tag:blogger.com,1999:blog-83993892678150591122024-03-19T03:36:29.235-05:00Algebra's FriendIdeas for Math ClassAlgebra's Friendhttp://www.blogger.com/profile/04729315514507170702noreply@blogger.comBlogger604125tag:blogger.com,1999:blog-8399389267815059112.post-50757252999414187292023-03-02T22:30:00.006-06:002023-03-02T22:30:44.369-06:00Pi Day Activities<p style="text-align: left;"><span style="font-family: arial; font-size: medium;">How will you celebrate PI Day on Tuesday, March 14? I'm sure you have the basic math ideas already ... but what about creative writing, games, and crafts? Here are a few ideas to consider ... </span></p><h3 style="text-align: left;"><span style="font-family: arial; font-size: medium;"><span style="background-color: white; color: #2f303a;">Idea 1 - a game:</span></span></h3><p style="text-align: left;"><span style="font-family: arial; font-size: medium;"><span style="background-color: white; color: #2f303a;">In groups, have students race to see who can be the first to roll the first 10 digits of pi. You’ll need some 10-sided dice </span><span style="background-color: white; color: #2f303a;">and a template for the first 10 digits like this:</span></span></p><p><span style="background-color: white; color: #2f303a;"><span style="font-family: arial;"></span></span></p><div class="separator" style="clear: both; font-size: 20.9px; text-align: center;"><span style="font-family: arial;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjusrJltMbbPc00uhgUbjlNKjO1h7D9SoyI9p4sOX5TR9eKlNWJtnB8iUlJ3eCuBQrEf7_-19-FIGX74mOpow2Ocxuqhx5o18T1ZIvxIgV9sh51GNVK0S0laCFj0PVimozs-pHAwFV_nINIYGzJz1QWL5YSj5JrJPLgg4GxjKkBJWHfwLSiexClOw" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="134" data-original-width="728" height="59" src="https://blogger.googleusercontent.com/img/a/AVvXsEjusrJltMbbPc00uhgUbjlNKjO1h7D9SoyI9p4sOX5TR9eKlNWJtnB8iUlJ3eCuBQrEf7_-19-FIGX74mOpow2Ocxuqhx5o18T1ZIvxIgV9sh51GNVK0S0laCFj0PVimozs-pHAwFV_nINIYGzJz1QWL5YSj5JrJPLgg4GxjKkBJWHfwLSiexClOw" width="320" /></a></span></div><h3 style="clear: both; text-align: left;"><span style="font-family: arial;"><span style="font-size: medium;">Idea 2 - a paper chain:</span></span></h3><p style="clear: both; text-align: left;"><span style="font-family: arial;"><span style="font-size: medium;">Create a PI DAY chain with loops of construction paper. Use a different color for each of the 10 digits. How long will your chain be?</span></span></p><p></p><h3 style="clear: both; color: #2f303a; text-align: left;"><span style="font-family: arial; font-size: medium;">Idea 3 - creative writing:</span></h3><div class="separator" style="clear: both;"><p style="clear: both; color: #2f303a; font-size: medium;"><span style="font-family: arial; font-size: medium;">Write "PI-Ku" poems ... modeled after Haiku. Who can write a meaningful poem using the first 10 digits of PI?</span></p><span style="font-family: arial; font-size: medium;">First line: 3 syllables<br />Second line: 1 syllable<br />Third line: 4 syllables</span></div><div class="separator" style="clear: both;"><span style="font-family: arial; font-size: medium;">Fourth line: 1 syllable</span></div><div class="separator" style="clear: both;"><span style="font-family: arial; font-size: medium;">Fifth line: 5 syllables</span></div><div class="separator" style="clear: both;"><span style="font-family: arial; font-size: medium;">And so on ... </span></div><div class="separator" style="clear: both;"><span style="font-family: arial; font-size: medium;"><br /></span></div><h3 style="clear: both; text-align: left;"><span style="font-family: arial; font-size: medium;">Idea 4 - music:</span></h3><div class="separator" style="clear: both;"><span style="font-family: arial; font-size: medium;">Create PI - Music. In pairs, assign students a digit 1 - 9. Let 0 = a rest. Each pair must come up with a unique sound for their digit, which might include a musical instrument if those are handy, electronic notes if computers are available, or tapping, clapping, or banging. Display the first 20 (or more digits of pi). Students "play" their sound when you point to a digit. Practice your PI symphony until students can play it smoothly.</span></div><div class="separator" style="clear: both;"><br /></div><h3 style="background-color: white; clear: both; color: #2f303a; font-family: arial;"><span style="font-size: medium;">Idea 5 - art:</span></h3><p style="background-color: white; clear: both; color: #2f303a; font-family: arial;"><span style="font-size: medium;">Using graph paper, fill in the blocks based on the first 20+ digits of PI. Color the books black. Then wash the paper with watercolors to represent the sky.</span></p><p style="background-color: white; clear: both; color: #2f303a; font-family: arial;"><span style="font-size: medium;"><br /></span></p><div class="separator" style="clear: both; text-align: center;"><span style="font-size: medium;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgcyxBiRXuzeZvnAkSsKE8ewXuPxycOKQbKOqr8g0H0RPgeM4lvaXw6VKRKzoR24txKVRl2-DozkPhKu0s2vOWMW4nQvFV7yRnULY-60XK_-UzGBEdDTz5Q1x5NdFG5kDhOZU1X7vibhORc4T61PspITXUhohUPDRZhHppnOlDa2HSiiTRNHylk2A" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="408" data-original-width="612" height="213" src="https://blogger.googleusercontent.com/img/a/AVvXsEgcyxBiRXuzeZvnAkSsKE8ewXuPxycOKQbKOqr8g0H0RPgeM4lvaXw6VKRKzoR24txKVRl2-DozkPhKu0s2vOWMW4nQvFV7yRnULY-60XK_-UzGBEdDTz5Q1x5NdFG5kDhOZU1X7vibhORc4T61PspITXUhohUPDRZhHppnOlDa2HSiiTRNHylk2A" width="320" /></a></span></div><div class="separator" style="clear: both; text-align: center;"><span style="font-size: medium;"><br /></span></div><p></p><h3 style="background-color: white; clear: both; color: #2f303a; font-family: arial;"><span style="font-size: medium;">Idea 6 - word fun:</span></h3><div><span style="color: #2f303a; font-family: arial; font-size: medium;"><span style="background-color: white;">In pairs or small groups, ask students to brainstorm as many words as they can that start with PI-. Then go around the room, each pair or group naming a unique word until there is a last group with one more PI- word. That group wins the prize!</span></span></div><div><span style="color: #2f303a; font-family: arial; font-size: medium;"><span style="background-color: white;"><br /></span></span></div><div><span style="color: #2f303a; font-family: arial; font-size: medium;"><span style="background-color: white;">Check out these books - for added fun!</span></span></div><div><span style="font-family: arial; font-size: medium;"><span style="background-color: white;"><div class="separator" style="clear: both; text-align: left;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEhoWJBEWKKUvGTWUW_ppCluFFLofrkgTolm5mVxzqohlOrCqIHZxQY0YNxUMiwZGIXo9vs-FZsW8CogL_hI3WZV7nOvQlZbOfoFXF6Fiwy-nYSC1cFhYfR_uIhNOQhTiSpDPcjQa9UIhfhzfyKf2KpWMZAh0Cj_bDwQskAMYV4faaUcG25qvWA-IQ" style="margin-left: 1em; margin-right: 1em;"><br /></a><div class="separator" style="clear: both; color: #2f303a; text-align: left;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEhoWJBEWKKUvGTWUW_ppCluFFLofrkgTolm5mVxzqohlOrCqIHZxQY0YNxUMiwZGIXo9vs-FZsW8CogL_hI3WZV7nOvQlZbOfoFXF6Fiwy-nYSC1cFhYfR_uIhNOQhTiSpDPcjQa9UIhfhzfyKf2KpWMZAh0Cj_bDwQskAMYV4faaUcG25qvWA-IQ" style="margin-left: 1em; margin-right: 1em;"></a><div class="separator" style="clear: both; text-align: right;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEhoWJBEWKKUvGTWUW_ppCluFFLofrkgTolm5mVxzqohlOrCqIHZxQY0YNxUMiwZGIXo9vs-FZsW8CogL_hI3WZV7nOvQlZbOfoFXF6Fiwy-nYSC1cFhYfR_uIhNOQhTiSpDPcjQa9UIhfhzfyKf2KpWMZAh0Cj_bDwQskAMYV4faaUcG25qvWA-IQ" style="margin-left: 1em; margin-right: 1em;"></a><a href="https://blogger.googleusercontent.com/img/a/AVvXsEipZZqwG3aqbPcUz52Wbiewm6kKXFPMJNQ6FHuOHciiX6EtdMflBPkZWGfedDTd4ceeG9XkNo32wxdyaSg8QUxPaoNRiV3X-y1xgfvaeiFzRndwr6Z11SeDMOXpidlcNkCUm_FWuRFL2g_Yj8lqtm3bZWThG8CInnL9Z3iqwAeO619X7b7-vztDKg" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img alt="" data-original-height="490" data-original-width="500" height="240" src="https://blogger.googleusercontent.com/img/a/AVvXsEipZZqwG3aqbPcUz52Wbiewm6kKXFPMJNQ6FHuOHciiX6EtdMflBPkZWGfedDTd4ceeG9XkNo32wxdyaSg8QUxPaoNRiV3X-y1xgfvaeiFzRndwr6Z11SeDMOXpidlcNkCUm_FWuRFL2g_Yj8lqtm3bZWThG8CInnL9Z3iqwAeO619X7b7-vztDKg" width="245" /></a><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjzRt0RCwqeg3DAhhdPQ6A5ikKqMzwAF7ukcpIes80FKbA4f0yVY3-bjzHXVjCRfEpd99Vk_WcTYFTdw0hyGiXZO7Uw3t4rDWSaDCTI2L8w10MdwV1cUodk0nYDrRYL1X0GIbPof567nrQwIhfUGVvvq18uYBq9GY0cUBUodFDhuUsMl3FwPAm44Q" style="clear: left; 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float: left; margin-bottom: 1em; margin-right: 1em;"><img alt="" data-original-height="291" data-original-width="260" height="214" src="https://blogger.googleusercontent.com/img/a/AVvXsEheGKSNAM1rMmAYjoa57Ls0QOwLkYYqGSIP8NIYpPvZJQ8BmT-d0drl0tyFFckX9Rm2VFx1_dXUkkOWUP1Q0b9YpCI9S1M2SLMJmcAunaw6ovwHSFO08RRp-FPqr6zvB0--nqw107NMFnM7-M1aJfADs6QA8Ed13J5HBo8zy_xwfo-0HB0peB3iww=w191-h214" width="191" /></a><a href="https://blogger.googleusercontent.com/img/a/AVvXsEg_DH0B_JaXfaUtIPIGPoIHbEPBv6Xp5Z0uhGghsu0tnMFNICXA_hB6CdoSQCfUe7EmaQkIkUaTroLsRgYPNGC9N2ebAKIH9e3IabjAwzSPz9KYmNtN_b2llyznIKODuUF66_N6-6UieQgH85NkV1msVMXIITOmfWcX8FGpi3BYIHTwH6ARLHRMTg" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="335" data-original-width="260" height="240" src="https://blogger.googleusercontent.com/img/a/AVvXsEg_DH0B_JaXfaUtIPIGPoIHbEPBv6Xp5Z0uhGghsu0tnMFNICXA_hB6CdoSQCfUe7EmaQkIkUaTroLsRgYPNGC9N2ebAKIH9e3IabjAwzSPz9KYmNtN_b2llyznIKODuUF66_N6-6UieQgH85NkV1msVMXIITOmfWcX8FGpi3BYIHTwH6ARLHRMTg" width="186" /></a></div></div></div><br /></div><br /><br /><br /><br /></span></span></div><p style="background-color: white; clear: both; color: #2f303a; font-family: arial;"><span style="font-size: medium;"><br /></span></p><div class="separator" style="clear: both; text-align: center;"></div><p><span style="background-color: white; color: #2f303a; font-family: Lato, proxima-nova-2, "Open Sans", "Helvetica Neue", Helvetica, Arial, sans-serif;"><br /></span></p>Algebra's Friendhttp://www.blogger.com/profile/04729315514507170702noreply@blogger.com0tag:blogger.com,1999:blog-8399389267815059112.post-5002268944528705122023-03-01T13:14:00.006-06:002023-03-01T13:17:56.785-06:00Introducing Quadratics<p><span style="font-family: arial; font-size: large;"> It is late in the year to introduce quadratics. These ideas might be something to save for next year.</span></p><p><span style="font-family: arial; font-size: large;">How can you activate multiple intelligences and involve students in thinking deeply about quadratics? Try using a variety of activities - hands-on, computer simulation, reading, critical thinking and/or a video.</span></p><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">What do you wonder, notice?</span><a href="https://drive.google.com/file/d/16Wftd8ff_jj9gjdk6bQVau9IptW8wSEa/view?usp=sharing" style="text-decoration: none;"><span style="-webkit-text-decoration-skip: none; background-color: transparent; color: #1155cc; font-family: Arial; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration-skip-ink: none; text-decoration: underline; vertical-align: baseline; white-space: pre;"> Examining pictures</span></a></p><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><br /></p><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">Starburst Lab -</span><a href="https://drive.google.com/file/d/0B-1saJM8fLPgbndGanRVb0dwNHc/view?usp=sharing&resourcekey=0-yvHBSA_dtduAgYH_3EF9pQ" style="text-decoration: none;"><span style="-webkit-text-decoration-skip: none; background-color: transparent; color: #1155cc; font-family: Arial; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration-skip-ink: none; text-decoration: underline; vertical-align: baseline; white-space: pre;"> Discover the pattern</span></a></p><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><br /></p><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">Essay to Read -</span><a href="https://plus.maths.org/content/101-uses-quadratic-equation" style="text-decoration: none;"><span style="-webkit-text-decoration-skip: none; background-color: transparent; color: #1155cc; font-family: Arial; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration-skip-ink: none; text-decoration: underline; vertical-align: baseline; white-space: pre;"> 101 Uses for a Quadratic Equation</span></a></p><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><br /></p><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">Video to Watch -</span><a href="https://youtu.be/He42k1xRpbQ" style="text-decoration: none;"><span style="-webkit-text-decoration-skip: none; background-color: transparent; color: #1155cc; font-family: Arial; font-size: 14pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration-skip-ink: none; text-decoration: underline; vertical-align: baseline; white-space: pre;"> Quadratics/Parabolas in the Real World</span></a></p><p><span style="font-family: Arial; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Guided Discovery -</span><a href="https://teacher.desmos.com/activitybuilder/custom/56e0b6af0133822106a0bed1?collections=featured-collections%2C5e73b204d560367270838c4b" style="text-decoration-line: none;"><span style="color: #1155cc; font-family: Arial; font-size: 14pt; font-variant-east-asian: normal; font-variant-numeric: normal; text-decoration-line: underline; text-decoration-skip-ink: none; vertical-align: baseline; white-space: pre-wrap;"> Will It Hit the Hoop Desmos Activity</span></a></p><p><br /></p><p><span style="font-size: large;">Then use <a href="https://docs.google.com/document/d/1_C-dt_q5qnBhXyODsj4hMUIXK9zlBlBgv-ueGDakHWk/copy" target="_blank">this chart to organize basic properties</a> - it will prompt you to make a copy.</span></p><br /><br />Algebra's Friendhttp://www.blogger.com/profile/04729315514507170702noreply@blogger.com0tag:blogger.com,1999:blog-8399389267815059112.post-55584217261682018322023-03-01T12:52:00.003-06:002023-03-01T12:52:21.957-06:00Looking for challenging problems?<p> Check out <a href="https://karendcampe.wordpress.com/" target="_blank">Reflections and Tangents</a> postings of "old" calendar problems! Search the name of the month in the search box on her blog. Here are two samples ... </p><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgnsiZj59WA44YrLNcxrDF2cs5TRcEH2G_0JegZYWc8vBBlg75ir3zZkiva-II8awJ4NGjqz_q28a-OXpTN5vX8XibEs7NC1opAZXiDFwF7V-HA34g4U_9sIq-j5f9lh3IXmo43AwGbPoCLnqHpOLzhhULPxceFt7xMAeEkXfGovFsw8UxkjQRBWg" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="786" data-original-width="1242" height="353" src="https://blogger.googleusercontent.com/img/a/AVvXsEgnsiZj59WA44YrLNcxrDF2cs5TRcEH2G_0JegZYWc8vBBlg75ir3zZkiva-II8awJ4NGjqz_q28a-OXpTN5vX8XibEs7NC1opAZXiDFwF7V-HA34g4U_9sIq-j5f9lh3IXmo43AwGbPoCLnqHpOLzhhULPxceFt7xMAeEkXfGovFsw8UxkjQRBWg=w557-h353" width="557" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></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/AVvXsEitY7GFYsuVSdO9vWvEmPdCrCL9LR9u0Fx1LGldIls1m0lB5kqM8WHJKsx93G8IXWJJTMZGtYvH8Sgc0K6a3udcJE-D3CvrYBMQN72oLSYaU20_8Tz7fhmHXroOmHAvuMVy69nwRYbXihZJ5NI-JUFXHeU6pe0lXI9O6Fdojh97FMEpV4d5hMV_kw" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="790" data-original-width="1256" height="340" src="https://blogger.googleusercontent.com/img/a/AVvXsEitY7GFYsuVSdO9vWvEmPdCrCL9LR9u0Fx1LGldIls1m0lB5kqM8WHJKsx93G8IXWJJTMZGtYvH8Sgc0K6a3udcJE-D3CvrYBMQN72oLSYaU20_8Tz7fhmHXroOmHAvuMVy69nwRYbXihZJ5NI-JUFXHeU6pe0lXI9O6Fdojh97FMEpV4d5hMV_kw=w541-h340" width="541" /></a></div><br /><br /></div><br /><br /><p></p>Algebra's Friendhttp://www.blogger.com/profile/04729315514507170702noreply@blogger.com0tag:blogger.com,1999:blog-8399389267815059112.post-85233761000803427422023-01-07T21:12:00.003-06:002023-01-07T21:12:25.507-06:00Closures - How you know they know ... <p>Almost two weeks ago I wrote about "hooks" also known as anticipatory sets or sometimes called warm-ups. The first few minutes of a lesson are critical for establishing student interest and engagement.</p><p><span style="background-color: white;">But what about closures?!?</span></p><p><a href="https://mathbythemountain.com/tag/math-exit-tickets-for-high-school/" target="_blank">Math By the Mountain </a>has developed several posts about the significance of using exit tickets in secondary math classes.</p><div style="background-color: white;">Shelli created an awesome set of prompts for exit tickets ... <a href="http://statteacher.blogspot.com/2016/08/ring-o-prompts.html" style="color: #9e4433; text-decoration-line: none;" target="_blank">check them out here</a>. Her prompts could be used not just for exit tickets but also for journal writing!</div><div style="background-color: white;"><br /></div><div style="background-color: white;">Sarah shared <a href="https://mathequalslove.net/free-exit-ticket-templates/" target="_blank">25+ Exit Ticket Templates</a> at Math Equals Love.</div><div style="background-color: white;"><br /></div><div style="background-color: white;">Ditch That Textbook has curated <a href="https://ditchthattextbook.com/10-ideas-for-digital-exit-tickets-and-some-analog-ones-too/" target="_blank">20 ideas for Exit Tickets</a> - not all math, but clearly, they might spark your own creativity!</div><div style="background-color: white;"><span face="Arial, Helvetica, sans-serif"><br /></span></div><div style="background-color: white;"><span face="Arial, Helvetica, sans-serif">Here are a few other ideas besides exit tickets - </span></div><div style="background-color: white;"><span face="Arial, Helvetica, sans-serif"><br /></span></div><div style="background-color: white;"><span face="Arial, Helvetica, sans-serif"><b>The Stoplight Method </b>works - students can post a response to a prompt as they are leaving. Check out this<a href="https://www.teachingchannel.org/videos/daily-lesson-assessment" style="color: #9e4433; text-decoration-line: none;" target="_blank"> one minute video description.</a></span></div><div style="background-color: white;"><span face="Arial, Helvetica, sans-serif"><br /></span></div><div style="background-color: white;"><span face="Arial, Helvetica, sans-serif"><b>Around the Room</b> is another one - students pass a ball around the room, stating one thing they learned that day.</span></div><div style="background-color: white;"><span face="Arial, Helvetica, sans-serif"><br /></span></div><div style="background-color: white;"><span face="Arial, Helvetica, sans-serif"><b>What's Inside -</b> pairs/groups of students receive an envelope and inside could be a vocabulary word, a concept, a problem. Students explain the connection to the lesson.</span></div><div style="background-color: white;"><span face="Arial, Helvetica, sans-serif"><br /></span></div><div style="background-color: white;"><span face="Arial, Helvetica, sans-serif">There are many more. Check out these lists:</span></div><div style="background-color: white;"><a href="http://www.edutopia.org/blog/22-powerful-closure-activities-todd-finley" style="color: #9e4433; text-decoration-line: none;" target="_blank">22 Powerful Closure Activities</a></div><div style="background-color: white;"><a href="http://teaching.colostate.edu/tips/tip.cfm?tipid=148" style="color: #9e4433; text-decoration-line: none;" target="_blank">Closure Activities</a></div><div style="background-color: white;"><a href="http://www.stma.k12.mn.us/documents/DW/Q_Comp/40_ways_to_leave_a_lesson.pdf" style="color: #9e4433; text-decoration-line: none;" target="_blank">40 Ways to Leave a Lesson</a></div><div style="background-color: white;"><span face="Arial, Helvetica, sans-serif"><a href="https://www.teachingchannel.org/videos/tips-on-closing-a-lesson" style="color: #9e4433; text-decoration-line: none;" target="_blank">Tips on Leaving a Lesson Effectively</a><br /><br />@LeeanneBranham mentioned the suggestion to start the next lesson with a closure to the previous one and she shared a 3-2-1 that worked for her.