tag:blogger.com,1999:blog-71942782067859232302024-03-05T16:18:18.781-08:00Second Grade Math at ParkerJennifer Gresenshttp://www.blogger.com/profile/09599007252984475124noreply@blogger.comBlogger11125tag:blogger.com,1999:blog-7194278206785923230.post-85408967416943448482014-05-09T02:37:00.000-07:002014-05-09T02:37:37.483-07:00Teacher for a day! As a teacher, I am always looking for ways to create opportunities for my students to showcase their abilities as well as demonstrate their knowledge. Designing projects and activities that develop higher-level thinking around a chosen topic is just one way to achieve this. Ideally, it's the students who create these projects and activities themselves. Just recently, the second grade math students were lucky enough to have the opportunity to learn something new and fascinating - yet this time, it was from one of their peers.<br />
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A student approached me with an interest in Fibonacci numbers. She was clearly interested in the concept and was eager to share this new information with her classmates. We discussed the material and after assessing she had a firm grasp of the information, I suggested that the following day she teach a lesson to the class explaining Fibonacci numbers. We talked about a structure for her lesson and what she would need to do to prepare. It was clear she was excited, and I knew this would be a valuable learning opportunity for all. After all, in order to teach something effectively, one must have a firm understanding of the material, and feel comfortable explaining it to others. What better way to extend one's knowledge than by having the opportunity to teach? <br />
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The next day the student arrived eager and ready. She wrote out the classroom morning message, outlining what would happen in math that day. She had even prepared hand-outs for the class as an extension to her lesson. As she began her lesson, her classmates listened attentively, asking questions and offering comments when appropriate. When it was time for them to complete the classwork, she circulated around the room, offering help and encouragement to her peers. I was amazed at the depth of knowledge that was gained from this experience. Beyond the mastery of the mathematical material, this type of activity can instill confidence and a level of engagement that comes with pursuing a genuine interest. The other students clearly benefited as well - watching a peer stand up in front of the class and direct a lesson was fascinating, engaging, and inspiring. After the lesson, we discussed the experience and I encouraged everyone to find an exciting mathematical concept or area of interest to present to the class. There were lots of ideas generated, and I'm hopeful that others will be inspired to follow suit. <br />
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<tr><td class="tr-caption" style="text-align: center;">morning message</td></tr>
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<tr><td class="tr-caption" style="text-align: center;">Fibonacci numbers are circled </td></tr>
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<tr><td class="tr-caption" style="text-align: center;">the prepared hand-out </td></tr>
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<tr><td class="tr-caption" style="text-align: center;">helping friends </td></tr>
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<tr><td class="tr-caption" style="text-align: center;">the proud teacher </td></tr>
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<tr><td class="tr-caption" style="text-align: center;">fully engaged students </td></tr>
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<tr><td class="tr-caption" style="text-align: center;">working together </td></tr>
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<tr><td class="tr-caption" style="text-align: center;">completed work, corrected by the teacher! </td></tr>
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While it’s unlikely that you have ever heard a person say, “that worksheet changed my life,” most people have an assignment from their childhood that they remember with pride because it was meaningful to them. More often than not, that memorable assignment was one that allowed them to express themselves and follow their passions. It's been a joy to watch the second graders find these passions and pursue them. Other passion projects in the works: a math newspaper, origami tutorial, game making 101, prime numbers, and multiplication charts! Jennifer Gresenshttp://www.blogger.com/profile/09599007252984475124noreply@blogger.com1tag:blogger.com,1999:blog-7194278206785923230.post-68334799419290053482014-04-28T18:52:00.000-07:002014-04-28T18:52:39.526-07:00<br /><br />The second graders approached our recent unit on fractions with their usual enthusiasm and curiosity. We explored the concepts of one whole, one half, one fourth, one third, as well as more complex fractions such as one eighth, two thirds, and three fourths. This was a unit where real life examples were useful and provided context for the students to think about these ideas. Half of a cookie, one quarter of a pizza, one third of an apple - these were all opportunities for the students to visualize what these fractions would look like in real life.<br /><br />After much exploration, the students made their own fraction books, an activity that provided additional practice and an opportunity to further display their understanding of the concepts. Each book was unique and detailed - some students wrote and illustrated stories exploring the concepts, others drew complex pictures of various fractions, and some even posed questions and answers to their readers. Creating these books allowed students to move beyond simply accessing this new information. Possession of facts cannot be the bulk of learning. What <i><b>is </b></i>an important skill is the ability to sift through abundant information, identify what is valid and meaningful, then use it to create meaning and express it. Writing and illustrating a book related to our topic, and presenting it to their peers, illustrated that deeper learning had occurred. This was another example of the importance of student creation.<br /><br /><span style="background-color: white; color: #1f1f1f; font-family: Arial; font-size: 15px; vertical-align: baseline; white-space: pre-wrap;"> </span><br />
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<tr><td class="tr-caption" style="text-align: center;">A student's book </td></tr>
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<tr><td class="tr-caption" style="text-align: center;">Hard at work!</td></tr>
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<tr><td class="tr-caption" style="text-align: center;">Making books </td></tr>
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<br /><br />The second graders have also been extremely interested and motivated to create their own math games to play with friends. Guidelines have been established to allow for personal creativity, yet still extend and broaden students' knowledge of the particular unit we may be studying (first fractions, now more complicated addition). Far beyond filling out answers on a worksheet, these assignments allow for individual talents and personality to shine through and provide students an additional way to illustrate their understanding of mathematical ideas. <br /><br />Math draws much of its meaning by relating to life in the world outside the classroom. Children seek to understand the world by inquiry and investigation. Giving students ample opportunities to develop sound investigative skills at an early age is essential to nurturing their ability to think critically and mathematically as they get older. Activities such as creating books, playing and developing math games, and other hands-on activities provides a wonderful and critical opportunity for learning. <div class="separator" style="clear: both; text-align: center;">
