{"id":2154,"date":"2022-05-25T07:00:00","date_gmt":"2022-05-25T12:00:00","guid":{"rendered":"https:\/\/mathisvisual.com\/?p=2154"},"modified":"2022-05-23T13:43:59","modified_gmt":"2022-05-23T18:43:59","slug":"growing-geometric-patterns","status":"publish","type":"post","link":"https:\/\/mathisvisual.com\/growing-geometric-patterns\/","title":{"rendered":"Growing Geometric Patterns"},"content":{"rendered":"\r\n<p><iframe loading=\"lazy\" title=\"Visual Patterns | Number Talk &amp; Practice Worksheet\" width=\"1104\" height=\"621\" src=\"https:\/\/www.youtube.com\/embed\/yGRP9mA8WEk?wmode=transparent&amp;rel=0&amp;feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/p>\r\n<h2><b>In This Set of Visual Number Talk Prompts\u2026<\/b><\/h2>\r\n<p><span style=\"font-weight: 400;\">Students will extend growing linear visual patterns, make near and far predictions and describe visual patterns in words.\u00a0<\/span><\/p>\r\n<h2><b>Intentionality\u2026<\/b><\/h2>\r\n<p><span style=\"font-weight: 400;\">Students will engage in a visual number talk using geometric patterns to develop a deeper understanding of the following big ideas.\u00a0<\/span><\/p>\r\n<ul>\r\n<li><span style=\"font-weight: 400;\">Patterns can be extended because they are repetitive by nature.<\/span><\/li>\r\n<li><span style=\"font-weight: 400;\">Pattern rules are generalizations about a pattern, and they can be described in words.<\/span><\/li>\r\n<li><span style=\"font-weight: 400;\">A pattern can be extended to make a prediction.\u00a0<\/span><\/li>\r\n<li><span style=\"font-weight: 400;\">For far predictions, calculations are required for efficiency.\u00a0<\/span><\/li>\r\n<li><span style=\"font-weight: 400;\">In a growing pattern, the values increase.<\/span><\/li>\r\n<li><span style=\"font-weight: 400;\">In a linear pattern, the values increase at the same rate.<\/span><\/li>\r\n<li><span style=\"font-weight: 400;\">Graphical representations of linear growing patterns appear as straight lines.<\/span><\/li>\r\n<\/ul>\r\n<h2>String of Related Problems<\/h2>\r\n<p><span style=\"font-weight: 400;\">Present the following visual patterns through the visual number talk prompt videos below. Leverage the day one context of an animal hoarding nuts, seeds or fruit in preparation for the winter. For each pattern, ask students to describe the pattern rule in words and predict the value of the 14th day and 21st day. Students are encouraged to justify their thinking and educators are encouraged to facilitate this visual number talk by modelling student thinking using the mathematical model that will help give others a window into that thinking.<\/span><\/p>\r\n<p><span style=\"font-weight: 400;\">While the <\/span><b><i>array model <\/i><\/b><span style=\"font-weight: 400;\">or <\/span><b><i>area model <\/i><\/b><span style=\"font-weight: 400;\">would best suit the visual patterns shared and therefore we want to be intentional about seeking ways to best emerge the use of this model, be sure to acknowledge other models that students may have used including linear or symbolic models.\u00a0<\/span><\/p>\r\n<p><span style=\"font-weight: 400;\">Look for opportunities to build efficiency. For example, rather than counting on or repeated addition, can students use partial products through scaling in the table? For example, the 14th term in the first pattern is the same as the fifth term, multiplied by two, plus the 4th term.\u00a0 Or see the multiplicative relationship between the term number and the term value?\u00a0<\/span><b>Facilitator note<\/b><span style=\"font-weight: 400;\">: The pattern rule can be described two ways. For example, start at 3, add three each time. Or multiply the term number (in this context, the day) by three (the <\/span><b><i>rate<\/i><\/b><span style=\"font-weight: 400;\">). <\/span><\/p>\r\n<h2><b>Visual Number Talk Prompt<\/b><\/h2>\r\n<p><span style=\"font-weight: 400;\">Student prompt:<\/span><\/p>\r\n<p style=\"padding-left: 40px;\"><b><i>Use manipulatives or draw what you think might come next.