{"id":1585,"date":"2021-07-02T19:38:35","date_gmt":"2021-07-03T00:38:35","guid":{"rendered":"https:\/\/mathisvisual.com\/?p=1585"},"modified":"2021-07-23T20:28:15","modified_gmt":"2021-07-24T01:28:15","slug":"revealing-rates","status":"publish","type":"post","link":"https:\/\/mathisvisual.com\/revealing-rates\/","title":{"rendered":"Revealing Rates Through Partitive Division"},"content":{"rendered":"\r\n<p>&nbsp;<\/p>\r\n\r\n<p><iframe loading=\"lazy\" title=\"How To Reveal a Rate From a Ratio Through Partitive Division | Visual Math Talk [SILENT SOLUTION]\" width=\"1104\" height=\"621\" src=\"https:\/\/www.youtube.com\/embed\/3qAjS94phhQ?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<p>&nbsp;<\/p>\r\n<h2>In This Set of Math Visual Prompts\u2026<\/h2>\r\n<p>Students will explore equivalent ratios and reveal rates through partitive division.<\/p>\r\n<h2>Intentionality\u2026<\/h2>\r\n<p><span style=\"font-weight: 400;\">This set of visual math talk prompts is taken from the Math Talk section of Day 2 in the Make Math Moments Problem Based Unit called <\/span><a href=\"https:\/\/learn.makemathmoments.com\/task\/planting-flowers\"><span style=\"font-weight: 400;\">Planting Flowers<\/span><\/a><span style=\"font-weight: 400;\">. The purpose of the Math Talk is to reinforce key concepts and big ideas from the first day of this problem based math unit including:\u00a0<\/span><\/p>\r\n<ul>\r\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">There are two types of ratios; composed unit and multiplicative comparison;<\/span><\/li>\r\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">A composed unit is often (not always) a ratio with two distinct units;\u00a0<\/span><\/li>\r\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">A composed unit can be scaled in tandem;\u00a0<\/span><\/li>\r\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Equivalent ratios are derived from the same rate;\u00a0<\/span><\/li>\r\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">When you divide a composed unit through partitive division, you reveal a rate.<\/span><\/li>\r\n<\/ul>\r\n<p><span style=\"font-weight: 400;\">This set of visual math talk prompts, we will explicitly emerge two strategies for revealing a rate from a ratio: through <strong>partitive division via fair sharing<\/strong> and through <strong>scaling in tandem on a double number line<\/strong>.<\/span><\/p>\r\n<h2>Preparing to Facilitate<\/h2>\r\n<p><span style=\"font-weight: 400;\">Present the following composed unit ratios one at a time. Create a context to define the units for each ratio. Focus on ratios with two distinct units at this time. Ask students to determine and justify one or more equivalent ratios for each composed unit. Equivalent ratios can be revealed by scaling the composed unit up or down. For each ratio, reveal the rate by leveraging partitive division.\u00a0<\/span><\/p>\r\n<p style=\"text-align: center;\"><b><i>8 : 4<\/i><\/b><\/p>\r\n<p style=\"text-align: center;\"><b><i>14 : 2<\/i><\/b><\/p>\r\n<p style=\"text-align: center;\"><b><i>27 : 3<\/i><\/b><\/p>\r\n<p style=\"text-align: center;\"><b><i>32 : 8\u00a0<\/i><\/b><\/p>\r\n<p style=\"text-align: center;\"><b><i>6 : 4\u00a0<\/i><\/b><\/p>\r\n<p><span style=\"font-weight: 400;\">As you\u2019ll notice with this set of animated Math Visual Prompts, we begin by introducing a composed unit ratio of 8 apples to 4 baskets which provides an extremely low floor for students to access and enter the problem.