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<tr><td class="tr-caption" style="text-align: center;">More books! </td></tr>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjal0hUYUlRVNHTi6mkQxphG5H6uwvm6WgCq9sClYKp8L2iwGwMfQMEpci-BxiyRaiLNT8f1Jv4-6FDpnBrzxwnU0NC8IqhXKtWOXxC1z8FOrAy-mHkfB4vng6wrutJQWACFfLL0QNC1pE/s1600/IMG_6871.JPG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjal0hUYUlRVNHTi6mkQxphG5H6uwvm6WgCq9sClYKp8L2iwGwMfQMEpci-BxiyRaiLNT8f1Jv4-6FDpnBrzxwnU0NC8IqhXKtWOXxC1z8FOrAy-mHkfB4vng6wrutJQWACFfLL0QNC1pE/s1600/IMG_6871.JPG" height="320" width="240" /></a><br />
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<tr><td class="tr-caption" style="text-align: center;">Math can even provide inspiration for creating new words! </td></tr>
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<tr><td class="tr-caption" style="text-align: center;">Students create their own math game </td></tr>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgiD0D_Jbk1ywucSdhijgm77tIDpvbtbc2q2kZqcvWRzk-Sro1UGwxZSMBDQWoV_NhyphenhyphenmP6WaK_6YCtLrPNzXBWV7EZ8CuYbadAYyqKYn9fZTUfBJ8V9J7XGe8LDm-I4iaGGinlXDvFO8JA/s1600/IMG_6896.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgiD0D_Jbk1ywucSdhijgm77tIDpvbtbc2q2kZqcvWRzk-Sro1UGwxZSMBDQWoV_NhyphenhyphenmP6WaK_6YCtLrPNzXBWV7EZ8CuYbadAYyqKYn9fZTUfBJ8V9J7XGe8LDm-I4iaGGinlXDvFO8JA/s1600/IMG_6896.JPG" height="240" width="320" /></a> </div>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjRgHDGM4nVAnIp5_a5LgnAO4AV_fEzfKOSrsJ_jkXLRFL0hZ1OG8CUB98Fpol05xYJlm5vEE2UmnQ1L8ZwA5kMX5P9_ZPHvUeUFOiNq0UPK_2GBexGutsF8_VTtxdyqFMpXUwlBohDepo/s1600/IMG_6997.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjRgHDGM4nVAnIp5_a5LgnAO4AV_fEzfKOSrsJ_jkXLRFL0hZ1OG8CUB98Fpol05xYJlm5vEE2UmnQ1L8ZwA5kMX5P9_ZPHvUeUFOiNq0UPK_2GBexGutsF8_VTtxdyqFMpXUwlBohDepo/s1600/IMG_6997.JPG" height="240" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">More addition games </td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjBhxiVQuEHRZlN6s75PHB3a7eHWOFB3wCSMOUXYVPKM5Kbmton6n641Jd-4NTBt3eK_MnmhrtKxbB16Zn7hPk4xQowdT-8hnKL9N2kCWFrHhNtIONBi_JjbzsET85H6tMBG49CBXC0pS8/s1600/IMG_6999.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjBhxiVQuEHRZlN6s75PHB3a7eHWOFB3wCSMOUXYVPKM5Kbmton6n641Jd-4NTBt3eK_MnmhrtKxbB16Zn7hPk4xQowdT-8hnKL9N2kCWFrHhNtIONBi_JjbzsET85H6tMBG49CBXC0pS8/s1600/IMG_6999.JPG" height="240" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Quizzing one another on math facts </td></tr>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjFcOeA4ltczb2TGsPBsqH0YM78h103j3GgGdAvnqPOKuBiKuTvzcP_NT0VWB2XRHpCTAU5pewMOYxQudCAwN-NClv_sW4-b4Lctklv2y2r7jFCJ4cUruS4t6AxW296eiczXIv0lFI9iAU/s1600/IMG_7002.JPG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjFcOeA4ltczb2TGsPBsqH0YM78h103j3GgGdAvnqPOKuBiKuTvzcP_NT0VWB2XRHpCTAU5pewMOYxQudCAwN-NClv_sW4-b4Lctklv2y2r7jFCJ4cUruS4t6AxW296eiczXIv0lFI9iAU/s1600/IMG_7002.JPG" height="240" width="320" /></a></div>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhywzfhHnPQ43vkQpsMJ4ZLrBUeIYAOtHSIUDK_9ZLoOtRBt7R2BQ5pnPk059EcV6XOHCm_pHfQjN-e7CZlyLuxJh20tOuqU4q07KXIsFADc5szYuRObOurH2rEpa0y7r3jrqJX94jI04c/s1600/IMG_6998.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhywzfhHnPQ43vkQpsMJ4ZLrBUeIYAOtHSIUDK_9ZLoOtRBt7R2BQ5pnPk059EcV6XOHCm_pHfQjN-e7CZlyLuxJh20tOuqU4q07KXIsFADc5szYuRObOurH2rEpa0y7r3jrqJX94jI04c/s1600/IMG_6998.JPG" height="240" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Practice makes perfect! </td></tr>
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<span id="goog_404536349"></span>Jennifer Gresenshttp://www.blogger.com/profile/09599007252984475124noreply@blogger.com0tag:blogger.com,1999:blog-7194278206785923230.post-79629681338272004432014-03-20T17:48:00.000-07:002014-03-20T17:52:03.834-07:00Games, graphs, and origami Amazing things happen when children are given the freedom to explore, notice, and create things of their own choosing. The unit we just finished, "How Many Tens? How Many Ones?" allowed students to explore our base ten number system, specifically in relation to 100. This meant addition and subtraction up to 100, counting by 2's, 5's, and 10's, skip counting, and the exploration of early multiplication and division concepts. Students all worked on mastering these ideas, but something equally important developed as well - passion to pursue one's own mathematical interests. <br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiKAurwLt8F6YHLd-WEl_sJFBiOd_e1LU_lQhCVLtXUHa65mq8KekO_83QYt8IWXEwOQBMrSjvlCoqhDuomoVe8ls_zxmm8jDNRSMmOgvSefL-MD74JULfwll8YF11mm3IJv8OlOvWy9do/s1600/IMG_6724.JPG" imageanchor="1" style="clear: left; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiKAurwLt8F6YHLd-WEl_sJFBiOd_e1LU_lQhCVLtXUHa65mq8KekO_83QYt8IWXEwOQBMrSjvlCoqhDuomoVe8ls_zxmm8jDNRSMmOgvSefL-MD74JULfwll8YF11mm3IJv8OlOvWy9do/s1600/IMG_6724.JPG" height="240" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Making origami </td></tr>
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It all started with curiosity about multiplication. Students began to notice certain patterns in the numbers and answers they were getting to problems. This led to further exploration, and for some, a personal journey into new material. One student began work on a prime number chart. Making a chart of all the prime numbers, testing and retesting findings, led this student to amazing discoveries along the way. A few students became passionate about origami - folding paper to make intricate and elaborate 2 and 3-dimensional structures. We counted the number of shapes and angles, and students were able to view their objects in a new, mathematical way. Students also worked together to make a math game, adding and subtracting, and solving math problems as they moved along their game board. Some students took favorite subject matter and decided to make thoughtful and detailed graphs.<br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjSetW7OAwctPrVz8bKjCP-8my6ZzH7rZ5g43LA7Efyt-u5Kr11JklJ1gsHJ_50i74Mu3fWF7qkG8Idtr4zRHxbMAAk9XMq5Xs9Rk3lhoMQChIy62niip7PSysXNoZpWBn4Bk7rSfktYkg/s1600/IMG_6719.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjSetW7OAwctPrVz8bKjCP-8my6ZzH7rZ5g43LA7Efyt-u5Kr11JklJ1gsHJ_50i74Mu3fWF7qkG8Idtr4zRHxbMAAk9XMq5Xs9Rk3lhoMQChIy62niip7PSysXNoZpWBn4Bk7rSfktYkg/s1600/IMG_6719.JPG" height="320" width="240" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Exploring multiplication </td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhVGLILiGV9tCsnkhA6XWGkC55eeDWnrBpVWm0nh3ZqrvlgEuqXaIeZa7MIFd2HrBsqqf_xbs_ez8EaCoZgKgQU347Gy8CxHOpNPXM0VWS609XptQ25JSVF9axOFExlljmrHQLBMDYbq9w/s1600/IMG_6723.JPG" imageanchor="1" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhVGLILiGV9tCsnkhA6XWGkC55eeDWnrBpVWm0nh3ZqrvlgEuqXaIeZa7MIFd2HrBsqqf_xbs_ez8EaCoZgKgQU347Gy8CxHOpNPXM0VWS609XptQ25JSVF9axOFExlljmrHQLBMDYbq9w/s1600/IMG_6723.JPG" height="240" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Brainstorming ideas for a graph</td></tr>
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This chance for free exploration of math concepts is critical for children to embrace math and enjoy the experience. Giving children a voice in the activities they wish to participate in allows them to make discoveries on their own. They notice patterns, make connections, and gain a deeper level of understanding when they have invested in their own area of interest and have opportunity to freely explore ideas. <br />
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<a href="http://www.theatlantic.com/education/archive/2014/03/5-year-olds-can-learn-calculus/284124/">This</a> is a wonderful article about this very idea. Looking at these photos, and spending time with these inquisitive and highly motivated children during math, clearly illustrates the benefit for free play, games, cooperation with peers, and choice. Math connections can be made everywhere, children just need the freedom to explore and find inspiration from a rich and social mathematical environment.<br />
