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	<title>problem-solving Archives - Shelley Gray</title>
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	<title>problem-solving Archives - Shelley Gray</title>
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		<title>Tackle Problem-Solving, Logical Reasoning, and Critical Thinking With These Fun Activities!</title>
		<link>https://shelleygrayteaching.com/logic-problems/</link>
					<comments>https://shelleygrayteaching.com/logic-problems/#comments</comments>
		
		<dc:creator><![CDATA[Shelley Gray]]></dc:creator>
		<pubDate>Sun, 22 Jan 2023 23:32:07 +0000</pubDate>
				<category><![CDATA[Logic and Problem Solving]]></category>
		<category><![CDATA[Math]]></category>
		<category><![CDATA[logic problems]]></category>
		<category><![CDATA[problem-solving]]></category>
		<guid isPermaLink="false">https://shelleygrayteaching.com/?p=13462</guid>

					<description><![CDATA[<p>When you think of problem-solving, logical reasoning, and critical thinking, do you visualize boring worksheets that students moan and groan about? Well, let&#8217;s put a stop to that! Logic problems are an engaging and interactive way to incorporate these essential skills into the math classroom, resulting in increased motivation and interest. They are also an effective [&#8230;]</p>
<p>The post <a href="https://shelleygrayteaching.com/logic-problems/">Tackle Problem-Solving, Logical Reasoning, and Critical Thinking With These Fun Activities!</a> appeared first on <a href="https://shelleygrayteaching.com">Shelley Gray</a>.</p>
]]></description>
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									<p>When you think of problem-solving, logical reasoning, and critical thinking, do you visualize boring worksheets that students moan and groan about? Well, let&#8217;s put a stop to that! <strong>Logic problems</strong> are an engaging and interactive way to incorporate these essential skills into the math classroom, resulting in increased motivation and interest. They are also an effective way to introduce algebraic thinking and help students develop the skills necessary for success in algebra in later grades. Too often the work that we give students consists of surface level thinking, where they simply regurgitate answers. But logic problems can provide a new type of challenge and encourage them to think in a much deeper way.</p>								</div>
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					<h2 class="elementor-heading-title elementor-size-default">How to Complete a Logic Problem Puzzle</h2>				</div>
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									<p>To complete the puzzle, students will quickly catch on that they must begin with symbols that they KNOW for certain. For example, in the puzzle below, we begin with solving for the gumball machines, since we know that 5+5=10. Now that we know the gumball machine equals 5, we can solve the second row. The heart equals 10, since 10+5=15. Lastly, we can solve the bottom row. Since we know the heart equals 10, we can conclude that the lollipop must be 6.</p>								</div>
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															<img fetchpriority="high" decoding="async" width="1024" height="576" src="https://shelleygrayteaching.com/wp-content/uploads/2023/01/2-1024x576.png" class="attachment-large size-large wp-image-13465" alt="" srcset="https://shelleygrayteaching.com/wp-content/uploads/2023/01/2-1024x576.png 1024w, https://shelleygrayteaching.com/wp-content/uploads/2023/01/2-300x169.png 300w, https://shelleygrayteaching.com/wp-content/uploads/2023/01/2-768x432.png 768w, https://shelleygrayteaching.com/wp-content/uploads/2023/01/2-1536x864.png 1536w, https://shelleygrayteaching.com/wp-content/uploads/2023/01/2-800x450.png 800w, https://shelleygrayteaching.com/wp-content/uploads/2023/01/2.png 1920w" sizes="(max-width: 1024px) 100vw, 1024px" />															</div>
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					<h2 class="elementor-heading-title elementor-size-default">Trickier Than They Seem</h2>				</div>
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									<p>Although the example above seems simple, it is not always easy for kids to think in this way, particularly once the puzzles get more difficult. <span style="color: var( --e-global-color-text ); font-family: var( --e-global-typography-text-font-family ), Sans-serif; font-weight: var( --e-global-typography-text-font-weight );">When deciding which puzzles to use with your students, remember that if they are not used to doing activities that involve logical reasoning, they will very likely find them challenging. Your grade 3-4 students might be sufficiently challenged with the numbers to 20 puzzles, even though they work with numbers in the thousands in other math activities. </span></p><p><span style="color: var( --e-global-color-text ); font-family: var( --e-global-typography-text-font-family ), Sans-serif; font-weight: var( --e-global-typography-text-font-weight );">I recommend making several levels of puzzles available to your students and allowing them to choose the ones that challenge their brains “just enough.” I typically find that students are eager to work to their full potential and will generally choose the ones that are best suited to their abilities.</span></p>								</div>
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					<h2 class="elementor-heading-title elementor-size-default">Ideas for Use</h2>				</div>
