tag:blogger.com,1999:blog-55192401757675838952024-03-27T13:52:49.656-05:00Explore. Wonder. Compute. Understand: MATHJennifer Gibsonhttp://www.blogger.com/profile/04128860663290797642noreply@blogger.comBlogger149125tag:blogger.com,1999:blog-5519240175767583895.post-6440688347990795222024-03-04T09:24:00.001-06:002024-03-04T09:27:16.646-06:00Mind Shifts<p><span style="font-family: Montserrat;">We have spent the better part of a year looking at new curriculum resources that will best support our students to become the best mathematicians they can be. </span></p><p><span style="font-family: Montserrat;"><b>A few takeaways that have been identified or reinforced after looking at a variety:</b></span></p><p><span style="font-family: Montserrat;">Each curriculum says it is aligned with the CCSS and math teaching practices.</span></p><p><span style="font-family: Montserrat;">Each curriculum resource has good and bad pieces to it. </span></p><p><span style="font-family: Montserrat;">If people just rely on the text in the teacher's manual to deliver instruction, they will not consistently be giving students what is best. </span></p><p><span style="font-family: Montserrat;"><i>Books are a RESOURCE. </i>The standards and math teaching practices are what is best, and the book is just a sequence and guide. Other resources should still be included. (Just because the book doesn't say to pull out a visual or manipulative doesn't mean you shouldn't...most students need these!)</span></p><p><span style="font-family: Montserrat;">Choosing the resource is not going to mean fabulous or not fabulous instruction.<i> It is what is done with the resource that will make the instruction meaningful to students.</i></span></p><p><span style="font-family: Montserrat;">Math discourse does not just mean having students turn and talk more.</span></p><p><span style="font-family: Montserrat;"><i>Pages of practice problems do not build problem-solvers. </i> They are not a necessary component of a curriculum resource.</span></p><p><span style="font-family: Montserrat;">3 Act Tasks are still important even though they are not included or referenced in most curriculums.</span></p><p><span style="font-family: Montserrat;"><i>Students need time to make sense in their own way first. </i> Once they have an idea of where to go, they may change that as they discuss and listen to classmates.</span></p><p><span style="font-family: Montserrat;">Culture has to be built in a classroom. It begins in August but is reinforced throughout the year and throughout all subjects. Telling students to persevere in September does not mean they will be able to in April. It needs to be part of every day with students.</span></p><p><span style="font-family: Montserrat;">Math should be an adventure--a combination of puzzles, games, practices, talking, and surprising connections that students make--not test scores.</span></p><p><span style="font-family: Montserrat;"><b><i>The person delivering instruction</i> still has to make the necessary shifts in their instruction in order to use a curriculum resource in a way that is fair and equitable to all students. </b></span></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiFz6YaNOrX4rhJ_XgwLcXUmv1j6YTdS1TDBswz2kQsy0BLH3EQxftgYh72NUNPrt262I6IcVFrBeHcZlOAnAiLNlRc8fX0csF1ct_DbrSCsKuSvc-ZeAZg-Rp1c2PgzaVaBb9mImOp_QdCIhNQsS4YBznyxpFFCuR5p8-8y1-z04BaqAeqYh3KrSsl6KE/s4032/IMG_3242.HEIC" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="4032" data-original-width="3024" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiFz6YaNOrX4rhJ_XgwLcXUmv1j6YTdS1TDBswz2kQsy0BLH3EQxftgYh72NUNPrt262I6IcVFrBeHcZlOAnAiLNlRc8fX0csF1ct_DbrSCsKuSvc-ZeAZg-Rp1c2PgzaVaBb9mImOp_QdCIhNQsS4YBznyxpFFCuR5p8-8y1-z04BaqAeqYh3KrSsl6KE/s320/IMG_3242.HEIC" width="240" /></a></div><br /><p><span style="font-family: Montserrat;">Have you been through this process? Have you found these to be true, too? <a href="https://drive.google.com/file/d/16uTklvMLem8Itmj1HnvBxDoPDmLV8UX-/view?usp=sharing" target="_blank">Teaching shifts need to occur no matter what curriculum resource teachers use. </a></span></p><p><br /></p>Jennifer Gibsonhttp://www.blogger.com/profile/04128860663290797642noreply@blogger.com0tag:blogger.com,1999:blog-5519240175767583895.post-13042635849554362502023-08-11T17:51:00.000-05:002023-08-11T17:51:13.019-05:00A new puzzle to consider<p><span style="font-family: Montserrat;">Recently, a friend introduced me to this game/puzzle, and I wanted to be sure to share it with you. It might be a great thing to use your PTO money or ask a generous parent to pick up for the class.</span></p><p><span style="font-family: Montserrat;">The only problem I really have with this game is its name: <a href="https://www.amazon.com/Genius-Star-Possible-Blockers-Complete/dp/B089B48NCX/ref=sr_1_1?crid=3AFU0H4XMOF4Z&keywords=genius+star&qid=1691793044&sprefix=genius+star%2Caps%2C646&sr=8-1" target="_blank">Genius Star.</a> I hate for that to cause students to believe they aren't capable of solving it, or vice-versa, that if they are able to solve it, it makes them a genius! </span></p><p><span style="font-family: Montserrat;">This puzzle explores spatial relationships which for so many of our students can be a challenge. It also offers students the opportunity to distinguish pieces they should prioritize as well as a trial in perseverance!</span></p><p><span style="font-family: Montserrat;">Here's how it works:</span></p><p><span style="font-family: Montserrat;">Roll the die that come with the game:</span></p><p><span style="font-family: Montserrat;"></span></p><div class="separator" style="clear: both; text-align: center;"><span style="font-family: Montserrat;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEj8sAu20u_tv3lZFbTzYYBmJCFRZc6ly9r1BTUcXXMi0qYZPMAI7gz7whLVGogzowSnySPGraieKvTfw1gKaELGXw3xuF0HiVZOfZZN_tgwwgh2zFKgsPOq2UqhmEW3uI4ICvQDbPgtXfHZ1oLnn-dJ9e1z8lps2zXUnFNsBBWtWP77q9oY7eV5c9SDU3A" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="866" data-original-width="1154" height="240" src="https://blogger.googleusercontent.com/img/a/AVvXsEj8sAu20u_tv3lZFbTzYYBmJCFRZc6ly9r1BTUcXXMi0qYZPMAI7gz7whLVGogzowSnySPGraieKvTfw1gKaELGXw3xuF0HiVZOfZZN_tgwwgh2zFKgsPOq2UqhmEW3uI4ICvQDbPgtXfHZ1oLnn-dJ9e1z8lps2zXUnFNsBBWtWP77q9oY7eV5c9SDU3A" width="320" /></a></span></div><span style="font-family: Montserrat;"><br />Lay the little white triangles onto the corresponding triangles on the board:</span><p></p><p><span style="font-family: Montserrat;"></span></p><div class="separator" style="clear: both; text-align: center;"><span style="font-family: Montserrat;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgBuWuvJEWxNblqdllZlBoh6RHuoltUXWD9Su_7cH_wxQpac2P5eIBvfs0myv5zsyWSA2efcM2-Ub74svLBRl2r9b-lYVaCbDBF-H7_Brwma5dqARHKN4fgG7KjOzZOD9PQ5F6ylo0hyQiIP8lLb2QNWYBerKviD7l4bBF77cjGT_X5z51LSvtJIREjpHY" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="866" data-original-width="1154" height="240" src="https://blogger.googleusercontent.com/img/a/AVvXsEgBuWuvJEWxNblqdllZlBoh6RHuoltUXWD9Su_7cH_wxQpac2P5eIBvfs0myv5zsyWSA2efcM2-Ub74svLBRl2r9b-lYVaCbDBF-H7_Brwma5dqARHKN4fgG7KjOzZOD9PQ5F6ylo0hyQiIP8lLb2QNWYBerKviD7l4bBF77cjGT_X5z51LSvtJIREjpHY" width="320" /></a></span></div><span style="font-family: Montserrat;">Now, I usually solve these on my own, and I don't recommend that it becomes a racing game, but students then take the 11 game pieces and place them on the board to cover in the star.</span><p></p><p><span style="font-family: Montserrat;"></span></p><div class="separator" style="clear: both; text-align: center;"><span style="font-family: Montserrat;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgAnppKnkeK6XlkR_O8FaA286O7zx0nh4ihtr4BiD5tbEyJMKZis4cwtSEWitko7vLZVdc9m-qDQJwT7ZcrP7Vf-TMgUJXSHq9MFj6lLJm9nva0cOEoMelEy1IJEQMnwahzS3rWup5R3xykYB42TA44HnEXChfCha7Uy4Nagt7768zCoa2b_s8IT1bL4Ww" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="866" data-original-width="1154" height="240" src="https://blogger.googleusercontent.com/img/a/AVvXsEgAnppKnkeK6XlkR_O8FaA286O7zx0nh4ihtr4BiD5tbEyJMKZis4cwtSEWitko7vLZVdc9m-qDQJwT7ZcrP7Vf-TMgUJXSHq9MFj6lLJm9nva0cOEoMelEy1IJEQMnwahzS3rWup5R3xykYB42TA44HnEXChfCha7Uy4Nagt7768zCoa2b_s8IT1bL4Ww" width="320" /></a></span></div><div class="separator" style="clear: both; text-align: center;"><span style="font-family: Montserrat;"><br /></span></div><div class="separator" style="clear: both; text-align: left;"><span style="font-family: Montserrat;">Students can compare their solutions to see what they did the same or different.</span></div><div class="separator" style="clear: both; text-align: left;"><span style="font-family: Montserrat;"><br /></span></div><div class="separator" style="clear: both; text-align: center;"><span style="font-family: Montserrat;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgOJgQLa5i7zkWdjNPJmoZU4FoKN9lzm1tJy9_QkdruwGYqmYgpE12I6X7MI8ci_oeYwd8ZMlk6QOc_f9kxvwm-d35VAgmJ-TZWXDEilgFC9-IR2CeNDtGnzunpjuZAIkGzrTQlpyOqLHeCP0c8Wihyi1cSe_nONCSypI6E3QBDPp5gNTM6k2TgEQZl3Yc" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="866" data-original-width="1154" height="240" src="https://blogger.googleusercontent.com/img/a/AVvXsEgOJgQLa5i7zkWdjNPJmoZU4FoKN9lzm1tJy9_QkdruwGYqmYgpE12I6X7MI8ci_oeYwd8ZMlk6QOc_f9kxvwm-d35VAgmJ-TZWXDEilgFC9-IR2CeNDtGnzunpjuZAIkGzrTQlpyOqLHeCP0c8Wihyi1cSe_nONCSypI6E3QBDPp5gNTM6k2TgEQZl3Yc" width="320" /></a></span></div><span style="font-family: Montserrat;"><br />Students can also reflect on what made the puzzle challenging or easy. </span><p></p><p><span style="font-family: Montserrat;">The box comes with two black trays to solve the puzzle on, but you could maybe get more than one game so that more students could work to solve. I find it quite fun, and it highlights the spatial skills of math. The company makes other similar games that will show up when you follow the above link to this game.</span></p><p><span style="font-family: Montserrat;">Students can solve the puzzle in pairs and discuss their findings, they can investigate the dice and the regions of the board that each one covers, they could create their own puzzle numbers that they think are unsolvable and ask classmates to prove them wrong, they could create fractional questions about the puzzle or its pieces, or you could use two solutions for the same numbers as a same/different discussion. It seems to me like there are a lot of ways that this little puzzle could be used!</span></p><p><span style="font-family: Montserrat;">Let me know in the comments if you have found or find other ways to use <a href="https://www.amazon.com/Genius-Star-Possible-Blockers-Complete/dp/B089B48NCX/ref=sr_1_1?crid=3AFU0H4XMOF4Z&keywords=genius+star&qid=1691793044&sprefix=genius+star%2Caps%2C646&sr=8-1" target="_blank">this puzzle</a> in the classroom!</span></p><p><span style="font-family: Montserrat;"><br /><br /></span></p>Jennifer Gibsonhttp://www.blogger.com/profile/04128860663290797642noreply@blogger.com0tag:blogger.com,1999:blog-5519240175767583895.post-58274488083005382742023-04-18T08:38:00.001-05:002023-04-18T08:38:58.433-05:00Removing Ability Grouping while increasing Problem-Solving<p><span style="font-family: Montserrat;">One of the biggest missteps that occurs in math core instruction is people trying to organize it the same as they do their reading workshop. </span></p><p><span style="font-family: Montserrat;">Traditionally in reading workshop, students are grouped by reading level and then called to the teacher to read and discuss a text at their level. The teacher's small group instruction is really concentrated during this time when meeting with a small group of students away from the rest of their classmates.</span></p><p><span style="font-family: Montserrat;">In math workshop, we do not recommend this kind of grouping for students often. In fact, <a href="https://buildingthinkingclassrooms.com/" target="_blank">through the work of Peter Liljedahl</a>, more and more teachers are reading and using the research around VRG: <b>Visibly Random Grouping.</b> In his book, <i>Building Thinking Classrooms in Mathematics</i>, he explains how he realized students are more successful this way.</span></p><div class="separator" style="clear: both; text-align: center;"><a href="https://www.amazon.com/Building-Thinking-Classrooms-Mathematics-Grades/dp/1544374836" imageanchor="1" style="margin-left: 1em; margin-right: 1em;" target="_blank"><img border="0" data-original-height="499" data-original-width="350" height="183" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhR3AoW0SeCV2LQeIYVwDc2FT9YEPAp7xDNHJb67NonE3FEvGa4IOeefveGKoidFArarqT9PedkTGhymw8eqsRi48PMahtkg5zwoO2UyMV6-wPyEENt740n_7gZCbM870bPlh0eE9ixsa7bhWwCCxf9pbIlNjDi4GDQFdUBJ66gNh1YoH01PtkSP37U/w128-h183/BTC.jpg" width="128" /></a></div><p><span style="font-family: Montserrat;">Visibly Random Grouping can be intimidating to some teachers because it means that they have to give up some of their control. Not like <i>let the room run crazy </i>loss of control, but letting students work with whomever they match with. Teachers have spent a lot of time organizing and reorganizing their groups for activities. The thought of just letting it be random might be a lot. However, once teachers begin to use VRG, they tend to love the results.</span></p><p><span style="font-family: Montserrat;">To begin with, the students should witness that the grouping has been random. There are apps that group students randomly(even Dojo), but you can always use playing cards, popsicle sticks, birthdays, or any other method that helps them see that you did not intentionally choose who was going to work together. Liljedahl's research shows that groups of 3 work best in most grades to get all students thinking. In the primary grades, he recommends groups of 2.</span></p><p><span style="color: #800180; font-family: Montserrat;">Here are some of the benefits of VRG:</span></p><ul style="box-sizing: border-box; color: #7c7c7c; font-size: 15px; letter-spacing: 0.1px; list-style-type: circle; margin: 16px 0px; padding: 0px 0px 0px 28px; text-align: left;"><li><span style="font-family: Montserrat;">Increased engagement</span></li><li><span style="font-family: Montserrat;">Improved collaboration skills</span></li><li><span style="font-family: Montserrat;">Reliance of students on each other more than on the teacher</span></li><li><span style="font-family: Montserrat;">Improved student ability to work with anyone and recognize the strengths that classmates possess</span></li><li><span style="font-family: Montserrat;">Better flow of learning with students not just sharing in their group but also with others in the room: the feeling of being on the same team</span></li><li><span style="font-family: Montserrat;"><u>Perception of the students that the teacher believes they can do it. </u> They don't have to be placed with a student who can "pull them along" or one that they need to support. No matter who they are with, they will be able to access the problem and move forward.</span></li></ul><div><span style="font-family: Montserrat;">As teachers begin to move towards more use of VRG, <a href="https://thinkthinkmath.blogspot.com/2021/01/removing-labels-from-students.html" target="_blank">they will find themselves removing labels from students.</a> This subtle shift in thinking will carry over into the students' views of each other, too. <a href="https://thinkthinkmath.blogspot.com/2018/09/rethinking-grouping-in-math-workshop.html" target="_blank">This video by Jo Boaler </a>offers somemre insight into the benefits of heterogenous grouping.</span></div><div><span style="font-family: Montserrat;"><br /></span></div><div><span style="font-family: Montserrat;">There are many teaching shifts that Liljedahl discusses in his book. Visibly Random Grouping is one that is a great first shift for all teachers, and it will help when they decide to give a Thinking Classroom a try.</span></div>Jennifer Gibsonhttp://www.blogger.com/profile/04128860663290797642noreply@blogger.com0tag:blogger.com,1999:blog-5519240175767583895.post-78849000979136644812023-03-07T21:30:00.004-06:002023-03-07T21:30:43.000-06:00March is Full of Palindromes this Year!<p><span style="font-family: Montserrat;"> As we approach the end of March, we come close to multiple school days which are palindromes. From 3-20-23 to 3-29-23, our dates will be palindromes, and they may offer opportunities for you and your students to explore palindromes!