</span></div><div style="background-color: white;"><blockquote class="twitter-tweet" data-lang="en"><div dir="ltr" lang="en"><span face="Arial, Helvetica, sans-serif"><a href="https://twitter.com/BridgetDunbar" style="color: #9e4433; text-decoration-line: none;">@BridgetDunbar</a> <a href="https://twitter.com/fractionfanatic" style="color: #9e4433; text-decoration-line: none;">@fractionfanatic</a> <a href="https://twitter.com/algebrasfriend" style="color: #9e4433; text-decoration-line: none;">@algebrasfriend</a> <a href="https://twitter.com/druinok" style="color: #9e4433; text-decoration-line: none;">@druinok</a> I have had great success with this. <a href="https://t.co/929nZPrP7m" style="color: #9e4433; text-decoration-line: none;">pic.twitter.com/929nZPrP7m</a></span></div><span face="Arial, Helvetica, sans-serif">— LeeanneBranham (@LeeanneBranham) <a href="https://twitter.com/LeeanneBranham/status/762878776145383424" style="color: #9e4433; text-decoration-line: none;">August 9, 2016</a></span></blockquote><span face="Arial, Helvetica, sans-serif">Beginnings and endings are significant - and possibly the moments we plan for the least.<br /><br />What ideas do you have to share? How do you reserve 5 to 10 minutes for closure consistently?</span></div>Algebra's Friendhttp://www.blogger.com/profile/04729315514507170702noreply@blogger.com0tag:blogger.com,1999:blog-8399389267815059112.post-29672790909936314442022-12-26T11:13:00.018-06:002022-12-26T11:15:24.118-06:00Beginnings - The HOOK!<span face="Verdana, sans-serif"><span id="docs-internal-guid-b29fe362-7fff-ebff-afb8-596ccb159a50"><p dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-family: Cambria, serif; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Brian Sztabnik is a highly recognized AP English Teacher. Here’s his quote about the first and last eight minutes of class:</span></p><br /><p dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-left: 72pt; margin-top: 0pt;"><span style="font-family: Cambria, serif; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">That is the crux of lesson planning right there—endings and beginnings. If we fail to engage students at the start, we may never get them back. If we don’t know the end result, we risk moving haphazardly from one activity to the next. Every moment in a lesson plan should tell.</span></p><br /><p dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-left: 72pt; margin-top: 0pt;"><span style="font-family: Cambria, serif; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">The eight minutes that matter most are the beginning and endings. If a lesson does not start off strong by activating prior knowledge, creating anticipation, or establishing goals, student interest wanes, and you have to do some heavy lifting to get them back. If it fails to check for understanding, you will never know if the lesson’s goal was attained.**</span></p><span style="font-family: Cambria, serif; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span> </span><span> </span><span> </span><span> </span><span> <span> </span></span></span><span style="font-family: Cambria, serif; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span></span></span><p>How do you engage or HOOK students in the first few minutes of class? One of my favorite ways was to use videos ... visual stimuli attract students' attention. Several years ago, I compiled a list of favorite Youtube videos that worked for my Algebra 2 curriculum. <a href="https://docs.google.com/spreadsheets/d/1cQOsDJtxcSOXAwFFTR6r5EE9EqFlUNL2SaAnQslfkA8/edit?usp=sharing" target="_blank">You can access the file here.</a></p><br /><span face="Verdana, sans-serif">You'll notice certain sources are repeated! Check out these sources for videos that fit your curriculum:</span><br /><span face="Verdana, sans-serif"><br /></span><a href="https://www.ted.com/topics/math" target="_blank"><span face="Verdana, sans-serif">TED</span></a><br /><a href="http://ed.ted.com/lessons?category=mathematics" target="_blank"><span face="Verdana, sans-serif">Ted Ed</span></a><br /><a href="http://www.numberphile.com/" target="_blank"><span face="Verdana, sans-serif">Numberphile</span></a><br /><a href="https://www.youtube.com/user/Vihart" target="_blank"><span face="Verdana, sans-serif">Vi Hart</span></a><br /><span face="Verdana, sans-serif"><br /></span><span face="Verdana, sans-serif">Do you have a video that inspires students in math class? If so, share the title/link in the comments!</span><div><span face="Verdana, sans-serif"><br /></span></div><div><span face="Verdana, sans-serif">And if you are looking for even more ideas ... check out these resources for hook strategies!</span></div><div><span face="Verdana, sans-serif"><br /></span></div><ul><li><span id="docs-internal-guid-d385cfc2-7fff-19f7-73de-37b0b956ddea">Talkin’ Chalk. (2018, September 9). Learning Hooks | Engage Students in the Classroom. YouTube. <a href="https://www.youtube.com/watch?v=GYiacSSLP9o&feature=youtu.be " target="_blank">https://www.youtube.com/watch?v=GYiacSSLP9o&feature=youtu.be </a></span> </li><li>Teach Starter. (2021, August 17). 9 Lesson Hook Strategies to Launch Learning. <a href="https://www.teachstarter.com/us/blog/lesson-hook-strategies-to-launch-learning/?queryID=ad3019fcf6bd045218cd34cf920cc3e6&objectID=1855798" target="_blank">https://www.teachstarter.com/us/blog/lesson-hook-strategies-to-launch-learning/?queryID=ad3019fcf6bd045218cd34cf920cc3e6&objectID=1855798 </a></li><li>Gonzalez, J. (2020, June 13). Know Your Terms: Anticipatory Set. Cult of Pedagogy. <a href="https://www.cultofpedagogy.com/anticipatory-set/">https://www.cultofpedagogy.com/anticipatory-set/</a> </li><li>Elliott, J. (2021, June 30). What is the Engagement Phase of the 5E Instructional Model. What I Have Learned. <a href="https://www.whatihavelearnedteaching.com/engagement-phase-5e-instructional-model/">https://www.whatihavelearnedteaching.com/engagement-phase-5e-instructional-model/ </a></li>Diede, M. D., & Risby, K. R. (2021, September 2). Captain of a hook: 10 engaging lesson introduction ideas. Ditch That Textbook. <a href="https://ditchthattextbook.com/lesson-hooks/">https://ditchthattextbook.com/lesson-hooks/</a><ul><br /></ul></ul><div>**<span style="font-family: Cambria, serif; font-size: 12pt; white-space: pre-wrap;">(Sztabnik, B. (2015, May 1). The 8 Minutes That Matter Most. Edutopia. </span><a href="https://www.edutopia.org/blog/8-minutes-that-matter-most-brian-sztabnik" style="text-decoration-line: none;"><span style="color: #1155cc; font-family: Cambria, serif; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; text-decoration-line: underline; text-decoration-skip-ink: none; vertical-align: baseline; white-space: pre-wrap;">https://www.edutopia.org/blog/8-minutes-that-matter-most-brian-sztabnik</span></a><span style="font-family: Cambria, serif; font-size: 12pt; white-space: pre-wrap;">)</span><span style="font-family: Cambria, serif; font-size: 12pt; white-space: pre-wrap;"> </span></div><div><span face="Verdana, sans-serif"> </span></div>Algebra's Friendhttp://www.blogger.com/profile/04729315514507170702noreply@blogger.com0tag:blogger.com,1999:blog-8399389267815059112.post-35344247318916233222022-12-22T22:38:00.002-06:002022-12-22T22:38:39.309-06:00Tips for January Back to School!<p> Returning to school after the winter break can be challenging for everyone. </p><p></p><ul style="text-align: left;"><li>Not everyone had a happy holiday; some students may have experienced great disappointments</li><li>If you feel reluctant, imagine how your students might feel the same way</li><li>It's hard to get back into the groove of a regular school schedule</li></ul><div>You can surely expect your middle/high schoolers to be tired!</div><div><br /></div><div>So how can you engage your students on that very first day? Here are ideas to think about - hopefully, they will spark your own creative ideas! Specifically, plan an "easy" first day back that provides opportunities for success, connection, and relationship building ...</div><div style="text-align: left;"><ol style="text-align: left;"><li>Start with a review game, including various problems from the first semester but especially some easy ones. Make the game fun -<a href="https://www.mrseteachesmath.com/2019/07/review-game-let-cards-decide.html" target="_blank"> Mrs. E Teaches Math has a free set of game cards </a>(sign up, free download) that adds a strong element of chance and fun. </li><li>OR start January with a math debate. Math is the most important subject. We don't need math now that we have portable computers (phones). Math is not relevant to our everyday lives. What was the most difficult topic you learned in first semester? If you have been studying parent functions - what is the coolest parent function you've learned so far? OR check out <a href="https://www.luzniak.com/stemdebatecards.html" target="_blank">this plethora of debate topics provided free!</a></li><li>OR use the <a href="https://www.nytimes.com/2022/11/10/learning/what-students-are-saying-about-the-value-of-math.html" target="_blank">New York Times Learning Network</a> guest opinion piece and writing prompt to explore the value of learning math.</li><li>OR use this first day back to explore mathematical mindsets. Use <a href="https://www.youcubed.org/mathematical-mindset-teaching-guide-teaching-video-and-additional-resources/" target="_blank">the guide at YouCubed!</a></li><li>OR If you already know your class likes mystery, intrigue, puzzles, start the new semester with a puzzle day - a day to warm up the brain! Sarah Carter (Math=Love) has<a href="https://mathequalslove.net/puzzles/" target="_blank"> a treasure trove of puzzles</a>! </li><li>Use the first class period or two to set fresh goals for the new semester. Students might review their work portfolio, grades, or work habits to determine areas to strengthen. <a href="https://www.mathgiraffe.com/blog/helping-students-set-goals" target="_blank">Math Giraffe has a great post</a> on teaching "smart" goals, a doodle worksheet to share, and tips for making it work in your classroom. "Teaching Expertise" suggests <a href="https://www.teachingexpertise.com/classroom-ideas/goal-setting-activities-for-high-school-students/" target="_blank">20 ways to do goal setting</a> if you are looking for another idea!</li></ol></div><p></p><p></p><div><br /></div><div>Most importantly, come to class with an attitude worth sharing! Spend a few minutes before that first day back listing your top three reasons for teaching. Organize your first week's outfits so those mornings are not so difficult. Buy a few healthy treats to add to your desk stash so that you have something to enjoy if/when you get a break in your day. Last, plan easy dinners for those few days back ... freezer meals, crock pot delights, your neighborhood eatery! A little self-care can go a long ways to a successful first week back to school!</div><div><br /></div><div>Please add your ideas to the comments section - </div><div><br /></div><div><br /></div><div><br /></div><div><br /></div><p></p>Algebra's Friendhttp://www.blogger.com/profile/04729315514507170702noreply@blogger.com0tag:blogger.com,1999:blog-8399389267815059112.post-19823830682323280982022-12-04T20:47:00.006-06:002022-12-04T20:47:35.957-06:00number sense in secondary educationUsually, when I think of building number sense, I think about primary math education. I know, though, number sense is something we all must work on all the time! I'm curating ideas for secondary math and building number sense.<br /><ol><br /> <li>Knowing how precisely a high school freshman can estimate the number of objects in a group gives you a good idea of how well he has done in math as far back as kindergarten, researchers at Johns Hopkins University found. This <a href="http://www.sciencedaily.com/releases/2008/09/080907211940.htm">Science Daily</a> article is quite interesting.</li><br /> <li>This is a go-to book for ideas: <a href="http://www.heinemann.com/products/E02662.aspx?catalog=120206&target=top">Building Powerful Numeracy for Middle and High School Students</a>, written by Harris and published by Heinemann. </li><br /> <li><a href="https://numberstrings.com/" target="_blank">This site</a> says it's a community for number string design!</li><br /> <li>The state of Texas has a well-developed academic competition developed by the University of Texas - one of which is number sense. Practice tests are available <a href="https://www.uiltexas.org/academics/stem/number-sense">online here</a>.<br /></li><br /><li>The San Francisco Unified School District Math Department has put together a page full of resources on number talks. <a href="https://www.sfusdmath.org/math-talks-resources.html" target="_blank">Check it out!</a></li><br /><li>Fawn Nguyen put together this set of <a href="https://docs.google.com/presentation/d/1I_zEnyFO-9BWZCeftIHnBDkZ2pa1ecD5ihqwnaAnBHo/edit#slide=id.g11e77be16ef_0_195">90-number talks</a> for middle schoolers — enough for a full school year if you do this routine every other day.</li></ol><div>What tools, routines, or materials do you use to build number sense in secondary students? How often do you work on number sense? How important is it in your math program?</div><br /><br />Algebra's Friendhttp://www.blogger.com/profile/04729315514507170702noreply@blogger.com7tag:blogger.com,1999:blog-8399389267815059112.post-79760753057287550012022-12-02T21:42:00.000-06:002022-12-03T10:34:01.770-06:00Writing in Math ClassReading and writing in math class helps to build, solidify, and deepen students' understanding of math concepts. In this post I share a few examples that I hope will spark your own ideas.<br />
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Writing frames support all math students in constructing short responses. These writing frames from science can be adapted to math. <a href="https://drive.google.com/a/roundrockisd.org/file/d/0ByJ71RI_wBc7N2hfNDNualFyaHNJZkxWWUlIeWh5aGp0WEpz/edit?usp=sharing">Here are 3 samples!</a> These samples are simplistic but great for teaching the structure of writing short responses!<br />
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Here are some specific examples of algebra 2 topics:<br />
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<b>Rational functions,</b> What is the horizontal asymptote of this function? Show this on the graph. What does this value represent in terms of the problem posed? Considering the problem, why does your value for the horizontal asymptote make sense?<br />
<b><br /></b><b>Exponential unit:</b> You have a rich Uncle that gives you $5000 to invest. You have researched two different banks to see which you want to use to help you make the most money. Describe when it would be better to choose MK Federal Credit Union and when it would be better to choose MCB National.<br />
<br /><b>Square root unit: </b>Does doubling the length of the skid double the speed the driver was going? Justify your response using tables, symbols, and graphs.<br />
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<b>Project idea:</b> Read an article about mathematics or a mathematician in the New York Times (http://topics.nytimes.com/top/news/science/topics/mathematics/). Create a mini-poster that illustrates the article. Include a “3-Part Source Integration” writing. A “3-Part Source Integration” is a three-sentence statement that includes the text's title, author’s name, author information, source material that is either paraphrased or directly quoted, and a brief statement explaining the significance of the paraphrase or quotation.<br />
<br />Past examples of students' writing ... <a href="http://algebrasfriend.blogspot.com/2013/10/math-munching-today.html">a blog post</a>. <br />
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I find that these short writing opportunities provide windows into students' thinking. How do you use short writing prompts?<br />
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In the article <a href="http://www-tc.pbs.org/teacherline/courses/rdla230/docs/session_6_brandenburg.pdf">"Advanced Math? Write!"</a> the author stresses starting small. She emphasizes journal writing. I have not tried journal writing with 150 students. Even when I had considerably fewer students, I found keeping up with responses to journals challenging. How could I begin journaling with students without feeling overwhelmed?<br />
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<br />Algebra's Friendhttp://www.blogger.com/profile/04729315514507170702noreply@blogger.com0tag:blogger.com,1999:blog-8399389267815059112.post-54202660043042809732022-12-01T11:00:00.000-06:002022-12-02T10:41:49.004-06:00Sharing Research With Our Students<div style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">When I was teaching high school, I asked my students to read a summary of Make It Stick by Peter Brown (or watch a video summary). Then I asked them what they noticed, what they wondered. Here are a few of their ideas.</div>
<div style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span face="Trebuchet MS, sans-serif"><br /></span><span style="background-color: transparent; color: black; font-style: normal; font-variant: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;"><span face="Trebuchet MS, sans-serif"><u>What I notice:</u></span></span></div>
<ul>
<li><span face="Trebuchet MS, sans-serif"><span style="font-weight: 400; line-height: 1.38;">“Make it Stick” focuses on how the student thinks about learning and goes about learning rather than how the material is taught </span></span></li>
<li><span face="Trebuchet MS, sans-serif"><span style="font-weight: 400; line-height: 1.38;">A majority of the chapters focus on how the student review or practice the content.</span></span></li>
<li><span face="Trebuchet MS, sans-serif"><span style="font-weight: 400; line-height: 1.38;"> Academic skill revolves more around environment and effort.</span></span></li>
<li><span face="Trebuchet MS, sans-serif"><span style="font-weight: 400; line-height: 1.38;">I notice how the author mentions that cramming information before a test the next day isn’t as potent as people believe.</span></span></li>
<li><span face="Trebuchet MS, sans-serif"><span style="line-height: 1.38;">I also notice how he mentions retrieval practice and how it should be more spread out. </span></span></li>
<li><span face="Trebuchet MS, sans-serif"><span style="line-height: 1.38;">I believe I have experienced “the illusion of knowing” after re-reading content as a study strategy</span></span></li>
<li><span face="Trebuchet MS, sans-serif"><span style="line-height: 1.38;">When I study, I notice that using the retrieval method is more difficult than other methods</span></span></li>
</ul>