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<tr><td class="tr-caption" style="text-align: center;">Double checking work </td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEicFSWPSTNAtmwDSm7RMud2cGw2RzadEG3XVPkLUCL3MynPdBUkpGMjj5CC0FSuEqBBr8GP5Ic-_3zt4cf2K9pv7Oxc_Mpnq4xU7x8ordzKWZgxKSAuMWeN8NAwmn4qLU1azb7GCpcVBaI/s1600/IMG_6417.JPG" imageanchor="1" style="clear: left; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEicFSWPSTNAtmwDSm7RMud2cGw2RzadEG3XVPkLUCL3MynPdBUkpGMjj5CC0FSuEqBBr8GP5Ic-_3zt4cf2K9pv7Oxc_Mpnq4xU7x8ordzKWZgxKSAuMWeN8NAwmn4qLU1azb7GCpcVBaI/s1600/IMG_6417.JPG" height="240" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Games! </td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhZviEq6c3xNJ6s5aztj_Rpm17VSDx6DMyuu_p-P3RqQOMBecpKYdXeJtw0OI8dr1xn46WE0RS6L0oSqpBy0uxtd-i6o686dn5hZftATtslCzSG5SJU96wTL3NP87kdV8GCNm3NRlwc4ME/s1600/IMG_6730.JPG" imageanchor="1" style="clear: left; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhZviEq6c3xNJ6s5aztj_Rpm17VSDx6DMyuu_p-P3RqQOMBecpKYdXeJtw0OI8dr1xn46WE0RS6L0oSqpBy0uxtd-i6o686dn5hZftATtslCzSG5SJU96wTL3NP87kdV8GCNm3NRlwc4ME/s1600/IMG_6730.JPG" height="320" width="240" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Counting coins</td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhscA67Ct2dP88mhbGv8GcVeF6Z2t1Gp5XP-MCiWWpFVe1tApgOHXDqFBijrpOV-1nfJk11HjMuuGhkqO4O_tPqNEuVsZ2bJCZaZm-C-pJAIgObaCJbALRldudG95fMgrUku9DBIA69Dmg/s1600/IMG_6814.JPG" imageanchor="1" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhscA67Ct2dP88mhbGv8GcVeF6Z2t1Gp5XP-MCiWWpFVe1tApgOHXDqFBijrpOV-1nfJk11HjMuuGhkqO4O_tPqNEuVsZ2bJCZaZm-C-pJAIgObaCJbALRldudG95fMgrUku9DBIA69Dmg/s1600/IMG_6814.JPG" height="320" width="240" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Playing a newly created game</td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEigGQtT8-fLA2rowEQUeLWaVv9piq2m6yt67J4PR-jLll_C3du5XMdwywfvxt6YG3DOIFKnnj27L9jkmxMrX3eWpTP0VZRAhzhxNFNuTQWnft-2P804RtEPUNWUQogkstrkTIE_Wmnk4Ko/s1600/IMG_6817.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEigGQtT8-fLA2rowEQUeLWaVv9piq2m6yt67J4PR-jLll_C3du5XMdwywfvxt6YG3DOIFKnnj27L9jkmxMrX3eWpTP0VZRAhzhxNFNuTQWnft-2P804RtEPUNWUQogkstrkTIE_Wmnk4Ko/s1600/IMG_6817.JPG" height="240" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">The graph takes shape</td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhzwtI2Ds42Fpqv9LbZacpknkmc1mHgivrnQaWn3a4ErFL4WkhfdWlpp7rAAXO7W4IFbBP5R1TWwWom8cX522AU0XgA4PPWnwcN4ofOM5w381nILisU29qH2oo0ib6U2Ei1gehJ8pO30AI/s1600/IMG_6427.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhzwtI2Ds42Fpqv9LbZacpknkmc1mHgivrnQaWn3a4ErFL4WkhfdWlpp7rAAXO7W4IFbBP5R1TWwWom8cX522AU0XgA4PPWnwcN4ofOM5w381nILisU29qH2oo0ib6U2Ei1gehJ8pO30AI/s1600/IMG_6427.JPG" height="320" width="240" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Exploring the concept of 100 </td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEio6us_HgWGPTVtm_ygFTkjhVA1x4jiY59I4kubWoGopCcMviiDd5pdDLLqBISspUs-9V6-ahevid0rIuR4vHfVhiMc5dJAWDgeYtn9JkkJHyi8cS4YcECn01_ucegUZ9pKQMmYxC1Gfpg/s1600/IMG_6729.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEio6us_HgWGPTVtm_ygFTkjhVA1x4jiY59I4kubWoGopCcMviiDd5pdDLLqBISspUs-9V6-ahevid0rIuR4vHfVhiMc5dJAWDgeYtn9JkkJHyi8cS4YcECn01_ucegUZ9pKQMmYxC1Gfpg/s1600/IMG_6729.JPG" height="320" width="240" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">We brainstormed a list of ideas </td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgsEp56wau1Uh_K8mCfaEVW4tMUDB3cPDkByyhMTa90D-UVDWGCviSI-TKsQSY-EmyHUFitLHMb0Sldop3esn6nREWrT2m4vztjuyjxjVdazOGp5SOFOPmrirxY74jpPlGwpXIsRqfFwRs/s1600/IMG_6419.JPG" imageanchor="1" style="clear: left; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgsEp56wau1Uh_K8mCfaEVW4tMUDB3cPDkByyhMTa90D-UVDWGCviSI-TKsQSY-EmyHUFitLHMb0Sldop3esn6nREWrT2m4vztjuyjxjVdazOGp5SOFOPmrirxY74jpPlGwpXIsRqfFwRs/s1600/IMG_6419.JPG" height="240" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">How many more cubes do we need to get to 100?</td></tr>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEindrS1YpQmx7oYNrN3ijgCXJlupcO7cZUwN4HPGsmoY7NNFrVgRNhVRUZwfzeneHpHpuUgbM6Go24s-x6O7ikOPAIvw43qi49Tbd0ubDsi6o_PFavS-Xx8A7B-8K61S6ny95XhUxWQxfI/s1600/IMG_6418.JPG" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEindrS1YpQmx7oYNrN3ijgCXJlupcO7cZUwN4HPGsmoY7NNFrVgRNhVRUZwfzeneHpHpuUgbM6Go24s-x6O7ikOPAIvw43qi49Tbd0ubDsi6o_PFavS-Xx8A7B-8K61S6ny95XhUxWQxfI/s1600/IMG_6418.JPG" height="400" width="300" /></a></div>
<!-- Blogger automated replacement: "https://images-blogger-opensocial.googleusercontent.com/gadgets/proxy?url=http%3A%2F%2F2.bp.blogspot.com%2F-AcMszbRK54M%2FUyq0DQ2KQdI%2FAAAAAAAAKIs%2FHCynueOHFKc%2Fs1600%2FIMG_6729.JPG&container=blogger&gadget=a&rewriteMime=image%2F*" with "https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEio6us_HgWGPTVtm_ygFTkjhVA1x4jiY59I4kubWoGopCcMviiDd5pdDLLqBISspUs-9V6-ahevid0rIuR4vHfVhiMc5dJAWDgeYtn9JkkJHyi8cS4YcECn01_ucegUZ9pKQMmYxC1Gfpg/s1600/IMG_6729.JPG" -->Jennifer Gresenshttp://www.blogger.com/profile/09599007252984475124noreply@blogger.com1tag:blogger.com,1999:blog-7194278206785923230.post-54743547950683610692014-02-09T15:27:00.000-08:002014-02-09T15:27:03.315-08:00Favorite pets, birding, and more! We recently completed our unit called <i>Pockets, Teeth, and Favorite Things</i>. The unit focused on data collection. The term data was explained to the students as the facts or information we collect about people and things in our world. There was ample opportunity for real world connection to clarify ideas in this unit. The students surveyed their friends about their favorite pets (or other favorite things), sorted, and then represented this data in ways that could be understood by others. <br />
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We started the unit with a brief survey of everyone's favorite weekend activity. The students wrote down their favorite activities and put them on our large classroom chart. Once everyone's activity was present, it was time to organize our data into a meaningful way that could be easily understood.<br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhXSdn0UOM5TkydOYbzrq-GPEks4d9iOZHKvgkN1GNeH0NcoN8GTB779NU-twC1j-0MqxLq0e1SGRodvbQFDzZ8ts2A0HG5YvIQGBaxO-3c5HiWKKEsyBdJjHUpTg8Udf69WO_ELwhZASM/s1600/IMG_6316.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhXSdn0UOM5TkydOYbzrq-GPEks4d9iOZHKvgkN1GNeH0NcoN8GTB779NU-twC1j-0MqxLq0e1SGRodvbQFDzZ8ts2A0HG5YvIQGBaxO-3c5HiWKKEsyBdJjHUpTg8Udf69WO_ELwhZASM/s1600/IMG_6316.JPG" height="320" width="240" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Placing data on our classroom chart</td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjczVOqVnHZG-CiKE_tdZqPw_9eQeMhgIaqh9oxd1Ey2o3LgKfggy1pa4BGFn3ruqidslfJuSRcANIdyd3D0WnuYmM_C6GSrpC394QdB5wGo-caiF707EDBkS3KyORCEr6VaofY3wzq7PE/s1600/IMG_6320.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjczVOqVnHZG-CiKE_tdZqPw_9eQeMhgIaqh9oxd1Ey2o3LgKfggy1pa4BGFn3ruqidslfJuSRcANIdyd3D0WnuYmM_C6GSrpC394QdB5wGo-caiF707EDBkS3KyORCEr6VaofY3wzq7PE/s1600/IMG_6320.JPG" height="320" width="240" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">The very beginnings of our class data collection</td></tr>
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In subsequent math classes, we made graphs of the data. The students noted that it was much easier to interpret and analyze the data once it was clearly organized in some way. <br />