</span></p><p><span style="font-family: Montserrat;">Students of all ages can look more closely at palindromes! I am going to focus on explorations with numbers, but your students might enjoy finding words that are palindromes, too. Here are a few books you might share with your students:</span></p><p></p><div class="separator" style="clear: both; text-align: center;"><span style="font-family: Montserrat;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgOa30YaPcJxCyOhwDX-fBg79k9TQ7T7B3bZyS81SDKJnbagr6EkKIjezL4CpirVPdjZtm6geeXNDFeAzW0ICGiwbaPDP9DkQkqtYIQPfgWD3zXtvVgQJXHIcduq5tO99MSiDHZ_1qiLW0zbbfcBt42amPEBLKVMtJeIwenM6wBdjMSHZsk7hWL0nID" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="982" data-original-width="1000" height="122" src="https://blogger.googleusercontent.com/img/a/AVvXsEgOa30YaPcJxCyOhwDX-fBg79k9TQ7T7B3bZyS81SDKJnbagr6EkKIjezL4CpirVPdjZtm6geeXNDFeAzW0ICGiwbaPDP9DkQkqtYIQPfgWD3zXtvVgQJXHIcduq5tO99MSiDHZ_1qiLW0zbbfcBt42amPEBLKVMtJeIwenM6wBdjMSHZsk7hWL0nID=w124-h122" width="124" /></a><a href="https://blogger.googleusercontent.com/img/a/AVvXsEhGzsnyiwF_A76iszp-9dhw-iNWir2OhhP7CB67W300BLN8xuDMR5j8p1MMKe3bQ4Z7bhXrGJjvJFj2RpA4mrvkMY9n65VGN3AI-K2EB6VskNRiqngMkiiVa-ciKLCbYD5FgGEJZA16EN08h6FzkFdOmxQHmlbKPecV43qHXc88M7_VUTWNXlzudGK8" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="400" data-original-width="644" height="153" src="https://blogger.googleusercontent.com/img/a/AVvXsEhGzsnyiwF_A76iszp-9dhw-iNWir2OhhP7CB67W300BLN8xuDMR5j8p1MMKe3bQ4Z7bhXrGJjvJFj2RpA4mrvkMY9n65VGN3AI-K2EB6VskNRiqngMkiiVa-ciKLCbYD5FgGEJZA16EN08h6FzkFdOmxQHmlbKPecV43qHXc88M7_VUTWNXlzudGK8=w247-h153" width="247" /></a><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjd60L5VdKcd0nN4Jf3QuvrbAnGGilKwGarCQkXs9zZAiV_4QChjEOXD7eFHWCeL5S_Mai7U5a0TY8A3OWWvxKJS2SSD9BcGa9s1wd5SwmaJM78N6ZD9yEu7OUMzMpdDKf4SRiACjnMBCKZ6TVD-N7poptXeLdYc2vr4EHfLq1npmLyGFXHHlkKlvhG" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="250" data-original-width="198" height="166" src="https://blogger.googleusercontent.com/img/a/AVvXsEjd60L5VdKcd0nN4Jf3QuvrbAnGGilKwGarCQkXs9zZAiV_4QChjEOXD7eFHWCeL5S_Mai7U5a0TY8A3OWWvxKJS2SSD9BcGa9s1wd5SwmaJM78N6ZD9yEu7OUMzMpdDKf4SRiACjnMBCKZ6TVD-N7poptXeLdYc2vr4EHfLq1npmLyGFXHHlkKlvhG=w131-h166" width="131" /></a></span><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEhGzsnyiwF_A76iszp-9dhw-iNWir2OhhP7CB67W300BLN8xuDMR5j8p1MMKe3bQ4Z7bhXrGJjvJFj2RpA4mrvkMY9n65VGN3AI-K2EB6VskNRiqngMkiiVa-ciKLCbYD5FgGEJZA16EN08h6FzkFdOmxQHmlbKPecV43qHXc88M7_VUTWNXlzudGK8" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: Montserrat;"><br /></span></a></div><span style="font-family: Montserrat;"><br /></span></div><span style="font-family: Montserrat;">Some of your students may get caught up in noticing individual words that are palindromes, but some may enjoy the word play involved in sayings and phrases that are palindromes. At either level, it is word work that many students find FUN!</span><p></p><p><span style="font-family: Montserrat;">For math explorations, you might not explain to your young students what a palindrome is, but let them discover! </span></p><p></p><ul style="text-align: left;"><li><span style="font-family: Montserrat;">Using your pattern blocks as a visual, you can give students numbers to "create" and allow them to notice what makes these numbers special. For example:</span></li></ul><p></p><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiTCxFBm39JXBlsfSzwz0lifL4npkW7pKNbabedXf9lwoKMVwB5fLYCxUXhHpKHMKMS6V1DAmy9DDsCVoe2zl14tXJmFT_6popTjN4yIXd7Nf8YWDDk96PRGjyjbYlTISRSKwH9Z-qOvg7TmiNJx7AedIqG-_VWDrmhzuYfNkDZYC6rGUbJffsEL1TS/s1758/palindrome1.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="810" data-original-width="1758" height="131" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiTCxFBm39JXBlsfSzwz0lifL4npkW7pKNbabedXf9lwoKMVwB5fLYCxUXhHpKHMKMS6V1DAmy9DDsCVoe2zl14tXJmFT_6popTjN4yIXd7Nf8YWDDk96PRGjyjbYlTISRSKwH9Z-qOvg7TmiNJx7AedIqG-_VWDrmhzuYfNkDZYC6rGUbJffsEL1TS/w286-h131/palindrome1.png" width="286" /></a><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhExGuJ7D8LVs9Cm7pyzByGu4f3Wr8KWQspMhl0AaM4zaEUtr_YpU2ctEnR0EPNPw3Fg760lYBDcwj-DRBEbmllmyn56AbrZnP5Ro82WT7C-ttvT70fUuD8g4Kf8hL3c-Lcxg1sXPe7LAEGxpENdhpsEN1KIPraNMxTFuinlVyz9_6g7pPsyce-1yY7/s1764/palindrome2.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="796" data-original-width="1764" height="127" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhExGuJ7D8LVs9Cm7pyzByGu4f3Wr8KWQspMhl0AaM4zaEUtr_YpU2ctEnR0EPNPw3Fg760lYBDcwj-DRBEbmllmyn56AbrZnP5Ro82WT7C-ttvT70fUuD8g4Kf8hL3c-Lcxg1sXPe7LAEGxpENdhpsEN1KIPraNMxTFuinlVyz9_6g7pPsyce-1yY7/w282-h127/palindrome2.png" width="282" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;"><span style="font-family: Montserrat;">If you display the pattern blocks to represent different digits, then you can dictate numbers and ask students to create them. Can they identify the pattern that makes palindromes special? Can they see with the March dates how they are palindromes?</span></div><div class="separator" style="clear: both; text-align: left;"><span style="font-family: Montserrat;"><br /></span></div><div class="separator" style="clear: both; text-align: left;"><ul style="text-align: left;"><li><span style="font-family: Montserrat;">Ask your students to find all of the palindromes between 0 and 100. What do they notice about two-digit palindromes? Is there a pattern in 3 digit palindromes?</span></li></ul><ul style="text-align: left;"><li><span style="font-family: Montserrat;">Will there be other palindromes this year? How about next year--What palindromes will there be? Is there ever a year without a palindrome date? What can your students find?</span></li></ul><ul style="text-align: left;"><li><span style="font-family: Montserrat;">Finding palindromic numbers <a href="https://mathforlove.com/" target="_blank">Math For Love</a> has a<a href="https://mathforlove.com/lesson/number-palindromes/" target="_blank"> great lesson exploration</a> opportunity where students search for different levels of palindromes. It offers a way for students to add, look for patterns, and have fun with numbers--all in one activity!</span></li></ul><div><div><br /></div></div><div><span style="font-family: Montserrat;">I hope you and your students find some time to explore the fascinating patterns and elements of palindromes in our words and numbers! You might want to consider ending with <a href="https://www.youtube.com/watch?v=JUQDzj6R3p4" target="_blank">this Weird Al video, Bob</a>, which is made entirely of palindromes.</span></div></div><p><br /></p>
<div style="text-align: center;"><iframe allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share" allowfullscreen="" frameborder="0" height="315" src="https://www.youtube.com/embed/JUQDzj6R3p4" title="YouTube video player" width="560"></iframe></div>Jennifer Gibsonhttp://www.blogger.com/profile/04128860663290797642noreply@blogger.com1tag:blogger.com,1999:blog-5519240175767583895.post-3323006743305693252022-11-29T20:06:00.004-06:002022-11-29T20:06:37.692-06:00Mathigon & Polypad & Puzzles...Oh My!<p><span style="font-family: Montserrat;">I have been a fan of <a href="https://mathigon.org/polypad" target="_blank">Mathigon's Polypad </a>for quite a while now, and have found many great ways for it to be used to help students build better mathematical understanding as well as to challenge their current understandings.</span></p><p><span style="font-family: Montserrat;">I want to share a few of the great resources available on Mathigon in hopes that you will find ways for them to work for you and your students!</span></p><p><span style="font-family: Montserrat;"><a href="https://mathigon.org/multiply" target="_blank">The Multiplication by Heart cards </a>(created by Math for Love) are great visual practice for students as they learn to understand and master their multiplication facts. </span></p><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEj51aP7ibeFJLkLlLcDcfKIrvcM4cdxFLIlKOJx18Ehjj9lFcdXGxVHr7U2OF5fnSDdSDruG66jA3Qxw_bCc9H31uqbkpYF5jOV_XwR5TaSjEAG1dZepKhShcQxSv7sk0-ypSRaGRBiDIClorT3RlAuJgk6OfQH6FpUzoym5Muvk_sryUFSIirLJGCw" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: Montserrat;"><img alt="" data-original-height="656" data-original-width="782" height="168" src="https://blogger.googleusercontent.com/img/a/AVvXsEj51aP7ibeFJLkLlLcDcfKIrvcM4cdxFLIlKOJx18Ehjj9lFcdXGxVHr7U2OF5fnSDdSDruG66jA3Qxw_bCc9H31uqbkpYF5jOV_XwR5TaSjEAG1dZepKhShcQxSv7sk0-ypSRaGRBiDIClorT3RlAuJgk6OfQH6FpUzoym5Muvk_sryUFSIirLJGCw=w200-h168" width="200" /></span></a></div><div class="separator" style="clear: both; text-align: left;"><span style="font-family: Montserrat;"><br /></span></div><div class="separator" style="clear: both; text-align: left;"><span style="font-family: Montserrat;">Of course, I also enjoy the<a href="https://mathigon.org/tangram" target="_blank"> Tangram Builder</a> which is located in the Activities section.</span></div><div class="separator" style="clear: both; text-align: center;"><span style="font-family: Montserrat;"><br /></span></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEj2QblKNZzrZGVoGgKHxKLUh8EHd6fLiK-DL10yM2it787t1utw-fScW9ByYBcp_YnNLgUIfgR1OV1Zk4gbtXJJLY4K5wlkeSY_9LyEPiWQXNYGTTBU_11rzZkF9dBtsGvjupG_yS-6zwGjeTig6OAcJVaWRacSSks4SQBsS0HKwIuanMHIecFXrhBB" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: Montserrat;"><img alt="" data-original-height="851" data-original-width="1410" height="121" src="https://blogger.googleusercontent.com/img/a/AVvXsEj2QblKNZzrZGVoGgKHxKLUh8EHd6fLiK-DL10yM2it787t1utw-fScW9ByYBcp_YnNLgUIfgR1OV1Zk4gbtXJJLY4K5wlkeSY_9LyEPiWQXNYGTTBU_11rzZkF9dBtsGvjupG_yS-6zwGjeTig6OAcJVaWRacSSks4SQBsS0HKwIuanMHIecFXrhBB=w200-h121" width="200" /></span></a></div><div class="separator" style="clear: both; text-align: center;"><span style="font-family: Montserrat;"><br /></span></div><div class="separator" style="clear: both; text-align: left;"><span style="font-family: Montserrat;"><a href="https://mathigon.org/course/exploding-dots/infinity" target="_blank">Exploding Dots </a>can also be found here. If you have not spent time in the Exploding Dots world by James Tanton, do yourself and your students a favor! It would make for a great exploration for your students. The Exploding Dots experience on Mathigon is an extension of <a href="https://www.explodingdots.org/" target="_blank">the actual website</a>, but still one to get you thinking.</span></div><div class="separator" style="clear: both; text-align: center;"><span style="font-family: Montserrat;"><br /></span></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjRZ5GFaqNPmiipyNcg5paB5dq8HUsaeoDlC-9Lpnx4N7LABEfz6-71lk1ibncokRaph7g9s9Ha6qOsNvzy-FW92F80MjbH03IvWK_iUaRfy1ak_xPGm-fCpxEICCbIGyZl4Ut1nMig9H_xjr-wr2-XLxM3Cbu78qcZHpk9Vfh8JJBH1yhihoUCJDBZ" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: Montserrat;"><img alt="" data-original-height="555" data-original-width="453" height="200" src="https://blogger.googleusercontent.com/img/a/AVvXsEjRZ5GFaqNPmiipyNcg5paB5dq8HUsaeoDlC-9Lpnx4N7LABEfz6-71lk1ibncokRaph7g9s9Ha6qOsNvzy-FW92F80MjbH03IvWK_iUaRfy1ak_xPGm-fCpxEICCbIGyZl4Ut1nMig9H_xjr-wr2-XLxM3Cbu78qcZHpk9Vfh8JJBH1yhihoUCJDBZ=w163-h200" width="163" /></span></a></div><div class="separator" style="clear: both; text-align: center;"><span style="font-family: Montserrat;"><br /></span></div><div class="separator" style="clear: both; text-align: left;"><span style="font-family: Montserrat;">What really got my attention on Mathigon is its <a href="https://mathigon.org/polypad" target="_blank">Polypad</a> section! It has so many unique manipulatives and tools to offer your students.</span></div><div class="separator" style="clear: both; text-align: left;"><span style="font-family: Montserrat;"><br /></span></div><div class="separator" style="clear: both; text-align: left;"><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjqcrG3MIOoGfuJHBfFTkaliW5V4NAnjUNVHZGa-aEk9495XNYaj0ayHr0wXoTzNrkveO75ld3NDqCZnc0DRpH6Ze9esx__cupNCJBjQcbtDv8Vv5pRwjEVZWvOEh3P3aepZx8LpWdXxG59cVteE_26FR0EmMRbLoeIX7pPfjS6dd92sebPeeuIPM80" style="margin-left: auto; margin-right: auto;"><span style="font-family: Montserrat;"><img alt="" data-original-height="756" data-original-width="989" height="245" src="https://blogger.googleusercontent.com/img/a/AVvXsEjqcrG3MIOoGfuJHBfFTkaliW5V4NAnjUNVHZGa-aEk9495XNYaj0ayHr0wXoTzNrkveO75ld3NDqCZnc0DRpH6Ze9esx__cupNCJBjQcbtDv8Vv5pRwjEVZWvOEh3P3aepZx8LpWdXxG59cVteE_26FR0EmMRbLoeIX7pPfjS6dd92sebPeeuIPM80=w320-h245" width="320" /></span></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><span style="font-family: Montserrat;">This polypad includes a balance scale and fraction bars. Each could be used separately.</span></td></tr></tbody></table><span style="font-family: Montserrat;"><br /></span><div class="separator" style="clear: both; text-align: center;"><span style="font-family: Montserrat;"><br /></span></div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEiAmon6la0tSetqq3ZuknW8siGthH4H66sMkkcclIy6eAbiIB1g3DJguhXCsnkyRobN5Fe9LswdnK7jgpgSnAL13w01V-xxfMr8jtzDPZpHN-JR6rQ2WoalLqE9fpc5h5XcD2rBJc6K4WiuX5ZNR75jSgY9ETI0aMxeXX_8K6HtKvfrrz4JYwyBLBNk" style="margin-left: auto; margin-right: auto;"><span style="font-family: Montserrat;"><img alt="" data-original-height="768" data-original-width="891" height="277" src="https://blogger.googleusercontent.com/img/a/AVvXsEiAmon6la0tSetqq3ZuknW8siGthH4H66sMkkcclIy6eAbiIB1g3DJguhXCsnkyRobN5Fe9LswdnK7jgpgSnAL13w01V-xxfMr8jtzDPZpHN-JR6rQ2WoalLqE9fpc5h5XcD2rBJc6K4WiuX5ZNR75jSgY9ETI0aMxeXX_8K6HtKvfrrz4JYwyBLBNk=w320-h277" width="320" /></span></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><span style="font-family: Montserrat;">Students can make music using these tools found in Polypad.</span></td></tr></tbody></table><span style="font-family: Montserrat;"><br /><br /><br /></span><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEg4dJ34vqv-F6xguIfxWKiSK3WqbwJkXdq9RXr1NCOaDa91LhrAc2_XIV38XJ-ohrSM1GrjZvaUKtsk_Fk2F3pBQrbU0XOaZec1USGu0Z9wCqAUOBg3OWezQmYpcgZsMKkNZAzWp0LJHYN3QWNh7HDkZHa29HN3T-TohYvm_vOSX50Vg2ga79JxJS9C" style="margin-left: auto; margin-right: auto;"><span style="font-family: Montserrat;"><img alt="" data-original-height="727" data-original-width="722" height="320" src="https://blogger.googleusercontent.com/img/a/AVvXsEg4dJ34vqv-F6xguIfxWKiSK3WqbwJkXdq9RXr1NCOaDa91LhrAc2_XIV38XJ-ohrSM1GrjZvaUKtsk_Fk2F3pBQrbU0XOaZec1USGu0Z9wCqAUOBg3OWezQmYpcgZsMKkNZAzWp0LJHYN3QWNh7HDkZHa29HN3T-TohYvm_vOSX50Vg2ga79JxJS9C=w317-h320" width="317" /></span></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><span style="font-family: Montserrat;">These Prime Factor Circles are a match to Prime Climb and can be decomposed (if composite) or combined as you wish to create new products.</span></td></tr></tbody></table><span style="font-family: Montserrat;"><br /><br />This is just the tip of the iceberg in this fabulous site. You can save and link activities that you make within the Polypad, but you can also use some of the many that are already prepared. One last thing to explore is the<a href="https://mathigon.org/tasks" target="_blank"> Lessons tab.</a> Inside of there you will find your way to a variety of puzzles and explorations for you and your students.</span></div><div class="separator" style="clear: both; text-align: left;"><span style="font-family: Montserrat;"><br /></span></div><div class="separator" style="clear: both; text-align: left;"><span style="font-family: Montserrat;">Take the time for your students and yourself to explore this site. You won't be disappointed!</span></div><span style="font-family: Montserrat;"><br /><br /></span></div><span style="font-family: Montserrat;"><br /><br /></span></div><span style="font-family: Montserrat;"><br /></span><br /><p></p>Jennifer Gibsonhttp://www.blogger.com/profile/04128860663290797642noreply@blogger.com0tag:blogger.com,1999:blog-5519240175767583895.post-45991517704818981802022-10-13T21:08:00.003-05:002022-10-16T19:36:29.818-05:00Building Math Culture<p><span style="font-family: Montserrat;"> I often talk to teachers about the importance of building a learning culture in their classrooms. It is so important that students feel safe and valued in their learning ideas.</span></p><p><span style="font-family: Montserrat;">Recently, I came upon <span style="color: #2b00fe;"><a href="https://www.mindsetkit.org/" target="_blank"><span>this website</span></a>, </span>which gives tips and has videos to guide teachers and families in promoting a growth mindset in students. I especially liked the examples within the section on<span> <span style="color: #2b00fe;"><a href="https://www.mindsetkit.org/topics/celebrate-mistakes" target="_blank">Celebrating Mistakes</a>.</span></span></span></p><p><span style="font-family: Montserrat;">It reminded me of a teacher I recently listened to excitedly explain the building of culture in her classroom. She talked about how she and her students cheer for each other's mistakes, how students grow in their ability to talk about math through the constant exposure to thinking problems, and how her students love math time in the classroom. There was no doubt that this excited teacher was talking from the positive experiences happening in her room, and that her students, too, had wonderful experiences as growing mathematicians!