<span style="background-color: transparent; color: black; font-style: normal; font-variant: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;"><span face="Trebuchet MS, sans-serif"><u>What I wonder:</u></span></span><br />
<ul style="margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-style: normal; font-variant: normal; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;"><span face="Trebuchet MS, sans-serif">
<li><span style="font-weight: 400; line-height: 1.38;">Can someone pick up study skills or do they have to be developed over time?</span></li>
<li><span style="font-weight: 400; line-height: 1.38;">Do genetics still influence how well someone does academically?</span></li>
<li dir="ltr" style="background-color: transparent; color: black; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: disc; vertical-align: baseline;"><span style="background-color: transparent; color: black; font-style: normal; font-variant: normal; font-weight: 400; vertical-align: baseline; white-space: pre-wrap;"><span face="Trebuchet MS, sans-serif">Does involvement in other non-academic activities have a positive influence on academic development?</span></span></li>
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<li dir="ltr" style="background-color: transparent; color: black; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: disc; text-decoration: none; vertical-align: baseline;"><span face="Trebuchet MS, sans-serif"><span style="background-color: transparent; color: black; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span id="docs-internal-guid-16ac3c81-69cf-eb52-081a-72b104b0483e"><span style="vertical-align: baseline;">Is a certain type of learning </span></span></span><span style="white-space: pre-wrap;">more powerful/memorable than another or if it is specific to the person?</span></span></li>
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<li dir="ltr" style="background-color: transparent; color: black; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: disc; text-decoration: none; vertical-align: baseline;"><span style="white-space: pre-wrap;"><span id="docs-internal-guid-20e76377-69d0-8faa-1eb0-0ee52e0cd7b1"><span style="vertical-align: baseline;"><span face="Trebuchet MS, sans-serif">Why does spacing out study sessions make your learning more potent causing your memory and learning to be stronger?</span></span></span></span></li>
<li><span face="'Trebuchet MS', sans-serif" style="line-height: 1.38;">I wonder why arduous effort in retaining memory is more effective than memorizing something. </span></li>
<li><span face="'Trebuchet MS', sans-serif" style="line-height: 1.38;">I also wonder why i’ve never been taught this before as it provides great information on how to keep your grades in superb shape.</span></li>
<li><span face="'Trebuchet MS', sans-serif" style="line-height: 1.38; white-space: pre-wrap;">How were these studying strategies thought of, and how many people did they test them on?</span></li>
<li><span face="'Trebuchet MS', sans-serif" style="line-height: 1.38; white-space: pre-wrap;">I wonder if there are any methods even more effective than retrieval practice?</span></li>
</ul>
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<span face="Trebuchet MS, sans-serif"><span style="line-height: 22.08px; white-space: pre-wrap;"><br /></span></span></div>
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<span face="'Trebuchet MS', Trebuchet, sans-serif" style="background-color: white; color: #27004e; font-size: 14px; line-height: 19.6px;"> Brown, P. (n.d.). </span><i style="background-color: white; color: #27004e; font-family: "Trebuchet MS", Trebuchet, sans-serif; font-size: 14px; line-height: 19.6px;">Make it stick: The science of successful learning</i><span face="'Trebuchet MS', Trebuchet, sans-serif" style="background-color: white; color: #27004e; font-size: 14px; line-height: 19.6px;">. </span></div><div><span face="'Trebuchet MS', Trebuchet, sans-serif" style="background-color: white; color: #27004e; font-size: 14px; line-height: 19.6px;"><br /></span></div><div><span face="'Trebuchet MS', Trebuchet, sans-serif" style="background-color: white; color: #27004e; font-size: 14px; line-height: 19.6px;"><b><i>How do you share the research you read with your students?</i></b></span></div>
<br />Algebra's Friendhttp://www.blogger.com/profile/04729315514507170702noreply@blogger.com0tag:blogger.com,1999:blog-8399389267815059112.post-47685724890012105162022-01-30T14:36:00.000-06:002022-01-30T14:36:03.026-06:00Curated Free Twos-Day Math Activities <div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEg6VKMRIksAEccJmwgM94a56Z54Yq9u_u89o-H1iIBkbtLWWDjZAhv_x4ivWXBbcJYlV54pvYLNACCYZEyu5QvGPcG-J5GQyOI6VFK8jOD-amx0VHo0IhA24EUKZg9gTqXlPeuaYId4c4zaeCJNzS4TPg2s_SKhh5t8DVi3sHzXfZ-ud1EK1hHbaQ=s800" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="400" data-original-width="800" height="320" src="https://blogger.googleusercontent.com/img/a/AVvXsEg6VKMRIksAEccJmwgM94a56Z54Yq9u_u89o-H1iIBkbtLWWDjZAhv_x4ivWXBbcJYlV54pvYLNACCYZEyu5QvGPcG-J5GQyOI6VFK8jOD-amx0VHo0IhA24EUKZg9gTqXlPeuaYId4c4zaeCJNzS4TPg2s_SKhh5t8DVi3sHzXfZ-ud1EK1hHbaQ=w640-h320" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><h3 style="background: rgb(255, 255, 255); border: 0px; box-sizing: border-box; color: #333033; font-family: "Cocogoose Pro", Helvetica, Arial, Lucida, sans-serif; font-size: 22px; font-weight: 500; line-height: 1.1em; margin: 0px; outline: 0px; padding: 0px 0px 10px; text-size-adjust: 100%; vertical-align: baseline;"><br /></h3><h2 style="text-align: left;">TUESDAY READ ALOUDS</h2><h3 style="background: rgb(255, 255, 255); border: 0px; box-sizing: border-box; color: #333033; font-family: "Cocogoose Pro", Helvetica, Arial, Lucida, sans-serif; font-size: 22px; font-weight: 500; line-height: 1.1em; margin: 0px; outline: 0px; padding: 0px 0px 10px; text-size-adjust: 100%; vertical-align: baseline;"><span style="background: transparent; border: 0px; box-sizing: border-box; font-weight: 700; margin: 0px; outline: 0px; padding: 0px; text-size-adjust: 100%; vertical-align: baseline;"><a href="https://www.amazon.com/gp/product/0395870828/ref=as_li_tl?ie=UTF8&camp=1789&creative=9325&creativeASIN=0395870828&linkCode=as2&tag=luckyl-20&linkId=2a3e7c7f0ac43a15ad338fd0254dc3c7" rel="noreferrer noopener" style="background: transparent; border: 0px; box-sizing: border-box; margin: 0px; outline: 0px; padding: 0px; text-decoration-line: none; text-size-adjust: 100%; vertical-align: baseline;" target="_blank">Tuesday by David Wiesner</a></span></h3><p><a href="https://www.amazon.com/gp/product/0395870828/ref=as_li_tl?ie=UTF8&camp=1789&creative=9325&creativeASIN=0395870828&linkCode=as2&tag=luckyl-20&linkId=212bdc6aafd0f9767a7a4ba18ff396d8" rel="noopener" style="background: rgb(255, 255, 255); border: 0px; box-sizing: border-box; color: #fa4fad; font-family: Pragmatica, Helvetica, Arial, Lucida, sans-serif; font-size: 18px; font-weight: 700; margin: 0px; outline: 0px; padding: 0px; text-decoration-line: none; text-size-adjust: 100%; vertical-align: baseline;" target="_blank"><img border="0" class="entered lazyloaded" data-lazy-src="//ws-na.amazon-adsystem.com/widgets/q?_encoding=UTF8&MarketPlace=US&ASIN=0395870828&ServiceVersion=20070822&ID=AsinImage&WS=1&Format=_SL250_&tag=luckyl-20" data-ll-status="loaded" data-pin-media="//ws-na.amazon-adsystem.com/widgets/q?_encoding=UTF8&MarketPlace=US&ASIN=0395870828&ServiceVersion=20070822&ID=AsinImage&WS=1&Format=_SL250_&tag=luckyl-20" data-pin-nopin="true" src="https://ws-na.amazon-adsystem.com/widgets/q?_encoding=UTF8&MarketPlace=US&ASIN=0395870828&ServiceVersion=20070822&ID=AsinImage&WS=1&Format=_SL250_&tag=luckyl-20" style="background: transparent; border: 0px; box-sizing: border-box; height: auto; margin: 0px; max-width: 100%; outline: 0px; padding: 0px; text-size-adjust: 100%; vertical-align: baseline;" /></a><span face="Pragmatica, Helvetica, Arial, Lucida, sans-serif" style="background-color: white; color: #333033; font-size: 18px;"></span></p><p style="background: rgb(255, 255, 255); border: 0px; box-sizing: border-box; color: #333033; font-family: Pragmatica, Helvetica, Arial, Lucida, sans-serif; font-size: 18px; margin: 0px; outline: 0px; padding: 0px 0px 1em; text-size-adjust: 100%; vertical-align: baseline;">Tuesday by Wiesner is mostly a wordless book, a mystery, maybe an opportunity to connect to problem-solving.</p><h3 style="background: rgb(255, 255, 255); border: 0px; box-sizing: border-box; color: #333033; font-family: "Cocogoose Pro", Helvetica, Arial, Lucida, sans-serif; font-size: 22px; font-weight: 500; line-height: 1.1em; margin: 0px; outline: 0px; padding: 0px 0px 10px; text-size-adjust: 100%; vertical-align: baseline;"><br /></h3><h3 style="background: rgb(255, 255, 255); border: 0px; box-sizing: border-box; color: #333033; font-family: "Cocogoose Pro", Helvetica, Arial, Lucida, sans-serif; font-size: 22px; font-weight: 500; line-height: 1.1em; margin: 0px; outline: 0px; padding: 0px 0px 10px; text-size-adjust: 100%; vertical-align: baseline;"><span style="background: transparent; border: 0px; box-sizing: border-box; font-weight: 700; margin: 0px; outline: 0px; padding: 0px; text-size-adjust: 100%; vertical-align: baseline;"><a href="https://www.amazon.com/gp/product/0807581585/ref=as_li_tl?ie=UTF8&camp=1789&creative=9325&creativeASIN=0807581585&linkCode=as2&tag=luckyl-20&linkId=681e249f8ae88d1fb6e9683dd3139863" rel="noreferrer noopener" style="background: transparent; border: 0px; box-sizing: border-box; margin: 0px; outline: 0px; padding: 0px; text-decoration-line: none; text-size-adjust: 100%; vertical-align: baseline;" target="_blank">Two of Everything Book by Lily Toy Hong</a></span></h3><p><a href="https://www.amazon.com/gp/product/0807581585/ref=as_li_tl?ie=UTF8&camp=1789&creative=9325&creativeASIN=0807581585&linkCode=as2&tag=luckyl-20&linkId=b0e0a8121b087214d296450a13435d72" rel="noopener" style="background: rgb(255, 255, 255); border: 0px; box-sizing: border-box; color: #fa4fad; font-family: Pragmatica, Helvetica, Arial, Lucida, sans-serif; font-size: 18px; font-weight: 700; margin: 0px; outline: 0px; padding: 0px; text-decoration-line: none; text-size-adjust: 100%; vertical-align: baseline;" target="_blank"><img border="0" class="entered lazyloaded" data-lazy-src="//ws-na.amazon-adsystem.com/widgets/q?_encoding=UTF8&MarketPlace=US&ASIN=0807581585&ServiceVersion=20070822&ID=AsinImage&WS=1&Format=_SL250_&tag=luckyl-20" data-ll-status="loaded" data-pin-media="//ws-na.amazon-adsystem.com/widgets/q?_encoding=UTF8&MarketPlace=US&ASIN=0807581585&ServiceVersion=20070822&ID=AsinImage&WS=1&Format=_SL250_&tag=luckyl-20" data-pin-nopin="true" src="https://ws-na.amazon-adsystem.com/widgets/q?_encoding=UTF8&MarketPlace=US&ASIN=0807581585&ServiceVersion=20070822&ID=AsinImage&WS=1&Format=_SL250_&tag=luckyl-20" style="background: transparent; border: 0px; box-sizing: border-box; height: auto; margin: 0px; max-width: 100%; outline: 0px; padding: 0px; text-size-adjust: 100%; vertical-align: baseline;" /></a><span face="Pragmatica, Helvetica, Arial, Lucida, sans-serif" style="background-color: white; color: #333033; font-size: 18px;"></span></p><p style="background: rgb(255, 255, 255); border: 0px; box-sizing: border-box; color: #333033; font-family: Pragmatica, Helvetica, Arial, Lucida, sans-serif; font-size: 18px; margin: 0px; outline: 0px; padding: 0px 0px 1em; text-size-adjust: 100%; vertical-align: baseline;">In this book, everything the main character puts in a magic pot doubles! This could be a fun book to correlate with input/output math tables!</p><h3 style="background: rgb(255, 255, 255); border: 0px; box-sizing: border-box; color: #333033; font-family: "Cocogoose Pro", Helvetica, Arial, Lucida, sans-serif; font-size: 22px; font-weight: 500; line-height: 1.1em; margin: 0px; outline: 0px; padding: 0px 0px 10px; text-size-adjust: 100%; vertical-align: baseline;"><br /></h3><h3 style="background: rgb(255, 255, 255); border: 0px; box-sizing: border-box; color: #333033; font-family: "Cocogoose Pro", Helvetica, Arial, Lucida, sans-serif; font-size: 22px; font-weight: 500; line-height: 1.1em; margin: 0px; outline: 0px; padding: 0px 0px 10px; text-size-adjust: 100%; vertical-align: baseline;"><span style="background: transparent; border: 0px; box-sizing: border-box; font-weight: 700; margin: 0px; outline: 0px; padding: 0px; text-size-adjust: 100%; vertical-align: baseline;"><a href="https://www.amazon.com/gp/product/059093998X/ref=as_li_tl?ie=UTF8&camp=1789&creative=9325&creativeASIN=059093998X&linkCode=as2&tag=luckyl-20&linkId=a83050cb48a3199c8b31c3b120eeaf2d" rel="noreferrer noopener" style="background: transparent; border: 0px; box-sizing: border-box; margin: 0px; outline: 0px; padding: 0px; text-decoration-line: none; text-size-adjust: 100%; vertical-align: baseline;" target="_blank">One Grain of Rice by Demi</a></span></h3><p><a href="https://www.amazon.com/gp/product/059093998X/ref=as_li_tl?ie=UTF8&camp=1789&creative=9325&creativeASIN=059093998X&linkCode=as2&tag=luckyl-20&linkId=da523fe887ff5f337b677ce602398ebf" rel="noopener" style="background: rgb(255, 255, 255); border: 0px; box-sizing: border-box; color: #fa4fad; font-family: Pragmatica, Helvetica, Arial, Lucida, sans-serif; font-size: 18px; font-weight: 700; margin: 0px; outline: 0px; padding: 0px; text-decoration-line: none; text-size-adjust: 100%; vertical-align: baseline;" target="_blank"><img border="0" class="entered lazyloaded" data-lazy-src="//ws-na.amazon-adsystem.com/widgets/q?_encoding=UTF8&MarketPlace=US&ASIN=059093998X&ServiceVersion=20070822&ID=AsinImage&WS=1&Format=_SL250_&tag=luckyl-20" data-ll-status="loaded" data-pin-media="//ws-na.amazon-adsystem.com/widgets/q?_encoding=UTF8&MarketPlace=US&ASIN=059093998X&ServiceVersion=20070822&ID=AsinImage&WS=1&Format=_SL250_&tag=luckyl-20" data-pin-nopin="true" src="https://ws-na.amazon-adsystem.com/widgets/q?_encoding=UTF8&MarketPlace=US&ASIN=059093998X&ServiceVersion=20070822&ID=AsinImage&WS=1&Format=_SL250_&tag=luckyl-20" style="background: transparent; border: 0px; box-sizing: border-box; height: auto; margin: 0px; max-width: 100%; outline: 0px; padding: 0px; text-size-adjust: 100%; vertical-align: baseline;" /></a><span face="Pragmatica, Helvetica, Arial, Lucida, sans-serif" style="background-color: white; color: #333033; font-size: 18px;"></span></p><p style="background: rgb(255, 255, 255); border: 0px; box-sizing: border-box; color: #333033; font-family: Pragmatica, Helvetica, Arial, Lucida, sans-serif; font-size: 18px; margin: 0px; outline: 0px; padding: 0px 0px 1em; text-size-adjust: 100%; vertical-align: baseline;">This book is about doubling and would go great with working on addition doubles or multiplying by 2, or exponential functions.</p><div><br /></div><h2 style="text-align: left;">PUZZLES AND MORE</h2><p style="text-align: left;"><span style="background-color: white; letter-spacing: 0.15px; white-space: pre-wrap;"><span style="font-family: arial; font-size: large;"><a href="https://www.mashupmath.com/blog/twosday-activities-2022" target="_blank">Mash-Up Math</a> has SIX free activities for K - 8.</span></span></p><p style="text-align: left;"><span style="background-color: white; letter-spacing: 0.15px; white-space: pre-wrap;"><span style="font-family: arial; font-size: large;"><br /></span></span></p><p style="text-align: left;"><span style="background-color: white; letter-spacing: 0.15px; white-space: pre-wrap;"><span style="font-family: arial; font-size: large;"><a href="https://mathequalslove.net/twosday-challenge-activity/" target="_blank">MATH = LOVE </a>HAS A TWOS-day puzzle.</span></span></p><p style="text-align: left;"><span style="background-color: white; letter-spacing: 0.15px; white-space: pre-wrap;"><span style="font-family: arial; font-size: large;"><br /></span></span></p><p style="text-align: left;"><span style="background-color: white; letter-spacing: 0.15px; white-space: pre-wrap;"><span style="font-family: arial; font-size: large;"><a href="https://donsteward.blogspot.com/search/label/halving" target="_blank">Don Steward</a> puzzle with "halving."</span></span></p><p style="text-align: left;"><span style="background-color: white; letter-spacing: 0.15px; white-space: pre-wrap;"><span style="font-family: arial; font-size: large;"><br /></span></span></p><p style="text-align: left;"><span style="background-color: white; letter-spacing: 0.15px; white-space: pre-wrap;"><span style="font-family: arial; font-size: large;"><a href="https://donsteward.blogspot.com/2015/03/doubling-and-halving.html" target="_blank">Don Steward</a> puzzle using both doubling and halving.</span></span></p><p style="text-align: left;"><span style="background-color: white; letter-spacing: 0.15px; white-space: pre-wrap;"><span style="font-family: arial; font-size: large;"><br /></span></span></p><p style="text-align: left;"><span style="background-color: white; letter-spacing: 0.15px; white-space: pre-wrap;"><span style="font-family: arial; font-size: large;"><a href="https://www.jjresourcecreations.com/-blog/cool-math-trick-where-your-answer-is-always-2#/" target="_blank">Cool Math Trick</a> (the answer is always 2!)</span></span></p><p style="text-align: left;"><span style="background-color: white; letter-spacing: 0.15px; white-space: pre-wrap;"><span style="font-family: arial; font-size: large;">BTW ... here's another version of a math trick that results in 2 every time ... why not ask students to create their OWN math trick that results in 2 every time!</span></span></p><h3 style="background-color: white; border: 0px; box-sizing: border-box; clear: both; color: #24292e; font-family: Lato, proxima-nova-2, "Open Sans", "Helvetica Neue", Helvetica, Arial, sans-serif; font-size: 18px; line-height: 25px; margin: 24px 0px 15px; outline: 0px; padding: 0px; vertical-align: baseline;">The Answer Is 2</h3><p><span style="background-color: white; letter-spacing: 0.15px; white-space: pre-wrap;"><span style="font-family: arial; font-size: large;"></span></span></p><ul class="" style="background-color: white; border: 0px; box-sizing: border-box; color: #2f303a; font-family: Lato, proxima-nova-2, "Open Sans", "Helvetica Neue", Helvetica, Arial, sans-serif; font-size: 19px; list-style: square; margin: 0px 0px 1.4em 20px; outline: 0px; padding: 0px; vertical-align: baseline;"><li style="border: 0px; box-sizing: border-box; font-family: inherit; font-style: inherit; font-weight: inherit; margin: 0px 0px 13.6875px; outline: 0px; padding: 0px; vertical-align: baseline;">Think of a whole number 1 through 10 (We’ll use 6)</li><li style="border: 0px; box-sizing: border-box; font-family: inherit; font-style: inherit; font-weight: inherit; margin: 0px 0px 13.6875px; outline: 0px; padding: 0px; vertical-align: baseline;">Double it (6×2=12)</li><li style="border: 0px; box-sizing: border-box; font-family: inherit; font-style: inherit; font-weight: inherit; margin: 0px 0px 13.6875px; outline: 0px; padding: 0px; vertical-align: baseline;">Add 4 (12+4=16)</li><li style="border: 0px; box-sizing: border-box; font-family: inherit; font-style: inherit; font-weight: inherit; margin: 0px 0px 13.6875px; outline: 0px; padding: 0px; vertical-align: baseline;">Divide by 2 (16÷2=8)</li><li style="border: 0px; box-sizing: border-box; font-family: inherit; font-style: inherit; font-weight: inherit; margin: 0px 0px 13.6875px; outline: 0px; padding: 0px; vertical-align: baseline;">Subtract the original number (8-6=2)</li><li style="border: 0px; box-sizing: border-box; font-family: inherit; font-style: inherit; font-weight: inherit; margin: 0px 0px 13.6875px; outline: 0px; padding: 0px; vertical-align: baseline;">The answer is always 2!