<\/i><\/b><\/p>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-2157 size-large\" src=\"https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-02-Visual-Math-Talk-Prompt-Image001-1024x576.jpeg\" alt=\"Growing Geometric Pattern - Proportional Relationship\" width=\"1024\" height=\"576\" srcset=\"https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-02-Visual-Math-Talk-Prompt-Image001-1024x576.jpeg 1024w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-02-Visual-Math-Talk-Prompt-Image001-300x169.jpeg 300w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-02-Visual-Math-Talk-Prompt-Image001-768x432.jpeg 768w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-02-Visual-Math-Talk-Prompt-Image001-1536x864.jpeg 1536w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-02-Visual-Math-Talk-Prompt-Image001-1104x621.jpeg 1104w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-02-Visual-Math-Talk-Prompt-Image001-366x205.jpeg 366w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-02-Visual-Math-Talk-Prompt-Image001-534x300.jpeg 534w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-02-Visual-Math-Talk-Prompt-Image001-165x92.jpeg 165w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-02-Visual-Math-Talk-Prompt-Image001-249x140.jpeg 249w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-02-Visual-Math-Talk-Prompt-Image001-232x130.jpeg 232w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-02-Visual-Math-Talk-Prompt-Image001-344x193.jpeg 344w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-02-Visual-Math-Talk-Prompt-Image001-533x300.jpeg 533w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-02-Visual-Math-Talk-Prompt-Image001-405x228.jpeg 405w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-02-Visual-Math-Talk-Prompt-Image001-139x78.jpeg 139w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-02-Visual-Math-Talk-Prompt-Image001.jpeg 1920w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/p>\r\n<p><span style=\"font-weight: 400;\">At this point, it is important for students to understand that there is really no way to <\/span><b><i>guarantee <\/i><\/b><span style=\"font-weight: 400;\">what will come next because we do not have enough information yet. Here are some of the predictions students might make and some possible reasoning:<\/span><\/p>\r\n<ul>\r\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">9 acorns because the pattern is growing by 3 acorns per day;<\/span><\/li>\r\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">12 acorns because the pattern is doubling each day.<\/span><\/li>\r\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">3 acorns because the pattern is repeating; and,<\/span><\/li>\r\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Other possibilities.<\/span><\/li>\r\n<\/ul>\r\n<p><span style=\"font-weight: 400;\">Next, show students the number of acorns in total on day 3 and ask them to make another prediction for how many acorns there will be on day 4.<\/span><\/p>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-2158 size-large\" src=\"https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-03-Visual-Math-Talk-Prompt-Image002-1024x576.jpeg\" alt=\"Growing Geometric Pattern - Proportional Relationship\" width=\"1024\" height=\"576\" srcset=\"https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-03-Visual-Math-Talk-Prompt-Image002-1024x576.jpeg 1024w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-03-Visual-Math-Talk-Prompt-Image002-300x169.jpeg 300w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-03-Visual-Math-Talk-Prompt-Image002-768x432.jpeg 768w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-03-Visual-Math-Talk-Prompt-Image002-1536x864.jpeg 1536w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-03-Visual-Math-Talk-Prompt-Image002-1104x621.jpeg 1104w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-03-Visual-Math-Talk-Prompt-Image002-366x205.jpeg 366w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-03-Visual-Math-Talk-Prompt-Image002-534x300.jpeg 534w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-03-Visual-Math-Talk-Prompt-Image002-165x92.jpeg 165w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-03-Visual-Math-Talk-Prompt-Image002-249x140.jpeg 249w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-03-Visual-Math-Talk-Prompt-Image002-232x130.jpeg 232w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-03-Visual-Math-Talk-Prompt-Image002-344x193.jpeg 344w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-03-Visual-Math-Talk-Prompt-Image002-533x300.jpeg 533w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-03-Visual-Math-Talk-Prompt-Image002-405x228.jpeg 405w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-03-Visual-Math-Talk-Prompt-Image002-139x78.jpeg 139w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-03-Visual-Math-Talk-Prompt-Image002.jpeg 1920w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/p>\r\n<p><span style=\"font-weight: 400;\">You may notice that more and more students update their predictions to a pattern increasing by 3 acorns per day (a rate of 3 acorns\/day).