<\/span><\/p>\r\n<p><a href=\"https:\/\/learn.makemathmoments.com\/task\/planting-flowers\" target=\"_blank\" rel=\"noopener\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1610 size-full aligncenter\" src=\"https:\/\/mathisvisual.com\/wp-content\/uploads\/2021\/07\/Planting-Flowers-Day-2-02-Dividing-Ratios-to-Reveal-a-Rate-8-apples-to-4-baskets.jpeg\" alt=\"Planting Flowers [Day 2] - 02 - Dividing Ratios to Reveal a Rate 8 apples to 4 baskets\" width=\"1920\" height=\"1080\" srcset=\"https:\/\/mathisvisual.com\/wp-content\/uploads\/2021\/07\/Planting-Flowers-Day-2-02-Dividing-Ratios-to-Reveal-a-Rate-8-apples-to-4-baskets.jpeg 1920w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2021\/07\/Planting-Flowers-Day-2-02-Dividing-Ratios-to-Reveal-a-Rate-8-apples-to-4-baskets-300x169.jpeg 300w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2021\/07\/Planting-Flowers-Day-2-02-Dividing-Ratios-to-Reveal-a-Rate-8-apples-to-4-baskets-1024x576.jpeg 1024w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2021\/07\/Planting-Flowers-Day-2-02-Dividing-Ratios-to-Reveal-a-Rate-8-apples-to-4-baskets-768x432.jpeg 768w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2021\/07\/Planting-Flowers-Day-2-02-Dividing-Ratios-to-Reveal-a-Rate-8-apples-to-4-baskets-1536x864.jpeg 1536w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2021\/07\/Planting-Flowers-Day-2-02-Dividing-Ratios-to-Reveal-a-Rate-8-apples-to-4-baskets-1104x621.jpeg 1104w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2021\/07\/Planting-Flowers-Day-2-02-Dividing-Ratios-to-Reveal-a-Rate-8-apples-to-4-baskets-366x205.jpeg 366w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2021\/07\/Planting-Flowers-Day-2-02-Dividing-Ratios-to-Reveal-a-Rate-8-apples-to-4-baskets-534x300.jpeg 534w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2021\/07\/Planting-Flowers-Day-2-02-Dividing-Ratios-to-Reveal-a-Rate-8-apples-to-4-baskets-165x92.jpeg 165w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2021\/07\/Planting-Flowers-Day-2-02-Dividing-Ratios-to-Reveal-a-Rate-8-apples-to-4-baskets-249x140.jpeg 249w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2021\/07\/Planting-Flowers-Day-2-02-Dividing-Ratios-to-Reveal-a-Rate-8-apples-to-4-baskets-232x130.jpeg 232w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2021\/07\/Planting-Flowers-Day-2-02-Dividing-Ratios-to-Reveal-a-Rate-8-apples-to-4-baskets-344x193.jpeg 344w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2021\/07\/Planting-Flowers-Day-2-02-Dividing-Ratios-to-Reveal-a-Rate-8-apples-to-4-baskets-533x300.jpeg 533w\" sizes=\"auto, (max-width: 1920px) 100vw, 1920px\" \/><\/a><\/p>\r\n<p><span style=\"font-weight: 400;\">It will almost seem obvious to many students that the 8:4 ratio they are given of apples to baskets is equivalent to 2:1.\u00a0<\/span><\/p>\r\n<p><a href=\"https:\/\/learn.makemathmoments.com\/task\/planting-flowers\" target=\"_blank\" rel=\"noopener\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1611 size-full\" src=\"https:\/\/mathisvisual.com\/wp-content\/uploads\/2021\/07\/Planting-Flowers-Day-2-03-Dividing-Ratios-to-Reveal-a-Rate-2-apples-to-1-baskets.jpeg\" alt=\"Planting Flowers [Day 2] - 03 - Dividing Ratios to Reveal a Rate 2 apples to 1 baskets\" width=\"1920\" height=\"1080\" srcset=\"https:\/\/mathisvisual.com\/wp-content\/uploads\/2021\/07\/Planting-Flowers-Day-2-03-Dividing-Ratios-to-Reveal-a-Rate-2-apples-to-1-baskets.jpeg 