</li></ul><p style="text-align: left;"><span style="background-color: white; letter-spacing: 0.15px; white-space: pre-wrap;"><span style="font-family: arial; font-size: large;"><a href="http://thewessens.net/ClassroomApps/Main/fourtwos.html" target="_blank">FOUR Twos</a> - what values can you make using only 4 twos?</span></span></p><h2 style="text-align: left;"><span style="background-color: white; letter-spacing: 0.15px; white-space: pre-wrap;"><span style="font-family: arial; font-size: large;"><br /></span></span><span style="background-color: white; letter-spacing: 0.15px; white-space: pre-wrap;"><span style="font-family: arial; font-size: large;">EXTRA Puzzles</span></span></h2><div><span style="font-family: arial; font-size: large;"><span style="background-color: white; letter-spacing: 0.15px; white-space: pre-wrap;">(1) Multiply the first three problems in the puzzle below. Can you determine the product for the last two using the pattern from your work?</span></span></div><div><span style="font-family: arial; font-size: large;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEhKtwIac2fo0fHCu33KxVHyiM44pLBE9lpc2Mi8FGlrX9rSxsnJqbk0FKL6WDpQpTOXKXjdd6g9IgkbW3tuFSez8noT11qD4MPKZfWQT93o_BaCVrtOPoECxoS6DLyrhidNoEqwemOkj4O177pfKG2z5ULFBwSAheJaCOMs3-UYpzDbJMB2SdMpdQ=s358" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="284" data-original-width="358" height="254" src="https://blogger.googleusercontent.com/img/a/AVvXsEhKtwIac2fo0fHCu33KxVHyiM44pLBE9lpc2Mi8FGlrX9rSxsnJqbk0FKL6WDpQpTOXKXjdd6g9IgkbW3tuFSez8noT11qD4MPKZfWQT93o_BaCVrtOPoECxoS6DLyrhidNoEqwemOkj4O177pfKG2z5ULFBwSAheJaCOMs3-UYpzDbJMB2SdMpdQ=s320" width="320" /></a></div>(2) Calculate - </span></div><div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjAG9zOVPpwtKEIlvZmXrAY2QjAFrOQJZtJXYOdraYCjaUl0cN0IzwuEqX0ssQzhNzmkEZy5iELQ_xPNgA-XDnPhOy3r8fY4-93u7JH_ANWPIRVuRlMwqGPtSyJ4cPXuemoWrS2bsn2A-NNDt1uqgjR2y2Q8ywXLKytXQPIqC37hcjTNKVuodTxRg=s1056" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="702" data-original-width="1056" height="266" src="https://blogger.googleusercontent.com/img/a/AVvXsEjAG9zOVPpwtKEIlvZmXrAY2QjAFrOQJZtJXYOdraYCjaUl0cN0IzwuEqX0ssQzhNzmkEZy5iELQ_xPNgA-XDnPhOy3r8fY4-93u7JH_ANWPIRVuRlMwqGPtSyJ4cPXuemoWrS2bsn2A-NNDt1uqgjR2y2Q8ywXLKytXQPIqC37hcjTNKVuodTxRg=w400-h266" width="400" /></a></div><h2 style="text-align: left;"><br />What other ideas are there? Please share in the comments!</h2></div>Algebra's Friendhttp://www.blogger.com/profile/04729315514507170702noreply@blogger.com0tag:blogger.com,1999:blog-8399389267815059112.post-49324654616966174972021-06-02T20:42:00.003-05:002021-06-02T20:42:31.064-05:00Why I Don't Like IXL<p><span style="font-family: arial; font-size: medium;"></span></p><div class="separator" style="clear: both; text-align: center;"><span style="font-family: arial; font-size: medium;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhvJ6_1Q2hqk3PxFw5-SstixQMk205qLpIwlr-625n8wwU0brIoOeZ95beFgkLSipSeUBxeGxklYoaoT8Sw8I59s-ALwYSUsXDjATo3BoL6Tczhr2xrSCYCOhyfGxVdOxTFYWIbO0XtGQ/s640/Ideas+for+Math+Class.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="240" data-original-width="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhvJ6_1Q2hqk3PxFw5-SstixQMk205qLpIwlr-625n8wwU0brIoOeZ95beFgkLSipSeUBxeGxklYoaoT8Sw8I59s-ALwYSUsXDjATo3BoL6Tczhr2xrSCYCOhyfGxVdOxTFYWIbO0XtGQ/s320/Ideas+for+Math+Class.jpg" width="320" /></a></span></div><span style="font-family: arial; font-size: medium;"><br /></span><span style="font-family: arial; font-size: large;">I'm not in the classroom. I'm retired. Why would my opinion on IXL matter? </span><p></p><p><span style="font-family: arial; font-size: medium;">I still work with students as a tutor. Sometimes, my students ask me to help them with their IXL assignments. There are three things I wish math teachers would consider before assigning IXL.</span></p><p><span style="font-family: arial; font-size: medium;">1) First, IXL promotes the lowest level math practice. I understand why some teachers find this useful - you can choose very specifically the skill you want students to practice. But IXL does not provide practice in critical or creative thinking or in problem solving, simply rote skills.</span></p><p><span style="font-family: arial; font-size: medium;">2) Second, IXL's scoring works against the student who struggles with basic facts. If students make errors they lose more points than when they get problems correct. The program punishes students for mistakes. What does that say about the value of learning from our mistakes? And since working out the problem is often not encouraged, all students have is the "one right answer" which eliminates again the importance of the process in the skills we teach.</span></p><p><span style="font-family: arial; font-size: medium;">Also related to the scoring algorithm, students spend an inordinate amount of time trying to achieve the cut off score set by their teacher, practicing the same mistakes over and over. Instead of encouraging students, this is demoralizing and discouraging. Our goal should be to increase students' interest in math, illustrating for them the beauty, the patterns, the connections between the concepts we teach. How might we provide worthwhile practice that supports students?</span></p><p><span style="font-family: arial; font-size: medium;">3) Both parents and students report that the support that IXL does provide in math, the explanations are not helpful, not clear. The last thing we need to promote is unclear instructions on how to perform basic arithmetic.</span></p><p><span style="font-family: arial; font-size: medium;">Bottom line, IXL is the opposite of what we know is empowering in math education. Need more evidence? Check out <a href="https://www.commonsensemedia.org/website-reviews/ixl/user-reviews/adult" target="_blank">Common Sense Media Parent reviews </a>- over 600 - with an average of 1 star. There are also over 2000 student reviews on that site - averaging 1 star out of five. </span></p><p><span style="font-family: arial; font-size: medium;">What can we do instead? <table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjgXi4wdftEiDxJ38Zyz6YHTooA_TQJ1QUaCWEl7ojsUli1M9Q51inMb37SV-qataMJTeVKbr9UI25DB901Hb07rxPB9tvgLf4valC_hubOObMVTOPPApoQ8w-4X4oIXiNBpY-9PPIZOA/s614/Screen+Shot+2021-06-02+at+8.35.50+PM.png" imageanchor="1" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" data-original-height="614" data-original-width="612" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjgXi4wdftEiDxJ38Zyz6YHTooA_TQJ1QUaCWEl7ojsUli1M9Q51inMb37SV-qataMJTeVKbr9UI25DB901Hb07rxPB9tvgLf4valC_hubOObMVTOPPApoQ8w-4X4oIXiNBpY-9PPIZOA/s320/Screen+Shot+2021-06-02+at+8.35.50+PM.png" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><b><i><span style="color: #990000;">Which one doesn't belong?</span></i></b></td></tr></tbody></table><br /></span></p><p><span style="font-family: arial; font-size: medium;">A) Know your students and their home lives. If they don't have support at home, don't assign homework on which they cannot be successful. Assign a few (5 to 10) review problems instead.</span></p><p><span style="font-family: arial; font-size: medium;">B) Check for understanding in your lessons to make sure that students are ready for the homework you want to assign. Don't assign homework over something that most of the class is not ready for. Instead, build in regular review.</span></p><p><span style="font-family: arial; font-size: medium;">C) If students are ready for homework over the day's lesson, why not give 5 to 8 problems instead of 20 to 30? Ask students to show their work. If you are virtual use @Classkick, @PearDeck, or @Nearpod. There are other tools as well - these are the ones with which I am most familiar.</span></p><p><span style="font-family: arial; font-size: medium;">D) As often as possible, differentiate homework. If students have already mastered the lesson, they don't need the same practice that students who have not achieved mastery yet.</span></p><p><span style="font-family: arial; font-size: medium;"><br /></span></p>Algebra's Friendhttp://www.blogger.com/profile/04729315514507170702noreply@blogger.com1tag:blogger.com,1999:blog-8399389267815059112.post-67308621855502888202021-04-22T10:46:00.001-05:002021-04-22T10:46:10.563-05:00YouTube Channel worth exploring ...<p> </p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiBDyfehIIfc18m31lygKTkggzdWAHOYPAxNa63q8QNzWv1n-W2eUF9QIMIMleNm56zH49ZnqvxXCkSAxdVr5OVc9KJ3n2sKiQ5-oSFlINGeSPvRDZGNcLQoaswRp74i3bWUBZUq0ISzQ/s640/Ideas+for+Math+Class.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="240" data-original-width="640" height="150" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiBDyfehIIfc18m31lygKTkggzdWAHOYPAxNa63q8QNzWv1n-W2eUF9QIMIMleNm56zH49ZnqvxXCkSAxdVr5OVc9KJ3n2sKiQ5-oSFlINGeSPvRDZGNcLQoaswRp74i3bWUBZUq0ISzQ/w400-h150/Ideas+for+Math+Class.jpg" width="400" /></a></div><br /><p></p><p>Looking for challenge problems that address SAT, ACT, AMC and a whole host of other ABCs??<br /><br />I like <a href="https://www.youtube.com/c/MathPrep/videos" target="_blank">this Youtube Channel</a> - I think you'll find interesting problems and complete solutions! <br /><br />How might you use this in class? </p><p>1) What if you used it as a bonus for each unit? Or an extension for students who master the required content early? </p><p>2) How about asking students if they can find a different way to solve - working on flexibility?</p><p>3) What about asking paired students to choose one problem (from your curated selection) to present to the class? Build in cooperative skills, presentation skills, as well as working on math skills?</p><p>4) Only half of your class present due to a field trip or other event? Don't want to teach "new" material? Use one of these challenge problems!</p><p>How else might you use them?</p><p>Here's a sample:</p><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="357" src="https://www.youtube.com/embed/4jk_rIUxn8U" width="480" youtube-src-id="4jk_rIUxn8U"></iframe></div><br /><p><br /></p>Algebra's Friendhttp://www.blogger.com/profile/04729315514507170702noreply@blogger.com1tag:blogger.com,1999:blog-8399389267815059112.post-57588577695081556812021-01-17T14:44:00.000-06:002021-01-17T14:44:04.111-06:00New to Lesson Planning?<div style="text-align: left;"><span style="font-family: verdana;"><div style="text-align: left;"><span style="font-family: verdana;"><br /></span></div><div style="text-align: left;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi-qiB_C0KWhb1qzFm8zjdhCWDG4m4UxnCC2W9DA4egVuUgsRQhm6KK_jUNUSIpUxmRSGL33Ww7B1vN6-RH_IfEbDlEoBCuJfVBIXuPzF2hyOKPbN_LK7yWukUElTHzBYxWLljOdE_TKw/s640/Ideas+for+Math+Class+%25281%2529.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="240" data-original-width="640" height="150" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi-qiB_C0KWhb1qzFm8zjdhCWDG4m4UxnCC2W9DA4egVuUgsRQhm6KK_jUNUSIpUxmRSGL33Ww7B1vN6-RH_IfEbDlEoBCuJfVBIXuPzF2hyOKPbN_LK7yWukUElTHzBYxWLljOdE_TKw/w400-h150/Ideas+for+Math+Class+%25281%2529.png" width="400" /></a></div><div style="text-align: left;"><br /></div>I work with teachers working on certification processes online. Just about every course, I meet teachers who for whatever reason never had instruction on how to write lesson plans. I put together a few resources for them ... thought they might be helpful to someone finding this blog. </div></span></div><div style="text-align: left;"><span style="font-family: verdana;"><br /><br /></span></div><p dir="ltr" style="background-color: white; line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; padding: 0pt 0pt 4pt 0pt;"><span style="background-color: transparent; color: #262626; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="font-family: verdana;">RESOURCE 1: Scholastic often has good ideas for new teachers. This outline for lesson planning is one of those ... written especially with elementary teachers in mind.</span></span></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhzh0ui24sEqUup9H9a3s4BQZQu26VA9blA_farJVjapZgbAJX3k8fJbGXneYbLjwTdGif6K6KDZly08GRQwDeOFGtBfjyfHG5hrE47XW8ygz7eepGmiVHuJlRPVI6ZVk70EFwRy98K0w/" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img alt="" data-original-height="1200" data-original-width="800" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhzh0ui24sEqUup9H9a3s4BQZQu26VA9blA_farJVjapZgbAJX3k8fJbGXneYbLjwTdGif6K6KDZly08GRQwDeOFGtBfjyfHG5hrE47XW8ygz7eepGmiVHuJlRPVI6ZVk70EFwRy98K0w/w214-h320/blog+graphic.png" width="214" /></a></div><p></p><p dir="ltr" style="background-color: white; line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; padding: 0pt 0pt 4pt 0pt;"><a href="https://www.scholastic.com/teachers/articles/teaching-content/new-teachers-guide-creating-lesson-plans/" style="text-decoration: none;"><span style="background-color: transparent; color: #2075a3; font-style: normal; font-variant: normal; font-weight: 400; text-decoration-skip-ink: none; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap;"><span style="font-family: verdana;">The New Teacher's Guide to Creating Lesson Plans</span></span></a></p><p dir="ltr" style="background-color: white; line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; padding: 0pt 0pt 4pt 0pt;"><span style="background-color: transparent; color: #262626; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="font-family: verdana;">Which of the ideas on this page is helpful to you?</span></span></p><p dir="ltr" style="background-color: white; line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; padding: 0pt 0pt 4pt 0pt;"> </p><p dir="ltr" style="background-color: white; line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; padding: 0pt 0pt 4pt 0pt;"><span style="background-color: transparent; color: #262626; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="font-family: verdana;">RESOURCE 2: This guide doesn't suggest a one "right" way but instead suggests ways to think about lesson planning.</span></span></p><p dir="ltr" style="background-color: white; line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; padding: 0pt 0pt 4pt 0pt;"><a href="https://writing.colostate.edu/guides/teaching/lesson_plans/" style="text-decoration: none;"><span style="background-color: transparent; color: #2075a3; font-style: normal; font-variant: normal; font-weight: 400; text-decoration-skip-ink: none; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap;"><span style="font-family: verdana;">Teaching Guide: Writing lesson plans</span></span></a></p><p dir="ltr" style="background-color: white; line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; padding: 0pt 0pt 4pt 0pt;"><span style="background-color: transparent; color: #262626; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="font-family: verdana;">Which section in this guide was most helpful to you?</span></span></p><p dir="ltr" style="background-color: white; line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; padding: 0pt 0pt 4pt 0pt;"> </p><p dir="ltr" style="background-color: white; line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; padding: 0pt 0pt 4pt 0pt;"><span style="background-color: transparent; color: #262626; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="font-family: verdana;">RESOURCE 3: Many of us are having to design online learning experiences. Using the 5Es to develop online learning activities is a great way to organize learning.</span></span></p><p dir="ltr" style="background-color: white; line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; padding: 0pt 0pt 4pt 0pt;"><a href="https://catlintucker.com/2020/03/designing-an-online-lesson/" style="text-decoration: none;"><span style="background-color: transparent; color: #2075a3; font-style: normal; font-variant: normal; font-weight: 400; text-decoration-skip-ink: none; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap;"><span style="font-family: verdana;">Tips for Designing an Online Learning Experience Using the 5 Es Instructional Model</span></span></a></p><p dir="ltr" style="background-color: white; line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; padding: 0pt 0pt 4pt 0pt;"><span style="background-color: transparent; color: #262626; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="font-family: verdana;">The author at this site has several videos to assist in understanding. Which video resonated with you?</span></span></p><p dir="ltr" style="background-color: white; line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; padding: 0pt 0pt 4pt 0pt;"><span style="font-family: verdana;"> </span></p><p dir="ltr" style="background-color: white; line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; padding: 0pt 0pt 4pt 0pt;"><span style="font-family: verdana;"><span style="background-color: transparent; color: #262626; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">RESOURCE 4: Maybe you have heard of "backwards planning" but are unsure how it is different from traditional planning. Check out this post:</span><a href="https://www.cultofpedagogy.com/backward-design-basics/" style="text-decoration: none;"><span style="background-color: transparent; color: #262626; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> </span><span style="background-color: transparent; color: #2075a3; font-style: normal; font-variant: normal; font-weight: 400; text-decoration-skip-ink: none; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap;">Backward Design: The Basics.</span></a></span></p><p dir="ltr" style="background-color: white; line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; padding: 0pt 0pt 4pt 0pt;"><span style="background-color: transparent; color: #262626; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="font-family: verdana;">What is your typical lesson planning method??</span></span></p><p dir="ltr" style="background-color: white; line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; padding: 0pt 0pt 4pt 0pt;"><span style="background-color: transparent; color: #262626; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-family: verdana;"><br /></span></span></p><p dir="ltr" style="background-color: white; line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; padding: 0pt 0pt 4pt 0pt;"><span style="font-family: verdana;"><span style="background-color: transparent; color: #262626; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">RESOURCE 5: Last, but not least - </span><span style="color: #262626; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">This website has some great information about</span><a href="https://www.edutopia.org/blog/9-ways-plan-transformational-lessons-todd-finley" style="text-decoration-line: none;"><span style="color: #262626; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> </span><span style="color: #2075a3; font-variant-east-asian: normal; font-variant-numeric: normal; text-decoration-line: underline; text-decoration-skip-ink: none; vertical-align: baseline; white-space: pre-wrap;">how to write "transformational" lessons!</span></a><span style="background-color: transparent; color: #262626; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> Which idea might you incorporate in your own lesson planning?