in">Formative assessment is the “formal and informal process teachers and students use to gather evidence for the purpose of improving learning” (Chappuis, Stiggins, Chappuis, & Arter, 2012, p. 6). </div>
<div> </div>
<div style="margin-left:.5in">Formative assessment is “frequent and onging assessment, completed en route to mastery; ongoing assessment could be considered as “checkpoints” on students’ progress and the foundation for feedback given – the most useful assessment teachers can provide for students and for their own teaching decisions” (Wormeli, 2006, p. 200).</div>
<div> </div>
<div style="margin-left:.5in">Formative assessment is “a process used by teachers and students during instruction that provides feedback to adjust ongoing teaching and learning to improve students’ achievement of intended instructional outcomes” (State Collaborative on Assessment and Student Standards, 2008, p. 3)</div>
<div style="margin-left:.5in"> </div>
<div style="margin-left:.5in">Formative assessment is “an assessment carried out during the instructional process for the purpose of improving teaching and learning…What makes formative assessment formative is that it is immediately used to make adjustments so as to form new learning (Shepard, 2008, p. 281).</div>
<div> </div>
<div>Assessment for learning (formative assessment) is identified by the Iowa Core as a characteristic of effective instruction and needs to be used by both teachers and students during instruction to monitor progress. An important point to stress is that formative assessment is not an add-on to instruction but rather an integrated part of the instructional process. Formative assessments are not instruments but rather practices that teachers and students must integrate into the classroom. </div>
<div> </div>
<div>So, the question is how do we integrate formative assessment into the classroom? Provided below are some formative assessment practices that teachers can integrate into the classroom so teachers and students can gauge their progress towards the intended learning goals. These practices are only formative if the results inform both teachers and students of progress and lead to necessary adjustments to instruction.</div>
<div> </div>
<div> </div>
<div><a href="/documents/filelibrary/blogs/blogs/Commit_and_Toss_Formative_Assessmen_9A7C1B1187AD0.docx">Commit and Toss Formative Assessment</a></div>
<div> </div>
<div><a href="/documents/filelibrary/blogs/blogs/First_Word_Formative_Assessment_A71D694F332DB.docx">First Word-Last Word Formative Assessment</a></div>
<div> </div>
<div><a href="/documents/filelibrary/blogs/blogs/Fishbowl_Think_Aloud_Formative_Asse_A24EB0A6B61E4.docx">Fishbowl Think Aloud Formative Assessment</a></div>
<div> </div>
<div><a href="/documents/filelibrary/blogs/blogs/One_Minute_Paper_Formative_Assessme_89885F0FCFBC1.docx">One Minute Paper Formative Assessment</a></div>
<div> </div>
<div><a href="/documents/filelibrary/blogs/blogs/RSQC2_Formative_Assessment_C89FE962F87E0.doc">RSQC^2 Formative Assessment</a></div>
<div> </div>
<div><a href="/documents/filelibrary/blogs/blogs/SOS_Summary_Formative_Assessment_DB4CD433F451A.pdf">SOS Summary Formative Assessment</a></div>
<div> </div>
<div><a href="/documents/filelibrary/blogs/blogs/Strategy_Harvest_Formative_Assessme_D51F7BEBC7CBF.docx">Strategy Harvest Formative Assessment</a></div>
<div> </div>
<div> </div>
<div> </div>
<div style="text-align: center;">Sources</div>
<div> </div>
<div>Chappuis, J., Stiggins, R., Chappuis, S., & Arter, J. (2011). <i>Classroom assessment for student learning</i>. Boston: Pearson.</div>
<div> </div>
<div>
<div><span style="background-color: white;">Keeley, P., & Tobey, C. R. (2011). </span><i>Mathematics formative assessment: 75 practical strategies for linking assessment, instruction, </i><i>and learning</i><span style="background-color: white;">. Thousand Oaks, Calif: Corwin Press.</span></div>
</div>
<div> </div>
<div>Shepard, L.A. (2008). Formative assessment: Caveat emptor. In C. Dwyer (ed.), <em>The future of assessment: Shaping teaching and </em><em>learning</em> (pp. 279-303). New York: Lawrence Erlbaum Associates.</div>