1920w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2021\/07\/Planting-Flowers-Day-2-03-Dividing-Ratios-to-Reveal-a-Rate-2-apples-to-1-baskets-300x169.jpeg 300w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2021\/07\/Planting-Flowers-Day-2-03-Dividing-Ratios-to-Reveal-a-Rate-2-apples-to-1-baskets-1024x576.jpeg 1024w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2021\/07\/Planting-Flowers-Day-2-03-Dividing-Ratios-to-Reveal-a-Rate-2-apples-to-1-baskets-768x432.jpeg 768w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2021\/07\/Planting-Flowers-Day-2-03-Dividing-Ratios-to-Reveal-a-Rate-2-apples-to-1-baskets-1536x864.jpeg 1536w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2021\/07\/Planting-Flowers-Day-2-03-Dividing-Ratios-to-Reveal-a-Rate-2-apples-to-1-baskets-1104x621.jpeg 1104w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2021\/07\/Planting-Flowers-Day-2-03-Dividing-Ratios-to-Reveal-a-Rate-2-apples-to-1-baskets-366x205.jpeg 366w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2021\/07\/Planting-Flowers-Day-2-03-Dividing-Ratios-to-Reveal-a-Rate-2-apples-to-1-baskets-534x300.jpeg 534w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2021\/07\/Planting-Flowers-Day-2-03-Dividing-Ratios-to-Reveal-a-Rate-2-apples-to-1-baskets-165x92.jpeg 165w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2021\/07\/Planting-Flowers-Day-2-03-Dividing-Ratios-to-Reveal-a-Rate-2-apples-to-1-baskets-249x140.jpeg 249w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2021\/07\/Planting-Flowers-Day-2-03-Dividing-Ratios-to-Reveal-a-Rate-2-apples-to-1-baskets-232x130.jpeg 232w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2021\/07\/Planting-Flowers-Day-2-03-Dividing-Ratios-to-Reveal-a-Rate-2-apples-to-1-baskets-344x193.jpeg 344w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2021\/07\/Planting-Flowers-Day-2-03-Dividing-Ratios-to-Reveal-a-Rate-2-apples-to-1-baskets-533x300.jpeg 533w\" sizes=\"auto, (max-width: 1920px) 100vw, 1920px\" \/><\/a><\/p>\r\n<p><span style=\"font-weight: 400;\">What students (and many educators) may not realize, is that while we have scaled this composed unit ratio from 8:4 down to 2:1 by \u201cfourthing\u201d the ratio, we can also quickly reveal a rate of 2 apples per basket through partitive division.\u00a0<\/span><\/p>\r\n<p><a href=\"https:\/\/learn.makemathmoments.com\/task\/planting-flowers\" target=\"_blank\" rel=\"noopener\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1612 size-full\" src=\"https:\/\/mathisvisual.com\/wp-content\/uploads\/2021\/07\/Planting-Flowers-Day-2-04-Dividing-Ratios-to-Reveal-a-Rate-double-number-line.jpeg\" alt=\"Planting Flowers [Day 2] - 04 - Dividing Ratios to Reveal a Rate double number line\" width=\"1920\" height=\"1080\" srcset=\"https:\/\/mathisvisual.com\/wp-content\/uploads\/2021\/07\/Planting-Flowers-Day-2-04-Dividing-Ratios-to-Reveal-a-Rate-double-number-line.jpeg 1920w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2021\/07\/Planting-Flowers-Day-2-04-Dividing-Ratios-to-Reveal-a-Rate-double-number-line-300x169.jpeg 300w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2021\/07\/Planting-Flowers-Day-2-04-Dividing-Ratios-to-Reveal-a-Rate-double-number-line-1024x576.jpeg 1024w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2021\/07\/Planting-Flowers-Day-2-04-Dividing-Ratios-to-Reveal-a-Rate-double-number-line-768x432.jpeg 768w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2021\/07\/Planting-Flowers-Day-2-04-Dividing-Ratios-to-Reveal-a-Rate-double-number-line-1536x864.jpeg 