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									<p>There are many ways you can store and use these puzzles in your classroom:</p><ul><li>Use at one of your math centers. Place the logic puzzles in the center of the table, and have students choose whichever ones they want to complete. To add differentiation, allow your students to choose between different sets of logic puzzles.</li><li>Store on a ring or in a folder and use an early finisher activity.</li><li>Post the puzzles around the room and use them for an <a href="https://shelleygrayteaching.com/using-gallery-walks-in-classroom/" target="_blank" rel="noopener">&#8220;Around the Room&#8221; gallery walk activity</a>. Have students circulate around the room, completing puzzles as they go! *Pro-tip: Give each student a clipboard if you have them available.</li><li>Use them as partner work. You will LOVE the amazing mathematical conversation that will occur as students talk about what each picture represents.</li></ul><div>Personally, I prefer to print these in color and laminate each card, but you may also wish to simply make black and white booklets for your students to keep inside their math folders.</div>								</div>
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									<p>If you&#8217;d like to try these puzzles in your classroom, but aren&#8217;t sure which set will work best, I&#8217;ve made a free sample available for you. T<span style="color: var( --e-global-color-text ); font-family: var( --e-global-typography-text-font-family ), Sans-serif; font-weight: var( --e-global-typography-text-font-weight );">ake them to your classroom and see how students respond before committing to purchasing an entire package or the full multi-grade bundle. In the free sample, you’ll receive one puzzle from each package . Download your free sample below!</span><span style="color: var( --e-global-color-text ); font-family: var( --e-global-typography-text-font-family ), Sans-serif; font-weight: var( --e-global-typography-text-font-weight ); font-size: 28px;"> </span></p><p> </p>								</div>
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									<p>If you are ready to use these puzzles in your classroom, I&#8217;ve included the links to the individual packages below. Each package of Logic Problems comes with 20 puzzles. Simply laminate, cut, and make copies of the recording sheets and you’ve got one of your math centers taken care of! </p><div> </div>								</div>
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									<span class="elementor-button-text">Or see the individual Logic Problem packages here.</span>
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		<p>The post <a href="https://shelleygrayteaching.com/logic-problems/">Tackle Problem-Solving, Logical Reasoning, and Critical Thinking With These Fun Activities!</a> appeared first on <a href="https://shelleygrayteaching.com">Shelley Gray</a>.</p>
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		<title>Making My Own Three-Act Task: What I Learned and Why You Should Try It</title>
		<link>https://shelleygrayteaching.com/making-my-own-three-act-task-what-i-learned-and-why-you-should-try-it/</link>
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		<dc:creator><![CDATA[Shelley Gray]]></dc:creator>
		<pubDate>Thu, 27 Jan 2022 19:13:05 +0000</pubDate>
				<category><![CDATA[Daily Math Routines]]></category>
		<category><![CDATA[Guest Post]]></category>
		<category><![CDATA[Math]]></category>
		<category><![CDATA[Dan Meyer]]></category>
		<category><![CDATA[problem-solving]]></category>
		<category><![CDATA[three-act tasks]]></category>
		<guid isPermaLink="false">https://shelleygrayteaching.com/?p=11964</guid>

					<description><![CDATA[<p>A three-act task is a whole group problem-solving activity, presented in three “acts” to engage and immerse students in authentic and meaningful math learning. Three-act tasks encourage curiosity, perseverance, and growth mindset (&#8220;We can do hard things!&#8221;). And even better &#8211; they are fun!   The Hero&#8217;s Journey My Hero’s Journey Begins As it turns [&#8230;]</p>
<p>The post <a href="https://shelleygrayteaching.com/making-my-own-three-act-task-what-i-learned-and-why-you-should-try-it/">Making My Own Three-Act Task: What I Learned and Why You Should Try It</a> appeared first on <a href="https://shelleygrayteaching.com">Shelley Gray</a>.</p>
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									<p><em><span style="font-weight: 400;">A three-act task is a whole group problem-solving activity, presented in three “acts” to engage and immerse students in authentic and meaningful math learning. Three-act tasks encourage curiosity, perseverance, and growth mindset (&#8220;We can do hard things!&#8221;). And even better &#8211; they are fun!