<\/span><\/p>\r\n<p><span style=\"font-weight: 400;\">Once we share how many acorns were collected over the first four days, we can ask students:<\/span><\/p>\r\n<p style=\"padding-left: 40px;\"><b><i>Assuming this pattern continues, describe the pattern rule in words to your neighbour<\/i><\/b><span style=\"font-weight: 400;\">.<\/span><\/p>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-2159 size-large\" src=\"https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-04-Visual-Math-Talk-Prompt-Image003-1024x576.jpeg\" alt=\"Growing Geometric Pattern - Proportional Relationship\" width=\"1024\" height=\"576\" srcset=\"https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-04-Visual-Math-Talk-Prompt-Image003-1024x576.jpeg 1024w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-04-Visual-Math-Talk-Prompt-Image003-300x169.jpeg 300w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-04-Visual-Math-Talk-Prompt-Image003-768x432.jpeg 768w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-04-Visual-Math-Talk-Prompt-Image003-1536x864.jpeg 1536w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-04-Visual-Math-Talk-Prompt-Image003-1104x621.jpeg 1104w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-04-Visual-Math-Talk-Prompt-Image003-366x205.jpeg 366w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-04-Visual-Math-Talk-Prompt-Image003-534x300.jpeg 534w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-04-Visual-Math-Talk-Prompt-Image003-165x92.jpeg 165w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-04-Visual-Math-Talk-Prompt-Image003-249x140.jpeg 249w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-04-Visual-Math-Talk-Prompt-Image003-232x130.jpeg 232w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-04-Visual-Math-Talk-Prompt-Image003-344x193.jpeg 344w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-04-Visual-Math-Talk-Prompt-Image003-533x300.jpeg 533w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-04-Visual-Math-Talk-Prompt-Image003-405x228.jpeg 405w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-04-Visual-Math-Talk-Prompt-Image003-139x78.jpeg 139w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-04-Visual-Math-Talk-Prompt-Image003.jpeg 1920w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/p>\r\n<p><span style=\"font-weight: 400;\">As students continue discussing how they might describe the pattern rule, you can extend this prompt to:<\/span><\/p>\r\n<p style=\"padding-left: 40px;\"><b><i>Describe what day 14 and what day 21 will look like.<\/i><\/b><\/p>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-2160 size-large\" src=\"https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-05-Visual-Math-Talk-Prompt-Image004-1024x576.jpeg\" alt=\"Growing Geometric Pattern - Proportional Relationship\" width=\"1024\" height=\"576\" srcset=\"https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-05-Visual-Math-Talk-Prompt-Image004-1024x576.jpeg 1024w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-05-Visual-Math-Talk-Prompt-Image004-300x169.jpeg 300w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-05-Visual-Math-Talk-Prompt-Image004-768x432.jpeg 768w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-05-Visual-Math-Talk-Prompt-Image004-1536x864.jpeg 1536w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-05-Visual-Math-Talk-Prompt-Image004-1104x621.jpeg 1104w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-05-Visual-Math-Talk-Prompt-Image004-366x205.jpeg 366w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-05-Visual-Math-Talk-Prompt-Image004-534x300.jpeg 534w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-05-Visual-Math-Talk-Prompt-Image004-165x92.jpeg 165w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-05-Visual-Math-Talk-Prompt-Image004-249x140.jpeg 249w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-05-Visual-Math-Talk-Prompt-Image004-232x130.jpeg 232w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-05-Visual-Math-Talk-Prompt-Image004-344x193.jpeg 344w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-05-Visual-Math-Talk-Prompt-Image004-533x300.jpeg 533w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-05-Visual-Math-Talk-Prompt-Image004-405x228.jpeg 