</span></p><p><span style="font-family: Montserrat;">Everyone in the room could feel the joy that this teacher exuded, and I'm sure, like me, they were wishing to have students (or be a student) who were a part of this classroom. As students grow and content becomes more and more, I think teachers find it more difficult to create this type of atmosphere, but by visiting the website, teachers might find just the motivation to build a stronger classroom learning culture. Even in October it is not too late!</span></p><p><span style="font-family: Montserrat;"><br /></span></p><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg822eBb3ShUw76Uw-BqATgUA_if7eDrWwiC_XHovfsNLwW0XxP0v0D6z295lLrciaLVY6Z6JyxJ0xMtcEkUtQCIviNCn0nKV6B8TFiFWN8uC-Gnx8cyLgYvrYI4RD_-TreSc1zzHNgRZT4KmcbVJOPre7XCVJSzP7FzvYajS_5A0R38yxnRYLtz3CH/s640/IMG_3179.JPG" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="480" data-original-width="640" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg822eBb3ShUw76Uw-BqATgUA_if7eDrWwiC_XHovfsNLwW0XxP0v0D6z295lLrciaLVY6Z6JyxJ0xMtcEkUtQCIviNCn0nKV6B8TFiFWN8uC-Gnx8cyLgYvrYI4RD_-TreSc1zzHNgRZT4KmcbVJOPre7XCVJSzP7FzvYajS_5A0R38yxnRYLtz3CH/s320/IMG_3179.JPG" width="320" /></a></div><br /><span style="font-family: Montserrat;"><br /></span><p></p>Jennifer Gibsonhttp://www.blogger.com/profile/04128860663290797642noreply@blogger.com0tag:blogger.com,1999:blog-5519240175767583895.post-75447338114479531662022-04-26T11:25:00.003-05:002023-04-18T07:43:30.949-05:00We are all math people!<p><span style="font-family: Montserrat;">Slowly, I am beginning to notice the phrase "math person" disappearing, and I am thrilled! We are all math people. It is not a subject for the elite--<u>all</u> of our lives involve math.</span></p><p><span style="font-family: Montserrat;">As is often said, people rarely go around and say, "I can't read," yet they have no issues with stating that they can't do math. I believe that people say this because they limit their definition of math. Math is such an important piece of our everyday lives. </span></p><p><span style="font-family: Montserrat;">Math is about <u>way more</u> than just computing. It is about logic and thinking and patterns. It is about shapes and sounds and data. It is about puzzles and perseverance. It is something we can all do. It is something that <u>all of our</u> students can do. It is just how this looks that may vary.</span></p><p><span style="font-family: Montserrat;">Computers were created by great thinkers so that we do not need to spend all of our time completing computation problems. The part that we need to do (and our students need to do) is think about the math: <span style="color: #800180;">What does this data tell us? How can we use this data? What do I need to do with these numbers? Which fraction is bigger? What fraction is smaller? What discount is better? Which measuring cup can I use when I can't find my half cup? About how much money will I need? How is symmetry used in art? How does logic help me solve a Wordle? </span> This is real world math. This is math that matters to us. Knowing that 7 x 9 is 63 is an important fact for sure, but it will only be relevant to a person as they age if it is necessary as part of their daily activities. Many carpenters know their 12s times tables for this reason.</span></p><p><span style="font-family: Montserrat;">So many other beautiful things that we do and experience daily involve math like baking, building, music, and art. Once we expand our thinking around the definition, we will see that <u>we are all math people</u>.</span></p><p><span style="font-family: Montserrat;"><br /></span></p><p><span style="font-family: Montserrat;">A t-shirt that I have seen many times says this:</span></p><p style="text-align: center;"><span style="color: #800180; font-family: Montserrat;">HOW TO BE A MATH PERSON:</span></p><p style="text-align: center;"><span style="color: #800180; font-family: Montserrat;">1. Do math. (any type)</span></p><p style="text-align: center;"><span style="color: #800180; font-family: Montserrat;">2. Be a person.</span></p>Jennifer Gibsonhttp://www.blogger.com/profile/04128860663290797642noreply@blogger.com0tag:blogger.com,1999:blog-5519240175767583895.post-22545600064977972932022-01-31T23:31:00.004-06:002023-04-18T07:43:58.347-05:00The Value of Routines<span style="font-family: Montserrat;">Classrooms with <a href="https://thinkthinkmath.blogspot.com/p/routines.html" target="_blank">strong routines</a> reap many benefits. This has become very evident this year as i have seen so many more classrooms begin math instruction each day with a routine.</span><div><span style="font-family: Montserrat;"><br /></span></div><div><span style="font-family: Montserrat;">In this year of continued chaos caused by the pandemic, teachers are finding that through routines, they can reinforce and review skills from previous grades. They are also able to use routines to preview skills that might not be coming until later in the year. So many free, well-designed routines are out there for teachers to use that it is easier than ever to find one that meets our students' needs.</span></div><div><span style="font-family: Montserrat;"><br /></span></div><div><span style="font-family: Montserrat;">Low-floor, high-ceiling routines are wonderful for engaging all students, and they usually involve a visual that helps students to all be able to "step-in" to the learning. Favorite examples of these types of routines include Which One Doesn't Belong and Same/Different. Teachers and students alike enjoy these routines because there are so many possibilities within one routine as they allow students to make sense of the problems in ways that make sense to them.</span></div><div><span style="font-family: Montserrat;"><br /></span></div><div><span style="font-family: Montserrat;">Many of the routines from <a href="https://stevewyborney.com/" target="_blank">Steve Wyborney</a> are also loved by teachers and students. These routines contain visuals, offer great exposure to vocabulary, and build number sense. Teachers love them because they are professionally made and easy to use, and students love them because they are fun! </span></div><div><span style="font-family: Montserrat;"><br /></span></div><div><span style="font-family: Montserrat;">Of course, Number Talks also are a routine that helps to build student discourse and fluency. Using the book as a guide for these helps students to develop and use strategies when they are ready. Doing Number Talks regularly has been shown to grow student fluency and flexibility in computation.</span></div><div><span style="font-family: Montserrat;"><br /></span></div><div><span style="font-family: Montserrat;">As students become more familiar with routines, there are many ways teachers can tweak the format. For example, they might decide to have students create their own following a favorite routine. (Creating your own Which One Doesn't Belong isn't as easy it might seem.) Students can create these routines and share them with other classrooms besides their own giving them a larger audience for their work. Teachers might also use routines as a daily warmup such as revealing one clue a day to an Estimystery and then discussing the students' thinking at the end of the week. I've even seen teacher print out images from routines and have students discuss them as they wait outside of a special class like PE or music. A routine image might be part of a weekly newsletter so that families can discuss it together. There are many ways that these routines can be used throughout a day's learning in addition to a warmup for math block.</span></div><div><span style="font-family: Montserrat;"><br /></span></div><div><span style="font-family: Montserrat;">All of these math class routines help to build a strong classroom culture of open, flexible thinking. They also strengthen students' number sense and confidence while expanding their math vocabulary. Teachers gain better insight to student development and can use these routines to help determine what next steps to take instructionally. They see quickly how students grow through the use of routines that meet their student needs; the routines may change from year to year. </span></div><div><span style="font-family: Montserrat;"><br /></span></div><div><span style="font-family: Montserrat;">Math routines help us to build mathematicians whose confidence help them to take on the math practice standards as part of who they are. </span></div><div><span style="font-family: georgia;"><br /></span></div><div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEj_M8uM68wqsoU2yHYSbNlm-Hf2UTTHqw1XBsJfF9HmSWh42ZjazX8qBDeX2sweqc5eqKQTBOiqqZhR0mgFPeQ_RWWbSdCnPuyY68mLrmSnopk6LqYij5NEVg8X1HiZ4YcRZPk2kJ85ihPxepH8cdMzs1utQ8i-gn9MmGXEQeOwBuJXVYFOXGS57x91=s711" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="711" data-original-width="600" height="320" src="https://blogger.googleusercontent.com/img/a/AVvXsEj_M8uM68wqsoU2yHYSbNlm-Hf2UTTHqw1XBsJfF9HmSWh42ZjazX8qBDeX2sweqc5eqKQTBOiqqZhR0mgFPeQ_RWWbSdCnPuyY68mLrmSnopk6LqYij5NEVg8X1HiZ4YcRZPk2kJ85ihPxepH8cdMzs1utQ8i-gn9MmGXEQeOwBuJXVYFOXGS57x91=s320" width="270" /></a></div><br /><span style="font-family: georgia;"><br /></span></div>Jennifer Gibsonhttp://www.blogger.com/profile/04128860663290797642noreply@blogger.com0tag:blogger.com,1999:blog-5519240175767583895.post-40136899512423841592021-05-10T21:25:00.001-05:002021-08-15T21:21:12.954-05:00Best Practices: Where can you grow?<p><span style="font-family: georgia;"> </span><span style="font-family: Montserrat;">It has been a crazy, stressful year. <u>The good news is that the end is in sight for this school year.</u> And, while we may still live with some restrictions when our new year arrives next fall, we anticipate that many things will return to a more typical format for instruction.</span></p><p><span style="font-family: Montserrat;">So--let's look with next year in sight. I know your summer is looking promising. You can't wait to just relax and enjoy all that the world has to offer without the weight of instruction on your mind. However--I imagine, like me, you find it difficult to totally <i>turn off school. </i>Here are some things you might consider looking into to grow as a math teacher for next year. <span style="color: #800180;">Think about these best practices</span>. Which ones seem reasonable for you as you continue on your math journey? You might choose two; you might choose seven. Do what works for you.</span></p><p><span style="font-family: Montserrat;"><br /></span></p><p><span style="font-family: Montserrat;"><b><span style="color: #0b5394;">Daily Routines:</span></b> Using the beginning moments of your workshop to get everyone thinking around an interesting problem is a great way to get the juices flowing! I would definitely include traditional number talks in these routines, but <a href="https://thinkthinkmath.blogspot.com/p/routines.html" target="_blank">there are so many others to consider</a>. Look for low floor/high ceiling routines that allow all students to enter into the problem and encourage creativity and fun for all.</span></p><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh-aXQ89ltfH-1uBdBxAPpke0xAI6X-RSW1C5ullUM3H8s_Oy29nanroVmFFuN8-PufSWO-6iDNRjDqPU277tG_XI5Y2Ic-9ESh7nplLE0m6Irp_pydHwKIYlKTDs3YE5EXZ548qSlUC_0/s4032/IMG_1216.HEIC" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: Montserrat;"><img border="0" data-original-height="4032" data-original-width="3024" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh-aXQ89ltfH-1uBdBxAPpke0xAI6X-RSW1C5ullUM3H8s_Oy29nanroVmFFuN8-PufSWO-6iDNRjDqPU277tG_XI5Y2Ic-9ESh7nplLE0m6Irp_pydHwKIYlKTDs3YE5EXZ548qSlUC_0/s320/IMG_1216.HEIC" /></span></a></div><span style="font-family: Montserrat;"><br /><span><br /></span></span><p></p><p><span style="font-family: Montserrat;"><b><span style="color: #0b5394;">More Manipulatives: </span></b> CRA Instruction "puts math in students' hands so they can understand it with their heads." <u>All</u> students benefit from this type of instruction, but sadly, we tend to move away from it too quickly. It is one of the best ways for students to gain conceptual understanding of concepts.</span></p><p><span style="font-family: Montserrat;"><b><span style="color: #0b5394;">Numberless Word Problems: </span></b> Key words are cancelled. They are not a good instructional practice because they do not encourage good thinking from our students. Taking some time to think around <a href="https://bstockus.wordpress.com/numberless-word-problems/" target="_blank">word problems that do not have numbers </a>is a fabulous strategy for our students. It not only shows the link between reading skills and math context, but it puts another tool in our students' toolboxes that they can use when they are confused by a word problem. Remove the numbers!</span></p><p><span style="font-family: Montserrat;"><b><span style="color: #0b5394;">Counting Collections: </span></b> The counting collections activity is way more complex than just counting, but it is also as simple as just counting. The CGI approach is really working hard in this activity that I love to use from K to 5th! (It could be used with older students, too!) It is an in-action practice of concrete, representational, and abstract. This can be done by individuals or in pairs, but as always, the sharing at the end is where the real learning occurs! You do not need anything fancy to count, so don't feel like this is something you have to go out and buy materials for.</span></p><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEijP61e1KWxD7Sx_DvLu7Vw_CwkhQuX8QAlOhdhZSxGeQ6g_2V6jyH3HIT17HydAnvMWF_rXEBCFJgH2ocPXgLoMdapOc26kY2iChIPklHef9wqtkIsHh7w0MXpMYtOQ_65bQ_8jVVps-M/s4032/IMG_1672.HEIC" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: Montserrat;"><img border="0" data-original-height="4032" data-original-width="3024" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEijP61e1KWxD7Sx_DvLu7Vw_CwkhQuX8QAlOhdhZSxGeQ6g_2V6jyH3HIT17HydAnvMWF_rXEBCFJgH2ocPXgLoMdapOc26kY2iChIPklHef9wqtkIsHh7w0MXpMYtOQ_65bQ_8jVVps-M/s320/IMG_1672.HEIC" /></span></a></div><span style="font-family: Montserrat;"><br /><span><br /></span></span><p></p><p><span style="font-family: Montserrat;"><b><span style="color: #0b5394;">More Visuals: </span></b> <u><a href="https://mathisvisual.com/how-to/" target="_blank">Math is visual.</a></u> Find ways to help students SEE the math in everything you do. From representations during Number Talks to <a href="https://mathvisuals.wordpress.com/" target="_blank">counting aloud visuals </a>to the <a href="https://samedifferentimages.wordpress.com/" target="_blank">Same/Different</a> routine to <a href="https://www.amazon.com/Math-for-Love-Prime-Climb/dp/B00PG9590G" target="_blank">Prime Climb</a> or <a href="https://www.amazon.com/Math-Love-Tiny-Polka-Dot/dp/B01N1UUHP4/ref=pd_lpo_21_t_1/137-4354703-9056816?_encoding=UTF8&pd_rd_i=B01N1UUHP4&pd_rd_r=db2eaaa7-a588-479c-b342-68fc8b665920&pd_rd_w=90I97&pd_rd_wg=CLFDq&pf_rd_p=a0d6e967-6561-454c-84f8-2ce2c92b79a6&pf_rd_r=6WF3EHC3TSC2GFH28WCT&psc=1&refRID=6WF3EHC3TSC2GFH28WCT" target="_blank">Tiny Polka Dot</a>, put the math out there in a way that students can engage with and understand. Visuals help all students to engage and step-in to the lesson.</span></p><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjh7qHeHOxJUGG0n7IKd4TI9KI15X9cPte3iCWbfAjpy952X-7TKL2fktJcXkFo-1DBpk6BNNzW03JzMILdVinuy1t6qI4dk97g-TdC6VVMBqpstWsd2O4XjQgbowbjgLb0Tv5jcYN_jQI/s4032/IMG_1270.HEIC" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: Montserrat;"><img border="0" data-original-height="4032" data-original-width="3024" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjh7qHeHOxJUGG0n7IKd4TI9KI15X9cPte3iCWbfAjpy952X-7TKL2fktJcXkFo-1DBpk6BNNzW03JzMILdVinuy1t6qI4dk97g-TdC6VVMBqpstWsd2O4XjQgbowbjgLb0Tv5jcYN_jQI/s320/IMG_1270.HEIC" /></span></a></div><span style="font-family: Montserrat;"><br /><span><br /></span></span><p></p><p><span style="font-family: Montserrat;"><span style="color: #0b5394; font-weight: bold;">Three Act Tasks: </span>These offer such a good opportunity for our students to make sense of math, and they do not follow the "I do, we do, you do" instructional format. There are so many available to choose from. The tab at the top of this blog is a rabbit hole that will take you to quite a few. How can you be more intentional about using them next year?</span></p><p><span style="font-family: Montserrat;"><span style="color: #0b5394;"><b>Heterogeneous Grouping: </b></span> Tracking students is not an equitable practice. All students need the opportunity to see and do high level tasks. Let's not limit our students. Be more intentional about grouping your students with students of varying strengths. Don't underestimate what your students can do.