<div> </div>
<div>State Collaborative on Assessment and Student Standards. (2008). Attributes of effective formative assessment. Washington, DC: Council of Chief State School Officers.</div>
<div> </div>
<div>Wormeli, R. (2006). <i>Fair isn't always equal assessing & grading in the differentiated classroom</i>. Portland, ME: Stenhouse Publishing.</div>
<div> </div>
<p> </p>
<div> </div>
<p> </p>Northwest AEASumDog Math Contest
http://www.nwaea.k12.ia.us/index.cfm/19662-1/8576/sumdog_math_contest
Mon, 21 Oct 2013 10:12:55 -0600Bloghttp://www.nwaea.k12.ia.us/index.cfm/19662-1/8576/sumdog_math_contest<h2><u><span style="color: rgb(0, 204, 255);"><strong>SUMDOG MATH COMPETITION</strong></span></u></h2>
<p> </p>
<p align="center" style="text-align:center" class="MsoBodyText">An exciting math contest is taking place for all schools in Northwest Iowa. It's free to take part and all students will get a fun participation reward!</p>
<p align="center" style="text-align:center" class="MsoBodyText">Students compete by playing <span class="il">Sumdog</span>'s free online <span class="il">math</span> games starting at <span data-term="goog_1415167907" class="aBn" tabindex="0"><span class="aQJ">8am on Friday November 8th until </span></span><span data-term="goog_1415167907" class="aBn" tabindex="0"><span class="aQJ">8pm November 15th</span></span>! - it will only take an hour so to get a competitive score.</p>
<p align="center" style="text-align:center" class="MsoBodyText">The games adapt to each student's level, giving everyone a fair chance of winning. </p>
<p align="center" style="text-align:center" class="MsoBodyText">Students will have fun practicing their math and there are prizes to be won!<span style="font-size:40.0pt;"><br />
</span></p>
<p align="center" style="margin-top:6.0pt;text-align:center;text-autospace:none"><span style="font-size:40.0pt;">Sign up now!</span></p>
<p align="center" style="text-align:center"><br />
In order to join in the fun, visit: <a target="_blank" href="http://www.sumdog.com/en/Contest_invitation/?hc">http://www.<span class="il">sumdog</span>.com/en/Conte<wbr></wbr>st_invitation/?hc</a></p>
<p align="center" style="text-align:center"><br />
If you have any questions or need help getting set up, you can email <a target="_blank" href="mailto:jeremy@sumdog.com">jeremy@<span class="il">sumdog</span>.com</a> or call <a target="_blank" value="+18779786364" href="tel:1-877-978-6364">1-877-978-6364</a>.</p>Northwest AEAIowa Core Alignment
http://www.nwaea.k12.ia.us/index.cfm/19662-1/8347/iowa_core_alignment
Thu, 19 Sep 2013 15:24:38 -0600Bloghttp://www.nwaea.k12.ia.us/index.cfm/19662-1/8347/iowa_core_alignment<p>Aligning to the Iowa Core is an arduous task and most districts are tackling this issue as we speak. In order to align your curriculum to the Iowa Core teachers must first grapple with the language of the Iowa Core and derive the true meaning and intent of the standard; teachers must “unpack” the standards. The Iowa Department of Education is adamant that the Iowa Core is a state-led effort but with local control. The local control component to the Iowa Core is the standard “unpacking” – Iowa is unique in the respect that the state department of education did not provide an “unpacked” curriculum to its districts. The autonomy that Iowa has granted its districts creates some challenges because it is difficult to “unpack” the standards in the Iowa Core. There are many resources out there and some are better then others so it is important to consult multiple resources when you begin to “unpack” the standards. <br />
<br />
Provided below are some resources to consult when you begin to “unpack” the Iowa Core Math standards. This list is only a small sampling of the resources available and you may find others that provide you with more information than these. Even though we adopted the Iowa Core it is important to keep in mind that the Iowa Core includes is a combination of all of the Common Core State Standards (CCSS) for math and 10 additional Iowa specific math standards (2 in 2nd grade and 8 in high school). When you are searching for resources do not just limit your search to Iowa Core math but rather expand your search to include Common Core State Standards math. <br />