</span></em></p><hr /><h2> </h2><h2>The Hero&#8217;s Journey</h2><p><b>My Hero’s Journey Begins</b></p><p><span style="font-weight: 400;">As it turns out, and as the literary lovers out there probably know, the Hero’s Journey is a mono-myth template developed by Joseph Campbell (Matthew Winkler on TEDEd summarizes it well </span><a href="https://www.youtube.com/watch?v=Hhk4N9A0oCA"><span style="font-weight: 400;">here</span></a><span style="font-weight: 400;">). What I need you to know is: it will also save your math lessons. </span></p><p><span style="font-weight: 400;">This past September I started a new gig that changed my life. I had been a full-time educator for seven years prior and, especially with the past couple of COVID years, “teaching” for me had started to become synonymous with “draining.” I kid you not I was digging deep and doing the work to make a career swap… and then I found my current school. Though I’m not technically a teacher anymore, I am still very much an educator. It’s just that now the learners call me a Guide. </span></p><p><em><span style="font-weight: 400;">So what exactly does a Guide do that is different from a teacher? </span></em></p><p><span style="font-weight: 400;">You may have heard of these expressions before, the “sage on the stage” or “meddler in the middle” &#8211; well, I am the “guide on the side.” Each refers back to various learning theories and tries to define the educator’s role in the classroom. The semantics might not seem like much, but for me, moving through the roles of traditional teacher to even a reformed meddler does not nearly compare to the dynamic power shift that occurs quite dramatically as a Guide. And if I’m being perfectly honest, I’m failing at this all the time because it requires that I step back from the learners and let them truly lead. And when things don’t work for the learners, I am supposed to step back some more. <strong>Failure is the goal</strong> because it will be their greatest teacher (not me). They are on a journey together as a community, and as a Guide, so am I. </span></p><p><b>The Call To Adventure!</b></p><p><span style="font-weight: 400;">In between considering leaving teaching and still teaching, I had been wanting to expand my approach to math education in particular. When I came across the practice of <strong>Three Act Math Tasks</strong> I was instantly intrigued. They are typically multimedia-driven, with a real-life hook, they capture EVERY learner’s attention and they make math accessible to all learners where they are using the power of intuition. And, cue serendipity, they often follow the Hero’s Journey as a template. When I found out that my new school uses this as the arc for every school year, every sessional quest, right down to the weekly and daily narratives too, I couldn’t help but feel that little spark from the universe that I was on the right path.</span></p><p><span style="font-weight: 400;"> </span></p><p><b>Assistance</b></p><p><span style="font-weight: 400;">Dan Meyer (one wise mentor I discovered on my journey) explains how this refreshing approach helps rectify many “</span><a href="https://www.ted.com/talks/dan_meyer_math_class_needs_a_makeover?language=en#t-122859"><span style="font-weight: 400;">symptoms</span></a><span style="font-weight: 400;">” you’ve likely encountered at some point in teaching mathematics. Though he is coming from a secondary perspective, I find the same applies for primary/junior-aged learners: </span></p><ul><li style="font-weight: 400;" aria-level="1"><span style="font-weight: 400;">They often hesitate to try something new or perceived as hard and,</span></li><li style="font-weight: 400;" aria-level="1"><span style="font-weight: 400;">give up easily, and/or,</span></li><li style="font-weight: 400;" aria-level="1"><span style="font-weight: 400;">don’t seem to truly make meaning of the math, and,</span></li><li style="font-weight: 400;" aria-level="1"><span style="font-weight: 400;">have easily caught on to the notion that “word problems” are the ones we boycott. </span></li></ul><h2>What is a Three-Act Task?</h2><p><span style="font-weight: 400;">So, <strong>what exactly is a Three-Act Task</strong> and how does it work? Simply put, this is a whole group problem-solving activity, presented to learners in three “acts” to engage and immerse them in authentic and meaningful math learning. Let’s dig in!</span></p><p><b>A Tasty Task</b></p><p><span style="font-weight: 400;"><em>Full disclosure:</em> when I was younger I used to eat A LOT of Starburst candies and my friends and I used to fold up and keep the wrappers. I kept them all these moons and finally found a use for them (no, I never did quite make them into origami or a purse).</span></p><p><span style="font-weight: 400;"><strong>ACT I</strong> &#8211; Present a teaser, a short clip, something recognizable from daily life but curious! Everyone can participate because we are bringing thinking down to shared experience and intuition.</span></p>								</div>
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									<p><strong>What do you notice and wonder about my candy wrapper collection? </strong></p><p><em><span style="font-weight: 400;">Side note: I just learned about the real power of the word </span><b>wonder</b><span style="font-weight: 400;"> from queen Brené’s new book where she says that, “wonder fuels our passion for exploration and learning, for curiosity and adventure” (Brown, p. 59, 2021). If the learners have nothing to wonder about, what do we expect them to learn? Furthermore, we might know what we hope they’ll ask about, but putting the power in their hands here is key. Whatever the learners decide they want to understand about your prompt is where we’ll head in Act II &#8211; so <strong>make sure the context is math rich</strong>! Inevitably, the learners ask me: how much candy did you eat, Ms. Mel!?