</span></p><p><span style="font-family: Montserrat;"><b><span style="color: #0b5394;">More Incorporation of Data: </span></b> Jo Boaler has added <a href="https://www.youcubed.org/resource/data-talks/" target="_blank">resources to her Youcubed website</a> around data. <a href="https://slowrevealgraphs.com/" target="_blank">SlowRevealgraphs.com </a> has a number of prepared slide decks for many different levels. These can be used in math class or incorporated into content areas. Teaching our students how to read, question, interpret, and create various data representations is an important 21st century skill.</span></p><p><span style="font-family: Montserrat;"><b style="color: #0b5394;">Desmos: </b>This platform offers so much for students, but also for teachers! The platform is manageable and you can find a large number of ready-made activities that go beyond DOK 1 on this site. I have many listed and aligned by standard in the Resources to support CCSS tab at the top of the page.</span></p><p><span style="font-family: Montserrat;"><b><span style="color: #0b5394;">Weeks of Inspirational Math: </span></b> I have blogged about this more than a few times. <a href="https://thinkthinkmath.blogspot.com/2017/08/try-week-of-inspirational-math.html" target="_blank">1st time</a> <a href="https://thinkthinkmath.blogspot.com/2018/07/looking-for-explorationsinvestigations.html" target="_blank">2nd time </a> <a href="https://thinkthinkmath.blogspot.com/2018/11/a-stepping-stone-to-more-student-driven.html" target="_blank">3rd time</a> I love these! I believe strongly you will, too, and so will your students.</span></p><p><span style="font-family: Montserrat;"><b><span style="color: #0b5394;">Puzzles:</span></b> Our students do not have enough experience with persevering through challenging problems, and <a href="https://thinkthinkmath.blogspot.com/search/label/puzzles" target="_blank">puzzles (both paper and tangible)</a> give them experience with this skill. Maybe you just add a jigsaw puzzle table next year, or maybe you take on KenKens--either way, your students will grow! (and probably have a little fun along the way)</span></p><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhOL9NpoCFeUP2lBsdh3DHdKjeOfkf64IJV7DGxUek-wYxbnYAuepzOq9qLUVxVaf7ul4e5JvuSFSjNomZZ3EZHyInQv0_Z3CljFiFAnQT8oLtSkvm3nUEO7ikAEXXRv1gSXs_X5RHRLXY/s4032/60045883566__6B4AD3BE-7E3B-4321-9B31-0D113AB2C9C6.JPG" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: Montserrat;"><img border="0" data-original-height="3024" data-original-width="4032" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhOL9NpoCFeUP2lBsdh3DHdKjeOfkf64IJV7DGxUek-wYxbnYAuepzOq9qLUVxVaf7ul4e5JvuSFSjNomZZ3EZHyInQv0_Z3CljFiFAnQT8oLtSkvm3nUEO7ikAEXXRv1gSXs_X5RHRLXY/s320/60045883566__6B4AD3BE-7E3B-4321-9B31-0D113AB2C9C6.JPG" width="320" /></span></a></div><span style="font-family: Montserrat;"><br /><span><br /></span></span><p></p><p><span style="vertical-align: inherit;"><span style="font-family: Montserrat; vertical-align: inherit;">Each year, we step into our classrooms with a fresh start and with plans of doing better than the year before. By challenging yourself to grow in your math instruction, you will not only grow, but so will your students! Good luck.</span></span></p><p><span style="font-family: georgia;"><br /></span></p>Jennifer Gibsonhttp://www.blogger.com/profile/04128860663290797642noreply@blogger.com0tag:blogger.com,1999:blog-5519240175767583895.post-81582923867916747672021-01-18T14:19:00.001-06:002021-08-15T21:24:32.337-05:00Removing Labels from Students<p><span style="font-family: Montserrat;">One thing that often challenges teachers is the way that they group students. After working with students, they tend to have a group that they consider "low" and a group that they consider "high." Sometimes this designation comes as a result of testing. This is an area where mindsets need to change. When we think of students in these terms, we tend to determine their track and limit or expand our expectations--depending on the group.</span></p><p><span style="font-family: Montserrat;"><b>I understand where this thinking comes from as it was taught to us as best practice for a while. </b>However, as Jo Boaler and other researchers point out, it is not what is in the best interests of our students as it pigeonholes them into believing that they are not good at math or that math should come easily to them. Students who are consistently told that math comes easily to them often don't know what to do when it doesn't, and students who are led to believe that math is a struggle for them will want to avoid it because they are "no good" at it. </span></p><p><span style="font-family: Montserrat;"><b>So how do we correct this mindset? </b>There are a number of things that can be done. <i> First,</i> we need to<span style="color: #2b00fe;"> be very deliberate when referring to students. We should work to no longer use terms like "high" or "low." </span>What I find is that most of our students have strengths and weaknesses. Just because they have difficulty with computation doesn't mean that they don't have a great eye for geometric thinking. </span></p><p><span style="font-family: Montserrat;"><i>Secondly, </i>every effort should be made <span style="color: #2b00fe;">to not group our students every day by what we perceive to be their ability level.</span> Students should be heterogeneously grouped so that they can all benefit from hearing the ideas and thinking of others. (Imagine if your principal always grouped teachers according to the strong teachers and the weaker teachers. How would the weaker teachers ever grow if they only had each other to get ideas from? And how would the stronger teachers develop better understanding of their craft if they had no one to think deeply with? Everyone brings something to the table.) Consider using <b>visibly random grouping--</b>an organizational structure researched, practiced, and encouraged by Peter Liljedahl as helping students become better problem solvers.</span></p><p><span style="font-family: Montserrat;"><i>Next, </i><span style="color: #2b00fe;">use low-floor/high ceiling problems </span>as much as possible with your students. From your opening routines to the rich tasks you ask your students to explore, find activities that all students can access and take to the level that they want. These tasks encourage creative thinking and offer may opportunities for rich mathematical discourse.</span></p><p><span style="font-family: Montserrat;">Being intentional in making these changes will lead to greater learning from our students and improved equity for all.</span></p>Jennifer Gibsonhttp://www.blogger.com/profile/04128860663290797642noreply@blogger.com0tag:blogger.com,1999:blog-5519240175767583895.post-55850306826883948822020-12-08T08:34:00.002-06:002021-08-15T21:24:57.553-05:00How have you changed?<p><span style="font-family: Montserrat;"><b>2020 has, in many ways, contained both stagnation and growth.</b> The stagnation is what seems to resonate with us. So much time at home, a limited circle of people to interact, and a school year that makes it challenging to see the desired growth in our students tend to overpower our thinking. It is easy to focus on these things, as they are such a part of our daily lives right now.</span></p><p><span style="font-family: Montserrat;">However, there are also so many ways that we have grown in the last year. We have gained more time for self-reflection, had time to actually pursue our interests, become quite adept at Zoom meetings, and for many of us, learned how to celebrate holidays with a small circle rather than our large family gatherings. While all of these opportunities have not been our choice, they have allowed us to look at our lives in a new light, and hopefully, there have been things we have done that we hope to continue well after this pandemic is in our rearview.</span></p><p><span style="font-family: Montserrat;"><b>But as a math teacher, what changes have you made that you want to stick around? </b> Have you eliminated pages of repeated problems? Have you put more time into the <i>hows</i> and <i>whys</i> of student work rather than the final results? Has making math visual been a priority in your instruction? Have you been more intentional with your practices and built in routines that fit your students' needs? Do your students see math as more than just computation? Have you offered more opportunities for creativity and critical thinking? Does your classroom culture celebrate mistakes as steps toward growth? </span></p><p><span style="font-family: Montserrat;">I am hopeful that some of these changes have occurred for you, and that you see the value in keeping these practices into the return of our post-pandemic world. While that world still may be many months away, these best practices are good now. Remote, hybird or in-person instruction. Polish them up so that you have them in good shape for our return to "normal" instruction. Whenever (and whatever) that may be. </span></p><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhdlhymIZU11TD4wgRgQufR1iE5PJgW-6aYAP4gLnMT9j9hS-NtiYYGVXPFCTumoIxKnheD_sqlYLGIuD_D1UfRVcerZKv4eoi8W0udTP3oKwMPh-4hfJXMQvoT8Mlxrjfkv1-Yy3w3HqE/s445/2020.PNG" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="210" data-original-width="445" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhdlhymIZU11TD4wgRgQufR1iE5PJgW-6aYAP4gLnMT9j9hS-NtiYYGVXPFCTumoIxKnheD_sqlYLGIuD_D1UfRVcerZKv4eoi8W0udTP3oKwMPh-4hfJXMQvoT8Mlxrjfkv1-Yy3w3HqE/s320/2020.PNG" width="320" /></a></div><br /><span style="font-family: georgia;"><br /></span><p></p><p><span style="font-family: georgia;"><br /></span></p><p><span style="font-family: georgia;"><br /></span></p>Jennifer Gibsonhttp://www.blogger.com/profile/04128860663290797642noreply@blogger.com0tag:blogger.com,1999:blog-5519240175767583895.post-76204742257628581252020-10-17T08:06:00.002-05:002021-08-15T21:25:23.537-05:00So much good in one place!<p><span style="font-family: georgia;"><br /></span></p><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj6wSCWMuaEn-Mbw9Wsmij4xs6BKbU8shR-jQHwbJlJXUJXbgUgoepxoXZS4wKpwQqAZwCbb4UaiyJKsNMO1bikffKRL5UGVNbGQhp4xII022nb0Czw1oz02Pgr-290rM3tTx4x3QVhWcM/s664/making+sense.PNG" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="602" data-original-width="664" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj6wSCWMuaEn-Mbw9Wsmij4xs6BKbU8shR-jQHwbJlJXUJXbgUgoepxoXZS4wKpwQqAZwCbb4UaiyJKsNMO1bikffKRL5UGVNbGQhp4xII022nb0Czw1oz02Pgr-290rM3tTx4x3QVhWcM/s320/making+sense.PNG" width="320" /></a></div><br /><span style="font-family: georgia;"><br /></span><p></p><p><span style="font-family: Montserrat;">Many of you are familiar with the beauty of <a href="https://stevewyborney.com/2017/02/splat/" target="_blank">Splat!</a> and all that it can offer our students. It also has the great quality of being a routine that can be used throughout school. It is certainly a routine that students, teachers, and this math specialist love due to its visual qualities, critical thinking elements, and engaging ways!</span></p><p><span style="font-family: Montserrat;">But the master behind Splat! has<i> many other great resources </i>available to teachers. They are opportunities to expose our students to many concepts and to encourage some rich discourse in our classrooms. And, best of all, Steve Wyborney shares his wonderful creations with us in the form of free downloads.</span></p><p><span style="font-family: Montserrat;">These resources are good in a normal year, but this year, they are especially nice to use in a virtual learning format.</span></p><p><span style="font-family: Montserrat;"><b>Here is a run-down of some of the things you can find from Mr. Wyborney:</b></span></p><p><span style="font-family: Montserrat;"><span style="color: black;"><a href="https://stevewyborney.com/2017/02/splat/" target="_blank"><b>Splat!:</b> </a> </span>Beginning with concept of missing addends, the Splat slides move from primary concepts to <a href="https://stevewyborney.com/2017/03/the-fraction-splat-series/" target="_blank">fractions</a> and <a href="https://stevewyborney.com/?s=nested+splat" target="_blank">algebra</a> as the slides become more complex. Students benefit from the visual nature of the slides, and they love the game feel of it all.</span></p><p><span style="font-family: Montserrat;"><b><span style="color: #ffa400;"><a href="https://stevewyborney.com/2018/11/esti-mysteries-estimation-meets-math-mysteries/" target="_blank">Esti-Mysteries:</a> </span></b> Another popular routine with students, esti-mysteries merge the skill of estimation with critical thinking. One clue is revealed at a time so that students can narrow down their choices. In the end, they still depend upon their estimating skills for a final decision. One thing I like about this routine is that once it has been taught, I think it can be used in many ways including revealing a clue a day with the final discussion occurring at the end of the week.</span></p><p><span style="font-family: Montserrat;"><b style="color: #04ff00;"><a href="https://stevewyborney.com/2018/04/the-estimation-clipboard/" target="_blank">Estimation Clipboard:</a> </b>This is one of my favorites! This routine again builds off of the concept of estimating and makes it fun for students to take the risks when making an estimate. An image is shown, students make an estimate, and then the answer is revealed. Another slide is shown with a change in the image, and the students adjust their estimate. This simple routine has hidden sophistication in that it often has hidden benchmarks for students to use to be able to make a better estimate. Many of the images are about number, but I especially recommend the slides that deal with length.</span></p><p><span style="font-family: Montserrat;"><b><span style="color: #2b00fe;"><a href="https://stevewyborney.com/2017/12/cube-conversations/" target="_blank">Cube Conversations:</a> </span></b> These 3D images are a great way for students to get an introduction to volume and to build their visual and grouping skills.</span></p><p><span style="font-family: Montserrat;"><span style="color: #800180;"><b><a href="https://stevewyborney.com/2017/01/tiled-area-questions/" target="_blank">Tiled Area Questions:</a></b></span> Beginning as <a href="https://stevewyborney.com/2017/01/primary-tile-questions/" target="_blank">general area problems</a>, these develop into more complex relationships between whole and fractional numbers. Again--an opportunity to stretch our students' thinking and their abilities to justify their thinking.</span></p><p><span style="font-family: Montserrat;">His<span style="color: black;"><a href="https://stevewyborney.com/2014/12/the-animated-multiplication-table/" style="font-weight: bold;" target="_blank"> </a><a href="https://stevewyborney.com/2014/12/the-animated-multiplication-table/" style="font-weight: bold;" target="_blank">animated multiplication chart</a></span> is a nice tool for students to explore patterns and be exposed to their facts.</span></p><p><span style="font-family: Montserrat;">I know that for many of you Splat! is a common routine used in your classroom, but I wanted you to be aware of some of the many other treasures that you can find on this website. If the past proves anything, I would bet we can look forward to other great ideas to be created by him in the future! Have fun exploring<a href="https://stevewyborney.com/" target="_blank"> this awesome sight</a>, but more importantly, have fun watching your students think, engage, and discuss mathematics in such fun ways!</span></p>Jennifer Gibsonhttp://www.blogger.com/profile/04128860663290797642noreply@blogger.com0tag:blogger.com,1999:blog-5519240175767583895.post-18246669076792304322020-09-17T09:31:00.004-05:002021-08-15T21:25:47.360-05:00Looking at Data<p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgdE3xkj60Gh8EeglF75OiOZ7VTwReqGbCAqMTSE9Ko_fY_yL4AS-27AmZKy02-9hpzEJR1u_qlQMkdJWHetgCdeY9hSCxI5EsUwAuQiLTbs_Jw3sIOVknw84rixoNmuzqE7vdk784HPKI/s869/numberlesslinegraph.PNG" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="527" data-original-width="869" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgdE3xkj60Gh8EeglF75OiOZ7VTwReqGbCAqMTSE9Ko_fY_yL4AS-27AmZKy02-9hpzEJR1u_qlQMkdJWHetgCdeY9hSCxI5EsUwAuQiLTbs_Jw3sIOVknw84rixoNmuzqE7vdk784HPKI/s320/numberlesslinegraph.PNG" width="320" /></a></div><span style="font-family: Montserrat;">While the post title might lead you to believe that this post is about looking at student data, that is not the case in this situation. Let's look at some resources for students looking at data!