1536w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2021\/07\/Planting-Flowers-Day-2-04-Dividing-Ratios-to-Reveal-a-Rate-double-number-line-1104x621.jpeg 1104w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2021\/07\/Planting-Flowers-Day-2-04-Dividing-Ratios-to-Reveal-a-Rate-double-number-line-366x205.jpeg 366w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2021\/07\/Planting-Flowers-Day-2-04-Dividing-Ratios-to-Reveal-a-Rate-double-number-line-534x300.jpeg 534w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2021\/07\/Planting-Flowers-Day-2-04-Dividing-Ratios-to-Reveal-a-Rate-double-number-line-165x92.jpeg 165w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2021\/07\/Planting-Flowers-Day-2-04-Dividing-Ratios-to-Reveal-a-Rate-double-number-line-249x140.jpeg 249w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2021\/07\/Planting-Flowers-Day-2-04-Dividing-Ratios-to-Reveal-a-Rate-double-number-line-232x130.jpeg 232w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2021\/07\/Planting-Flowers-Day-2-04-Dividing-Ratios-to-Reveal-a-Rate-double-number-line-344x193.jpeg 344w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2021\/07\/Planting-Flowers-Day-2-04-Dividing-Ratios-to-Reveal-a-Rate-double-number-line-533x300.jpeg 533w\" sizes=\"auto, (max-width: 1920px) 100vw, 1920px\" \/><\/a><\/p>\r\n<p><span style=\"font-weight: 400;\">The goal here is to give students an opportunity to work with ratios using their intuition. Also we aim to help them realize that while we can scale any ratio up or down to find an infinite number of equivalent ratios, scaling to a unit ratio provides access to reveal a rate through partitive division (without really having to divide at all).\u00a0<\/span><\/p>\r\n<p><span style=\"font-weight: 400;\">We also emerge the double number line as a <\/span><b><i>tool<\/i><\/b> <b><i>for thinking<\/i><\/b><span style=\"font-weight: 400;\"> as well as a <\/span><b><i>tool to represent thinking<\/i><\/b><span style=\"font-weight: 400;\">.\u00a0<\/span><\/p>\r\n<p><span style=\"font-weight: 400;\">Although there are five (5) ratios to work through in this animated Math Visual Prompt sets where we use partitive division via fair sharing (distributing apples equally to each basket) as well as through scaling in tandem on the double number line, be sure to dive into the final ratio where we reveal a fractional rate of apples per basket.<\/span><\/p>\r\n<p><a href=\"https:\/\/learn.makemathmoments.com\/task\/planting-flowers\" target=\"_blank\" rel=\"noopener\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1613 size-full\" src=\"https:\/\/mathisvisual.com\/wp-content\/uploads\/2021\/07\/Planting-Flowers-Day-2-02-Ratio-5-Revealing-a-Rate-6-apples-to-4-baskets.jpeg\" alt=\"Planting Flowers [Day 2] - 02 - Ratio 5 Revealing a Rate 6 apples to 4 baskets\" width=\"1920\" height=\"1080\" srcset=\"https:\/\/mathisvisual.com\/wp-content\/uploads\/2021\/07\/Planting-Flowers-Day-2-02-Ratio-5-Revealing-a-Rate-6-apples-to-4-baskets.jpeg 1920w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2021\/07\/Planting-Flowers-Day-2-02-Ratio-5-Revealing-a-Rate-6-apples-to-4-baskets-300x169.jpeg 300w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2021\/07\/Planting-Flowers-Day-2-02-Ratio-5-Revealing-a-Rate-6-apples-to-4-baskets-1024x576.jpeg 1024w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2021\/07\/Planting-Flowers-Day-2-02-Ratio-5-Revealing-a-Rate-6-apples-to-4-baskets-768x432.jpeg 