</span></span></p>Algebra's Friendhttp://www.blogger.com/profile/04729315514507170702noreply@blogger.com0tag:blogger.com,1999:blog-8399389267815059112.post-84013466757451176422020-11-07T14:09:00.006-06:002020-11-07T14:09:38.297-06:00Writing in Math Class<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj4yfZLx3q8tz0cfRtvqCsbaZfIDY1ENESemj5fM2z_1S-Bv0Guync4EAlNTa1-TX1H_JP3-q1uB3lvVbKP1f9uMHWAdK31fptoBO-J4hzclMzFcgKNmG9BP4Jc4TCf5UqWLSEtXcs13A/s640/Ideas+for+Math+Class+%25281%2529.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="240" data-original-width="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj4yfZLx3q8tz0cfRtvqCsbaZfIDY1ENESemj5fM2z_1S-Bv0Guync4EAlNTa1-TX1H_JP3-q1uB3lvVbKP1f9uMHWAdK31fptoBO-J4hzclMzFcgKNmG9BP4Jc4TCf5UqWLSEtXcs13A/s320/Ideas+for+Math+Class+%25281%2529.png" width="320" /></a></div><h3 style="text-align: left;"><span style="color: #050505;"><span style="background-color: white; font-size: 15px; white-space: pre-wrap;">In a conversation in a FB group about math, this list of writing topics was shared. Do you ask students to write in math class? Blog? Essay? Why or why not?</span></span></h3><div class="o9v6fnle cxmmr5t8 oygrvhab hcukyx3x c1et5uql ii04i59q" style="background-color: white; color: #050505; font-family: system-ui, -apple-system, system-ui, ".SFNSText-Regular", sans-serif; font-size: 15px; margin: 0.5em 0px 0px; overflow-wrap: break-word; white-space: pre-wrap;"><div dir="auto" style="font-family: inherit;">01] My Math Autobiography</div></div><div class="o9v6fnle cxmmr5t8 oygrvhab hcukyx3x c1et5uql ii04i59q" style="background-color: white; color: #050505; font-family: system-ui, -apple-system, system-ui, ".SFNSText-Regular", sans-serif; font-size: 15px; margin: 0.5em 0px 0px; overflow-wrap: break-word; white-space: pre-wrap;"><div dir="auto" style="font-family: inherit;">02] When I Graduate, I Want To ...</div></div><div class="o9v6fnle cxmmr5t8 oygrvhab hcukyx3x c1et5uql ii04i59q" style="background-color: white; color: #050505; font-family: system-ui, -apple-system, system-ui, ".SFNSText-Regular", sans-serif; font-size: 15px; margin: 0.5em 0px 0px; overflow-wrap: break-word; white-space: pre-wrap;"><div dir="auto" style="font-family: inherit;">03] Math in the Kitchen</div></div><div class="o9v6fnle cxmmr5t8 oygrvhab hcukyx3x c1et5uql ii04i59q" style="background-color: white; color: #050505; font-family: system-ui, -apple-system, system-ui, ".SFNSText-Regular", sans-serif; font-size: 15px; margin: 0.5em 0px 0px; overflow-wrap: break-word; white-space: pre-wrap;"><div dir="auto" style="font-family: inherit;">04] A World Without Math (describe in detail)</div></div><div class="o9v6fnle cxmmr5t8 oygrvhab hcukyx3x c1et5uql ii04i59q" style="background-color: white; color: #050505; font-family: system-ui, -apple-system, system-ui, ".SFNSText-Regular", sans-serif; font-size: 15px; margin: 0.5em 0px 0px; overflow-wrap: break-word; white-space: pre-wrap;"><div dir="auto" style="font-family: inherit;">05] Math and the Weather</div></div><div class="o9v6fnle cxmmr5t8 oygrvhab hcukyx3x c1et5uql ii04i59q" style="background-color: white; color: #050505; font-family: system-ui, -apple-system, system-ui, ".SFNSText-Regular", sans-serif; font-size: 15px; margin: 0.5em 0px 0px; overflow-wrap: break-word; white-space: pre-wrap;"><div dir="auto" style="font-family: inherit;">06] Open Math Topic</div></div><div class="o9v6fnle cxmmr5t8 oygrvhab hcukyx3x c1et5uql ii04i59q" style="background-color: white; color: #050505; font-family: system-ui, -apple-system, system-ui, ".SFNSText-Regular", sans-serif; font-size: 15px; margin: 0.5em 0px 0px; overflow-wrap: break-word; white-space: pre-wrap;"><div dir="auto" style="font-family: inherit;">07] My Favorite Thing (singular) About Math</div></div><div class="o9v6fnle cxmmr5t8 oygrvhab hcukyx3x c1et5uql ii04i59q" style="background-color: white; color: #050505; font-family: system-ui, -apple-system, system-ui, ".SFNSText-Regular", sans-serif; font-size: 15px; margin: 0.5em 0px 0px; overflow-wrap: break-word; white-space: pre-wrap;"><div dir="auto" style="font-family: inherit;">08] What the Math Monster Might Say (draw a cartoon)</div></div><div class="o9v6fnle cxmmr5t8 oygrvhab hcukyx3x c1et5uql ii04i59q" style="background-color: white; color: #050505; font-family: system-ui, -apple-system, system-ui, ".SFNSText-Regular", sans-serif; font-size: 15px; margin: 0.5em 0px 0px; overflow-wrap: break-word; white-space: pre-wrap;"><div dir="auto" style="font-family: inherit;">09] About My Q1 Project</div></div><div class="o9v6fnle cxmmr5t8 oygrvhab hcukyx3x c1et5uql ii04i59q" style="background-color: white; color: #050505; font-family: system-ui, -apple-system, system-ui, ".SFNSText-Regular", sans-serif; font-size: 15px; margin: 0.5em 0px 0px; overflow-wrap: break-word; white-space: pre-wrap;"><div dir="auto" style="font-family: inherit;">10] Math and Sports</div></div><div class="o9v6fnle cxmmr5t8 oygrvhab hcukyx3x c1et5uql ii04i59q" style="background-color: white; color: #050505; font-family: system-ui, -apple-system, system-ui, ".SFNSText-Regular", sans-serif; font-size: 15px; margin: 0.5em 0px 0px; overflow-wrap: break-word; white-space: pre-wrap;"><div dir="auto" style="font-family: inherit;">11] What Math Shape Am I? (choose shape, describe how you match its qualities)</div></div><div class="o9v6fnle cxmmr5t8 oygrvhab hcukyx3x c1et5uql ii04i59q" style="background-color: white; color: #050505; font-family: system-ui, -apple-system, system-ui, ".SFNSText-Regular", sans-serif; font-size: 15px; margin: 0.5em 0px 0px; overflow-wrap: break-word; white-space: pre-wrap;"><div dir="auto" style="font-family: inherit;">12] Math and Smoking/Vaping</div></div><div class="o9v6fnle cxmmr5t8 oygrvhab hcukyx3x c1et5uql ii04i59q" style="background-color: white; color: #050505; font-family: system-ui, -apple-system, system-ui, ".SFNSText-Regular", sans-serif; font-size: 15px; margin: 0.5em 0px 0px; overflow-wrap: break-word; white-space: pre-wrap;"><div dir="auto" style="font-family: inherit;">13] The Thing (singular) That Frustrates Me Most About Math...</div></div><div class="o9v6fnle cxmmr5t8 oygrvhab hcukyx3x c1et5uql ii04i59q" style="background-color: white; color: #050505; font-family: system-ui, -apple-system, system-ui, ".SFNSText-Regular", sans-serif; font-size: 15px; margin: 0.5em 0px 0px; overflow-wrap: break-word; white-space: pre-wrap;"><div dir="auto" style="font-family: inherit;">14] Math and Vacations</div></div><div class="o9v6fnle cxmmr5t8 oygrvhab hcukyx3x c1et5uql ii04i59q" style="background-color: white; color: #050505; font-family: system-ui, -apple-system, system-ui, ".SFNSText-Regular", sans-serif; font-size: 15px; margin: 0.5em 0px 0px; overflow-wrap: break-word; white-space: pre-wrap;"><div dir="auto" style="font-family: inherit;">15] Open Math Topic</div></div><div class="o9v6fnle cxmmr5t8 oygrvhab hcukyx3x c1et5uql ii04i59q" style="background-color: white; color: #050505; font-family: system-ui, -apple-system, system-ui, ".SFNSText-Regular", sans-serif; font-size: 15px; margin: 0.5em 0px 0px; overflow-wrap: break-word; white-space: pre-wrap;"><div dir="auto" style="font-family: inherit;">16] Why is PEMDAS So Hard to Keep Straight?</div></div><div class="o9v6fnle cxmmr5t8 oygrvhab hcukyx3x c1et5uql ii04i59q" style="background-color: white; color: #050505; font-family: system-ui, -apple-system, system-ui, ".SFNSText-Regular", sans-serif; font-size: 15px; margin: 0.5em 0px 0px; overflow-wrap: break-word; white-space: pre-wrap;"><div dir="auto" style="font-family: inherit;">17] Math Bumper Stickers (draw one funny, one thoughtful)</div></div><div class="o9v6fnle cxmmr5t8 oygrvhab hcukyx3x c1et5uql ii04i59q" style="background-color: white; color: #050505; font-family: system-ui, -apple-system, system-ui, ".SFNSText-Regular", sans-serif; font-size: 15px; margin: 0.5em 0px 0px; overflow-wrap: break-word; white-space: pre-wrap;"><div dir="auto" style="font-family: inherit;">18] Dear Egbert, You Should Do Your Homework (to a friend)</div></div><div class="o9v6fnle cxmmr5t8 oygrvhab hcukyx3x c1et5uql ii04i59q" style="background-color: white; color: #050505; font-family: system-ui, -apple-system, system-ui, ".SFNSText-Regular", sans-serif; font-size: 15px; margin: 0.5em 0px 0px; overflow-wrap: break-word; white-space: pre-wrap;"><div dir="auto" style="font-family: inherit;">19] Math of Buying/Owning a Car</div></div><div class="o9v6fnle cxmmr5t8 oygrvhab hcukyx3x c1et5uql ii04i59q" style="background-color: white; color: #050505; font-family: system-ui, -apple-system, system-ui, ".SFNSText-Regular", sans-serif; font-size: 15px; margin: 0.5em 0px 0px; overflow-wrap: break-word; white-space: pre-wrap;"><div dir="auto" style="font-family: inherit;">20] About My Q2 Project</div></div><div class="o9v6fnle cxmmr5t8 oygrvhab hcukyx3x c1et5uql ii04i59q" style="background-color: white; color: #050505; font-family: system-ui, -apple-system, system-ui, ".SFNSText-Regular", sans-serif; font-size: 15px; margin: 0.5em 0px 0px; overflow-wrap: break-word; white-space: pre-wrap;"><div dir="auto" style="font-family: inherit;">21] Are Boys or Girls Better At Math?</div></div><div class="o9v6fnle cxmmr5t8 oygrvhab hcukyx3x c1et5uql ii04i59q" style="background-color: white; color: #050505; font-family: system-ui, -apple-system, system-ui, ".SFNSText-Regular", sans-serif; font-size: 15px; margin: 0.5em 0px 0px; overflow-wrap: break-word; white-space: pre-wrap;"><div dir="auto" style="font-family: inherit;">22] Open Math Topic</div></div><div class="o9v6fnle cxmmr5t8 oygrvhab hcukyx3x c1et5uql ii04i59q" style="background-color: white; color: #050505; font-family: system-ui, -apple-system, system-ui, ".SFNSText-Regular", sans-serif; font-size: 15px; margin: 0.5em 0px 0px; overflow-wrap: break-word; white-space: pre-wrap;"><div dir="auto" style="font-family: inherit;">23] Math and Law Enforcement</div></div><div class="o9v6fnle cxmmr5t8 oygrvhab hcukyx3x c1et5uql ii04i59q" style="background-color: white; color: #050505; font-family: system-ui, -apple-system, system-ui, ".SFNSText-Regular", sans-serif; font-size: 15px; margin: 0.5em 0px 0px; overflow-wrap: break-word; white-space: pre-wrap;"><div dir="auto" style="font-family: inherit;">24] I Want To Become Better at Math So That ....</div></div><div class="o9v6fnle cxmmr5t8 oygrvhab hcukyx3x c1et5uql ii04i59q" style="background-color: white; color: #050505; font-family: system-ui, -apple-system, system-ui, ".SFNSText-Regular", sans-serif; font-size: 15px; margin: 0.5em 0px 0px; overflow-wrap: break-word; white-space: pre-wrap;"><div dir="auto" style="font-family: inherit;">25] Math and the Media</div></div><div class="o9v6fnle cxmmr5t8 oygrvhab hcukyx3x c1et5uql ii04i59q" style="background-color: white; color: #050505; font-family: system-ui, -apple-system, system-ui, ".SFNSText-Regular", sans-serif; font-size: 15px; margin: 0.5em 0px 0px; overflow-wrap: break-word; white-space: pre-wrap;"><div dir="auto" style="font-family: inherit;">26] Math and Contagious Viruses</div></div><div class="o9v6fnle cxmmr5t8 oygrvhab hcukyx3x c1et5uql ii04i59q" style="background-color: white; color: #050505; font-family: system-ui, -apple-system, system-ui, ".SFNSText-Regular", sans-serif; font-size: 15px; margin: 0.5em 0px 0px; overflow-wrap: break-word; white-space: pre-wrap;"><div dir="auto" style="font-family: inherit;">27] Why Are Word Problems Necessary?</div></div><div class="o9v6fnle cxmmr5t8 oygrvhab hcukyx3x c1et5uql ii04i59q" style="background-color: white; color: #050505; font-family: system-ui, -apple-system, system-ui, ".SFNSText-Regular", sans-serif; font-size: 15px; margin: 0.5em 0px 0px; overflow-wrap: break-word; white-space: pre-wrap;"><div dir="auto" style="font-family: inherit;">28] Open Math Topic</div></div><div class="o9v6fnle cxmmr5t8 oygrvhab hcukyx3x c1et5uql ii04i59q" style="background-color: white; color: #050505; font-family: system-ui, -apple-system, system-ui, ".SFNSText-Regular", sans-serif; font-size: 15px; margin: 0.5em 0px 0px; overflow-wrap: break-word; white-space: pre-wrap;"><div dir="auto" style="font-family: inherit;">29] My Math Day (encountered in a single day)</div></div><div class="o9v6fnle cxmmr5t8 oygrvhab hcukyx3x c1et5uql ii04i59q" style="background-color: white; color: #050505; font-family: system-ui, -apple-system, system-ui, ".SFNSText-Regular", sans-serif; font-size: 15px; margin: 0.5em 0px 0px; overflow-wrap: break-word; white-space: pre-wrap;"><div dir="auto" style="font-family: inherit;">30] Math and Hospitality (restaurants, hotels, etc)</div></div><div class="o9v6fnle cxmmr5t8 oygrvhab hcukyx3x c1et5uql ii04i59q" style="background-color: white; color: #050505; font-family: system-ui, -apple-system, system-ui, ".SFNSText-Regular", sans-serif; font-size: 15px; margin: 0.5em 0px 0px; overflow-wrap: break-word; white-space: pre-wrap;"><div dir="auto" style="font-family: inherit;">31] My Favorite Topic in This Course This Year</div></div><div class="o9v6fnle cxmmr5t8 oygrvhab hcukyx3x c1et5uql ii04i59q" style="background-color: white; color: #050505; font-family: system-ui, -apple-system, system-ui, ".SFNSText-Regular", sans-serif; font-size: 15px; margin: 0.5em 0px 0px; overflow-wrap: break-word; white-space: pre-wrap;"><div dir="auto" style="font-family: inherit;">32] Dear BFF, Here's What to Expect in Mr./Mrs. --- Class Next Year.</div></div>Algebra's Friendhttp://www.blogger.com/profile/04729315514507170702noreply@blogger.com1tag:blogger.com,1999:blog-8399389267815059112.post-11322702332608302602020-08-25T11:44:00.018-05:002020-11-07T14:07:28.056-06:00Curated Ideas for Engaging Students from a Distance<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjUg49QSH1UED6E6lbl8uQ0hroZyoJsv7lkuCmyprG85ihJEyOt3M6Jx4BmMlri166AOb9Frszz4F3m7f4VwRPOd1qV3dyRE-YRsfn6NWpxfNoDR80OMoJHzRLhHCc7lcrXH47JktGeLw/s640/Ideas+for+Math+Class+%25281%2529.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="240" data-original-width="640" height="150" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjUg49QSH1UED6E6lbl8uQ0hroZyoJsv7lkuCmyprG85ihJEyOt3M6Jx4BmMlri166AOb9Frszz4F3m7f4VwRPOd1qV3dyRE-YRsfn6NWpxfNoDR80OMoJHzRLhHCc7lcrXH47JktGeLw/w400-h150/Ideas+for+Math+Class+%25281%2529.png" width="400" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><h2 style="clear: both; text-align: center;"><span style="color: #b45f06;">MTBoS BLAUGUST</span></h2><p> Today I saw a slide show how to engage students in distance learning. There are quite a few ideas curated from various blogs and such. The presentation is not original with me. I am sharing it with permission of <a href="https://www.facebook.com/groups/445786889466638/?post_id=608322029879789&comment_id=608411383204187&__cft__[0]=AZVv55ZAGxbG6CU50FcVYiaO15HF1CEBJwctbWBq23aminUuDyxLMM3-rIXo5O9VX2D-RtP1zZwe6DTeb5Z3t683vf8kdqhwg9RtgF8vMVorjv_KydDFSr2JinAMvVtL8OE&__tn__=R]-R">the author</a>. The Facebook group where I saw it is a public group called Amazing Educational Resources. <br /><br />I hope that some of the ideas in the presentation are helpful to all of you working so hard to capture the hearts and minds of your students while delivering required content ... from a computer screen. No easy feat for sure!</p><p>If you want to download the presentation, <a href="https://docs.google.com/presentation/d/1a0H6LW-tCJ1vr4XUfYhKVf47bj4S7b5lExEu4wOYxOE/copy">click here and make a copy.</a></p>
<iframe allowfullscreen="true" frameborder="0" height="480" mozallowfullscreen="true" src="https://docs.google.com/presentation/d/e/2PACX-1vTul8NV63H-cKljw2CVZyGbSnqshDf0X-qZGmaZiPm4XPFeX30rWd7nXs_aWYfz9-uU0dSAXjf4Fc6B/embed?start=true&loop=true&delayms=5000" webkitallowfullscreen="true" width="576"></iframe>Algebra's Friendhttp://www.blogger.com/profile/04729315514507170702noreply@blogger.com2tag:blogger.com,1999:blog-8399389267815059112.post-52165817669423118772020-08-24T19:37:00.006-05:002020-11-07T14:10:35.443-06:00Just for fun ... brain teasers<p></p><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi54mlTkMmYU3kjaxUiK_o9ewogrTJtXDOp4yi-pMNT7Lyq_IA5IBhTtK43cMZzbmwdM106bmSV7MiReCFemvfrP9Mz4Ty7htq0CpJWVx1Fhc_DmaKCbUMB_tsIT8dvBVMiPGCvBFvzQw/s640/Ideas+for+Math+Class+%25281%2529.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="240" data-original-width="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi54mlTkMmYU3kjaxUiK_o9ewogrTJtXDOp4yi-pMNT7Lyq_IA5IBhTtK43cMZzbmwdM106bmSV7MiReCFemvfrP9Mz4Ty7htq0CpJWVx1Fhc_DmaKCbUMB_tsIT8dvBVMiPGCvBFvzQw/s320/Ideas+for+Math+Class+%25281%2529.png" width="320" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><br /></div><h1 style="clear: both; text-align: center;">MTBoS BLAUGUST</h1><div class="separator" style="clear: both; text-align: left;"><a href="https://twitter.com/druinok/status/1297887276463271936?s=20">Awesome Shelli asked early today</a> if anyone has a slide show of brain teasers that could be used as an "away" screen on Google Meet.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">Her ask resonated with me ... felt like a challenge that I wanted to tackle today.<br /><br />So ... I pulled together a few brain teasers today that might be interesting to a wide range of students.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">You are <a href="https://docs.google.com/presentation/d/17Ko7S3Ta8tImmlLBTMWERqg1K-_UytS1wotu_nANiqc/copy" target="_blank">welcome to copy this slide show</a>, use it, modify it, add to it!</div><p></p>
<iframe allowfullscreen="true" frameborder="0" height="480" mozallowfullscreen="true" src="https://docs.google.com/presentation/d/e/2PACX-1vRI8XNyW2zI7-SavUWqqtHr98CVqhntJ9p2oMJ-BfcZM5yAjHWTfXUBrOj5SVLloRRbODnCj8vB0kox/embed?start=true&loop=true&delayms=10000" webkitallowfullscreen="true" width="576"></iframe>