</span><p></p><p><span style="font-family: Montserrat;">Last fall, I met with some representatives of a major company in my community to discuss math education in our schools. The number one take-away: <i>We want workers who know the answer to the question, "What does the data tell you?" </i></span></p><p><span style="font-family: Montserrat;">It is common for teachers to present math pictures or problems to students and ask them "What do you notice? What do you wonder?" But this post focuses on true data and how we can get students to look at it more thoughtfully, with the ultimate goal being that they can use the information to be better informed about the world around them.</span></p><p><span style="font-family: Montserrat;">Jo Boaler and youcubed have come up with data talk images! Here is<a href="https://www.youcubed.org/resource/data-talks/?utm_source=Youcubed+Updates&utm_campaign=270417ed8b-EMAIL_CAMPAIGN_2020_09_15_06_44_COPY_01&utm_medium=email&utm_term=0_230e567c40-270417ed8b-163691881" target="_blank"> a link to their page</a> of images (which I am sure will grow...) Displaying these data images to students not only is great practice with graphs and infographics, but it also allows them to be better readers and understanders of data. While these might make a great start to a math lesson, they can also be wonderfully embedded into content areas such as social studies and science--all with the simple questions, <b><span style="color: #2b00fe;">"What do you notice?"</span> <span style="color: #800180;">"What do you wonder?"</span></b></span></p><p><span style="font-family: Montserrat;">Another resource that I often lead teachers to is <a href="https://slowrevealgraphs.com/read-about-it/">numberless graphs</a>. Much like numberless word problems, numberless graphs force students to think and make relationships about the things they know from the graph while still missing key information. Also much like a numberless word problem, the data is slowly revealed to them to help them make sense of it all in a thoughtful way.</span></p><p><span style="font-family: Montserrat;">No matter the grade you teach, what are you doing to engage your students in reading and understanding data? Consider trying some of the links above, and watch the lightbulbs go off!</span></p>Jennifer Gibsonhttp://www.blogger.com/profile/04128860663290797642noreply@blogger.com0tag:blogger.com,1999:blog-5519240175767583895.post-69749314900430192752020-07-31T04:00:00.002-05:002021-08-15T21:26:10.653-05:00Here we go!<font face="Montserrat">Tomorrow is August, and that typically means the beginning to a school year. And Oh! what a school year it is to be. Like one we have never experienced before.</font><div><font face="Montserrat"><br /></font></div><div><font face="Montserrat">As we think about our students, safety is our priority, of course. However, we also must keep in mind learning--as that is the reason the new year begins.</font></div><div><font face="Montserrat"><br /></font></div><div><font face="Montserrat">Instead of getting caught up in the things that our students missed without in-school learning last spring, let's think about what we as teachers always have done; let's meet our students where they are and move them forward. We don't have to worry about teaching a third of the content from the grade before us. Let's pick them up where they are and move them into new thinking, into new content.</font></div><div><font face="Montserrat"><br /></font></div><div><font face="Montserrat">2020 is one that will always be remembered, we know that. Let's not burden our students by making them feel behind or like they aren't ready for their new grade. Let's build them up, and build them into students with knowledge and understanding. It is what is best, and it will relieve the pressure on them--and you. </font></div><div><font face="Montserrat"><br /></font></div><div><font face="Montserrat">Good luck in 2020 whether it be in-person, online, or a little bit of both!</font></div><div><font face="georgia"><br /></font></div><div><font face="georgia"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiUAnV68-nxWgok_Q7VGn-s2u4JpUVJSWe2F-LL4Nba4gTGxTSi_u1wj8xSH5WD7-IH0I-d2njiaUZGlH3gob-SVjt26U5MuDMYAj1oP_2xK5vhxYb_6_ADsIg2Gk4MRrK0QrPPKBIGfbg/s641/wordcloud.PNG" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="600" data-original-width="641" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiUAnV68-nxWgok_Q7VGn-s2u4JpUVJSWe2F-LL4Nba4gTGxTSi_u1wj8xSH5WD7-IH0I-d2njiaUZGlH3gob-SVjt26U5MuDMYAj1oP_2xK5vhxYb_6_ADsIg2Gk4MRrK0QrPPKBIGfbg/s320/wordcloud.PNG" width="320" /></a></div> </font></div><div><font face="georgia"><br /></font></div><div><font face="georgia"><br /></font></div>Jennifer Gibsonhttp://www.blogger.com/profile/04128860663290797642noreply@blogger.com0tag:blogger.com,1999:blog-5519240175767583895.post-75112951779993123992020-07-03T18:02:00.002-05:002021-08-15T21:26:37.382-05:00Individual student toolkits for CRA instruction<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi6aLbhsDxWGLApJxJkNVoZLWMr4SRrf3Uh0jFbke1z_Wfnpk8TX70FVlXN5IWPqJ_kntWUQBnlIUYKaavDFiF1BaoUGwFHpxmlED4noNoYG8kqViK7Mq_Ib72aB1XNjPQMc3p10kXsWJc/s1600/counting+puzzles.PNG" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="445" data-original-width="740" height="192" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi6aLbhsDxWGLApJxJkNVoZLWMr4SRrf3Uh0jFbke1z_Wfnpk8TX70FVlXN5IWPqJ_kntWUQBnlIUYKaavDFiF1BaoUGwFHpxmlED4noNoYG8kqViK7Mq_Ib72aB1XNjPQMc3p10kXsWJc/s320/counting+puzzles.PNG" width="320" /></a></div>
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<span style="font-family: Montserrat;"><span>If students are in your classroom in August, it will be worth your time to have some sort of math tool kits prepared for your students because it is not recommended that students share resources, and you don't want to be cleaning them every night. What you are able to put in the kits will depend on your resources. </span><br />
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<span style="font-family: Montserrat;"><span>We know that <b>CRA instruction</b> is vital for conceptual understanding of mathematical concepts. Just because we will have some limits in place (for everyone's safety), doesn't mean we should abandon best practices. We just need to adjust and do what we can for our students.</span><br />
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<span style="font-family: Montserrat;"><span>As I have said before, <a href="https://thinkthinkmath.blogspot.com/2020/05/looking-for-virtual-manipulatives.html" target="_blank">the use of virtual manipulatives</a> will probably increase in your instruction even if you are seeing students in person. This is especially true for those manipulatives where students usually need a lot of them to do their work--like pattern blocks and base ten blocks. I recommend that you use the virtual versions some in the classroom so that students are comfortable with the websites if they should need to use them from home without your direct support.</span><br />
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<span style="font-family: Montserrat;">You might also consider paper versions of some of these tools to have in students's toolkits. Not only can you get them easily and cheaply for the classroom, but you can also send them home if you need to without the worry of losing valuable manipulatives.</span></div>
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<span style="font-family: Montserrat;">You may not start the year with all of the items in the toolkits. You might add some as students are introduced to new concepts. <span style="color: purple;">Here are some things you might consider putting into individual toolkits for your students:</span></span></div>
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<span style="color: red; font-family: Montserrat;"><b>K:</b></span></div>
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<span style="font-family: Montserrat;"><a href="https://wps.ablongman.com/wps/media/objects/3464/3547873/blackline_masters/BLM_09.pdf" target="_blank">five frame</a></span></div>
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<span style="font-family: Montserrat;"><a href="https://wps.ablongman.com/wps/media/objects/3464/3547873/blackline_masters/BLM_10.pdf" target="_blank">ten frame</a></span></div>
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<span style="font-family: Montserrat;"><a href="https://nrich.maths.org/content/id/8506/1-100_NumberGrid.pdf" target="_blank">hundred grid</a><span> from nrich.maths.org</span></span></div>
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<span style="font-family: Montserrat;"><a href="https://drive.google.com/file/d/19K0OKtFx3U8Zocp4iDKc6md6ZvgBBk8K/view" target="_blank">number path 1-20</a> by Berkeley Everett</span></div>
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<span style="font-family: Montserrat;">ten counters (unifix cubes?)</span></div>
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<span style="font-family: Montserrat;">rekenrek</span></div>
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<span style="font-family: Montserrat;"><span>real or </span><a href="http://mathwire.com/templates/patternblocktemplate.pdf" target="_blank">paper pattern blocks</a><span> by Mathwire</span></span></div>
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<span style="font-family: Montserrat;"><a href="https://drive.google.com/file/d/14D0VgiQ2tq4mZxe8bBAKWb97SoAjLd7X/view" target="_blank">+/- Math Flips cards (+/- 1)</a> by Berkeley Everett<br /><a href="https://1woqu41bs5kerai2f3lyxkm7-wpengine.netdna-ssl.com/wp-content/uploads/2018/07/EMC_QuantityCards_1-5_ALL.pdf" target="_blank">Quantity Cards</a> from Erickson Early Math Collaborative</span></div>
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<span style="font-family: Montserrat;">pair of dice</span></div>
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<span style="color: red; font-family: Montserrat;"><b>1:</b></span></div>
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<a href="https://wps.ablongman.com/wps/media/objects/3464/3547873/blackline_masters/BLM_10.pdf" target="_blank"><span style="font-family: Montserrat;">ten frame</span></a></div>
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<a href="https://wps.ablongman.com/wps/media/objects/3464/3547873/blackline_masters/BLM_11.pdf" target="_blank"><span style="font-family: Montserrat;">double ten-frame</span></a></div>
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<span style="font-family: Montserrat;"><a href="https://nrich.maths.org/content/id/8506/1-100_NumberGrid.pdf" target="_blank">hundred grid</a><span> from nrich.maths.org</span></span></div>
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<span style="font-family: Montserrat;"><a href="https://drive.google.com/file/d/19K0OKtFx3U8Zocp4iDKc6md6ZvgBBk8K/view" target="_blank">number path 1-20</a><span> by Berkeley Everett</span></span></div>
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<span style="font-family: Montserrat;">twenty counters (unifix cubes ?)</span></div>
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<span style="font-family: Montserrat;">rekenrek</span></div>
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<span style="font-family: Montserrat;">beaded number line</span></div>
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<span style="font-family: Montserrat;">small clock face <a href="https://docs.google.com/document/d/1Pj95Ivyor8SGB49zDFl5dmsrwtdT39ZzeUjOJEeQEEQ/edit?usp=sharing" target="_blank">paper version</a></span></div>
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<span style="font-family: Montserrat;"><span>real or </span><a href="http://mathwire.com/templates/patternblocktemplate.pdf" target="_blank">paper pattern blocks</a><span> by Mathwire</span></span></div>
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<span style="font-family: Montserrat;">+/- Math Flips cards <span style="font-size: x-small;">(<a href="https://drive.google.com/file/d/1QXPwUXebBfVSs5AJB8ygTSYJwjj6W99Q/view" target="_blank">Count on within 10</a>) (<a href="https://drive.google.com/file/d/1HAq7oVjHaLFdNgTKD0cWa_AWKubpCBrn/view?usp=drive_open" target="_blank">+/- 1 or 10 within 100</a>) (<a href="https://drive.google.com/file/d/1jWC_JulcGiarqAx6md2-IswbMPIDZD-_/view?usp=sharing" target="_blank">subtraction within 10</a>)</span></span></div>
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<span style="font-family: Montserrat;">pair of dice</span></div>
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<span style="color: red; font-family: Montserrat;"><b>2:</b></span></div>
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<span style="font-family: Montserrat;"><a href="https://wps.ablongman.com/wps/media/objects/3464/3547873/blackline_masters/BLM_11.pdf" target="_blank">double ten-frame</a></span></div>
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<span style="font-family: Montserrat;"><a href="https://nrich.maths.org/content/id/8506/1-100_NumberGrid.pdf" target="_blank">hundred grid</a><span> from nrich.maths.org</span></span></div>
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<span style="font-family: Montserrat;"><a href="https://2nd-grade-math-salamanders.s3-us-west-1.amazonaws.com/Number-Lines-2nd/Number-Line-0-to-20/number-line-0-to-20-printable-1b.pdf" target="_blank">number line 1-20</a> by Math Salamanders</span></div>
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<span style="font-family: Montserrat;">twenty counters (cm cubes?)</span></div>
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<span style="font-family: Montserrat;">rekenrek</span></div>
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<span style="font-family: Montserrat;">beaded number line</span></div>
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<span style="font-family: Montserrat;"><span>small clock face </span><a href="https://docs.google.com/document/d/1Pj95Ivyor8SGB49zDFl5dmsrwtdT39ZzeUjOJEeQEEQ/edit?usp=sharing" target="_blank">paper version</a></span></div>
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<span style="font-family: Montserrat;">play coins, dollar bills</span></div>
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<span style="font-family: Montserrat;">ruler</span></div>
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<span style="font-family: Montserrat;"><span>real or </span><a href="http://mathwire.com/templates/patternblocktemplate.pdf" target="_blank">paper pattern blocks</a><span> by Mathwire</span></span></div>
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<span style="font-family: Montserrat;"><span><span>real or </span><a href="https://www.timvandevall.com/wp-content/uploads/2014/04/Printable-Place-Value-Blocks.pdf" target="_blank">paper base ten blocks</a> from </span><span>Tim Van de Vall</span></span></div>
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<span style="font-family: Montserrat;"><span>+/- Math Flips cards by Berkeley Everett <span style="font-size: x-small;">(<a href="https://drive.google.com/file/d/1PJ2FkAOKfplbhTqX-u1RGbZnSK02riOZ/view?usp=drive_open" target="_blank">Doubles/Near Doubles</a>) (<a href="https://drive.google.com/file/d/1hXELz6anhu3RGQqv3-9yZ6Sgimg5j0q7/view?usp=drive_open" target="_blank">make 10 with 2 addends</a>) </span></span><span style="font-size: x-small;"><span>(</span><a href="https://drive.google.com/file/d/1mFs0eT2NxUZ8csr7zEjRS96YItsVeDti/view?usp=drive_open" target="_blank">make 10 with 3 addends</a><span>) (<a href="https://drive.google.com/open?id=1FduStNfnKnAKuCwQAzFH463K77PRRdYV" target="_blank">2 digit + 1 digit</a>) (<a href="https://drive.google.com/file/d/1OAm4UY-DvKkMIf-QrJO4ndehNvqTQNba/view" target="_blank">2 digit + 2 digit</a>) (<a href="https://drive.google.com/file/d/1kwN7_-20d_GFj4QKOROlmtmtZypmmTUb/view?usp=sharing" target="_blank">subtraction within 20</a>) (<a href="https://drive.google.com/file/d/19clH4tl7D98rO_Qdr76BTq876d6JWm5s/view?usp=sharing" target="_blank">subtraction within 100</a>)</span></span><span> </span></span></div>
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<span style="font-family: Montserrat;">pair of dice</span></div>
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<span style="color: red; font-family: Montserrat;"><b>3:</b></span></div>
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<a href="https://wps.ablongman.com/wps/media/objects/3464/3547873/blackline_masters/BLM_10.pdf" target="_blank"><span style="font-family: Montserrat;">ten frame</span></a></div>
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<span style="font-family: Montserrat;"><a href="https://wps.ablongman.com/wps/media/objects/3464/3547873/blackline_masters/BLM_23.pdf" target="_blank">hundred grid</a> </span></div>