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We also talked about Venn diagrams and how to sort data by different attributes. The students made their own Venn diagrams and sorted data by two attributes. Partners took turns guessing attributes and sorting information. This early work in classification provided experiences in considering only certain attributes of an object while ignoring others. <br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgBuJ-X59nEsr4fTVSJYOcbur8bwwHj2KTBww4Phvkxr0o4ubLrAqlJYbR22WtZbSPnV7weKs2pjt5cD_x46qRh5De6Ul_HCrHOKc-RDnz7t4RWAKrUfmV4NoD1ULFNar44RsjNFogouoY/s1600/IMG_6336.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgBuJ-X59nEsr4fTVSJYOcbur8bwwHj2KTBww4Phvkxr0o4ubLrAqlJYbR22WtZbSPnV7weKs2pjt5cD_x46qRh5De6Ul_HCrHOKc-RDnz7t4RWAKrUfmV4NoD1ULFNar44RsjNFogouoY/s1600/IMG_6336.JPG" height="240" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Sorting objects by their attributes</td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi9N0xlW6zLxNh4E6qKSIBQZxq88BaMXJ9kq-d7M381Hk4ca1qZH8pERroT129wEoQF_hi4S3djxzTvOqbRZwGg9fpgPX3R7HYqd3-KVVWIZS34oFZlH_fJB8whk8RKp9J4cKoxUHS_YqY/s1600/IMG_6334.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi9N0xlW6zLxNh4E6qKSIBQZxq88BaMXJ9kq-d7M381Hk4ca1qZH8pERroT129wEoQF_hi4S3djxzTvOqbRZwGg9fpgPX3R7HYqd3-KVVWIZS34oFZlH_fJB8whk8RKp9J4cKoxUHS_YqY/s1600/IMG_6334.JPG" height="320" width="240" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Using Venn diagrams to help sort the data</td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhLJAk1wx4NJFWHUJuoWmJh8P33gcbdCLjCrrlYoovAIGTVcPjVJxZfHhU8cfIME3P9223tINFMtkIlu0iaMM1zPw100rv2cgjz_I1Fx2B2Vprrg_4RYw8AVUc7JvGy90AyiWLsUCRo37g/s1600/IMG_6329.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhLJAk1wx4NJFWHUJuoWmJh8P33gcbdCLjCrrlYoovAIGTVcPjVJxZfHhU8cfIME3P9223tINFMtkIlu0iaMM1zPw100rv2cgjz_I1Fx2B2Vprrg_4RYw8AVUc7JvGy90AyiWLsUCRo37g/s1600/IMG_6329.JPG" height="320" width="240" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">More sorting and discussion about attributes</td></tr>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhw2q2rL0KryPoVRb1kj9DVtVaAP2sFrhGRNW9muJ_Xd_6xcHBd0F5JlwuheF7lR-dotWNbBta4nY12BjYi2owD_FdP-fkMb5YutkYq5yccb0YDPDLfswOZfaE3bacQX06CRZmjLSK0IH4/s1600/IMG_6333.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhw2q2rL0KryPoVRb1kj9DVtVaAP2sFrhGRNW9muJ_Xd_6xcHBd0F5JlwuheF7lR-dotWNbBta4nY12BjYi2owD_FdP-fkMb5YutkYq5yccb0YDPDLfswOZfaE3bacQX06CRZmjLSK0IH4/s1600/IMG_6333.JPG" height="320" width="240" /></a></div>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgJbnYTpWsHOZt8Kg9TI45vAv_2X_yNZkB2f81AtTogtVlt7rpXXM6_7jn0nQQZRNeXhGE8sSkVGRIJFqQ2iLwzYwqrjTnqkb2n3W54h-tBu07Y6o0d47CgqW35ZyJ9-aXwThCI7By2Io4/s1600/IMG_6331.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgJbnYTpWsHOZt8Kg9TI45vAv_2X_yNZkB2f81AtTogtVlt7rpXXM6_7jn0nQQZRNeXhGE8sSkVGRIJFqQ2iLwzYwqrjTnqkb2n3W54h-tBu07Y6o0d47CgqW35ZyJ9-aXwThCI7By2Io4/s1600/IMG_6331.JPG" height="320" width="240" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Noticing differences in data</td></tr>
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To further connect this unit to real life, we took advantage of our beautiful surroundings</div>
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and went outside on our monthly bird walk. This time even the 3rd graders joined us on our adventure. Students keep track of what birds we see outside, and back inside we enter the data on the e<i>bird</i> website and incorporate it in our classroom bird graph. </div>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiktsEZL0f9CyviqmoP3tfH-gSsADrNstfIzbv3BQLDlrjTyl8lv1FgAGfwSA8x4qGMXYKbcoyUH088t7avGHr3tZH5oV61e2NXNYb8nuXxuVRRMLg6gf8gbFdNtJj1KaNUlIN5xEaakP8/s1600/IMG_6347.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiktsEZL0f9CyviqmoP3tfH-gSsADrNstfIzbv3BQLDlrjTyl8lv1FgAGfwSA8x4qGMXYKbcoyUH088t7avGHr3tZH5oV61e2NXNYb8nuXxuVRRMLg6gf8gbFdNtJj1KaNUlIN5xEaakP8/s1600/IMG_6347.JPG" height="240" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Outside on our bird walk</td></tr>
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Now it was time to represent our data clearly. Students used a variety of representations: line plots, bar graphs, pictures, pop up charts, and other creative means to show the amount of birds that were spotted. It was wonderful to see how each student approached this task with gusto and enthusiasm. The data we had collected held real meaning for them (these were birds we saw on our school property, after all!), and they each worked to their fullest potential to display the data clearly. <br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhmx4c_Bb7F5a37C64fxkSW1lZk4ZYOeXQOlBvupbBTRcWoKO1FLbyqj9zyDOdYSW9p1i1B04yP4R2EOKvqig_-A0f-6qHFiWImLqpxJBa2nqbL5y5S5R6GMsLeg5Cqrio8GJduFQ4so7s/s1600/IMG_6362.JPG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhmx4c_Bb7F5a37C64fxkSW1lZk4ZYOeXQOlBvupbBTRcWoKO1FLbyqj9zyDOdYSW9p1i1B04yP4R2EOKvqig_-A0f-6qHFiWImLqpxJBa2nqbL5y5S5R6GMsLeg5Cqrio8GJduFQ4so7s/s1600/IMG_6362.JPG" height="320" width="240" /></a><br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjpMy63xUtd3Ndn-MOEMDrtkMjrH8ipG_X-1PRPKmBwQtcFFXNb8-M4oX8lLXwBZAhnHATniEKfdDH-fx_p-WuwiHjH8Bg5w0I1NuQbqv4l85tc3BrPoyMFQJoZebWVDLALXF-8BlTpRng/s1600/IMG_6363.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjpMy63xUtd3Ndn-MOEMDrtkMjrH8ipG_X-1PRPKmBwQtcFFXNb8-M4oX8lLXwBZAhnHATniEKfdDH-fx_p-WuwiHjH8Bg5w0I1NuQbqv4l85tc3BrPoyMFQJoZebWVDLALXF-8BlTpRng/s1600/IMG_6363.JPG" height="320" width="240" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Beginning to represent our data</td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjyfMIcPZPoCT8-pucDf4pdAWcoWcctw5i0RLioe2O_4nkZxCA3QrDROjVlYzjRlGB3KfSIqsXi0cWnxqZykWxENXEmbYW6qsHsy0q_Vrbi8gjnOvuDvqGHPehEKFmDPjRFVhk_JT4BsqY/s1600/IMG_6356.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjyfMIcPZPoCT8-pucDf4pdAWcoWcctw5i0RLioe2O_4nkZxCA3QrDROjVlYzjRlGB3KfSIqsXi0cWnxqZykWxENXEmbYW6qsHsy0q_Vrbi8gjnOvuDvqGHPehEKFmDPjRFVhk_JT4BsqY/s1600/IMG_6356.JPG" height="240" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">A variety of representations were used</td></tr>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEijESgc8XioGei_qccoUGRQcAbdNlNLevp1kY6QjiS0ZdsKcAt5DssS2_8wgAXNYBaMm4S-bp8udLM1y731tH1OOfjQcAhjUkHNE5K_dlrs4whohNl25B3-AruCRCkLI554IpnM5P_riI0/s1600/IMG_6359.JPG" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEijESgc8XioGei_qccoUGRQcAbdNlNLevp1kY6QjiS0ZdsKcAt5DssS2_8wgAXNYBaMm4S-bp8udLM1y731tH1OOfjQcAhjUkHNE5K_dlrs4whohNl25B3-AruCRCkLI554IpnM5P_riI0/s1600/IMG_6359.JPG" height="320" width="240" /></a><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj-Z-OZvrXnkxB0hpK82H8MnCrPiEdM-m6tpl6UaZCSMRWiQd0-kPfDC9Sh7ef_dhjcpAnRZbn8N0JNmRUEIuTxUXrtyEanSEfhA4C608TrXcDfrsyb29KHa8pgNe0PJojlIxBKdKvQWMk/s1600/IMG_6354.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj-Z-OZvrXnkxB0hpK82H8MnCrPiEdM-m6tpl6UaZCSMRWiQd0-kPfDC9Sh7ef_dhjcpAnRZbn8N0JNmRUEIuTxUXrtyEanSEfhA4C608TrXcDfrsyb29KHa8pgNe0PJojlIxBKdKvQWMk/s1600/IMG_6354.JPG" height="320" width="240" /></a></div>
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During this unit, students were introduced to various frequency distributions in which each piece of data is represented by one symbol (e.g., an X, a picture, a sticker, a square, or even a sticky note). In using this kind of representation, students have to think through the meaning of two ways numbers are used in describing data: Some numbers indicate the value of a piece of data; other numbers indicate how often a particular data value occurs. The Second graders were able to describe the data by considering the frequency of each value, the mode, and the highest and lowest values. <br />
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By participating in an entire data investigation from start to finish, students encounter many of the same issues encountered by statisticians as they decide how to collect, keep track of, organize, represent, describe, and interpret their data. All this while having real life experiences to tie things together - interviewing friends, talking about their favorite things, and bird watching! <br />
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<tr><td class="tr-caption" style="text-align: center;">Sentiments from a Second grade mathematician</td></tr>