405w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-05-Visual-Math-Talk-Prompt-Image004-139x78.jpeg 139w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-05-Visual-Math-Talk-Prompt-Image004.jpeg 1920w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/p>\r\n<p><span style=\"font-weight: 400;\">Articulate to students that the purpose of a pattern rule is to help someone easily understand how a pattern changes from day to day (or stage to stage, or figure to figure). In the case of a geometric pattern (or visual pattern), it is also helpful to describe how the <\/span><a href=\"https:\/\/www.visualpatterns.org\"><span style=\"font-weight: 400;\">visual pattern<\/span><\/a><span style=\"font-weight: 400;\"> is growing without necessarily being able to \u201csee\u201d the pattern with their own eyes.<\/span><\/p>\r\n<p><span style=\"font-weight: 400;\">Some students might be able to articulate that day 14 should be a long 3 acorn by 14 acorn rectangle.\u00a0<\/span><\/p>\r\n<p><span style=\"font-weight: 400;\">Since we promote students <\/span><b><i>building number fluency and flexibility<\/i><\/b><span style=\"font-weight: 400;\"> each and every day, this is an excellent opportunity for them to apply the multiplication strategy of partial products which leverages the distributive property to decompose the factor of 14 into smaller parts.<\/span><\/p>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-2162 size-large\" src=\"https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-06-Visual-Math-Talk-Prompt-Image005-1024x576.jpeg\" alt=\"Growing Geometric Pattern - Proportional Relationship\" width=\"1024\" height=\"576\" srcset=\"https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-06-Visual-Math-Talk-Prompt-Image005-1024x576.jpeg 1024w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-06-Visual-Math-Talk-Prompt-Image005-300x169.jpeg 300w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-06-Visual-Math-Talk-Prompt-Image005-768x432.jpeg 768w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-06-Visual-Math-Talk-Prompt-Image005-1536x864.jpeg 1536w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-06-Visual-Math-Talk-Prompt-Image005-1104x621.jpeg 1104w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-06-Visual-Math-Talk-Prompt-Image005-366x205.jpeg 366w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-06-Visual-Math-Talk-Prompt-Image005-534x300.jpeg 534w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-06-Visual-Math-Talk-Prompt-Image005-165x92.jpeg 165w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-06-Visual-Math-Talk-Prompt-Image005-249x140.jpeg 249w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-06-Visual-Math-Talk-Prompt-Image005-232x130.jpeg 232w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-06-Visual-Math-Talk-Prompt-Image005-344x193.jpeg 344w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-06-Visual-Math-Talk-Prompt-Image005-533x300.jpeg 533w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-06-Visual-Math-Talk-Prompt-Image005-405x228.jpeg 405w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-06-Visual-Math-Talk-Prompt-Image005-139x78.jpeg 139w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-06-Visual-Math-Talk-Prompt-Image005.jpeg 1920w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/p>\r\n<p><span style=\"font-weight: 400;\">Above, you can see that this particular example shows 14 acorns decomposed into parts of 10 and 4 which ultimately produces the following equivalent expression:<\/span><\/p>\r\n<p style=\"padding-left: 40px;\"><b><i>3(10 + 4)<\/i><\/b><\/p>\r\n<p><span style=\"font-weight: 400;\">Not only does this promote an opportunity for students to multiply without a calculator to build fluency and flexibility with multiplication, but it also allows us to revisit order of operations and how blindly following the rules can actually create more work for us at times.\u00a0<\/span><\/p>\r\n<p><span style=\"font-weight: 400;\">For example, if we simplify what is \u201cinside the <\/span><b>B<\/b><span style=\"font-weight: 400;\">rackets\u201d (or <\/span><b>P<\/b><span style=\"font-weight: 400;\">arentheses) as BEDMAS (or PEDMAS) would require, we would actually be doing ourselves a disservice.<\/span><\/p>\r\n<p><span style=\"font-weight: 400;\">Here, we know that 3 groups of 10 acorns is 30 acorns and 3 groups of 4 acorns is 12 acorns, resulting in 42 acorns total.