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<span style="font-family: Montserrat;">twenty or more counters (cm cubes?)</span></div>
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<span style="font-family: Montserrat;">beaded number line</span></div>
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<span style="font-family: Montserrat;"><span>small clock face </span><a href="https://docs.google.com/document/d/1Pj95Ivyor8SGB49zDFl5dmsrwtdT39ZzeUjOJEeQEEQ/edit?usp=sharing" target="_blank">paper version</a></span></div>
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<span style="font-family: Montserrat;">play coins, dollar bills</span></div>
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<span style="font-family: Montserrat;">ruler</span></div>
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<span style="font-family: Montserrat;"><a href="https://wps.ablongman.com/wps/media/objects/3464/3547873/blackline_masters/BLM_27.pdf" target="_blank">10 x 10 array</a> (laminate)</span></div>
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<span style="font-family: Montserrat;"><span>real or </span><a href="http://mathwire.com/templates/patternblocktemplate.pdf" target="_blank">paper pattern blocks</a><span> by Mathwire</span></span></div>
<div>
<span style="font-family: Montserrat;"><span><span>real or </span><a href="https://www.timvandevall.com/wp-content/uploads/2014/04/Printable-Place-Value-Blocks.pdf" target="_blank">paper base ten blocks</a> </span><span>from </span><span>Tim Van de Vall</span></span></div>
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<span style="font-family: Montserrat;"><span>paper </span><a href="https://s3-us-west-1.amazonaws.com/math-salamanders/Fractions/Fraction-Resources/Fraction-Strips/fraction-strips-up-to-twelfths.pdf" target="_blank">Fraction Strip</a><span> from Math Salamander (blank version)</span></span></div>
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<span style="font-family: Montserrat;">paper Fraction Circle Pieces <a href="https://wps.ablongman.com/wps/media/objects/3464/3547873/blackline_masters/BLM_24.pdf" target="_blank">Page 1 </a> <a href="https://wps.ablongman.com/wps/media/objects/3464/3547873/blackline_masters/BLM_25.pdf" target="_blank">Page 2</a> <a href="https://wps.ablongman.com/wps/media/objects/3464/3547873/blackline_masters/BLM_26.pdf" target="_blank">Page 3</a></span></div>
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<span style="font-family: Montserrat;">+/- Math Flips cards by Berkeley Everett (if needed from previous grades)</span></div>
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<span style="font-family: Montserrat;"><span> x Math Flips cards by Berkeley Everett (<a href="https://drive.google.com/open?id=1niLQthRKuwe86eTf3alpmpjs911Qk0T0" target="_blank">2s,5s, and 10s</a>) (<a href="https://drive.google.com/file/d/1PqBlbAHXGDcGRHJhFAfw2A2i7MCjMNNo/view?usp=drive_open" target="_blank">4s, 6s,& 8s</a></span><span>) (</span><a href="https://drive.google.com/open?id=1WfdDQXzSnruYkWmHWYAE4VyHOkXNElcD" target="_blank">3s & 6s</a><span>) (<a href="https://drive.google.com/open?id=14Pj6tDRfICULCoB9Wutyg2IGPc7pz5E2" target="_blank">9s & 4s</a>)</span></span></div>
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<span style="font-family: Montserrat;">pair of dice</span></div>
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<span style="font-family: Montserrat;"><br /></span></div>
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<span style="color: red; font-family: Montserrat;"><b>4:</b></span></div>
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<span style="font-family: Montserrat;"><a href="https://wps.ablongman.com/wps/media/objects/3464/3547873/blackline_masters/BLM_23.pdf" target="_blank">hundred grid</a><span> </span></span></div>
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<span style="font-family: Montserrat;"><span>thirty-six counters </span><span>(cm cubes?)</span></span></div>
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<span style="font-family: Montserrat;">beaded number line</span></div>
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<span style="font-family: Montserrat;">ruler</span></div>
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<span style="font-family: Montserrat;"><a href="https://wps.ablongman.com/wps/media/objects/3464/3547873/blackline_masters/BLM_27.pdf" target="_blank">10 x 10 array</a><span> (laminate)</span></span></div>
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<span style="font-family: Montserrat;"><span>real or </span><a href="http://mathwire.com/templates/patternblocktemplate.pdf" target="_blank">paper pattern blocks</a><span> by Mathwire</span></span></div>
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<span style="font-family: Montserrat;"><span><span>real or </span><a href="https://www.timvandevall.com/wp-content/uploads/2014/04/Printable-Place-Value-Blocks.pdf" target="_blank">paper base ten blocks</a> </span><span>from </span><span>Tim Van de Vall</span></span></div>
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<span style="font-family: Montserrat;">paper <a href="https://s3-us-west-1.amazonaws.com/math-salamanders/Fractions/Fraction-Resources/Fraction-Strips/fraction-strips-up-to-twelfths.pdf" target="_blank">Fraction Strip</a> from Math Salamander</span></div>
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<span style="font-family: Montserrat;"><span>paper Fraction Circle Pieces </span><a href="https://wps.ablongman.com/wps/media/objects/3464/3547873/blackline_masters/BLM_24.pdf" target="_blank">Page 1 </a><span> </span><a href="https://wps.ablongman.com/wps/media/objects/3464/3547873/blackline_masters/BLM_25.pdf" target="_blank">Page 2</a><span> </span><a href="https://wps.ablongman.com/wps/media/objects/3464/3547873/blackline_masters/BLM_26.pdf" target="_blank">Page 3</a></span></div>
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<span style="font-family: Montserrat;">+/- Math Flips cards by Berkeley Everett (if needed from previous grades)</span></div>
<div>
<span style="font-family: Montserrat;"> <a href="https://drive.google.com/file/d/10O9H8jmQ-dmj9gDL8C-m6a37NJG5_laN/view?usp=drive_open" target="_blank">x Math Flips cards</a> by Berkeley Everett</span></div>
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<span style="font-family: Montserrat;">pair of dice</span></div>
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<span style="color: red; font-family: Montserrat;"><b>5:</b></span></div>
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<div>
<span style="font-family: Montserrat;"><a href="https://wps.ablongman.com/wps/media/objects/3464/3547873/blackline_masters/BLM_23.pdf" target="_blank">hundred grid</a><span> </span></span></div>
<div>
<span style="font-family: Montserrat;"><span>thirty-six counters </span><span>(cm cubes?)</span></span></div>
</div>
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<span style="font-family: Montserrat;">beaded number line</span></div>
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<span style="font-family: Montserrat;">ruler</span></div>
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<span style="font-family: Montserrat;"><span>real or </span><a href="http://mathwire.com/templates/patternblocktemplate.pdf" target="_blank">paper pattern blocks</a><span> by Mathwire</span></span></div>
<div>
<span style="font-family: Montserrat;"><span><span>real or </span><a href="https://www.timvandevall.com/wp-content/uploads/2014/04/Printable-Place-Value-Blocks.pdf" target="_blank">paper base ten blocks</a> </span><span>from </span><span>Tim Van de Vall</span></span></div>
<div>
<span style="font-family: Montserrat;">paper <a href="https://s3-us-west-1.amazonaws.com/math-salamanders/Fractions/Fraction-Resources/Fraction-Strips/fraction-strips-up-to-twelfths.pdf" target="_blank">Fraction strip</a> from Math Salamander</span></div>
<div>
<span style="font-family: Montserrat;"><span>paper Fraction Circle Pieces </span><a href="https://wps.ablongman.com/wps/media/objects/3464/3547873/blackline_masters/BLM_24.pdf" target="_blank">Page 1 </a><span> </span><a href="https://wps.ablongman.com/wps/media/objects/3464/3547873/blackline_masters/BLM_25.pdf" target="_blank">Page 2</a><span> </span><a href="https://wps.ablongman.com/wps/media/objects/3464/3547873/blackline_masters/BLM_26.pdf" target="_blank">Page 3</a></span></div>
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<span style="font-family: Montserrat;">Math Flips cards by Berkeley Everett (if needed from previous grades)</span></div>
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<span style="font-family: Montserrat;">pair of dice</span></div>
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<span style="font-family: Montserrat; font-size: large;"><b><br /></b></span></div>
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<span style="font-family: Montserrat;">If you laminate many of the paper tools, students could use a dry erase marker to create representations.</span></div>
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<span style="font-family: Montserrat; font-size: large;"><b>What am I forgetting?</b></span></div>
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<span style="font-family: georgia, "times new roman", serif;"><br /></span></div>
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Jennifer Gibsonhttp://www.blogger.com/profile/04128860663290797642noreply@blogger.com0tag:blogger.com,1999:blog-5519240175767583895.post-12747857197121135992020-05-17T10:24:00.001-05:002021-08-15T21:45:39.334-05:00Looking for Virtual Manipulatives?<div class="separator" style="clear: both; text-align: left;">
<span style="font-family: Montserrat;">While we are still unsure how our instruction will be delivered in the fall, there is one thing we are sure of....student's involvement in the concrete phase of learning math is important!</span></div>
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<span style="font-family: Montserrat;">Sending home concrete manipulatives for all of our students may be too costly for most schools. Purchasing enough to send home is not the only problem: we know it is doubtful that many of these tools will return to our buildings. With that in mind, here I am going to highlight some of the best virtual manipulatives I have been able to find and use.</span></div>
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<span style="font-family: Montserrat;">I highly recommend using these with students this fall even if we are face to face. Allowing for guided use now will make it easier should they need to use them again at some point in the year.</span></div>
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<span style="font-family: Montserrat;">I have always been a fan of <a href="https://www.mathlearningcenter.org/resources/apps" target="_blank">Math Learning Center Apps</a>, and I have shared these apps with many teachers before! These apps have always been free and easy to access and use. Because of the pandemic's rise in at-home schooling, they have added an extra feature! Sharing! Four of the apps can be set and shared with students and/or students can share with you. There is a video explaining how this works, and I have had success with it myself. There are many great apps here. Some of my favorites include the Number Rack, the Number Line, and the Partial Product Finder. However, I can think of many great uses of the other apps. I just have not used them myself in a classroom.</span></div>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><span style="margin-left: auto; margin-right: auto;"><a href="https://www.mathlearningcenter.org/resources/apps" target="_blank"><span style="font-family: Montserrat;"><img border="0" data-original-height="487" data-original-width="986" height="158" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjjs1XMwBmT5-vtXTBsUKZ0MQLkH0EyWq4u3ZwiBwxfZtUtqE9YlX1jT5CddHQ3IgwNf0ou8-wuCjhfReZ7kqBu4gDBQMrjk0NPgCcYVFswghyphenhyphena4o1FczdQxOKH_-wegH5YvgDepYrndXg/s320/MLCapps.PNG" width="320" /></span></a></span></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><a href="https://www.mathlearningcenter.org/resources/apps" target="_blank"><span style="font-family: Montserrat;">These are the apps that allow sharing at this time.</span></a></td></tr>
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<span style="font-family: Montserrat;"><span><a href="https://toytheater.com/category/teacher-tools/virtual-manipulatives/" target="_blank">Toy Theater</a> also has a great selection of virtual manipulatives. I do not have as much experience with these, but it has some great ones such as interactive hundreds and mulitiplication charts, a variety of counters, dice, <span style="text-align: center;">and some graphing apps. I think it could meet a lot of needs!</span></span><br />
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<tr><td style="text-align: center;"><span style="margin-left: auto; margin-right: auto;"><a href="https://toytheater.com/category/teacher-tools/virtual-manipulatives/" target="_blank"><span style="font-family: Montserrat;"><img border="0" data-original-height="606" data-original-width="989" height="196" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjOGC2xfU3Vc7O1vUurY_hPW1FR3tLkBPexc4chvCCCO7MWboRfnHBByIoDzQr90BmGq9BpU4DcJQnfIndA9TO_w_C2LHWaTOC8g-odEomJGurCMcY4HfnYAT59-10FGR9yW2BhHculkVk/s320/toytheaterapps.PNG" width="320" /></span></a></span></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><a href="https://toytheater.com/category/teacher-tools/virtual-manipulatives/" target="_blank"><span style="font-family: Montserrat;">A great variety</span></a></td></tr>
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<span style="font-family: Montserrat;"><a href="https://www.didax.com/math/virtual-manipulatives.html" target="_blank">Didax</a> also has free online manipulatives. I have only found these while I've been sheltering at home, so I do not have experience in the classroom with them. You'll find many that are available above, but here you will also find linking cubes and a math balance! It also has algebra tiles and prime factor tiles that can be used in middle grades. (because manipulatives are just as important there!)</span></div>
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<a href="https://www.didax.com/math/virtual-manipulatives.html" target="_blank"><span style="font-family: Montserrat;"><img border="0" data-original-height="464" data-original-width="1120" height="132" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjO0inhG3pETIbASuhhnxV1rK4wT9koQr_Fv3E3rqHp6iD3ruW9e8nL3ReRno5TfUrqjAXn_vK3WHl4rzU6pXhJsl5H9G8Bt8xPghzRh8eM1SyD8pHn-B23dk3f4XFSgdNlfRLrWBYiFPA/s320/Didaxmanip.PNG" width="320" /></span></a></div>
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<span style="font-family: Montserrat;">A few other places that you can find specialty links:</span></div>
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<tr><td style="text-align: center;"><span style="margin-left: auto; margin-right: auto;"><a href="http://mathtoybox.com/numblox/NumBlox.html#.Xra9TGi6PIU" target="_blank"><span style="font-family: Montserrat;"><img border="0" data-original-height="583" data-original-width="1171" height="159" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhDOgZ5VlGlVJ-_p5v66SNWzD2eSltqaA1vKJv0ntowaWY3Sh6MOgScvYF1n9OxIn0spG-uf3jAxaR0wGxazvUrc4s4oLQK9Ds8M2xIJ88c448t_sVXV_zC-9I9d4HYE1FWXOaGnK0gPxo/s320/MathToybox.PNG" width="320" /></span></a></span></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><a href="http://mathtoybox.com/numblox/NumBlox.html#.Xra9TGi6PIU" target="_blank"><span style="font-family: Montserrat;">MathToybox has a Cuisenaire rods app.</span></a></td></tr>
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<tr><td style="text-align: center;"><span style="margin-left: auto; margin-right: auto;"><a href="https://www.abcya.com/games/fraction_percent_decimal_tiles" target="_blank"><span style="font-family: Montserrat;"><img border="0" data-original-height="492" data-original-width="749" height="210" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi2wcg5AwwHVsKepBRIDrwChejJuYx-vz9yvoky1HN3YI_1a6PxiiZgHZT3nj1JJNiQP8VIKHCjzrUvp79_WAtWTrdgsrV-My_ltWeGzKZmiERlCAwqBoq7oA-ceqdeTmcLGdFlgt5Y2Xg/s320/ABCYA.PNG" width="320" /></span></a></span></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><a href="https://www.abcya.com/games/fraction_percent_decimal_tiles" target="_blank"><span style="font-family: Montserrat;">ABCYa has some fraction tiles that are nice.</span></a></td></tr>