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Jennifer Gresenshttp://www.blogger.com/profile/09599007252984475124noreply@blogger.com0tag:blogger.com,1999:blog-7194278206785923230.post-2574094121698127452014-01-12T16:46:00.000-08:002014-01-12T16:47:29.864-08:00In the Zone......The weeks leading up to winter break were busy ones for our Second grade mathematicians. The students were challenged with mastering many new concepts in our latest unit. They experienced first hand what it felt like to gain mastery of something after what initially felt new and even frustrating at times. <br />
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Second graders are continuing to make sense of and develop various strategies to solve addition and subtraction problems with totals amounting to 50 and over. We've practiced numerous ways to add and subtract larger numbers, with students having opportunities to find a way that makes sense to them. <br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgYDJo1XuQ1yFZPuuspx6DXsmjXHp7XUJVGfBPQPOO1c-dRhW8S-BuQn0GN8pIgvTL_AHYYodA0QXJ_qE9st8wqJC71JLUrNIrGindDl3IPoasbZ3JStKXFox8G-CCGTfti_AJLX374Si8/s1600/IMG_6132.JPG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgYDJo1XuQ1yFZPuuspx6DXsmjXHp7XUJVGfBPQPOO1c-dRhW8S-BuQn0GN8pIgvTL_AHYYodA0QXJ_qE9st8wqJC71JLUrNIrGindDl3IPoasbZ3JStKXFox8G-CCGTfti_AJLX374Si8/s1600/IMG_6132.JPG" height="240" width="320" /></a><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiNv4E1aV2kXO4c2MTB5AKvWveO92p0PYeDWsbof5hW24-Yu7pBf9Qorh4DPMhniQxkSkIX168QhLhCoxarIVuw6Fhzrx4UZRehrpoiivuZpwCejRpoZVsc17K7hrvp_fEpT3cGauvzZ2M/s1600/IMG_6120.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiNv4E1aV2kXO4c2MTB5AKvWveO92p0PYeDWsbof5hW24-Yu7pBf9Qorh4DPMhniQxkSkIX168QhLhCoxarIVuw6Fhzrx4UZRehrpoiivuZpwCejRpoZVsc17K7hrvp_fEpT3cGauvzZ2M/s1600/IMG_6120.JPG" height="320" width="240" /></a></div>
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We spent time discussing and learning about even and odd numbers, and investigating those numbers in terms of being broken into equal groups of two. We used real life examples within the context of partners (groups of two) and teams (two equal groups) to reinforce this. We looked at the number of students in our class and members of our family to provide meaning for the students. Classroom games also became a reinforcement to provide additional practice with even and odd numbers. <br />
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This investigation led to developing fluency with skip counting by 2s, 5s, and 10s. We counted bags of objects and materials in our classroom to gain mastery of this concept. Students soon realized that counting a set of 100 objects in groups of 5 or 10 is much easier than counting each and every object! Students became familiar with tally marks to represent groups of 5 and keep track of their counting. <br />
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Perhaps one of the most important break throughs this past month has been the ability to become deeply immersed in our learning, or as we call it, "being in the zone." During class one day, a particularly challenging concept was introduced. One of the students continued to get frustrated and complained of not understanding the material, saying, "It's too hard. I can't do it." This was clearly an opportunity for the entire class to learn about perseverance and not giving up when things get difficult. We talked through the concept again as a class, and had another go at the problem. The class was silent, each student working to his or her full potential. After some time had gone by, a visitor came to the door, and some students stopped what they were doing to greet the visitor. This same student, the one who felt the task was impossible, said "Wow, I actually forgot where I even was and what I was doing until I heard voices." He was so "in the zone" that time slipped away and it just became him and his math work. We then talked as a class about this idea of being in the zone. This is the place where effort and enthusiasm meet, and where students engage in thinking at the deepest level. This is a place I see more and more of our second graders - a place where I may need to give them 2, 3, even 4 reminders to finish up their work because they are so deeply involved. <br />
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My goal for the Second graders is to see learning as a journey, not a place that can always be reached immediately. Giving students time to reflect about the challenges they've faced, and the mistakes and revisions they've made, will give them the confidence to continue when things are difficult. When we persevere, we also need to celebrate the success. After this particular day, we congratulated one another on hanging in there, and reflected on the pride and sense of accomplishment that everyone felt. It was an amazing learning opportunity for all. <br />
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Jennifer Gresenshttp://www.blogger.com/profile/09599007252984475124noreply@blogger.com0tag:blogger.com,1999:blog-7194278206785923230.post-17310950785153446632013-11-26T02:59:00.000-08:002013-11-26T02:59:43.043-08:00Exploring geometry!The second graders recently finished up our unit on 2D and 3D geometry. This unit provided us with many rich opportunities for hands on learning as the students searched for shapes around our classroom and at home, read books about the subject, created 3D rectangles out of paper, and used mirrors to explore symmetry. There were many highlights of this unit - here are some of our favorites......<br />
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After introducing solid shapes, we read the book <i>Sir Cumference and the Sword in the Cone</i>, by Cindy Neuscwander. A Swiss mathematician, Leonhard Euler, created a formula that expressed a relationship between the faces, vertices and edges of solid shapes. He discovered that adding the numbers of flat faces of any solid shape to its corresponding vertices (or corner points) and then subtracting that sum from the number of straight edges, the result would be represented by a total of two. When the result was two, that meant that the solid shape could be classified as a polyhedron. Any solid shapes whose totals were not two cannot be considered polyhedrons. After reading the book, we discussed and carefully studied the shapes presented in the story. We created a chart to fill out the number of faces, vertices and edges of each shape, and then applied the equation and gave each shape the "Two's Test." This gave the students opportunity to carefully examine each shape as well as practice with making advanced and intricate calculations. This activity quickly became a favorite. When reflecting back at the end of the unit, many students claimed the Two's Test was their favorite part of studying geometry! <br />
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<tr><td class="tr-caption" style="text-align: center;">Taking the "Two's Test"<br />
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Another thought provoking and fun activity was to create "tricky triangles" or rectangles, and find hidden shapes within shapes. The students learned there are usually more shapes present than initially thought. They also devised wonderful strategies to find the various hidden shapes. <br />
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<tr><td class="tr-caption" style="text-align: center;">Finding hidden triangles</td></tr>
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When initially asked to put a group of rectangles in order from smallest to largest, students normally will choose the order based on height. After we discussed the concept of area and determined how to measure the area of a rectangle by using 1 inch square color tiles, students realized that the tallest rectangles were not always the largest. This was an excellent exercise on making and testing a prediction. <br />