<br />
<strong>Progressions Documents for the Common Core Math Standards</strong><br />
<a href="http://ime.math.arizona.edu/progressions/">http://ime.math.arizona.edu/progressions/</a><br />
<br />
These documents can explain why standards are sequenced the way they are, point out cognitive difficulties and pedagogical solutions, and give more detail on particularly knotty areas of the mathematics.<br />
<br />
<br />
<strong>Common Core Flip Books</strong><br />
<a href="http://www.ksde.org/Default.aspx?tabid=5646">http://www.ksde.org/Default.aspx?tabid=5646</a><br />
<br />
These resources were developed by the Kansas Association of Teachers of Mathematics (KATM) and make links between the mathematical practices and the content of the Kansas Common Core Standards. They include instructional strategies and examples for each standard at each grade level. They may also be found on the KATM website (www.katm.org) under their "Common Core Resources" page.<br />
<br />
<br />
<strong>Oregon Department of Education – CCSS Toolkit</strong><br />
<a href="http://www.ode.state.or.us/search/page/?id=3511">http://www.ode.state.or.us/search/page/?id=3511</a><br />
<br />
The documents on this page were developed by other CCSS states to assist their teachers in more deeply understanding the standards. These grade-level documents "deconstruct" the standards, one standard at a time, providing explanations and examples. <br />
<br />
<br />
<strong>Public Schools of North Carolina – CCSS Mathematics Wiki</strong><br />
<a href="http://maccss.ncdpi.wikispaces.net/home">http://maccss.ncdpi.wikispaces.net/home<br />
</a><br />
This side provides links to various mathematics resources for teachers, administrators, teacher educators and others who are interested in the mathematics education.<br />
<br />
<br />
<strong>Illustrative Mathematics</strong><br />
<a href="http://www.illustrativemathematics.org/">http://www.illustrativemathematics.org/</a><br />
<br />
Illustrative Mathematics provides guidance to states, assessment consortia, testing companies, and curriculum developers by illustrating the range and types of mathematical work that students experience in a faithful implementation of the Common Core State Standards, and by publishing other tools that support implementation of the standards.<br />
<br />
<br />
<strong>Inside Mathematics</strong><br />
<a href="http://insidemathematics.org/">http://insidemathematics.org/</a><br />
<br />
Inside Mathematics opens those doors:<br />
• to tested demonstration lessons presented to children and groups of observing teachers;<br />
• to guided tours of reflective mathematics practice, identifying what makes teaching, learning, and improving instruction in mathematics a difficult enterprise and providing resources for teachers to improve their practice;<br />
• to mathematics teaching and learning tools and resources to support classroom teachers', math coaches', and administrators' daily practices;<br />
• and to a professional learning community in which you are invited to open your own classroom door and engage in conversation about your own mathematics teaching and learning.<br />
<br />
<strong>Mathematics Assessment Project</strong><br />
<a href="http://map.mathshell.org.uk/materials/index.php">http://map.mathshell.org.uk/materials/index.php</a><br />
<br />
The Mathematics Assessment Program (MAP) aims to bring to life the Common Core State Standards (CCSSM) in a way that will help teachers and their students turn their aspirations for achieving them into classroom realities. MAP is a collaboration between the University of California, Berkeley and the Shell Center team at the University of Nottingham, with support from the Bill & Melinda Gates Foundation. <br />