768w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2021\/07\/Planting-Flowers-Day-2-02-Ratio-5-Revealing-a-Rate-6-apples-to-4-baskets-1536x864.jpeg 1536w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2021\/07\/Planting-Flowers-Day-2-02-Ratio-5-Revealing-a-Rate-6-apples-to-4-baskets-1104x621.jpeg 1104w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2021\/07\/Planting-Flowers-Day-2-02-Ratio-5-Revealing-a-Rate-6-apples-to-4-baskets-366x205.jpeg 366w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2021\/07\/Planting-Flowers-Day-2-02-Ratio-5-Revealing-a-Rate-6-apples-to-4-baskets-534x300.jpeg 534w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2021\/07\/Planting-Flowers-Day-2-02-Ratio-5-Revealing-a-Rate-6-apples-to-4-baskets-165x92.jpeg 165w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2021\/07\/Planting-Flowers-Day-2-02-Ratio-5-Revealing-a-Rate-6-apples-to-4-baskets-249x140.jpeg 249w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2021\/07\/Planting-Flowers-Day-2-02-Ratio-5-Revealing-a-Rate-6-apples-to-4-baskets-232x130.jpeg 232w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2021\/07\/Planting-Flowers-Day-2-02-Ratio-5-Revealing-a-Rate-6-apples-to-4-baskets-344x193.jpeg 344w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2021\/07\/Planting-Flowers-Day-2-02-Ratio-5-Revealing-a-Rate-6-apples-to-4-baskets-533x300.jpeg 533w\" sizes=\"auto, (max-width: 1920px) 100vw, 1920px\" \/><\/a><\/p>\r\n<p><span style=\"font-weight: 400;\">Through partitive division and the fair sharing strategy, you can quickly see that each basket will receive 1 and 1 half apples, revealing a rate of 1 \u00bd apples per basket:<\/span><\/p>\r\n<p><a href=\"https:\/\/learn.makemathmoments.com\/task\/planting-flowers\" target=\"_blank\" rel=\"noopener\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1614 size-full\" src=\"https:\/\/mathisvisual.com\/wp-content\/uploads\/2021\/07\/Planting-Flowers-Day-2-03-Ratio-5-Revealing-a-Rate-1-and-a-half-apples-to-1-baskets.jpeg\" alt=\"Planting Flowers [Day 2] - 03 - Ratio 5 Revealing a Rate 1 and a half apples to 1 baskets\" width=\"1920\" height=\"1080\" srcset=\"https:\/\/mathisvisual.com\/wp-content\/uploads\/2021\/07\/Planting-Flowers-Day-2-03-Ratio-5-Revealing-a-Rate-1-and-a-half-apples-to-1-baskets.jpeg 1920w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2021\/07\/Planting-Flowers-Day-2-03-Ratio-5-Revealing-a-Rate-1-and-a-half-apples-to-1-baskets-300x169.jpeg 300w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2021\/07\/Planting-Flowers-Day-2-03-Ratio-5-Revealing-a-Rate-1-and-a-half-apples-to-1-baskets-1024x576.jpeg 1024w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2021\/07\/Planting-Flowers-Day-2-03-Ratio-5-Revealing-a-Rate-1-and-a-half-apples-to-1-baskets-768x432.jpeg 768w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2021\/07\/Planting-Flowers-Day-2-03-Ratio-5-Revealing-a-Rate-1-and-a-half-apples-to-1-baskets-1536x864.jpeg 1536w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2021\/07\/Planting-Flowers-Day-2-03-Ratio-5-Revealing-a-Rate-1-and-a-half-apples-to-1-baskets-1104x621.jpeg 1104w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2021\/07\/Planting-Flowers-Day-2-03-Ratio-5-Revealing-a-Rate-1-and-a-half-apples-to-1-baskets-366x205.jpeg 366w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2021\/07\/Planting-Flowers-Day-2-03-Ratio-5-Revealing-a-Rate-1-and-a-half-apples-to-1-baskets-534x300.jpeg 