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<span style="font-family: Montserrat;"><span style="color: purple;">I hope you can take some time to explore these apps and find the ones that will work best for you and your students' needs! </span> It might be a good way to start the school year, whether we are virtual or in-person, to spend some time walking students through these tools, how to get to them, and how to use them. That way, when the time arises, they will be able to use them more independently! Remind them that they can use them and explore with them whenever they want. Exploring these tools independently helps students to see relationships and make sense of it all on their own.</span></div>
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<span style="font-family: Montserrat;">The other thing that is great about these virtual tools is that you can use them to create your visuals for your SMART docs, Google slides, or student tasks. <span style="color: purple;">Math is visual</span>, and these provide us with good ways to show the math to our students.</span></div>
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<span style="font-family: Montserrat;"><span style="color: red;">I hope we have the chance to use concrete manipulatives in August with our students</span>, but now is the time to prepare in case we don't. I hope you can find tools at some of these sites that match the ones your students typically use in the classroom.</span></div>
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Jennifer Gibsonhttp://www.blogger.com/profile/04128860663290797642noreply@blogger.com0tag:blogger.com,1999:blog-5519240175767583895.post-35339790388714077332020-04-03T21:41:00.002-05:002021-08-15T21:32:46.668-05:00In These Uncertain Times...<span style="font-family: Montserrat;"><span>The world is so unsettled now, as we try to maneuver through these scary waters. As teachers, we are doing all that we can to help our students feel safe even though we have to do this through technology. I think what unsettles everyone the most is not knowing how long this will last. We hear different predictions and ideas every day about the length of this stay at home world. We just want to see our students and have some closure to our school year. However, this is not in our control either.</span><br />
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<span>What is in our control is offering some normalcy to our lives and our student lives. As we do this though, we may sometimes become overzealous and expect things from our students that they don't have the support to complete from home. Give yourself some grace. You can't make up for the interaction that would have happened if we were in our schools. If you are meeting with your students online or giving them tasks to complete, keep it simple. Read a book, write a letter, solve a puzzle, play a game, help fix dinner tonight...these are all appropriate assignments that keep our students and their parents from being overwhelmed by school as well as by world events. </span><br />
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<span>I hope this ends sooner rather than later. I hope that a vaccine is found. I know that when it is found, teachers are some of the people who helped to develop the doctor who finds the vaccine. This has always been true because teachers believe in their students. </span><br />
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<span>I also know that the entire world is holding its breath right now. Do what you can to help your students feel safe. Don't feel obligated to have them complete large amounts of work. Believe in them and that they will be okay when this is over. All will be okay. </span></span>Jennifer Gibsonhttp://www.blogger.com/profile/04128860663290797642noreply@blogger.com0tag:blogger.com,1999:blog-5519240175767583895.post-32142866151732138312020-03-10T08:28:00.002-05:002021-08-15T21:45:20.583-05:00Math is Visual<div style="text-align: center;">
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhrgi_If2822XVpdDmYux9x3_kEiXEzUAwmlJ9KxSbGKRwP4MmsGkWBkbqjzQcN0NgAu54E8uiG0Z0YFjM6SEOVFxMP_QOvg69-s2-rDOL0QBLmvtV2Jm1s2JbF7cKdXcHs3ikeQjizOZw/s1600/Screenshot+2020-03-10+at+8.24.59+AM.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="642" data-original-width="855" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhrgi_If2822XVpdDmYux9x3_kEiXEzUAwmlJ9KxSbGKRwP4MmsGkWBkbqjzQcN0NgAu54E8uiG0Z0YFjM6SEOVFxMP_QOvg69-s2-rDOL0QBLmvtV2Jm1s2JbF7cKdXcHs3ikeQjizOZw/s320/Screenshot+2020-03-10+at+8.24.59+AM.png" width="320" /></a></div>
<span style="font-family: Montserrat;"><span>Our students need access to math visually as much as possible. This can come in different ways. Drawing, manipulatives and online components are some places to start.</span><br />
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<span>I spend a lot of time in classrooms working around word problems. One of the things I find myself constantly coming back to with students is "Think like a reader:" use schema, make predictions, infer, VISUALIZE...that is what good thinkers do. Asking students to draw what they are seeing happening in the problem is an important step. That drawing can be a true drawing, a number line, a tape diagram, or anything else that helps them make sense. Are they thinking through the problem or are they just pulling the numbers and computing without making sense? </span><br />
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<span>I also use numberless word problems a lot. Numberless word problems give students the opportunity to see the problem as a story and to make sense of it without worrying about the numbers. Once you have practiced this strategy in class, it is a strategy they can refer to independently when they come across a word problem that confuses them.</span><br />
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<span>Manipulatives are important, too. <a href="https://thinkthinkmath.blogspot.com/search/label/CRA" target="_blank"> CRA instruction</a> helps us to build the visual into the child's mind by using tools to represent the math. This is important for all students and provides equity in instruction.</span><br />
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<span>There are many websites with visual representations. One of the best is <a href="https://mathvisuals.wordpress.com/" target="_blank">Math Visuals</a>. Berkeley Everett has created a treasure trove of visuals for the K-5 classroom. His short videos to accompany skills like counting and computing are a fabulous resource, but they are just the beginning. He brings visual supports to understanding mathematical properties and making connections through visuals, too. In addition, his <a href="https://mathvisuals.wordpress.com/math-flips/" target="_blank">Math Flips cards </a>are well worth the time to cut out and use with all of your students.</span><br />
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<span>Many other awesome websites exist, too, that are very visual. <a href="http://mathisvisual.com/" target="_blank">Math is Visual</a>, <a href="http://fractiontalks.com/" target="_blank">Fraction Talks</a>, <a href="https://samedifferentimages.wordpress.com/" target="_blank">Same or Different</a>, <a href="http://ntimages.weebly.com/suites--strings.html" target="_blank">Number Talk Images</a>, and <a href="https://slowrevealgraphs.com/" target="_blank">Slow Reveal Graphs</a> are just a few of the visual resources that may help you and your students make more sense of mathematical concepts.</span><br />
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<span>Visual math is for all students. We have to be careful not to assume they can see it in their heads. We have to help them see it in their heads...Visuals help students to make sense. They help students to look for patterns. Visuals help students to answer the question, "What does the data tell us?"</span><br />
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<span>In what ways can you provide your students with more visuals? This is an important area for all of us to grow.</span></span>Jennifer Gibsonhttp://www.blogger.com/profile/04128860663290797642noreply@blogger.com0tag:blogger.com,1999:blog-5519240175767583895.post-48461981744518220462020-02-20T07:46:00.001-06:002021-08-15T21:32:29.724-05:00Counting Connections<span style="font-family: Montserrat;"><span>I love choral counting! This is confirmed every time I participate in one in a classroom. It doesn't matter if it is a Kindergarten or 5th grade. Choral counting gets everyone thinking--including the teacher!</span><br />
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<span>One piece to choral counting that I have found to be important is the connections that can be made between different choral counts.</span><br />
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<span>For example, this was an eye-opening choral count for some 2nd graders. We began with the confidence builder of counting by 5s. We broke it down by looking for patterns. A lot of good talk and discussion here, but it really kicked up a notch when I challenged them to count by 5s off-decade. We began slowly, but then the students were able to idenify patterns and get going. We looked for patterns in this count, too, and then I pulled the two counts up side by side. The ahas! that the students had were quite exciting! So important for students to make these connections.</span><br />
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<span>I did another one recently in a 5th grade classroom where we counted by 21s.</span><br />
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<span style="font-family: Montserrat;">Students stepped up to the challenge of counting by 21s and looking for patterns. But the real excitement came when I asked them to do another count by 2.1. (I had copied the first count onto a clean page before we had found its patterns.) Students kind of gasped, but then I pulled up the clean screen of our previous count. They counted by 2.1 as I added decimal points into the numbers. When we were done, we made connections between the two counts and place value. We also discussed what would have happened if I had asked them to count by 210. These place value concepts were things that they "knew," but when we put it on paper, it really clicked for them!</span></div>
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<span style="font-family: Montserrat;">Because I am in and out of classrooms, I did these "double-counts" in one session making the choral count a little longer than usual. I certainly think that it would work for a teacher to do one one day and the second one the next day. The importance is the time taken to connect the two counts, and following-up in later days with similar counts in order to help cement the counts into students' minds.</span></div>
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<span style="font-family: Montserrat;">Beginning with choral counting is your first step. Give one a try! Once you get past that hurdle, you will feel more comfortable moving into a double-count!</span></div>
<br />Jennifer Gibsonhttp://www.blogger.com/profile/04128860663290797642noreply@blogger.com0tag:blogger.com,1999:blog-5519240175767583895.post-88686840589428771222019-12-30T08:13:00.001-06:002021-08-15T21:46:00.761-05:00An exploration for 4th grade<span style="font-family: Montserrat;"><span>A site that I often frequent for good math inquiry problems is <a href="http://www.inquirymaths.org/">http://www.inquirymaths.org/</a>.</span><br />
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<span><a href="http://www.inquirymaths.org/home/number-prompts/24-x-21-42-x-12">This</a> is a good inquiry I found there for 4th (and 5th) graders.</span><br />
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<span style="font-family: Montserrat; font-size: large;"><span style="background-color: white; color: #666666;"> </span><span style="background-color: white; color: blue;">24 x 21 = 42 x 12</span></span></div>
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<span style="font-family: Montserrat;"><span><a href="http://www.inquirymaths.org/home/number-prompts/24-x-21-42-x-12">The link</a> gives good directions and discusses the importance of student conjectures and exploration. But it leads me to another idea: How much more valuable is solving this problem and thinking about it deeply than doing a page full of double-digit multiplication? We sometimes practice the way we were taught, but many times, there are way better ways. Students, in this case, solve two multiplication problems, look for patterns, develop conjectures, and then work to test those conjectures. More math problems are being practiced while students are doing some important noticing and thinking. <span style="color: purple;">So much better than a sheet full of double-digit problems. </span></span><br /></span>
<br />Jennifer Gibsonhttp://www.blogger.com/profile/04128860663290797642noreply@blogger.com0tag:blogger.com,1999:blog-5519240175767583895.post-48552070243504639802019-12-06T09:35:00.001-06:002021-08-15T21:46:53.309-05:00Sorts<span style="font-family: Montserrat;"><span>Sorts are a great way for students to make sense of things around them. It could be images or numbers or objects or words....the point is to get them thinking about a subject and have them make sense of it in some way.</span><br />
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<span>Here are some ideas for sorts. Don't think that these are just for Littles. Older students enjoy them. They offer a non-threatening way for students to look at things, and they offer us good insight into our students' thinking. Sorting is very mathematical even when it is not about numbers. It is about looking at things carefully, finding patterns, and making sense--that's math!</span><br />
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<span>SORT:</span><br />
<span>pattern blocks</span><br />
<a href="https://www.simpsondoor.com/find-a-door/"><span>doors</span></a><br />
<span>coins</span><br />
<span>book characters</span><br />
<a href="https://sites.google.com/site/womiworldwide/drain-covers"><span>drain covers</span></a><br />
<span>shapes--2D and 3D</span><br />
<span>numbers (odd/even) (prime/composite) (square/not square) (multiples)</span><br />
<a href="https://www.freepik.com/free-vector/cars-icons-set_3886851.htm"><span>vehicles</span></a><br />
<span>words</span><br />
<a href="http://www.visualpatterns.org/"><span>patterns</span></a><br />
<a href="https://getemoji.com/"><span>emojis</span></a><br />
<span>food</span><br />
<span>volume/area/perimeter</span><br />
<span>shoes</span><br />
<a href="http://semmonogramming.com/Hyperlink_Pages/Alphabet%20Lettering/50%20State%20Outline.htm"><span>states</span></a><br />
<span><a href="https://visme.co/blog/types-of-graphs/">types of graphs </a>(no numbers or titles are necessary)</span><br />
<span>expressions</span><br />
<span>angles</span><br />
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<br />Jennifer Gibsonhttp://www.blogger.com/profile/04128860663290797642noreply@blogger.com0tag:blogger.com,1999:blog-5519240175767583895.post-35694049299075555212019-11-25T07:00:00.001-06:002021-08-15T21:47:09.261-05:00Cutting the holiday pie<span style="font-family: Montserrat;"><span>A good opportunity for exploration and problem-solving for your students.</span><br />
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<span>With one straight cut, you can cut a pie into two pieces. Cutting it again and having the second cut cross the first cut gives you four pieces. With three cuts, you might get up to seven pieces. <b>What is the maximum number of pieces you can get with 6 straight cuts?</b></span><br />
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Your cuts do not need to produce equal pieces. Once students identify the solution, can they keep going with more cuts? Is there a pattern that begins to emerge?</span><br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhndXxExCxUzA98W_8XptSHU4OedA895WdPPvONt707P3B3a963o0JmZfp4hkyaSxZiTE1PlD0tHSoJOPWLM40HC3emEcrWHwjGHR6Oq7UNMDXYYNrOeUuokbsoOuD7e_rRgUqIHRbFPb4/s1600/alex-loup-aX_ljOOyWJY-unsplash.jpg" style="margin-left: auto; margin-right: auto;"><span style="font-family: Montserrat;"><img border="0" data-original-height="1600" data-original-width="1067" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhndXxExCxUzA98W_8XptSHU4OedA895WdPPvONt707P3B3a963o0JmZfp4hkyaSxZiTE1PlD0tHSoJOPWLM40HC3emEcrWHwjGHR6Oq7UNMDXYYNrOeUuokbsoOuD7e_rRgUqIHRbFPb4/s320/alex-loup-aX_ljOOyWJY-unsplash.jpg" width="213" /></span></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-family: Montserrat;">Photo by Alex Loup on Unsplash</span></td></tr>