\u00a0<\/span><\/p>\r\n<p><span style=\"font-weight: 400;\">Of course, students are not limited to the <\/span><b><i>distributive property <\/i><\/b><span style=\"font-weight: 400;\">here and are more than welcome to leverage other multiplication strategies such as doubling and halving or other strategies that feel helpful.\u00a0<\/span><\/p>\r\n<p><span style=\"font-weight: 400;\">The description of day 21 is similar to that of day 14 and students might leverage similar or different multiplication strategies to yield their total number of acorns.<\/span><\/p>\r\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-2163 size-large\" src=\"https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-07-Visual-Math-Talk-Prompt-Image006-1024x576.jpeg\" alt=\"Growing Geometric Pattern - Proportional Relationship\" width=\"1024\" height=\"576\" srcset=\"https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-07-Visual-Math-Talk-Prompt-Image006-1024x576.jpeg 1024w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-07-Visual-Math-Talk-Prompt-Image006-300x169.jpeg 300w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-07-Visual-Math-Talk-Prompt-Image006-768x432.jpeg 768w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-07-Visual-Math-Talk-Prompt-Image006-1536x864.jpeg 1536w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-07-Visual-Math-Talk-Prompt-Image006-1104x621.jpeg 1104w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-07-Visual-Math-Talk-Prompt-Image006-366x205.jpeg 366w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-07-Visual-Math-Talk-Prompt-Image006-534x300.jpeg 534w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-07-Visual-Math-Talk-Prompt-Image006-165x92.jpeg 165w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-07-Visual-Math-Talk-Prompt-Image006-249x140.jpeg 249w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-07-Visual-Math-Talk-Prompt-Image006-232x130.jpeg 232w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-07-Visual-Math-Talk-Prompt-Image006-344x193.jpeg 344w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-07-Visual-Math-Talk-Prompt-Image006-533x300.jpeg 533w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-07-Visual-Math-Talk-Prompt-Image006-405x228.jpeg 405w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-07-Visual-Math-Talk-Prompt-Image006-139x78.jpeg 139w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2022\/05\/Acorn-Hoarding-Day-2-Purposeful-Practice-07-Visual-Math-Talk-Prompt-Image006.jpeg 1920w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/p>\r\n<h2>\u00a0<\/h2>\r\n<h2>Want to Explore These Concepts &amp; Skills Further?<\/h2>\r\n<p><b><i>Two (2) additional number talk prompts are available<\/i><\/b><span style=\"font-weight: 400;\"> in <\/span><a href=\"https:\/\/learn.makemathmoments.com\/task\/acorn-hoarding-day2\"><span style=\"font-weight: 400;\">Day 2<\/span><\/a><span style=\"font-weight: 400;\"> of the <\/span><a href=\"https:\/\/learn.makemathmoments.com\/task\/acorn-hoarding\"><span style=\"font-weight: 400;\">Acorn Hoarding problem based math unit<\/span><\/a><span style=\"font-weight: 400;\"> that you can dive into now.\u00a0<\/span><\/p>\r\n<p><span style=\"font-weight: 400;\">Why not start from the beginning of this contextual 5-day unit of <\/span><a href=\"https:\/\/learn.makemathmoments.com\/tasks\"><span style=\"font-weight: 400;\">real world lessons<\/span><\/a><span style=\"font-weight: 400;\"> from the Make Math Moments Problem Based Units page.<\/span><\/p>\r\n<p><span style=\"font-weight: 400;\">Did you use this in your classroom or at home? How\u2019d it go? Post in the comments!<\/span><\/p>\r\n<p><b>Math IS Visual. Let\u2019s teach it that way.<\/b><\/p>","protected":false},"excerpt":{"rendered":"<p>Visual Number Talk Prompts emerging Growing Proportional Geometric Patterns where students will describe pattern rules and make predictions.<\/p>\n","protected":false},"author":1,"featured_media":2170,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[68,23],"tags":[50,61,51,52,53,32,33,34],"series":[54,94,95],"class_list":["post-2154","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-algebra","category-number","tag-grade-2","tag-grade-3","tag-grade-4","tag-grade-5","tag-grade-6","tag-grade-7","tag-grade-8","tag-grade-9","series-number-talk","series-patterning","series-proportional-relationships"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.1.1 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Growing Proportional Geometric Patterns | 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