<div><br /></div><div>The last slide has links to the resources from which I borrowed these teasers. They are not original with me. I don't have solutions for most of htem.</div>Algebra's Friendhttp://www.blogger.com/profile/04729315514507170702noreply@blogger.com0tag:blogger.com,1999:blog-8399389267815059112.post-74418268304457665802020-08-17T16:15:00.001-05:002020-11-07T14:14:14.486-06:00Exploring Patterns ... extending thinking <p> </p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi-qiB_C0KWhb1qzFm8zjdhCWDG4m4UxnCC2W9DA4egVuUgsRQhm6KK_jUNUSIpUxmRSGL33Ww7B1vN6-RH_IfEbDlEoBCuJfVBIXuPzF2hyOKPbN_LK7yWukUElTHzBYxWLljOdE_TKw/s640/Ideas+for+Math+Class+%25281%2529.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="240" data-original-width="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi-qiB_C0KWhb1qzFm8zjdhCWDG4m4UxnCC2W9DA4egVuUgsRQhm6KK_jUNUSIpUxmRSGL33Ww7B1vN6-RH_IfEbDlEoBCuJfVBIXuPzF2hyOKPbN_LK7yWukUElTHzBYxWLljOdE_TKw/s320/Ideas+for+Math+Class+%25281%2529.png" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><br />Patterns are EVERYWHERE! Some suggest that the study of mathematics is the study of patterns ... identifying them, categorizing them, generalizing them.<br /><br />Five universal generalizations are true about patterns:<br /><ul style="text-align: left;"><li>patterns have segments that are repeated</li><li>patterns allow for prediction</li><li>patterns have an internal order</li><li>patterns may have symmetry</li><li>patterns are everywhere</li></ul>In fact, patterns make a great curriculum organizer for interdisciplinary work since patterns are evident in language, science, history, music, art, and more!<br /><div><br />Here are a few ideas for exploring patterns in math in introductory ways ... <br /><br />1). Read children's books! I love to connect with students using a read aloud ... talking through a picture book before getting started with math. AND yes! It works well even in middle and high school!</div><div>Some of these are more sophisticated than others ... and the last one (bottom right corner) is a coloring book.</div><div class="separator" style="clear: both;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgtehKl3p9p_h4vkIvh_w7c9r1_oi42kXQuQ_vr-ANdw96MdmaljyU4tdWhjPZlGN92xCNVxP-BdmCE2DNSPPtt3svbap0SidSNQzaENgyPoE0ja5KMk1Hyabq-TRC8nNr2iTk-lmsfpQ/s2048/47FEA079-C6CB-46FF-85F8-9CBA640BB6B9.JPG" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="2048" data-original-width="2048" height="262" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgtehKl3p9p_h4vkIvh_w7c9r1_oi42kXQuQ_vr-ANdw96MdmaljyU4tdWhjPZlGN92xCNVxP-BdmCE2DNSPPtt3svbap0SidSNQzaENgyPoE0ja5KMk1Hyabq-TRC8nNr2iTk-lmsfpQ/w262-h262/47FEA079-C6CB-46FF-85F8-9CBA640BB6B9.JPG" width="262" /></a><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjSRVB7dM1oiBC9fM0h4sUF6qkTSQVC56tizWqNcZ-ETyDZ4SUBu7FshnNBXBuvIG8B-9eZb9sFAQOwVxSZGk2L3oOcKQmGWH3JoVBc8e4Y6Zf67h5F7nquPQb57PIjOJxNmgsZQJbt6A/s2048/F37645F5-E37F-42DB-B247-1EA326521155.JPG" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="2048" data-original-width="2048" height="262" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjSRVB7dM1oiBC9fM0h4sUF6qkTSQVC56tizWqNcZ-ETyDZ4SUBu7FshnNBXBuvIG8B-9eZb9sFAQOwVxSZGk2L3oOcKQmGWH3JoVBc8e4Y6Zf67h5F7nquPQb57PIjOJxNmgsZQJbt6A/w262-h262/F37645F5-E37F-42DB-B247-1EA326521155.JPG" width="262" /></a></div><div class="separator" style="clear: both;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgtehKl3p9p_h4vkIvh_w7c9r1_oi42kXQuQ_vr-ANdw96MdmaljyU4tdWhjPZlGN92xCNVxP-BdmCE2DNSPPtt3svbap0SidSNQzaENgyPoE0ja5KMk1Hyabq-TRC8nNr2iTk-lmsfpQ/s2048/47FEA079-C6CB-46FF-85F8-9CBA640BB6B9.JPG"><span style="color: black;"><br /></span></a><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgtehKl3p9p_h4vkIvh_w7c9r1_oi42kXQuQ_vr-ANdw96MdmaljyU4tdWhjPZlGN92xCNVxP-BdmCE2DNSPPtt3svbap0SidSNQzaENgyPoE0ja5KMk1Hyabq-TRC8nNr2iTk-lmsfpQ/s2048/47FEA079-C6CB-46FF-85F8-9CBA640BB6B9.JPG">2)</a> Explore polygonal or figurate numbers. I have a task I've used with students ... you may find it helpful. <a href="https://docs.google.com/document/d/1ND6CdVttwbC7JfDp-vk-eb5ofWugOJ1nft13ZE2dAUg/copy">"Explore Numbers in Shapes."</a></div><div class="separator" style="clear: both;"><br /></div><p></p><iframe src="https://docs.google.com/document/d/e/2PACX-1vRwp_QdYGSDvfqOlEzSdxsscRz9CaQ8d522QHP1Hkj7rXC-znonV6WnSwO8VToAGcmr1N5ga-B8fB_J/pub?embedded=true" width="512"></iframe><div><br /></div><div>3). Check out the <a href="https://www.youcubed.org/tasks/">activities, explorations in YouCubed</a> ... there are more than a dozen pattern activities ready to implement in your classroom.</div><div><br /></div><div>4). <a href="http://www.visualpatterns.org/">Visual Patterns </a>is an excellent site ... set up to use regularly as a key activity in your math program.</div><div><br /></div><div>5). <a href="https://mathigon.org/course/sequences/introduction">Mathigon</a> has a great series of lessons, interactive, free ... ready to use to enrich students' understanding of patterns.</div><div><br /></div><div>6) NRich is another excellent source for problem solving, stretching students' thinking and exploring topics. They have <a href="https://nrich.maths.org/search/?search=patterns&tab=2&fs=111110000000111">numerous pattern activities at all levels</a> ... perfect for differentiating!</div><div><br /></div><div>I am sure there are other great resources! What sources to you recommend for exploring patterns with students?</div>Algebra's Friendhttp://www.blogger.com/profile/04729315514507170702noreply@blogger.com0tag:blogger.com,1999:blog-8399389267815059112.post-40326152789385715512020-08-16T13:42:00.006-05:002020-11-07T14:14:49.631-06:00Always Sometimes Never ... which is it for you?<p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi-qiB_C0KWhb1qzFm8zjdhCWDG4m4UxnCC2W9DA4egVuUgsRQhm6KK_jUNUSIpUxmRSGL33Ww7B1vN6-RH_IfEbDlEoBCuJfVBIXuPzF2hyOKPbN_LK7yWukUElTHzBYxWLljOdE_TKw/s640/Ideas+for+Math+Class+%25281%2529.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="240" data-original-width="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi-qiB_C0KWhb1qzFm8zjdhCWDG4m4UxnCC2W9DA4egVuUgsRQhm6KK_jUNUSIpUxmRSGL33Ww7B1vN6-RH_IfEbDlEoBCuJfVBIXuPzF2hyOKPbN_LK7yWukUElTHzBYxWLljOdE_TKw/s320/Ideas+for+Math+Class+%25281%2529.png" width="320" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><b style="background-color: white; color: #27004e; line-height: 19.6px; text-align: left;">Always, Sometimes, Never</b><span style="background-color: white; color: #27004e; line-height: 19.6px; text-align: left;"> are statements that allow students to justify thinking using prediction, inference, and testing hypotheses. Several summers ago I began curating ASN statements. Today I updated the <a href="https://asnmath.blogspot.com/">Almost Sometimes Never blog site </a>to make it more user friendly.</span></div><p><span face="arial, helvetica, sans-serif" style="color: #27004e;">Originally, I set up the site to be used one slide at a time. There are 179 statements in 13 categories: </span><span style="background-color: white; color: #27004e; line-height: 19.6px;"><span face="arial, helvetica, sans-serif">Absolute Value, Conic Sections, Exponential Functions, Financial Literacy, Functions, Geometry, Linear Equations, Number Properties, Polynomials, Real Number System, Systems of Equations, Trigonometry, and Trig Identities. </span></span></p><p><span face="arial, helvetica, sans-serif" style="color: #27004e;"><span style="background-color: white;">But I realized that you may want several slides and it's a pain to copy them one by one. So today, I created a page with<a href="https://asnmath.blogspot.com/p/asn-slide-shows.html"> LINKS to SLIDE SHOWS </a>... one for each topic. You can make a copy of my slide shows ... embed them in your assignments. I hope this will make the site more useful to everyone.<br /><br />I've been thinking about expanding the site. <a href="https://twitter.com/pamjwilson/status/1294979908683411457?s=20">@PamJWilson </a>tweeted about using ASN statements and wrote about using <a href="https://pamjwilson.wordpress.com/2020/08/16/always-sometimes-never-mtbosblaugust/">NON-Math ASN statements today in her blog post</a> ... and is creating a shared document. What a great idea to continue collecting, sharing, posting ASN statements ... mathy ones, non-mathy ones!<br /><br /></span></span></p><div><span face="arial, helvetica, sans-serif">When using ASN statements ... </span><br /><ul><span face="arial, helvetica, sans-serif"><li>encourage students to talk math with one another, agreeing, questioning each other, helping others to think through their reasoning</li><li>suggest that students consider working through examples, use modeling, tables, graphs, equations to justify their work</li><li>ask probing questions to help students clarify their thinking or to develop their vocabulary</li><li>possibly review expected vocabulary before beginning the activity</li><li>obviously the key is for all students to explain their thinking!</li></span></ul><span face="arial, helvetica, sans-serif"></span></div><div><span face="arial, helvetica, sans-serif">What is a favorite Always, Sometimes, Never statement or instructional routine that you might share with us?</span></div>Algebra's Friendhttp://www.blogger.com/profile/04729315514507170702noreply@blogger.com0tag:blogger.com,1999:blog-8399389267815059112.post-81853751319935294052020-08-15T05:00:00.014-05:002020-11-07T14:15:24.468-06:00Fun with Exponential Functions<p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi-qiB_C0KWhb1qzFm8zjdhCWDG4m4UxnCC2W9DA4egVuUgsRQhm6KK_jUNUSIpUxmRSGL33Ww7B1vN6-RH_IfEbDlEoBCuJfVBIXuPzF2hyOKPbN_LK7yWukUElTHzBYxWLljOdE_TKw/s640/Ideas+for+Math+Class+%25281%2529.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="240" data-original-width="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi-qiB_C0KWhb1qzFm8zjdhCWDG4m4UxnCC2W9DA4egVuUgsRQhm6KK_jUNUSIpUxmRSGL33Ww7B1vN6-RH_IfEbDlEoBCuJfVBIXuPzF2hyOKPbN_LK7yWukUElTHzBYxWLljOdE_TKw/s320/Ideas+for+Math+Class+%25281%2529.png" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div> <p></p><p>I enjoy teaching exponential functions! Here are some ideas for exploring exponentials ...</p><p>-</p><h3 style="text-align: left;">Mini Poster Projects</h3>CHOOSE JUST ONE of the FOLLOWING Ideas (A, B, C, OR D) and create a mini poster in a class<br />slides presentation. Include a title, table of values, graph, and art to illustrate the problem.<div><a href="https://docs.google.com/document/d/1H2HgEWq2W0RNVl5Wzn7fTbwHUWB2KE-vrIdrhgYuvH4/copy">Access the activity here.</a><br /><div><br /></div><iframe src="https://docs.google.com/document/d/e/2PACX-1vTTZMohemFHI0xFgIp3yufmxhWc0vhlFyWiYNSW-rh4LK6TI8rvIrY0yrAr8pRRsHTWPvTqQJwzwbT2/pub?embedded=true" width="512"></iframe><div><br /></div><h3 style="text-align: left;"><span></span>-</h3><h3 style="text-align: left;">Always, Sometimes, Never Exponential Statements</h3><div><a href="https://docs.google.com/presentation/d/1oAWY4hkXkdERKzuFhGLVoYjr6x_Wb-7Qwh_eSJ1tiiU/copy">Access the slide show here.</a></div><div><br /></div><iframe allowfullscreen="true" frameborder="0" height="512" mozallowfullscreen="true" src="https://docs.google.com/presentation/d/e/2PACX-1vRFAi5cKIKxF7vCuaAvT_f0I0Shx9Bo5PmZHlOkyEc-wcazt06g2gg4tYyB1X-q_6qpYfEHH--iiC9I/embed?start=false&loop=false&delayms=3000" webkitallowfullscreen="true" width="512"></iframe><div><br /></div><h3 style="text-align: left;"><span></span>-</h3><h3 style="text-align: left;">A few critical thinking questions</h3><div><a href="https://docs.google.com/document/d/1WM_bsjCRpqQCgFJj1lUhLwiBPMIxnXFmUmMcY4uyn9M/copy">Access the document here.</a></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgP-Avl1RpLk5KskUI1-s6k4tqzqKm6IHteIQfAP3PJ3eLl1SGET5CCu9l2iEIEXbjXXqhMTIeXZlsnykT1ufO2Xusl0VORwDeGsnqG5WlN-Z68EhAZQMRTYMxHMwxFR9oENtxuFWT7bA/s1476/Screen+Shot+2020-08-14+at+7.57.22+PM.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="718" data-original-width="1476" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgP-Avl1RpLk5KskUI1-s6k4tqzqKm6IHteIQfAP3PJ3eLl1SGET5CCu9l2iEIEXbjXXqhMTIeXZlsnykT1ufO2Xusl0VORwDeGsnqG5WlN-Z68EhAZQMRTYMxHMwxFR9oENtxuFWT7bA/s640/Screen+Shot+2020-08-14+at+7.57.22+PM.png" width="640" /></a></div><div><br /></div><div><br /></div><div><br /></div></div>Algebra's Friendhttp://www.blogger.com/profile/04729315514507170702noreply@blogger.com0tag:blogger.com,1999:blog-8399389267815059112.post-35813111245053869512020-08-14T05:00:00.001-05:002020-08-14T14:06:47.867-05:00#MTBoSBlaugust To Infinity and Beyond! An enrichment project idea<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEivuheUGKD4dz06rURk9hSj7J8Mfn56zfMIiuTRUn02nkS7UynEv-KI2erq-zAN9aOdrkUl9jejd_Ssyhc7yDfifwU_wgjHgLVQKplXykfxN_Ueob1rLFkirBRlK3TlYqhizXlm-oPmFg/s512/Blaugust2020.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="182" data-original-width="512" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEivuheUGKD4dz06rURk9hSj7J8Mfn56zfMIiuTRUn02nkS7UynEv-KI2erq-zAN9aOdrkUl9jejd_Ssyhc7yDfifwU_wgjHgLVQKplXykfxN_Ueob1rLFkirBRlK3TlYqhizXlm-oPmFg/s0/Blaugust2020.png" /></a></div><div><br /></div><div><br /></div>A favorite picture book is,Infinity and Me, by Kate Hosford. If you haven't read it, do so! If you teach math, buy it for your classroom. Many of us teach sets of numbers early in the year. We talk about infinity in domain and range. Infinity is one of those topics that makes for a great enrichment project!<br />
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Here is an example of a "choice board" that you could use as a project in your class ...<br />
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You can <a href="https://docs.google.com/document/u/0/d/1329AWT3seDHtshKT2cLK-jWnO5rEq74QTv3ziqDg1Kc/copy">access the Google Doc here </a>... just copy it to your Google Drive.<br />
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<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: center;">
<span face="" style="background-color: transparent; color: black; font-family: arial; font-size: 24px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">To INFINITY, and BEYOND!</span></div>
<b id="docs-internal-guid-ba76d7ef-be9b-926d-9464-33f9d0536681" style="font-weight: normal;"><br /></b>
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<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span face="" style="background-color: transparent; color: black; font-family: arial; font-size: 18.6667px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Complete three activities making a tic-tac-toe from the Choice Board. Use at least three of the following resources. Create a reference page for the resources you use.</span></div>
<b style="font-weight: normal;"><br /></b>
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<li dir="ltr" style="background-color: transparent; color: black; font-family: arial; font-size: 16px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: disc; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span face="" style="background-color: transparent; color: black; font-family: arial; font-size: 16px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Angier, N. (2012, December 31). The Life of Pi, and Other Infinities. Retrieved August 24, 2016, from</span><a href="http://www.nytimes.com/2013/01/01/science/the-life-of-pi-and-other-infinities.html" style="text-decoration: none;"><span face="" style="background-color: transparent; color: black; font-family: arial; font-size: 16px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> </span><span face="" style="background-color: transparent; color: #1155cc; font-family: arial; font-size: 16px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap;">http://www.nytimes.com/2013/01/01/science/the-life-of-pi-and-other-infinities.html</span></a></div>
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<li dir="ltr" style="background-color: transparent; color: black; font-family: arial; font-size: 16px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: disc; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span face="" style="background-color: transparent; color: black; font-family: arial; font-size: 16px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Chartier, T. (2014, April 14). Mime-matics - the infinite rope. Retrieved August 24, 2016, from </span><a href="https://www.youtube.com/watch?v=--nbhhuabHo" style="text-decoration: none;"><span face="" style="background-color: transparent; color: #1155cc; font-family: arial; font-size: 16px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap;">https://www.youtube.com/watch?v=--nbhhuabHo</span></a><span face="" style="background-color: transparent; color: black; font-family: arial; font-size: 16px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> </span></div>
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<li dir="ltr" style="background-color: transparent; color: black; font-family: arial; font-size: 16px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: disc; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span face="" style="background-color: transparent; color: black; font-family: arial; font-size: 16px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Hosford, K., & Swiatkowska, G. (2012). </span><span face="" style="background-color: transparent; color: black; font-family: arial; font-size: 16px; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Infinity and me</span><span face="" style="background-color: transparent; color: black; font-family: arial; font-size: 16px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">. Minneapolis: Carolrhoda Books.</span></div>
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<li dir="ltr" style="background-color: transparent; color: black; font-family: arial; font-size: 16px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: disc; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span face="" style="background-color: transparent; color: black; font-family: arial; font-size: 16px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">How big is infinity? - Dennis Wildfogel. (n.d.). Retrieved August 24, 2016, from</span><a href="http://ed.ted.com/lessons/how-big-is-infinity" style="text-decoration: none;"><span face="" style="background-color: transparent; color: black; font-family: arial; font-size: 16px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> </span><span face="" style="background-color: transparent; color: #1155cc; font-family: arial; font-size: 16px; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap;">http://ed.ted.com/lessons/how-big-is-infinity</span></a></div>
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<li dir="ltr" style="background-color: transparent; color: black; font-family: arial; font-size: 16px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: disc; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span face="" style="background-color: transparent; color: black; font-family: arial; font-size: 16px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">The Infinite Hotel Paradox - Jeff Dekofsky. (n.d.). Retrieved August 24, 2016, from</span><a href="http://ed.ted.com/lessons/the-infinite-hotel-paradox-jeff-dekofsky" style="text-decoration: none;"><span face="" style="background-color: transparent; color: black; font-family: arial; font-size: 16px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> </span><span face="" style="background-color: transparent; color: #1155cc; font-family: arial; font-size: 16px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap;">http://ed.ted.com/lessons/the-infinite-hotel-paradox-jeff-dekofsky</span></a></div>
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<li dir="ltr" style="background-color: transparent; color: black; font-family: arial; font-size: 16px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: disc; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span face="" style="background-color: transparent; color: black; font-family: arial; font-size: 16px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Vi Hart. (2014, June 6). Retrieved August 24, 2016, from</span><a href="http://vihart.com/how-many-kinds-of-infinity-are-there/" style="text-decoration: none;"><span face="" style="background-color: transparent; color: black; font-family: arial; font-size: 16px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> </span><span face="" style="background-color: transparent; color: #1155cc; font-family: arial; font-size: 16px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap;">http://vihart.com/how-many-kinds-of-infinity-are-there/</span></a></div>