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<br />Jennifer Gibsonhttp://www.blogger.com/profile/04128860663290797642noreply@blogger.com0tag:blogger.com,1999:blog-5519240175767583895.post-15044755363383486572019-11-18T14:36:00.000-06:002020-03-16T13:02:30.435-05:00What Does the Data Tell Us?<span style="font-family: Georgia, Times New Roman, serif;">In a recent conversation with some representatives from a major nationwide business company, we were discussing the needs in elementary math education to help lead students to be productive workers in tomorrow's business world.</span><br />
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<span style="font-family: Georgia, Times New Roman, serif;">The big question they said that students need to learn to answer is, "What does the data tell us?" We also discussed the importance of probability and statistics, but in the end, they said that they are looking for workers who can answer this question.</span><br />
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<span style="font-family: Georgia, Times New Roman, serif;">What would this look like in an elementary classroom? I think it just reframes our questioning. In many of our activities, we already expose students to real-world information. We just need to be sure to be more intentional in our questioning in order to get them to look at data.</span><br />
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<span style="font-family: Georgia, Times New Roman, serif;">For example, look at this picture. I took it thinking that it would be a good one for students to determine what was the best deal. What does it tell us? What are some possible reasons a person would be willing to pay more for 3 Peep trees when they can get 9 for such a better deal? </span></div>
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<span style="font-family: Georgia, Times New Roman, serif;">Noticing and wondering is a classroom routine that really benefits our students. When they notice and wonder, you can ask them what the picture tells them. Make them infer from the data that they have. Numberless graphs are a good method of providing data that the students have to make sense of. Here is a <a href="http://undercovercalculus.com/numberless-word-problem-2/" target="_blank">good example </a>of a 2nd grade lesson regarding them. You can find lots of examples and ideas for using them by reading some of the posts listed <a href="https://slowrevealgraphs.com/read-about-it/">here.</a></span></div>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhOofc6iMd7iIKxbnhKgeCmBQviR_fDW-tfr4cRXDK8-MjCVQEj_ju5XBYziFOe_ePT4R_ufvPNk8etGRQ_XQv0BeNNQ2tud5bvfIaGz4voOvoV54JjudrdoBHu31ADUTd-0J4KWmlyZKU/s1600/Screenshot+2019-11-18+at+1.43.01+PM.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><span style="font-family: Georgia, Times New Roman, serif;"><img border="0" data-original-height="228" data-original-width="529" height="137" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhOofc6iMd7iIKxbnhKgeCmBQviR_fDW-tfr4cRXDK8-MjCVQEj_ju5XBYziFOe_ePT4R_ufvPNk8etGRQ_XQv0BeNNQ2tud5bvfIaGz4voOvoV54JjudrdoBHu31ADUTd-0J4KWmlyZKU/s320/Screenshot+2019-11-18+at+1.43.01+PM.png" width="320" /></span></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">What do you notice about this data? What do you wonder?</span></td></tr>
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<span style="font-family: Georgia, Times New Roman, serif;">We want our students to be able to compute and do basic math, but not at the expense of good math thinking and discussion. These are the skills that will carry them into the future--not only in their career, but also in their roles as consumers and citizens.</span><br />
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<span style="font-family: Georgia, Times New Roman, serif;">How can you incorporate statistics and probability into your classroom (whether it is a K classroom or a 5th classroom) by framing your questions and your students' thinking around the question, "What does the data tell us?"</span></div>
<br />Jennifer Gibsonhttp://www.blogger.com/profile/04128860663290797642noreply@blogger.com0tag:blogger.com,1999:blog-5519240175767583895.post-71731815329310757162019-11-05T09:55:00.001-06:002020-03-16T13:02:53.441-05:00Continuing Thoughts on Math Facts<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgt58v5X5f0M3_SMXzib8K4xNngbSM6WTOtE1f41EpzlRcVJLidUl_BXWew4AVHrs_G86d0YR-nvi8gVbioUCYlEz0870vT3kYK6CuCTvPD-wqNCZQ2Wq4ODvf64HAe-nyqxMXdTuN4NQw/s1600/Screenshot+2019-11-05+at+8.21.40+AM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="471" data-original-width="489" height="308" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgt58v5X5f0M3_SMXzib8K4xNngbSM6WTOtE1f41EpzlRcVJLidUl_BXWew4AVHrs_G86d0YR-nvi8gVbioUCYlEz0870vT3kYK6CuCTvPD-wqNCZQ2Wq4ODvf64HAe-nyqxMXdTuN4NQw/s320/Screenshot+2019-11-05+at+8.21.40+AM.png" width="320" /></a></div>
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<span style="font-family: Georgia, Times New Roman, serif;">Some of the biggest concerns I get from teachers revolve around math facts. Oftentimes, when they hear my response, they think that I am saying that math fact fluency is not important. That is not true. I do believe math fact fluency is important; I just don't believe that most of our class time should be spent on rote math fact practice.</span><br />
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<span style="font-family: Georgia, Times New Roman, serif;">This is a topic of much discussion among math educators, and books continue to be written addressing the ways to build true math fluency. Graham Fletcher and Tracy Zager are piloting<a href="https://gfletchy.com/2019/09/25/building-fact-fluency-the-right-way/" target="_blank"> a math fluency kit</a> that should be available soon, and I can't wait to see it in action!</span><br />
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<span style="font-family: Georgia, Times New Roman, serif;">I have been recently reading <u>No More Math Fact Frenzy </u>by Davenport, Henry, Clements, and Sarama. It reinforces the ideas that I continue to communicate to teachers. Rote memorization is not a method for students to best learn their math facts. It does not lead to a true understanding or flexibility of number that defines fluency.</span><br />
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<b><span style="font-family: Georgia, Times New Roman, serif;">Some ideas to consider:</span></b><br />
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<span style="font-family: Georgia, Times New Roman, serif;"><span style="color: purple;"><b>Count</b>. </span>Choral counting is a great way to build number fluency. Counting forwards, backwards, by different multiples....This not only allows students to think about the strings of numbers, but it helps to build a mental number line for students which is so helpful for future success with mathematics. Learn more about choral counting <a href="https://thinkthinkmath.blogspot.com/2019/04/building-number-sense-through-choral.html" target="_blank">here</a>.</span><br />
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<span style="font-family: Georgia, Times New Roman, serif;"><span style="color: purple;"><b>Make your fact practice visual.</b> </span>Create structure that students are familiar with, and have them <span style="color: red;">see</span> the fact rather than just memorize the fact. For example:</span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhSTTKzirWehRE2iYgyE9D0AVEz1nkzk9WgxAYe_Wbqc-r8fSbhP7BuMW5Kzg0G9nvnZI5PxGgb6ke9iS89h0F4eql1ZtJKmeiSwtDQB5UDuDRy0XrfIan_il0e0VL8nGxd7XNCDUHNoEg/s1600/Screenshot+2019-11-05+at+9.09.46+AM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: Georgia, Times New Roman, serif;"><img border="0" data-original-height="243" data-original-width="561" height="138" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhSTTKzirWehRE2iYgyE9D0AVEz1nkzk9WgxAYe_Wbqc-r8fSbhP7BuMW5Kzg0G9nvnZI5PxGgb6ke9iS89h0F4eql1ZtJKmeiSwtDQB5UDuDRy0XrfIan_il0e0VL8nGxd7XNCDUHNoEg/s320/Screenshot+2019-11-05+at+9.09.46+AM.png" width="320" /></span></a></div>
<span style="font-family: Georgia, Times New Roman, serif;">Seeing 7 x 6 this way helps students to visualize how knowing 7 x 5 can help them get the answer for 7 x 6. Using subitizing is still important as students get older!</span><br />
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<span style="font-family: Georgia, Times New Roman, serif;">Rekenrek and ten frame visuals are also great for addition and subtraction facts. There is nothing wrong with students using fingers for a while either. They are a built-in tool. We hope that they eventually gain the confidence to know the sums and differences without their fingers, but if using their fingers helps it to make sense, let them!</span><br />
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<span style="font-family: Georgia, Times New Roman, serif;"><b><span style="color: purple;">Use number talks.</span> </b>Asking students to use dot cards to make sense of math facts is important because it allows them to decompose numbers in different ways and to hear different people's strategies. The above image could be an example of a dot card number strategy for older students, but more simple dot cards for primary will also allow for students to see the fact. Traditional number talks with numbers written horizontally also build fact fluency through exposure to multiple strategies. For example:</span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhQdcWJvyoSgT_QhkObbDLfczRQe8cFZNyrS5DPjB3bFh_8-jXwm_1AsD0TyhI53_C0RMaQ-yfW0DUPgya7Xap-QcozG9m-ewmOY0175VmUTi5CFCyE-qgAUnowLMcoQ9Akz2OE1hazIXI/s1600/Screenshot+2019-11-05+at+9.16.09+AM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: Georgia, Times New Roman, serif;"><img border="0" data-original-height="103" data-original-width="292" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhQdcWJvyoSgT_QhkObbDLfczRQe8cFZNyrS5DPjB3bFh_8-jXwm_1AsD0TyhI53_C0RMaQ-yfW0DUPgya7Xap-QcozG9m-ewmOY0175VmUTi5CFCyE-qgAUnowLMcoQ9Akz2OE1hazIXI/s1600/Screenshot+2019-11-05+at+9.16.09+AM.png" /></span></a></div>
<span style="font-family: Georgia, Times New Roman, serif;">When students discuss the way that they solved a problem like this, they gain a better understanding of number. Maybe one student added 7 + 7 and then added one more. Another decomposed 7 into 2 and 5 so they could make 10 + 5. Maybe another started at 7 and counted up to 8. Number talks give students opportunities to make sense of problems in ways that make sense to them, but they also give you the opportunity to make connections between the strategy they used and those that their classmates used. The goal is for students to not only think more flexibly but also to look for a more efficient method.</span><br />
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<b><span style="color: purple;">Make connections: </span> </b>Help students to see the connection between operations. How does addition help us to do subtraction? How is multiplication related to addition? How are subtraction and division related? Not only asking these questions, but having students explore with manipulatives and discover these relationships will help students to have a better conceptual understanding of the relationship between operations.</span><br />
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<span style="font-family: Georgia, Times New Roman, serif;"><b><span style="color: purple;">Play games: </span> </b>Games that practice math facts are always good not only because students get the opportunity to use their facts, but also because they get to practice important social skills like taking turns, good sportsmanship, and taking care of materials. The best games include students having to use strategy besides knowledge of facts. Encourage parents to play games at home with their children. This is one of the best ways for parents to help their children become better mathematical thinkers.</span><br />
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<b><span style="color: purple;">Make it real: </span> </b>Find as many examples as you can in the real world to help students see how the operations are used. Adding the chairs at one table to the chairs at the other table, finding an array in a display of student work, and talking through the math of your lunch count are all real world ways for the students to make more sense of their math.</span><br />
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<span style="font-family: Georgia, Times New Roman, serif;">Trying some or all of these ideas should help students to gain more flexibility and fluency with their math facts. I believe it is better use of time than pages of math facts, repeated rote practice on a computer program, or timed tests. Knowing your math facts fluently does free up some brain space as you work through more complicated mathematical concepts, but conceptual understanding is much more important than rapid fire!</span><br />
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<b><span style="font-family: Georgia, Times New Roman, serif;">Reminder of math fact progessions:</span></b><br />
<span style="font-family: Georgia, Times New Roman, serif;">Kindergarten: Fluency of +/- facts within 5</span><br />
<span style="font-family: Georgia, Times New Roman, serif;">1st grade: Fluency of +/- facts within 10</span><br />
<span style="font-family: Georgia, Times New Roman, serif;">2nd grade: Fluency of +/- facts within 20</span><br />
<span style="font-family: Georgia, Times New Roman, serif;">3rd grade: Fluency of x and / facts within 100</span><br />
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<br />Jennifer Gibsonhttp://www.blogger.com/profile/04128860663290797642noreply@blogger.com1tag:blogger.com,1999:blog-5519240175767583895.post-66960699559807153742019-10-18T14:44:00.000-05:002020-03-16T13:03:17.224-05:00Playing with Numbers<span style="font-family: Georgia, Times New Roman, serif;">After reading the book Math Recess by Sunil Singh and Dr. Christopher Brownell, I realized the importance of giving students time to explore numbers by playing with them. This post shares a couple of ideas for these explorations.</span><br />
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<tr><td class="tr-caption" style="text-align: center;"><span style="font-family: Georgia, Times New Roman, serif;">This book is a great read and will make you rethink your instructional practices!</span></td></tr>
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<span style="font-family: Georgia, Times New Roman, serif;"><b><u><span style="color: red;">Abundant Numbers:</span></u></b> Have students search for ABUNDANT NUMBERS. A number is considered abundant if the sum of its divisors is greater than the number. For example, twelve is abundant because its divisors (1,2,3,4, and 6) is greater than 12.How many can your students find?</span><br />
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<span style="font-family: Georgia, Times New Roman, serif;"><b><u><span style="color: red;">Circular Primes:</span></u></b> A circular prime is one that remains prime with the relocation of the first digit to the end. So for example, 113 is a circular prime: 113 is prime. When I move the 1 to the end of the number, my new number is 131, which is also prime. When I again move the first digit to the end, I get the number 311. It is also prime; so it means that all 3 of those numbers are CIRCULAR PRIMES.</span></div>
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<span style="font-family: Georgia, Times New Roman, serif;"><span style="color: red;"><b><u>Happy Numbers</u></b></span>: 19 is a HAPPY NUMBER. How do I know? To find a happy number, square each digit and find the sum. Continue doing until you find the final number. If it is 1, then the number is happy. </span><br />
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<span style="color: purple; font-family: Georgia, Times New Roman, serif;"><b>Click <a href="https://drive.google.com/file/d/1o5rzpgdozt_384A2RkvjA2ZWU4UOhHWC/view?usp=sharing" target="_blank">here</a> to see how I know 19 is happy!</b></span></div>
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<span style="font-family: "georgia" , "times new roman" , serif;">Make it a goal to give your students some time with these ideas. Can they find more of any type of number? How many can your class find this week? before winter break? this school year? Can they prove that the numbers they found fit the definition provided?</span></span><br />
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<span style="font-family: Georgia, Times New Roman, serif;">Let your students spend time playing and thinking about numbers. </span></div>
Jennifer Gibsonhttp://www.blogger.com/profile/04128860663290797642noreply@blogger.com0