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<tr><td class="tr-caption" style="text-align: center;">Ordering rectangles<br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEixtyw20wmsnCNZ3qLmJM4cyqauvYE1FsIRtQbmDHTpeAxHYqVDKFu4qaySj8y_SsovvRNVCoV3CQwYaZvTQ8G4KgbG6yNx0wQb3ILL-rB9t1IW2BUpBF2i6-4CFS1pz1zT6G7MqA6baRA/s1600/IMG_5927.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEixtyw20wmsnCNZ3qLmJM4cyqauvYE1FsIRtQbmDHTpeAxHYqVDKFu4qaySj8y_SsovvRNVCoV3CQwYaZvTQ8G4KgbG6yNx0wQb3ILL-rB9t1IW2BUpBF2i6-4CFS1pz1zT6G7MqA6baRA/s1600/IMG_5927.JPG" height="240" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Which rectangle is the biggest?</td></tr>
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<tr><td class="tr-caption" style="text-align: center;">Finding the area of a rectangle by using color tiles</td></tr>
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The students made 3 dimensional rectangles out of various sizes of paper. This activity proved challenging at first. The students weren't sure how to approach creating a 3 dimensional object out of something 2 dimensional. They needed to fit the sides together, create a top and a bottom, and finally tape it all together so it would eventually become a 3 dimensional box. After some effort and perseverance, the results were amazing - we had rectangles of all sizes, animals made out of paper shapes, fairy houses, doll beds, and colorful cubes, just to name a few of the creations. What started out as a challenge, ended up being a class favorite. The possibilities were endless! <br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjKWFu1iTCsb554Dc1Leo8k4ded8lZsrEWqwfLcUsfgS8vIUijuBBytT9pmpAt18w5zGo6I79tFhml_yJ7BwXpVQ2d10tfKiyUNVk-NagGTWcCVdGiti53IsU0qH8vub3a5mX0jBGjy0nw/s1600/IMG_5946.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjKWFu1iTCsb554Dc1Leo8k4ded8lZsrEWqwfLcUsfgS8vIUijuBBytT9pmpAt18w5zGo6I79tFhml_yJ7BwXpVQ2d10tfKiyUNVk-NagGTWcCVdGiti53IsU0qH8vub3a5mX0jBGjy0nw/s1600/IMG_5946.JPG" height="320" width="240" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">colorful cubes!</td></tr>
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<tr><td class="tr-caption" style="text-align: center;">"Mousey house"</td></tr>
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<tr><td class="tr-caption" style="text-align: center;">Working on creating a box out of paper</td></tr>
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Finally, we explored symmetry, and the properties of symmetrical objects and shapes. We used mirrors to create perfectly symmetrical designs out of pattern blocks and color tiles. This was another hands on learning experience that illustrated a mathematical concept in a very tangible way for the students.<br />
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<tr><td class="tr-caption" style="text-align: center;">mirror images</td></tr>
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<tr><td class="tr-caption" style="text-align: center;">Exploring symmetry </td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgeDVY646sGyCycyI1F-D6GkYA7tIfzidX8cce2D_bHIW9GNklGDxsHXKqrDCubeOJ6B7ia-kiuuNSd8x0-1DreqG0h5NgOxU3KVWFT8VOCIK49Uo6pIa4p0TBxeiaIeqXUHFWykZ30FD4/s1600/IMG_5977.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgeDVY646sGyCycyI1F-D6GkYA7tIfzidX8cce2D_bHIW9GNklGDxsHXKqrDCubeOJ6B7ia-kiuuNSd8x0-1DreqG0h5NgOxU3KVWFT8VOCIK49Uo6pIa4p0TBxeiaIeqXUHFWykZ30FD4/s1600/IMG_5977.JPG" height="320" width="240" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Making a chart about symmetry<br />
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I can safely say that the 2nd graders are now experts in geometry. Looking ahead, we will explore more complicated addition and subtraction story problems, using larger numbers. I have no doubt they will approach this unit with ethusiasm and meet any challenges head on! <br />
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Jennifer Gresenshttp://www.blogger.com/profile/09599007252984475124noreply@blogger.com0tag:blogger.com,1999:blog-7194278206785923230.post-24192836869766308342013-10-27T16:03:00.001-07:002013-10-27T16:03:36.619-07:00<br />
<h2 style="text-align: center;">
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The second grade mathematicians have successfully mastered our first unit, Counting, Coins, and Combinations. They have developed an understanding of the magnitude and sequence of numbers up to 100, developed strategies to solve addition and subtraction problems with totals up to 50 (and beyond!), mastered their combinations of 10, and explored doubling a quantity. These goals were met through a variety of ways. We solved problems in our journals, presented ideas to our classmates, played math games, read and discussed relevant books, and explored materials.<br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgPDWtgpi4kt8jX96jjtRlMDA-BEiD9HsREcc40vVRJdHiV3uf30zW58qA9AiYt17X1kY9TFN-Pu1BxDEU1YVAltLzYJBgEV5aojHDt3MXPrirTlsUKBMILLFhkj99R6wYyk04o8eaUYso/s1600/IMG_5863.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgPDWtgpi4kt8jX96jjtRlMDA-BEiD9HsREcc40vVRJdHiV3uf30zW58qA9AiYt17X1kY9TFN-Pu1BxDEU1YVAltLzYJBgEV5aojHDt3MXPrirTlsUKBMILLFhkj99R6wYyk04o8eaUYso/s1600/IMG_5863.JPG" height="320" width="240" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Doubling </td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEik06Kl8HEqnBXlbyP7fhuY5G1xSRQYZSkzxWrTjUl-r2cEKcR5faNuaalElBVS46amLO3lSLpEbUL-aDA_GftTPxHtgEdMf4hZN7vgazfyOmfa4FgrRcRBfqYmw7lsNnzSJqMChc_pMG4/s1600/IMG_5857.JPG" imageanchor="1" style="clear: left; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEik06Kl8HEqnBXlbyP7fhuY5G1xSRQYZSkzxWrTjUl-r2cEKcR5faNuaalElBVS46amLO3lSLpEbUL-aDA_GftTPxHtgEdMf4hZN7vgazfyOmfa4FgrRcRBfqYmw7lsNnzSJqMChc_pMG4/s1600/IMG_5857.JPG" height="320" width="240" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Working at the doubling center</td></tr>
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<tr><td class="tr-caption" style="text-align: center;">Journal work</td></tr>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj6rZQ3bcN0kqwKHA1cEa6enyAPK2pbfHjY3_GOPozFUGUzu9QTRjKRVi-V5dtLBYBKYVCesop7jHWPUTvsIvg0erQjEz0kb02SsXNt_jOEC87UYG6_GPyBCthQipQkEQgnHOaOV5vhFMk/s1600/IMG_5864.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj6rZQ3bcN0kqwKHA1cEa6enyAPK2pbfHjY3_GOPozFUGUzu9QTRjKRVi-V5dtLBYBKYVCesop7jHWPUTvsIvg0erQjEz0kb02SsXNt_jOEC87UYG6_GPyBCthQipQkEQgnHOaOV5vhFMk/s1600/IMG_5864.JPG" height="320" width="240" /></a><br />
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<tr><td class="tr-caption" style="text-align: center;">Playing Plus 1 or 2 Bingo </td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgcDpGRuE2laYAa8d03lBlYwj_yzTOhv6vgv2WVLtkoR8jpwEGhvaUN7LGb6w-CKrIP_8a5uxwmD48oaRLdDLnMcIJdQvv_AKKZzNn1Sv0-DNWzovZuEoysjcmmtxm4VG3UXq7c5agYo2s/s1600/IMG_5853.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgcDpGRuE2laYAa8d03lBlYwj_yzTOhv6vgv2WVLtkoR8jpwEGhvaUN7LGb6w-CKrIP_8a5uxwmD48oaRLdDLnMcIJdQvv_AKKZzNn1Sv0-DNWzovZuEoysjcmmtxm4VG3UXq7c5agYo2s/s1600/IMG_5853.JPG" height="240" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Playing "Double It"</td></tr>
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<span style="font-size: 13px;"> </span><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgibp1GXqP7KtgfqPFO36zvcbUIzMdV8kaeQKCXb9-_3u5qvcAG7GvnpxoblLv4l6W2SyCjzGJubkd9mGU6QwJ1YqFAfPkGspU596ZuqdSQturcYEog-LaoG2T0aLtfEikbn94n44kiQ-8/s1600/IMG_5849.JPG" imageanchor="1" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgibp1GXqP7KtgfqPFO36zvcbUIzMdV8kaeQKCXb9-_3u5qvcAG7GvnpxoblLv4l6W2SyCjzGJubkd9mGU6QwJ1YqFAfPkGspU596ZuqdSQturcYEog-LaoG2T0aLtfEikbn94n44kiQ-8/s1600/IMG_5849.JPG" height="240" width="320" /></a></h2>
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<tr><td class="tr-caption" style="text-align: center;">Working on doubles arrays <br />
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<tr><td class="tr-caption" style="text-align: center;">Playing "Double It"</td></tr>