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<li dir="ltr" style="background-color: transparent; color: black; font-family: arial; font-size: 16px; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: disc; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span face="" style="background-color: transparent; color: black; font-family: arial; font-size: 16px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Weltman, A. (2014, February 20). Talk Like a Computer, Infinite Hotel, and Video Contest. Retrieved August 24, 2016, from</span><a href="https://mathmunch.org/2014/02/20/talk-like-a-computer-infinite-hotel-and-video-contest/" style="text-decoration: none;"><span face="" style="background-color: transparent; color: black; font-family: arial; font-size: 16px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> </span><span face="" style="background-color: transparent; color: #1155cc; font-family: arial; font-size: 16px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap;">https://mathmunch.org/2014/02/20/talk-like-a-computer-infinite-hotel-and-video-contest/</span></a></div>
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<span face="" style="background-color: transparent; color: black; font-family: arial; font-size: 24px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">To INFINITY, and BEYOND! Choice Board</span></div>
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<table style="border-collapse: collapse; border: none; width: 672px;"><colgroup><col width=""></col><col width=""></col><col width=""></col></colgroup><tbody>
<tr style="height: 0px;"><td style="border-color: rgb(0, 0, 0); border-style: solid; border-width: 1px; padding: 7px; vertical-align: top;"><div dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;">
<span face="" style="background-color: transparent; color: black; font-family: arial; font-size: 18.6667px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> </span><span face="" style="background-color: transparent; color: black; font-family: arial; font-size: 18.6667px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><img alt="checkerboard-1297808_640.png" height="147" src="https://lh4.googleusercontent.com/Oebw5Q7lDS_eZs4tjH_QIv8LSyFhXrq2XkmfRuqHt5ctkdbcVNqnMiY--ewtHH8JrEUEF-zyNUhwAXNEoO-mi9L_-qK37alVjMThp1NuxS3GJhppSiQ-juxrCuB2_1ZrpgVo_yw" style="border: none; transform: rotate(0rad);" width="147" /></span></div>
<div dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;">
<span face="" style="background-color: transparent; color: black; font-family: arial; font-size: 18.6667px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Define infinity for a 1st grader. Define it for a 6th grader. Define it for a high schooler. How do your definitions change?</span></div>
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<div dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;">
<span face="" style="background-color: transparent; color: black; font-family: arial; font-size: 18.6667px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><img alt="characters-1036501_640.png" height="53" src="https://lh6.googleusercontent.com/WVEbU7uJjRcM2Mfygk1voY2o1sZXjR1MAb70DfYl2y4LKWJ5p-Jp7GeHldR3XeI5kwbPmzwc4-dw-ypE3_ODiRocI_zQpBjCUC_DPMvJ3On-3LExQqPEoMvjSvk6cNNmtPPaBO4" style="border: none; transform: rotate(0rad);" width="209" /></span></div>
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<div dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;">
<span face="" style="background-color: transparent; color: black; font-family: arial; font-size: 18.6667px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Explain the infinity symbol. What is it’s name? How did it originate?</span></div>
</td><td style="border-color: rgb(0, 0, 0); border-style: solid; border-width: 1px; padding: 7px; vertical-align: top;"><div dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;">
<span face="" style="background-color: transparent; color: black; font-family: arial; font-size: 18.6667px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><img alt="palette-1482678_640.png" height="147" src="https://lh6.googleusercontent.com/WHdMVJzCp7-7sFHngX9e57Th4QI-tpk7g7G4nmqZ0PG7BJ3Dh7JEOiLjZnfjMVPgQbLLv0WlIynodkEtM7V_PGuS3fLkCc1jOUZbBnAX5saWqzeoSif6JDjDd3LurDGdWd2D010" style="border: none; transform: rotate(0rad);" width="209" /></span><span face="" style="background-color: transparent; color: black; font-family: arial; font-size: 18.6667px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">What does infinity look like to you? Draw a picture that captures infinity.</span></div>
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<tr style="height: 0px;"><td style="border-color: rgb(0, 0, 0); border-style: solid; border-width: 1px; padding: 7px; vertical-align: top;"><div dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;">
<span face="" style="background-color: transparent; color: black; font-family: arial; font-size: 18.6667px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">N. Angier says in her New York Times post, “... there are infinities, multiplicities of the limit-free that come in a vast variety of shapes, sizes, purposes and charms.” What is meant by “different” infinities?</span></div>
</td><td style="border-color: rgb(0, 0, 0); border-style: solid; border-width: 1px; padding: 7px; vertical-align: top;"><div dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;">
<span face="" style="background-color: transparent; color: black; font-family: arial; font-size: 18.6667px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> </span><span face="" style="background-color: transparent; color: black; font-family: arial; font-size: 18.6667px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><img alt="Screen Shot 2016-08-24 at 5.10.28 PM.png" height="97" src="https://lh3.googleusercontent.com/hqykE0wUlFuxTCR0A5BuLIEiKFmqZfdmth-eI2tSCDN4p-3HZ500_qzJRl5hTh9OAHB9C5zLxgsRqn6Fnfd24hwsfqpWL1GFLyRFDD80rqHtK4ZRspoNg3jwPyG4aG0Ur2rv6xs" style="border: none; transform: rotate(0rad);" width="160" /></span><span face="" style="background-color: transparent; color: black; font-family: arial; font-size: 18.6667px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Select either the infinite hotel paradox or Zeno’s Paradox. Write a story, poem, or essay about the one your choice.</span></div>
</td><td style="border-color: rgb(0, 0, 0); border-style: solid; border-width: 1px; padding: 7px; vertical-align: top;"><div dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;">
<span face="" style="background-color: white; color: black; font-family: arial; font-size: 18.6667px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> </span><span face="" style="background-color: white; color: black; font-family: arial; font-size: 18.6667px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><img alt="twins.png" height="154" src="https://lh5.googleusercontent.com/CsS4F4Zz4XzOTUWMzrFghPbcW4pytgD2wVkxaefI54BG0VNAVznJPayBzMgFmtfakxW-b2GuNQ-0xeSdWG5OQZp4ua8AWW1lDXxSSOR5V8MpSj7MFyeG82YZEbz-ozD9CvAJ9ks" style="border: none; transform: rotate(0rad);" width="124" /></span><span face="" style="background-color: white; color: black; font-family: arial; font-size: 18.6667px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">What is a doppelgänger, and why does the existence of an infinite universe suggest yours might exist?</span></div>
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<tr style="height: 240px;"><td style="border-color: rgb(0, 0, 0); border-style: solid; border-width: 1px; padding: 7px; vertical-align: top;"><div dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;">
<span face="" style="background-color: white; color: #333333; font-family: arial; font-size: 18.6667px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Make a list of quantities that you believe are infinite and present that list to a group of classmates. Invite your classmates to debate whether or not the quantities are finite or infinite, and if infinite, which kind of infinity.</span></div>
</td><td style="border-color: rgb(0, 0, 0); border-style: solid; border-width: 1px; padding: 7px; vertical-align: top;"><div dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;">
<span face="" style="background-color: white; color: #333333; font-family: arial; font-size: 18.6667px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Mime Tim Chartier uses movement to explore and express the idea of infinity. Watch his youtube video. Then, create your own skit or mime to convey how you see infinity.</span></div>
</td><td style="border-color: rgb(0, 0, 0); border-style: solid; border-width: 1px; padding: 7px; vertical-align: top;"><div dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;">
<span face="" style="background-color: transparent; color: black; font-family: arial; font-size: 18.6667px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> </span><span face="" style="background-color: transparent; color: black; font-family: arial; font-size: 18.6667px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><img alt="infinite sum.png" height="148" src="https://lh5.googleusercontent.com/0s0W_-3BwLg_Wy7fvuvvI1U9yaIjcH3W7fANvNKLOQH32bVQqvAU8R6qQ44w3rP_TN6G9UDkuPSvolr4uJ7J5_R1JrS3C-dWjbPJtDSbAPRziAdutS5uMuf5Dye9cC3G3LgrxZE" style="border: none; transform: rotate(0rad);" width="152" /></span></div>
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<div dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;">
<span face="" style="background-color: transparent; color: black; font-family: arial; font-size: 18.6667px; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Is it possible to find the sum of an infinite series? Explain.</span></div>
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<span face="" style="font-family: arial, helvetica, sans-serif; font-size: x-small;">Reference: <span style="color: black; line-height: 22.08px; vertical-align: baseline; white-space: pre-wrap;">Teaching the Mathematics of Infinity. (0604). Retrieved August 24, 2016, from</span><a href="http://learning.blogs.nytimes.com/2013/01/30/teaching-the-mathematics-of-infinity/" style="line-height: 22.08px; text-decoration: none;"><span style="color: black; vertical-align: baseline; white-space: pre-wrap;"> </span><span style="color: #1155cc; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap;">http://learning.blogs.nytimes.com/2013/01/30/teaching-the-mathematics-of-infinity/</span></a></span>Algebra's Friendhttp://www.blogger.com/profile/04729315514507170702noreply@blogger.com0tag:blogger.com,1999:blog-8399389267815059112.post-88199970460025339462020-08-12T20:02:00.007-05:002020-08-13T12:47:09.314-05:00Creating a Working Document for Quadratics Unit<p> </p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhp8J-E4-2Ahc_NQBng_xkgyEd5DX_qlrHT7VB1u9uLHJcAJHXiegy2PXEkR3IXQagcFgq8M0CCl6OATPz4jRZ2D4ETDKZGeGlMg1eEAhk7vtPEN0ZtlyYSKafDqk6knr5sRDeUYU5-Rw/s512/Blaugust2020.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="182" data-original-width="512" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhp8J-E4-2Ahc_NQBng_xkgyEd5DX_qlrHT7VB1u9uLHJcAJHXiegy2PXEkR3IXQagcFgq8M0CCl6OATPz4jRZ2D4ETDKZGeGlMg1eEAhk7vtPEN0ZtlyYSKafDqk6knr5sRDeUYU5-Rw/s0/Blaugust2020.png" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">I decided to try out a hyperlinked document to experiment with how to put together a unit for students. I started with a familiar one. I am working on a series of enrichment lessons for gifted middle schoolers who are already accelerated in basic math. I found this "notebook" style to be challenging and yet, it may be useful. <br /><br />I'm curious how you are organizing lessons?<br /><br /><br /></div><p></p>
<iframe allowfullscreen="true" frameborder="0" height="749" mozallowfullscreen="true" src="https://docs.google.com/presentation/d/e/2PACX-1vQIV167GxZse3yxB7Qu1aQV29vOqDNJ0BsFkUxMFIP8nxriKiElnsC70jUO0thLz2WCnACP0bsLsJ5T/embed?start=false&loop=false&delayms=3000" webkitallowfullscreen="true" width="576"></iframe><div><br /></div><div>The part I struggled with is how students would keep notes, share thoughts and so on. In the document above I refer to Padlet a couple of times. And I do like that site for sharing whole class.<br /><br />BUT just now I saw how one school created a Google Doc for a whole unit ... as a "scrapbook" for students to keep all of their unit work together. I can't publish theirs here but in the next few days I want to create that kind of document for this unit. We'll see how that goes :). (If you want to track down an example of the Google Doc scrapbook, <a href="https://sites.google.com/innovatesd.org/distancelearning">check out this link </a>... high school integrated math 1.</div>Algebra's Friendhttp://www.blogger.com/profile/04729315514507170702noreply@blogger.com1tag:blogger.com,1999:blog-8399389267815059112.post-24207073276175758012020-08-10T05:00:00.029-05:002020-08-10T12:55:44.955-05:00Structuring Lessons for Virtual Instruction<p></p><div class="separator" style="clear: both;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjnn6d4TBc7P5g3MErg7DDpTagvDTwuHkx6UhN4hMQjuISUJNbTul1YFfI_itF-5u8U0Kx22f_2TOi5I32t8LgUGakbCpWkP1OMIZTrTvdIFdSXMpkK1JbOYwbZDt_Y0f_yKfYtW-ML_g/s512/Blaugust2020.png" style="display: block; padding: 1em 0px;"><img border="0" data-original-height="182" data-original-width="512" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjnn6d4TBc7P5g3MErg7DDpTagvDTwuHkx6UhN4hMQjuISUJNbTul1YFfI_itF-5u8U0Kx22f_2TOi5I32t8LgUGakbCpWkP1OMIZTrTvdIFdSXMpkK1JbOYwbZDt_Y0f_yKfYtW-ML_g/s0/Blaugust2020.png" /></a></div><span face="" style="background-color: white; color: #3162f5; font-family: arial, tahoma, helvetica, freesans, sans-serif; font-size: 22px;"><br /></span><p></p><p><span face="" style="background-color: white; color: #3162f5; font-family: arial, tahoma, helvetica, freesans, sans-serif; font-size: 22px;">Structuring Lessons for Virtual Instruction</span></p><div class="post-header" style="background-color: white; font-family: arial, tahoma, helvetica, freesans, sans-serif; font-size: 13px; line-height: 1.6; margin: 0px 0px 1em;"><div class="post-header-line-1"></div></div><div class="post-body entry-content" id="post-body-8242383229350186774" itemprop="" style="background-color: white; line-height: 1.4; position: relative; width: 586px;"><span style="font-family: arial;">I'm working with a group of teachers about planning a differentiated lesson. While discussing lesson planning, I realized that we go about that process differently, organize our work differently, create different styles of lesson plans.</span></div><div class="post-body entry-content" id="post-body-8242383229350186774" itemprop="" style="background-color: white; line-height: 1.4; position: relative; width: 586px;"><span style="font-family: arial;"><br /></span></div><div class="post-body entry-content" id="post-body-8242383229350186774" itemprop="" style="background-color: white; line-height: 1.4; position: relative; width: 586px;"><span style="font-family: arial;">On top of that, many teachers are planning for online delivery. How might that look different from f2f classes?<br /><br />While I have been teaching online for a university for 16 years, I do not have experience delivering classroom instruction K12 online. So take my thoughts with a grain of salt :)</span></div><div class="post-body entry-content" id="post-body-8242383229350186774" itemprop="" style="background-color: white; line-height: 1.4; position: relative; width: 586px;"><span style="font-family: arial;"><br /></span></div><div class="post-body entry-content" id="post-body-8242383229350186774" itemprop="" style="background-color: white; line-height: 1.4; position: relative; width: 586px;"><span style="font-family: arial;">The first thing that is significant to me is organization. Teachers and students are both flustered by technology. How might lessons be organized so no one is guessing what to do, when to do it, where to find it?<br /><br />A Hyperdoc might be a good idea at this point. Hyperdocs can look different. I'm going to suggest a couple of ways of organizing lessons.</span></div><div class="post-body entry-content" id="post-body-8242383229350186774" itemprop="" style="background-color: white; line-height: 1.4; position: relative; width: 586px;"><span style="font-family: arial;"><br /></span></div><div class="post-body entry-content" id="post-body-8242383229350186774" itemprop="" style="background-color: white; line-height: 1.4; position: relative; width: 586px;"><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/b/R29vZ2xl/AVvXsEi9UtvhkprM7gg8K4VOFs8BP-0iKLNDYNvRnpRcrBsReEVfBsfCXOhCWSMuWYh6Zd_mufrifzfk8kCfS92xwpGhedAkl0Qg17BOvhB_KLeGOuWWEP8uH95id8wiVqy1cxnwDKwf_ao1Dg/s520/why+hyperdoc.png" style="display: block; margin-left: auto; margin-right: auto; padding: 1em 0px; text-align: center;"><img border="0" data-original-height="520" data-original-width="520" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi9UtvhkprM7gg8K4VOFs8BP-0iKLNDYNvRnpRcrBsReEVfBsfCXOhCWSMuWYh6Zd_mufrifzfk8kCfS92xwpGhedAkl0Qg17BOvhB_KLeGOuWWEP8uH95id8wiVqy1cxnwDKwf_ao1Dg/d/why+hyperdoc.png" title="borrowed from https://www.aoptech.org/michele-kiss.html" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Borrowed from <a href="https://www.aoptech.org/michele-kiss.html">https://www.aoptech.org/michele-kiss.html</a><br /></td></tr></tbody></table><span style="font-family: arial;"><br />I've used three different sets of labels to set up a basic Hyperdoc model.<br /><ul style="text-align: left;"><li><span style="font-family: arial;"><a href="https://docs.google.com/document/d/1az5VqVWGj6BKCUt7nwHMGI0EafGIKTUKn8unBZrESxA/edit?usp=sharing">5E model </a></span></li><li><span style="color: #27004e; font-family: arial; line-height: 19.6px;"><a href="https://docs.google.com/document/d/1SD4UFA41auMWWFEJEXv9cizUQ_0i0NZU32B06Hf4zME/edit?usp=sharing">EELDRC or Enroll, Explore, Label, Demonstrate, Review, and Celebrate</a></span></li><li><span style="color: #27004e; font-family: arial;"><a href="https://docs.google.com/document/d/15jjKDsWCcnCnOz2t9SfNBMXYnMDZd5jlWGI4vROhJNQ/edit?usp=sharing">Upside Down Version to I Do, We Do, You Do</a></span></li></ul></span></div><div class="post-body entry-content" id="post-body-8242383229350186774" itemprop="" style="background-color: white; line-height: 1.4; position: relative; width: 586px;"><br /></div><div class="post-body entry-content" id="post-body-8242383229350186774" itemprop="" style="background-color: white; line-height: 1.4; position: relative; width: 586px;"><span style="color: #27004e; font-family: arial;">In each of these models, the teacher plans out lessons inviting students to participate by accessing links, videos, forms, online tutorials, online practice, and more. In addition students can snap and insert photos, respond and/or reflect right in the document itself. It becomes not only an organizer for the lesson plan but also could be an organizer for brief notes for the student.<br /><br />If you want to improve upon those Hyperdoc ideas ... check out<a href="https://slidesmania.com/free-hyperdoc-handbook-template-for-google-slides-or-powerpoint/"> Slides Mania's Hyperdoc Notebook</a> ... You could create a notebook for each unit. <a href="https://twitter.com/SlidesManiaSM">Her work </a>is amazing and it is shared freely!