<br />
<br />
<strong>Learn Zillion</strong><br />
<a href="http://learnzillion.com/">http://learnzillion.com/</a><br />
<br />
LearnZillion is a learning platform that combines video lessons, assessments, and progress reporting. Each lesson highlights a Common Core standard, starting with math in grades 3-9. Teachers can gain access to the site by registering (free) and then examine the videos, this provides another example of how a particular standards is being interpreted.</p>Northwest AEAPhase 2 of the Smarter Balanced Practice Test
http://www.nwaea.k12.ia.us/index.cfm/19662-1/8214/phase_2_of_the_smarter_balanced_practice_test
Fri, 30 Aug 2013 11:31:54 -0600Bloghttp://www.nwaea.k12.ia.us/index.cfm/19662-1/8214/phase_2_of_the_smarter_balanced_practice_test<p><span style="font-size:10.0pt;Arial","sans-serif"">Phase 2 of the Smarter Balanced Practice Test was successfully implemented this weekend and can be found at <a target="_blank" href="http://sbac.portal.airast.org/practice-test/">http://sbac.portal.airast.<wbr></wbr>org/practice-test/</a>. <span style="background:white">Phase 2 updates include expanded accommodations to cover all grades and the addition of Mathematics performance tasks and associated scoring rubrics. </span></span></p>
<p> </p>
<p><span style="font-size:10.0pt;Arial","sans-serif"">Please feel free to review the items and use them for professional learning. They provide much needed insight on assessing the intent and rigor of the Common Core portion of the Iowa Core. In particular, the accommodations included in this version are very interesting.</span></p>
<p> </p>
<p><span style="font-size:10.0pt;Arial","sans-serif"">For questions on the Practice Test, you can contact the Help Desk toll-free at <a target="_blank" value="+18558331969" href="tel:1-855-833-1969">1-855-833-1969</a> or email us at <a target="_blank" href="mailto:smarterbalancedhelpdesk@ets.org">smarterbalancedhelpdesk@ets.<wbr></wbr>org</a> . <br />
</span></p>
<p> </p>Northwest AEACount Around the Circle
http://www.nwaea.k12.ia.us/index.cfm/19662-1/7257/count_around_the_circle
Mon, 22 Apr 2013 13:11:11 -0600Bloghttp://www.nwaea.k12.ia.us/index.cfm/19662-1/7257/count_around_the_circle<p> </p>
<p><b>Count Around the Circle</b></p>
<p> </p>
<p>Count Around the Circle is a number sense routine that is easy to implement. Jessica F. Shumway described how to establish the Count Around the Circle in her book <i>Number Sense Routines: Numerical Numeracy Every Day in Grades K-3</i>. </p>
<p> </p>
<p>Students/Teacher stand in a circle and the teacher designates what will be counted by. At the beginning and in lower grades you can count by ones, fives, twos, threes, etc., starting at zero. Then move to starting at various points other than zero. Counting backwards, fractions, whole numbers, decimal numbers, mixed numbers, hundreds, and thousands are other ways to count as it progresses into older grades. </p>
<p> </p>
<p>The fun part for the teacher is incorporating some estimation into the counting. Ask students questions like, “<i>If we start counting by ones and go all the way around the circle, what number to you think we will say last?” </i>(Do students make a connection with the number of people in the class?) or, Count by tens around the circle once, then ask, <i>“If we go around again, what number will be said last?”</i></p>
<p> </p>
<p>Teachers can also look at patterns. In this video from the Teaching Channel, <a href="https://www.teachingchannel.org/videos/teaching-number-patterns?fd=1">https://www.teachingchannel.org/videos/teaching-number-patterns?fd=1</a> this 3<sup>rd</sup> grade teacher records the counting sequence (instead of counting in a circle) and the students look for patterns using number sense.</p>
<p> </p>
<p>This is one of many number sense routines Jessica F. Shumway discusses in her book. There are also many great examples of lessons teaching the Iowa Core on the teaching channel. I encourage all teachers to check them out.</p>
<p> </p>Northwest AEA