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Another new development in math this month has been the introduction of "Math Workshop." After new concepts and topics have been introduced, explored, mastered, and summarized, students have the opportunity to participate in Math Workshop, consisting of various math centers (usually about 4) pertaining to our unit. A center may have a game to play with a partner, free exploration of math materials and manipulatives, math journal work, or "challenge problems." This has provided a wonderful opportunity for the students to work with partners, share ideas, and further explore mathematical concepts. <br />
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Looking ahead, we are just beginning our unit on geometry. Students will explore the characteristics and attributes of 2-dimensional and 3-dimensional shapes. We will do in-depth work with rectangles and rectangular prisms and investigate symmetry. This has already captured the interest of the second graders, and I'm looking forward to witnessing and guiding their interest, creativity, and enthusiasm! <br />
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<tr><td class="tr-caption" style="text-align: center;">Playing Tens Go Fish<br />
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<tr><td class="tr-caption" style="text-align: center;">Exploring and drawing geoblocks</td></tr>
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<tr><td class="tr-caption" style="text-align: center;">Tens Go Fish<br />
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Jennifer Gresenshttp://www.blogger.com/profile/09599007252984475124noreply@blogger.com0tag:blogger.com,1999:blog-7194278206785923230.post-15798278960069626212013-10-06T17:45:00.000-07:002013-10-06T17:45:47.039-07:00We started the week with an activity called "counting pockets." We counted the amount of pockets each student had, and recorded the total number. This was a great exercise on estimating, counting, comparing and combining, as the students collected, represented and interpreted data.<br />
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Later in the week, we read the book <i>Math Curse</i>, by Jon Scieszka and Lane Smith. It is a story about a girl who starts to think of everything as a math problem, and believes her teacher has given her a "math curse." We talked about how everything can appear to be a math problem when you start thinking this way. Inspired by the book, we made up our own math problems and shared them with the class. This was an amazing exercise as the students had to think about ways to express themselves and their mathematical ideas. The problems had to be relevant, challenging enough but not too challenging, and interesting for their peers to solve. The students loved coming up to the front of the class to write out and present their problems. <br />
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Plus 1 or 2 Bingo was also a favorite this week. We worked on our addition combinations while playing games with our friends. Looking ahead to next week, we'll be learning more games to assist us with combinations of 10.<br />
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In closing, here is a link to an excellent article discussing the beauty of math. Enjoy! <br />
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<a href="http://blogs.kqed.org/mindshift/2013/10/finding-the-beauty-in-math/">http://blogs.kqed.org/mindshift/2013/10/finding-the-beauty-in-math/</a><br />
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<tr><td class="tr-caption" style="text-align: center;">Writing our own problem on the board</td></tr>
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<tr><td class="tr-caption" style="text-align: center;">Presenting our problem!</td></tr>
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<tr><td class="tr-caption" style="text-align: center;">Finding a solution in our journals</td></tr>
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<tr><td class="tr-caption" style="text-align: center;">Problem solving</td></tr>
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<tr><td class="tr-caption" style="text-align: center;">Playing Plus 1 or 2 Bingo</td></tr>
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<span style="color: #0000ee;"><u><br /></u></span><a href="http://blogs.kqed.org/mindshift/2013/10/finding-the-beauty-in-math/"></a><br />
<br />Jennifer Gresenshttp://www.blogger.com/profile/09599007252984475124noreply@blogger.com0tag:blogger.com,1999:blog-7194278206785923230.post-13231657005125751972013-09-29T16:55:00.000-07:002013-09-29T16:55:32.551-07:00<div>
This week we started to explore coins and their values. We sorted and counted the various coins and learned two games - Collect 25 Cents and Roll for $1.00. This provided the children with practical experience adding up coins and making trades for the different coins. <br />
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We also started our year long service project - observing and counting birds through eBird.org. We'll be going outdoors to take a monthly bird count on the Parker property and entering the data into a national database on the eBird website. We will be graphing our results back in the classroom, as well as completing word problems and other relevant activities. On our first outing we spotted almost 30 birds! Now we just have to get better at identifying them. ;) <br />
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<tr><td class="tr-caption" style="text-align: center;">Carefully counting coins</td></tr>
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<tr><td class="tr-caption" style="text-align: center;">Sorting coins</td></tr>
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<tr><td class="tr-caption" style="text-align: center;">More sorting</td></tr>
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<tr><td class="tr-caption" style="text-align: center;">Counting birds on the Parker property</td></tr>
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<tr><td class="tr-caption" style="text-align: center;">Taking careful notes</td></tr>
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<tr><td class="tr-caption" style="text-align: center;">Playing Roll for $1.00</td></tr>
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<br />Jennifer Gresenshttp://www.blogger.com/profile/09599007252984475124noreply@blogger.com0tag:blogger.com,1999:blog-7194278206785923230.post-73767154567165558022013-09-22T14:22:00.000-07:002013-09-23T02:38:01.188-07:00Another great week in 2nd Grade math! This week there was a strong emphasis on counting. We tried out various strategies for counting large sets of objects, and determined what worked best for each of us. Some students counted by 2's, 5's or 10's. Others sorted by color, counted up the groups, and added them together. Others learned to keep track by keeping a running list of numbers while counting (this strategy was developed after a very frustrating experience of losing track of our count after getting beyond 100!). It was great to see the engagement of the children and the way they approached this activity. We also counted large numbers of objects grouped in bags, and determined if there would be enough for the class. Obviously with our small class there always was, so the next question was "How many cubes will be left over?" This posed another challenge, and yet another opportunity for problem solving and strategy. <br />
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A favorite game has become "Guess My Number." We think of a number (usually between 1-30) and with clues, our partner makes a guess. The object is to guess the number with as few guesses as possible. To help us we used number lines, and even 100 charts, to narrow down and visualize the numbers. We talked about the terminology <i>greater than</i> and <i>less than</i>, and the corresponding symbols. Try this game at home - your 2nd grader will love it! </div>