</span></div><div class="post-body entry-content" id="post-body-8242383229350186774" itemprop="" style="background-color: white; font-size: 13px; line-height: 1.4; position: relative; width: 586px;"><span style="font-family: arial;"><br /></span></div><div class="post-body entry-content" id="post-body-8242383229350186774" itemprop="" style="background-color: white; line-height: 1.4; position: relative; width: 586px;"><span style="font-family: arial;">The last suggestion for organizing lessons is using <a href="https://deck.toys/">Deck Toys</a>! This site is new to me but I enjoyed playing with it. I created a sample lesson on <a href="https://deck.toys/bethtestclass6550">Babylonian Numbers</a> ... it's not great - just my first time. By the way, you can embed video, require answering before continuing, embed Desmos, and Delta Math! I also found several already created for secondary math! You will want to check those out! Anyway ...if you are looking for a way to organize lessons this may be a great one!</span></div><div class="post-body entry-content" id="post-body-8242383229350186774" itemprop="" style="background-color: white; line-height: 1.4; position: relative; width: 586px;"><span style="font-family: arial;"><br /></span></div><div class="post-body entry-content" id="post-body-8242383229350186774" itemprop="" style="background-color: white; line-height: 1.4; position: relative; width: 586px;"><span style="font-family: arial;">How are you building lessons online? What structure are you using? What ideas might you share with a first year teacher?</span></div><div class="post-body entry-content" id="post-body-8242383229350186774" itemprop="" style="background-color: white; line-height: 1.4; position: relative; width: 586px;"><span style="font-family: arial;"><br /></span></div><div class="post-body entry-content" id="post-body-8242383229350186774" itemprop="" style="background-color: white; line-height: 1.4; position: relative; width: 586px;"><span style="font-family: arial;">By the way, I wrote about <a href="http://algebrasfriend.blogspot.com/2016/06/lesson-planning-structures.html">Lesson Planning Structures</a> in a previous blog post. You might find it interesting if you are new to lesson planning!</span></div>Algebra's Friendhttp://www.blogger.com/profile/04729315514507170702noreply@blogger.com0tag:blogger.com,1999:blog-8399389267815059112.post-62362402443727032322020-08-09T12:15:00.001-05:002020-08-09T12:15:23.491-05:00Resources to Extend Thinking with Quadratics<p> </p><div class="separator" style="clear: both;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjEZ2u6CghywSeyCQgW263VNvRy3_1rLR1cnElp5yNArNnU45iWNHFNOOABR5vLfGSqeDScrGoysq1DyJLV6TyfQMVwf93_YECIt_ERrTIE_bX-YeJ-E4N46GZafrFoBtkk30dstRGf8A/s512/Blaugust2020.png" style="display: block; padding: 1em 0px;"><img border="0" data-original-height="182" data-original-width="512" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjEZ2u6CghywSeyCQgW263VNvRy3_1rLR1cnElp5yNArNnU45iWNHFNOOABR5vLfGSqeDScrGoysq1DyJLV6TyfQMVwf93_YECIt_ERrTIE_bX-YeJ-E4N46GZafrFoBtkk30dstRGf8A/s0/Blaugust2020.png" /></a><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjEZ2u6CghywSeyCQgW263VNvRy3_1rLR1cnElp5yNArNnU45iWNHFNOOABR5vLfGSqeDScrGoysq1DyJLV6TyfQMVwf93_YECIt_ERrTIE_bX-YeJ-E4N46GZafrFoBtkk30dstRGf8A/s512/Blaugust2020.png" style="display: block; padding: 1em 0px;"><br /></a><span style="font-size: x-large;">Here are a few activities that I've used to extend thinking in our work with the Quadratic Function ...</span></div><div class="separator" style="clear: both;">----------------------</div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;"><a href="https://docs.google.com/document/d/1qT-z8SSbtfPVM4_z-89uyNR2YWf4SLUoccb5kgtE29E/edit?usp=sharing">True False Statements Sorting Activity</a> - Characteristics of Quadratics</div><div class="separator" style="clear: both;"><br /></div><p></p>
<iframe src="https://docs.google.com/document/d/e/2PACX-1vSUGAscLQbpcEd5mGjNhrIjr4D-F9xthc09UZcTfbGmJXo32r_r3PX1atJLhA7npi44pNsYzF-ga2PN/pub?embedded=true" width="512"></iframe><div><br /></div><div>----------------------</div><div><br /></div><div><a href="https://docs.google.com/document/d/1Y8EVnxyaqobaUF4GZaudt91TOaEMjm9JKRDKceDDgmg/edit?usp=sharing">Odd One Out Activities</a> give students opportunity to analyze, build vocabulary, and develop a discerning eye for mathematics.</div><div><br /></div>
<iframe src="https://docs.google.com/document/d/e/2PACX-1vQTW9SlEXzSWce7__bbA1XZctdZoujqBJEF3Pe_jWLoQSsGbs1VsHeU87XZ3cqCYc3hTA2EbgKc-BeU/pub?embedded=true" width="512"></iframe><div><br /></div><div>---------------------</div><div><br /></div><div><a href="https://docs.google.com/document/d/1F6SujoO5Ut2TvVyy6yXfdRKAdNupmBpNoB8eCuPfHt8/edit?usp=sharing">Partner Discussions or "He Said She Said" Activity</a> asks students to analyze 2 problems, discuss them and then debrief.</div><div><br /></div><div><br /></div><iframe src="https://docs.google.com/document/d/e/2PACX-1vQPdr7MaHc2klic3VlxEeFeM0ccSsg7wvoXtrNzdjRTObFSozp4ahbIQ4XvJFCVh4DghpgV8vrEl1dn/pub?embedded=true" width="512"></iframe><div><br /></div><div>----------------------</div><div><br /></div><div><a href="https://docs.google.com/presentation/d/1z7KJTaaupzLXzNhSbdzs8Vkj52W73_hLQVpo7j7y1Fw/edit?usp=sharing">Always, Sometimes, Never statements</a> are great for helping students think deeply about quadratics.</div><div><br /></div><iframe allowfullscreen="true" frameborder="0" height="480" mozallowfullscreen="true" src="https://docs.google.com/presentation/d/e/2PACX-1vT5FOyRL7n9ae5oqRXjiHn9U1w2JNCrXFCWHHZ2x-St4kkuwDuuoiH0kr2G1erkp3nwS3ufGnsuIvxg/embed?start=false&loop=false&delayms=3000" webkitallowfullscreen="true" width="512"></iframe><div><br /></div><div>-----------------------</div><div><br /></div><div>Last ... Here is a collection of questions to promote critical thinking:</div><div><br /></div><div>1) Write three different quadratic functions whose graphs have the line x = 4 as an axis of symmetry but have different y - intercepts.</div><div>2) The points (2, 3) and (-4, 3) lie on the graph of a quadratic function. Explain how these points can be sued to find an equation of the axis of symmetry.<br />3) Write a quadratic function that has as roots, x = 2a and x = -5b.</div><div>4) For what nonzero whole number m does the quadratic equation x^2 + 3mx + (9/2)m = 0 have exactly one real solution for x?</div><div>5) What characteristics are most easily determined from a quadratic function written in standard form? In factored form? In vertex form?</div><div>6) The point (1, 5) lies on the graph of a quadratic function whose axis of symmetry is x = -1. Your classmate says the vertex could be (0, 5). Is your classmate correct? Explain.</div>Algebra's Friendhttp://www.blogger.com/profile/04729315514507170702noreply@blogger.com0tag:blogger.com,1999:blog-8399389267815059112.post-30983797816630919082020-08-08T13:31:00.011-05:002020-08-08T13:33:53.298-05:00Extending Thinking with Systems of Equations<p> </p><div class="separator" style="clear: both;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjtJnzfeWJVYvAfhgYzVIFQKTrFx3OAu_AsXKo2JjaU2e-F3gRUPPQsAbkuKjcEU5y6DswgXBft9LyDmQ52ZrP0n15iGsJ16Oeawsi6_JRE66Pt-k2o0yNbZAliM2YSwQyjK3PkcHbNJA/s512/Blaugust2020.png" style="display: block; padding: 1em 0px;"><img border="0" data-original-height="182" data-original-width="512" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjtJnzfeWJVYvAfhgYzVIFQKTrFx3OAu_AsXKo2JjaU2e-F3gRUPPQsAbkuKjcEU5y6DswgXBft9LyDmQ52ZrP0n15iGsJ16Oeawsi6_JRE66Pt-k2o0yNbZAliM2YSwQyjK3PkcHbNJA/s0/Blaugust2020.png" /></a><h3 style="text-align: center;">Systems of Equations can be fun to explore. </h3><h3 style="text-align: center;">Here are some ideas for extending thinking...</h3><div style="text-align: center;">-------------------</div><div><br /></div></div><h4 style="clear: both; text-align: left;"><a href="https://docs.google.com/document/d/1K6YxQt-ij312dYoBYuazaPAtyE9cxtWk1NzhTNFHIkY/edit?usp=sharing">Odd One Out</a> is always a great discussion starter!</h4><p></p>
<iframe src="https://docs.google.com/document/d/e/2PACX-1vRCgedR_JtkWYQpXdxiab1Udx7EhC0HlhfVBAIMWwDJG9CxkOl5Cf90GjosWQafNIWAbXl_VMr8fvWa/pub?embedded=true" width="512"></iframe><div><br /></div><h4 style="text-align: left;"><span style="font-weight: 400; text-align: center;">-------------------</span></h4><h4 style="text-align: left;">Another critical thinking activity ... <a href="https://docs.google.com/document/d/1TGFThvtHNYbYHtDrCr7rm06RdRUpRcpyqMDBFwg75lg/edit?usp=sharing">"Partner Talk or He Said, She Said"</a> ... students analyze problems on their own, pair up to discuss, and then debrief as a class:</h4><div><br /></div>
<iframe src="https://docs.google.com/document/d/e/2PACX-1vSR-LbTOUm6tHeLQwBgViW5o7QgGFIwbYFrlJS14CxpCwzHNtJzOTpjKoPTL2XIOHQWKa-X4WXzOW8-/pub?embedded=true" width="512"></iframe><div><br /></div><h4 style="text-align: left;"><span style="font-weight: 400; text-align: center;">-------------------</span></h4><h4 style="text-align: left;"><a href="https://docs.google.com/document/d/1Q7UmxY572OGOiRCSNQdZjdnlnWxZpyZrYl45YSyGGBw/edit?usp=sharing">This Tic Tac Toe board</a> offers students opportunities to explain their understanding of systems of equations. How might you use something like this in distance learning?</h4><div><br /></div>
<iframe src="https://docs.google.com/document/d/e/2PACX-1vQ0r2S_71yYCIrEA-behXu_ilFibndIctUr8mKWYdTXHmIrhp65INqbJHtGudQv5n9Y4J1Hxu9G-zXJ/pub?embedded=true" width="512"></iframe><div style="text-align: center;"><br /></div><h4 style="text-align: left;"><span style="font-weight: 400; text-align: center;">-------------------</span></h4><h4 style="text-align: left;"><a href="https://drive.google.com/file/d/1aXCF5rSrI9R63c-GrC4joDL7w3ngnOOb/view?usp=sharing">My Analysis Task</a> asks students to complete several activities to demonstrate mastery of systems of equations:</h4><div><br /></div>
<iframe height="480" src="https://drive.google.com/file/d/1aXCF5rSrI9R63c-GrC4joDL7w3ngnOOb/preview" width="512"></iframe><div style="text-align: center;"><br /></div><h4 style="text-align: left;"><span style="font-weight: 400; text-align: center;">-------------------</span></h4><h4 style="text-align: left;">Last ... if you like using <a href="https://drive.google.com/file/d/0B-1saJM8fLPgeXVIR3pfWWZ3Ymc/view?usp=sharing">"Always, sometimes, never" statements,</a> here are a set of 10!</h4><div><br /></div>
<iframe height="480" src="https://drive.google.com/file/d/0B-1saJM8fLPgeXVIR3pfWWZ3Ymc/preview" width="512"></iframe>Algebra's Friendhttp://www.blogger.com/profile/04729315514507170702noreply@blogger.com1tag:blogger.com,1999:blog-8399389267815059112.post-88747278782508299502020-08-07T07:00:00.002-05:002020-08-07T07:00:00.304-05:00More Data Collection Ideas ... Old and NEW<br /><div class="separator" style="clear: both;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEglIVriNTisYIF_psynG4lYedq02Bqh3P099wRhlvmxA1F7gfrJeqhxtizJ1WxWbWSyNqQt2nY3kqRIBaNDV74b8gZ7WuGjXNj_MyFOxrcgC2la6roCnNDFEC84ZbRyiIgG3uRN51xF6Q/s512/Blaugust2020.png" imageanchor="1" style="display: block; padding: 1em 0px;"><img border="0" data-original-height="182" data-original-width="512" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEglIVriNTisYIF_psynG4lYedq02Bqh3P099wRhlvmxA1F7gfrJeqhxtizJ1WxWbWSyNqQt2nY3kqRIBaNDV74b8gZ7WuGjXNj_MyFOxrcgC2la6roCnNDFEC84ZbRyiIgG3uRN51xF6Q/s0/Blaugust2020.png" /></a>Data Collection Activities are great for introducing functions. I wonder if you were teaching remotely, how it might work to collect and analyze data? I wonder if students were given time to assemble the supplies and collect data at home, if then you could analyze it together online?<br /><h3 style="text-align: left;">A couple of ideas new to me</h3></div><div class="separator" style="clear: both;"><a href="https://www.eupschools.org/cms/lib/MI17000134/Centricity/Domain/29/allExperiments.pdf">M & M's, Balloons, Cups and More </a> is a pdf of several activities published several years ago by NCTM. This is a series of six different activities where students collect data, graph the data points, determine which family of functions it belongs to and find an equation for the data. The functions include linear, quadratic, and exponential.</div><div class="separator" style="clear: both;"><br /></div><div class="separator" style="clear: both;">By the way, I found that activity on this site, <a href="https://www.eupschools.org/Page/1530">Mathematics - Algebra for All</a>. There are a number of great activities linked there. Definitely a place to bookmark!</div><br /><a href="https://uen.instructure.com/courses/314069/files/70596584/download?verifier=7L4Ym8KnsuIGrZXPkM9oUnco2ERY9FJ1SFlqI2sl&wrap=1">Walk the Plank</a> - When one end of a wooden board is placed on a bathroom scale and the other end is suspended on a textbook, students can "walk the plank" and record the weight measurement as their distance from the scale changes. The results are unexpected— the relationship between the weight and distance is linear, and all lines have the same x‑intercept. This investigation leads to a real world occurrence of negative slope, examples of which are often hard to find.<div><br /></div><div>And from a previous post ... <br /><br /></div><div><h3 style="background-color: white; font-family: arial, tahoma, helvetica, freesans, sans-serif; margin: 0px; position: relative;"><span face="" style="font-family: arial, helvetica, sans-serif;">Linear (and Quadratic) Function: Pass the Ball</span></h3>All the information needed for this activity is <a href="http://algebrasfriend.blogspot.com/2014/07/70days-day-1-fast-approaching.html">in this blog post.</a> Students pass a ball to one person, timing the event. Then to two people, three people, etc. This is a very easy lab to set up.<div><br /></div><div>Another activity is<a href="https://themathlab.com/Algebra/linear%20functions%20regressions%20slope/regression%20lessons/day1.htm" target="_blank"> the message/whisper chain</a>. Students will enjoy this lab!</div><div><a href="https://drive.google.com/drive/folders/1BA1Xc1KmNoyxsUSnkHOPhHHFgcs2yJC-" target="_blank">The Wave Lab</a> is also a great introductory lab suitable for linear functions!</div><div><a href="https://drive.google.com/drive/folders/1BA1Xc1KmNoyxsUSnkHOPhHHFgcs2yJC-" target="_blank">Pass the Book</a> is similar to the previous two!</div><div><br /></div><div>If you teach Algebra 2 and want to review both linear and quadratic functions in a single activity ... consider this <a href="https://drive.google.com/open?id=1Sw-Vh9NQI2wvlqpDl6YBwqq7TiHHMteO" target="_blank">looking through a tube idea!</a><br /><h3 style="background-color: white; font-family: arial, tahoma, helvetica, freesans, sans-serif; margin: 0px; position: relative;"><span face="" style="font-family: arial, helvetica, sans-serif;"><br /></span></h3><div><span face="" style="font-family: arial, helvetica, sans-serif;"><br /></span></div><h3 style="background-color: white; font-family: arial, tahoma, helvetica, freesans, sans-serif; margin: 0px; position: relative;"><span face="" style="font-family: arial, helvetica, sans-serif;">Quadratic Function: Stacking Starbursts and Kangaroo Conundrum</span></h3>Both of these activities are simple, table top activities that result in quadratic patterns. I provide instructions <a href="http://algebrasfriend.blogspot.com/2013/11/unit-planning-characteristics-of.html">in this blog post.</a><div><br /></div><div><a href="https://docs.google.com/document/d/1pdQ8QJLncgSaAb0EsjyDASmPd7CQC_Gj5ysj1ZbFaOg/edit" target="_blank">The Water Flow Lab</a> looks fascinating ... </div><div>And EVERYONE loves a catapult! Check out<a href="https://courtneyelmendorf.weebly.com/hands-on-activity.html" target="_blank"> this data collection </a>opportunity!<br /><h3 style="background-color: white; font-family: arial, tahoma, helvetica, freesans, sans-serif; margin: 0px; position: relative;"><span face="" style="font-family: arial, helvetica, sans-serif;"><br /></span></h3><div><span face="" style="font-family: arial, helvetica, sans-serif;"><br /></span></div><h3 style="background-color: white; font-family: arial, tahoma, helvetica, freesans, sans-serif; margin: 0px; position: relative;"><span face="" style="font-family: arial, helvetica, sans-serif;">Square Root Functions: Inclined Plane Data Collection</span></h3>A copy of the instructions <a href="https://drive.google.com/file/d/0B-1saJM8fLPgZzJsc2FHbVprems/edit">can be found here</a>. Students roll a marble on an inclined plane - varying the distance of the roll, and measuring the time it takes to reach 0.</div><div><br /></div><div>You can <a href="http://www.txar.org/training/materials/Algebra_II/09MAPSquareRootFunctionsStudentLesson3-19-07.pdf" target="_blank">model the movement of a metronome here using a bottle and spring</a>!</div><div><br /></div><div>Here's <a href="https://afmmath.files.wordpress.com/2015/02/pendulum-lab-key.pdf" target="_blank">another version of a pendulum lab</a>!</div><div><br /></div><div><a href="http://phet.colorado.edu/sims/pendulum-lab/pendulum-lab_en.html" target="_blank">PhET has a pendulum virtual lab </a>worth investigating if you don't have materials!<br /><h3 style="background-color: white; font-family: arial, tahoma, helvetica, freesans, sans-serif; margin: 0px; position: relative;"><span face="" style="font-family: arial, helvetica, sans-serif;"><br /></span></h3><div><span face="" style="font-family: arial, helvetica, sans-serif;"><br /></span></div><h3 style="background-color: white; font-family: arial, tahoma, helvetica, freesans, sans-serif; margin: 0px; position: relative;"><span face="" style="font-family: arial, helvetica, sans-serif;">Exponential Functions: M 'n M Data Collection</span></h3>This is popular for obvious reasons - students love to eat the m 'n ms after the experiment is complete. We do both parts ... exponential growth and decay. The handouts with instructions can be found <a href="https://drive.google.com/file/d/0ByJ71RI_wBc7aHZraDJoZXBPdzQ/view">here</a> and <a href="https://drive.google.com/file/d/0ByJ71RI_wBc7akJoTmdxNlMyTlk/view">here</a>.</div><div><br /></div><div><a href="http://lhsblogs.typepad.com/files/exponential-growth-lab---paper-folding.pdf" target="_blank">Paper folding </a>also works for exponential functions ... and requires little preparation or materials!</div><div><br /></div><div>Mathy Cathy explains how she uses <a href="http://www.mathycathy.com/blog/2015/12/exponential-growth-similarity-and-a-partridge/" target="_blank">the Sierpinski Triangle </a>to model exponential functions!<br /><br /><br /><h3 style="background-color: white; font-family: arial, tahoma, helvetica, freesans, sans-serif; margin: 0px; position: relative;">Rational Functions: Spaghetti Cantilevers</h3><div style="background-color: white; font-family: arial, tahoma, helvetica, freesans, sans-serif; font-size: 13px;">Instructions <a href="http://www.txar.org/training/materials/Algebra_II/11MAPRationalsStudentLesson02.19.2007.pdf" style="color: #9e4433; text-decoration-line: none;" target="_blank">are online.</a> Students bundle 2, 3, 4, 5, 6 pieces of spaghetti and hang a weight from the end without breaking the spaghetti. They collect the data and analyze it. The rational function is the model for the cantilever. </div><br /><h3>MORE IDEAS!</h3>Several labs are shared in <a href="http://s3.amazonaws.com/conference-handouts/2017-nctm-san-antonio/pdfs/1538-2111.pdf" target="_blank">this conference handout!</a><br /><div><br /></div><div>Also check out <a href="https://twitter.com/mathequalslove/status/1103766297421193216?s=20" target="_blank">this Twitter thread </a>where folks shared ideas for labs!</div></div></div></div><div><br /></div>Algebra's Friendhttp://www.blogger.com/profile/04729315514507170702noreply@blogger.com1