</span></em></p><p><span style="font-weight: 400;"><strong>ACT II</strong> &#8211; Continue by asking what information is missing? This gets some problem-solving going; what information matters and does not matter, what do we keep and what do we toss? The learners, again, drive the sub-steps and are not given them (or even “taught” them) in advance! What mathematical processes would help us determine how many there are? What information is missing or hidden? As they ask questions, provide more information.</span></p><p><span style="font-weight: 400;"><strong>ACT III</strong> &#8211; Similar to the consolidation part in a three-part lesson, bring everyone together to discuss strategies and solutions. Bonus points if you have monitored learner thinking and selected or sequenced the sharing to portray a coherent storyline (another blog post on the</span><a href="https://www.nctm.org/Store/Products/The-5-Practices-in-Practice--Successfully-Orchestrating-Mathematical-Discussion-in-your-Middle-School-Classroom/"><span style="font-weight: 400;"> The 5 Practices</span></a><span style="font-weight: 400;"> soon to come!). Even if you just invite a show and tell style discussion, as Meyer says, “The math serves the conversation, the conversation doesn’t serve the math.” If no one gets to the goal (there are 792 wrappers by the way), the discussions about why not are just as powerful in terms of turning students&#8217; mathematical reasoning on and grounding it in something interesting to them. </span></p>								</div>
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									<h2>My Three-Act Task: What I Learned</h2><p><span style="font-weight: 400;"><em>What Failed:</em> I have used this in a traditional Grade 6 Math classroom and in an alternative multi-age studio, and both times the learners never quite got to the strategies I was hoping they would. I anticipated they would use measurement concepts like area and volume to make precise estimates based on Metric measurements of the container and/or an individual wrapper. While there were accurate estimates and some smaller case arguments, the advanced spatial reasoning wasn’t captured and shared as I had hoped. </span></p><p><span style="font-weight: 400;"><em>What Worked:</em> Everyone participated. Everyone shared an idea. Everyone was excited. Some of us made connections between area and perimeter. Some of us built smaller models. We practiced other important rituals like “say more about that” and asking questions of our peers. Learners had fun in the Math Lab.</span></p><h2><b>A Challenge to You!</b></h2><p><span style="font-weight: 400;">So, next time you’re planning a mathematics activity, I challenge you to try to:</span></p><ul><li style="font-weight: 400;" aria-level="1"><span style="font-weight: 400;">Incorporate real-life multimedia into your problem-solving</span></li><li style="font-weight: 400;" aria-level="1"><span style="font-weight: 400;">Extend the invitation to all learners with a sense of wonder and the three-act template</span></li><li style="font-weight: 400;" aria-level="1"><span style="font-weight: 400;">Let the learners drive the questions</span></li><li style="font-weight: 400;" aria-level="1"><span style="font-weight: 400;">Let them struggle (it is a Hero’s Journey after all!)</span></li></ul><p><span style="font-weight: 400;">If you try it out, let us know how it goes in the comment section below! </span></p><hr /><p><b>Resources</b></p><p><em><strong>For the readers:</strong></em></p><p><span style="font-weight: 400;">From </span><i><span style="font-weight: 400;">Teaching Children Mathematics Volume 24 Number 2 </span></i><span style="font-weight: 400;">(2017) check out the </span><a href="https://drive.google.com/file/d/1VS8KD4JXfqPH70mY67BAKsrxV_xNQ5WT/view"><span style="font-weight: 400;">article</span></a><span style="font-weight: 400;"> “Trying Three-Act Tasks with Primary Students”</span></p><p><em><strong>For the grab and goers: </strong></em></p><p><span style="font-weight: 400;">Explore these banks of free tasks for primary/junior learners:</span></p><p><a href="https://gfletchy.com/3-act-lessons/"><span style="font-weight: 400;">Graham Fletcher</span></a></p><p><a href="https://whenmathhappens.com/3-act-math/"><span style="font-weight: 400;">Dane Ehlert</span></a></p><p><b>References</b></p><p><span style="font-weight: 400;">Brown, B. (2021). </span><i><span style="font-weight: 400;">Atlas of the heart. </span></i><span style="font-weight: 400;">New York. </span></p><p><span style="font-weight: 400;">Meyer, D. (n.d.). </span><i><span style="font-weight: 400;">Math class needs a makeover</span></i><span style="font-weight: 400;">. TED. Retrieved January 23, 2022, from https://www.ted.com/talks/dan_meyer_math_class_needs_a_makeover?language=en#t-122859 </span></p><p><span style="font-weight: 400;">TEDEducation. (2012, December 4). </span><i><span style="font-weight: 400;">What makes a hero? &#8211; Matthew Winkler. YouTube</span></i><span style="font-weight: 400;">. Retrieved January 23, 2022, from https://www.youtube.com/watch?v=Hhk4N9A0oCA</span></p>								</div>
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						FREE MULTIPLICATION ACTIVITIES					</h2>
				
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		<p>The post <a href="https://shelleygrayteaching.com/making-my-own-three-act-task-what-i-learned-and-why-you-should-try-it/">Making My Own Three-Act Task: What I Learned and Why You Should Try It</a> appeared first on <a href="https://shelleygrayteaching.com">Shelley Gray</a>.</p>
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