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We'll start the next week talking about money and coin values, providing us with further opportunity to develop an understanding of the magnitude and sequence of numbers up to 100. </div>
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<tr><td class="tr-caption" style="text-align: center;">Counting by groups of color</td></tr>
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<tr><td class="tr-caption" style="text-align: center;"> Counting by 10's</td></tr>
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<tr><td class="tr-caption" style="text-align: center;"> Playing Guess My Number</td></tr>
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<tr><td class="tr-caption" style="text-align: center;"> More Guess My Number </td></tr>
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<tr><td class="tr-caption" style="text-align: center;">Studying the 100 chart</td></tr>
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<tr><td class="tr-caption" style="text-align: center;">Filling in the class 100 chart</td></tr>
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<tr><td class="tr-caption" style="text-align: center;">Using our number lines</td></tr>
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<tr><td class="tr-caption" style="text-align: center;"> Guess My Number while using number lines</td></tr>
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<tr><td class="tr-caption" style="text-align: center;">Working in our math journals</td></tr>
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Jennifer Gresenshttp://www.blogger.com/profile/09599007252984475124noreply@blogger.com0tag:blogger.com,1999:blog-7194278206785923230.post-26930689307726664792013-09-15T17:41:00.000-07:002013-09-15T17:41:30.701-07:00We had a wonderful first week in Second Grade math. We learned about combinations of 10, reviewed geometry, and played some new math games. The children are curious and eager - we're off to an amazing start!<br />
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<tr><td class="tr-caption" style="text-align: center;">exploring cubes</td></tr>
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<tr><td class="tr-caption" style="text-align: center;">playing a new math game - Make 10.</td></tr>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi8uz-DKY7LUrLuvtKuavmgxhUI7Ud49SnR4DjVKViMW-n_O6wdBRpTiPe0rp-V9STDLtEBoQgbAEdPbqZ3A7Uuxi2Cqj985xt6ADf151YZwKis85iMjw2gdr1QNOs_f7rBb7IJ1U2qPPo/s1600/IMG_5668.JPG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi8uz-DKY7LUrLuvtKuavmgxhUI7Ud49SnR4DjVKViMW-n_O6wdBRpTiPe0rp-V9STDLtEBoQgbAEdPbqZ3A7Uuxi2Cqj985xt6ADf151YZwKis85iMjw2gdr1QNOs_f7rBb7IJ1U2qPPo/s1600/IMG_5668.JPG" height="320" width="240" /></a><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgaeyljybHMSRG0cNMuRRswvQXKnDZNJKjDwZETvddayBbq3KIhQz1pzpnje683x5irqP8KKn_S2wL3f0Uv_ODJrIOBnuDtC0CWMp4f12ytOiG0MAAyjYfIkguJsdFDXfOAs75qkug_FUE/s1600/IMG_5673.JPG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgaeyljybHMSRG0cNMuRRswvQXKnDZNJKjDwZETvddayBbq3KIhQz1pzpnje683x5irqP8KKn_S2wL3f0Uv_ODJrIOBnuDtC0CWMp4f12ytOiG0MAAyjYfIkguJsdFDXfOAs75qkug_FUE/s1600/IMG_5673.JPG" height="320" width="240" /></a></div>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEghg0Sm-BNtIcPz56T88JTEvTKezHntW_UMTvczj_Gwb6yOQosU9eLqHS_kqr59oUXEN2irOi2P7Vn8DXnsA4Y3Yc4-mqUnZZ-D3Viex4CxvB9tegy2zfUis5aju1L_FDGEwD6JfczOAP0/s1600/IMG_5675.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEghg0Sm-BNtIcPz56T88JTEvTKezHntW_UMTvczj_Gwb6yOQosU9eLqHS_kqr59oUXEN2irOi2P7Vn8DXnsA4Y3Yc4-mqUnZZ-D3Viex4CxvB9tegy2zfUis5aju1L_FDGEwD6JfczOAP0/s1600/IMG_5675.JPG" height="320" width="240" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">working together on creating intricate structures out of pattern blocks. </td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhw3uo20qq8K3zTIYqZuuMoUia8ZSdrLTlcvPm8ZtqZBkebm-LlRaSiWMOhAV0Pjxpu-wqQDkkt9jjfCvoHRMsLJsQQf0pIqAFG68dWhzH5nAbDH5Nl6-6DFS28euP0OpKvxweVCM9mzHY/s1600/IMG_5670.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhw3uo20qq8K3zTIYqZuuMoUia8ZSdrLTlcvPm8ZtqZBkebm-LlRaSiWMOhAV0Pjxpu-wqQDkkt9jjfCvoHRMsLJsQQf0pIqAFG68dWhzH5nAbDH5Nl6-6DFS28euP0OpKvxweVCM9mzHY/s1600/IMG_5670.JPG" height="320" width="240" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">working in our math journals. </td></tr>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgahswel7SMyRmLLwRth-Wkf41BY__xw9AxYfsb651jA0T2Van66N9iG6Gpv2sGWkWKMqaXgIKI9NwQJD-ipK-42DQT7yqRPridUs0dnZhOw2RvyVwgASbMkBVauK8kzeEa2r5U6yS0Loc/s1600/IMG_5669.JPG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgahswel7SMyRmLLwRth-Wkf41BY__xw9AxYfsb651jA0T2Van66N9iG6Gpv2sGWkWKMqaXgIKI9NwQJD-ipK-42DQT7yqRPridUs0dnZhOw2RvyVwgASbMkBVauK8kzeEa2r5U6yS0Loc/s1600/IMG_5669.JPG" height="320" width="240" /></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjz7UmFEPXIZ1uHcZjiN3kG7A4r5JM7WIfD9MFLXbUE1xobU6KanTwUxBlg1Vevk3cBTnXjFVbBUaFQGy-nwVGu6V3QoVkxz6PX-o1zYFNDS7PZrLCo9J5AfCQA2sf13KZuAwM5R-KpNJM/s1600/IMG_5671.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjz7UmFEPXIZ1uHcZjiN3kG7A4r5JM7WIfD9MFLXbUE1xobU6KanTwUxBlg1Vevk3cBTnXjFVbBUaFQGy-nwVGu6V3QoVkxz6PX-o1zYFNDS7PZrLCo9J5AfCQA2sf13KZuAwM5R-KpNJM/s1600/IMG_5671.JPG" height="320" width="240" /></a></div>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEinm5QRHPPOGbbw4rIMASvtbL5opoqc-vyOT6eNHGHo5NqxMVRPAiVEfIntiIWZcW_2GivAD9Fyu0GxMWlb2K5k2ZeqpJs_xRyTNx4caQSeVaWiLgYCBkr7QZmONJSmYvPN7TNks0bhsVQ/s1600/IMG_5658.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEinm5QRHPPOGbbw4rIMASvtbL5opoqc-vyOT6eNHGHo5NqxMVRPAiVEfIntiIWZcW_2GivAD9Fyu0GxMWlb2K5k2ZeqpJs_xRyTNx4caQSeVaWiLgYCBkr7QZmONJSmYvPN7TNks0bhsVQ/s1600/IMG_5658.JPG" height="320" width="240" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">fun with geometry </td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjOnIzqsBqWiKTbB04ccQIHjZ1Zn-Zcto_YKBbM80L_67VSCo9Cg5rW_DaHFXarcg8z5WrsnLh3lKNGC_WgVRIHPtHEazsD8H7AWWkBZnzRIpZDA3joJWvalGPQKFMsY8A7pwJNH_SpPS8/s1600/IMG_5646.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjOnIzqsBqWiKTbB04ccQIHjZ1Zn-Zcto_YKBbM80L_67VSCo9Cg5rW_DaHFXarcg8z5WrsnLh3lKNGC_WgVRIHPtHEazsD8H7AWWkBZnzRIpZDA3joJWvalGPQKFMsY8A7pwJNH_SpPS8/s1600/IMG_5646.JPG" height="320" width="240" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">solving problems on the board</td></tr>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgcB1SR_Dz8qcE_ecIqQ3iqsK3jIQ8JqGK-W7tKISHnZJ54MzPH7W1LIMlfnmD6TIP8VSwB73evc_UOyPCNHp1eQTWW4M_pWmCUKqQxhbZ1051XWMi7nIAOTP_k0ykk3m1aGAmmKpxZEtw/s1600/IMG_5651.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgcB1SR_Dz8qcE_ecIqQ3iqsK3jIQ8JqGK-W7tKISHnZJ54MzPH7W1LIMlfnmD6TIP8VSwB73evc_UOyPCNHp1eQTWW4M_pWmCUKqQxhbZ1051XWMi7nIAOTP_k0ykk3m1aGAmmKpxZEtw/s1600/IMG_5651.JPG" height="320" width="240" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">reviewing geometry and filling out charts</td></tr>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgYiJ4-GjGOrYsJeR49_qi-3llODbvtBfIrQu8mw4AUo_NjHq1ySPOGo_S2OHTsVELMiZTv3XeJRhzh7ISRUgq_kjEU_0dTkVAF_ZDf4-X3nwqKNhyphenhyphenRS2Zb20I2NfeELmzpM03myCHxFGo/s1600/IMG_5653.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgYiJ4-GjGOrYsJeR49_qi-3llODbvtBfIrQu8mw4AUo_NjHq1ySPOGo_S2OHTsVELMiZTv3XeJRhzh7ISRUgq_kjEU_0dTkVAF_ZDf4-X3nwqKNhyphenhyphenRS2Zb20I2NfeELmzpM03myCHxFGo/s1600/IMG_5653.JPG" height="320" width="240" /></a><br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjuR-ZMb6AVd9NhtgmZa95wmJ6PPiUKtxD5v5mUy37ucCkVcicP55OQ6nsFpK8xRCbc_NsUobxGz8F-IQIv4UGNwIQVqSXQlu33XFWRN9iIf43JRzYCmUNeWRAuzZdJs6SL111BkskKQrg/s1600/IMG_5661.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjuR-ZMb6AVd9NhtgmZa95wmJ6PPiUKtxD5v5mUy37ucCkVcicP55OQ6nsFpK8xRCbc_NsUobxGz8F-IQIv4UGNwIQVqSXQlu33XFWRN9iIf43JRzYCmUNeWRAuzZdJs6SL111BkskKQrg/s1600/IMG_5661.JPG" height="320" width="240" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">making designs out of pattern blocks<br />
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Jennifer Gresenshttp://www.blogger.com/profile/09599007252984475124noreply@blogger.com1