534w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2021\/07\/Planting-Flowers-Day-2-03-Ratio-5-Revealing-a-Rate-1-and-a-half-apples-to-1-baskets-165x92.jpeg 165w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2021\/07\/Planting-Flowers-Day-2-03-Ratio-5-Revealing-a-Rate-1-and-a-half-apples-to-1-baskets-249x140.jpeg 249w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2021\/07\/Planting-Flowers-Day-2-03-Ratio-5-Revealing-a-Rate-1-and-a-half-apples-to-1-baskets-232x130.jpeg 232w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2021\/07\/Planting-Flowers-Day-2-03-Ratio-5-Revealing-a-Rate-1-and-a-half-apples-to-1-baskets-344x193.jpeg 344w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2021\/07\/Planting-Flowers-Day-2-03-Ratio-5-Revealing-a-Rate-1-and-a-half-apples-to-1-baskets-533x300.jpeg 533w\" sizes=\"auto, (max-width: 1920px) 100vw, 1920px\" \/><\/a><\/p>\r\n<p><span style=\"font-weight: 400;\">Scaling in tandem by halving twice (or \u201cfourthing\u201d) reveals an equivalent ratio of 1.5:1 apples to baskets:<\/span><\/p>\r\n<p><a href=\"https:\/\/learn.makemathmoments.com\/task\/planting-flowers\" target=\"_blank\" rel=\"noopener\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1615 size-full\" src=\"https:\/\/mathisvisual.com\/wp-content\/uploads\/2021\/07\/Planting-Flowers-Day-2-04-Ratio-5-Revealing-a-Rate-1-and-a-half-apples-to-1-baskets-double-number-line.jpeg\" alt=\"Planting Flowers [Day 2] - 04 - Ratio 5 Revealing a Rate 1 and a half apples to 1 baskets double number line\" width=\"1920\" height=\"1080\" srcset=\"https:\/\/mathisvisual.com\/wp-content\/uploads\/2021\/07\/Planting-Flowers-Day-2-04-Ratio-5-Revealing-a-Rate-1-and-a-half-apples-to-1-baskets-double-number-line.jpeg 1920w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2021\/07\/Planting-Flowers-Day-2-04-Ratio-5-Revealing-a-Rate-1-and-a-half-apples-to-1-baskets-double-number-line-300x169.jpeg 300w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2021\/07\/Planting-Flowers-Day-2-04-Ratio-5-Revealing-a-Rate-1-and-a-half-apples-to-1-baskets-double-number-line-1024x576.jpeg 1024w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2021\/07\/Planting-Flowers-Day-2-04-Ratio-5-Revealing-a-Rate-1-and-a-half-apples-to-1-baskets-double-number-line-768x432.jpeg 768w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2021\/07\/Planting-Flowers-Day-2-04-Ratio-5-Revealing-a-Rate-1-and-a-half-apples-to-1-baskets-double-number-line-1536x864.jpeg 1536w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2021\/07\/Planting-Flowers-Day-2-04-Ratio-5-Revealing-a-Rate-1-and-a-half-apples-to-1-baskets-double-number-line-1104x621.jpeg 1104w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2021\/07\/Planting-Flowers-Day-2-04-Ratio-5-Revealing-a-Rate-1-and-a-half-apples-to-1-baskets-double-number-line-366x205.jpeg 366w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2021\/07\/Planting-Flowers-Day-2-04-Ratio-5-Revealing-a-Rate-1-and-a-half-apples-to-1-baskets-double-number-line-534x300.jpeg 534w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2021\/07\/Planting-Flowers-Day-2-04-Ratio-5-Revealing-a-Rate-1-and-a-half-apples-to-1-baskets-double-number-line-165x92.jpeg 165w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2021\/07\/Planting-Flowers-Day-2-04-Ratio-5-Revealing-a-Rate-1-and-a-half-apples-to-1-baskets-double-number-line-249x140.jpeg 249w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2021\/07\/Planting-Flowers-Day-2-04-Ratio-5-Revealing-a-Rate-1-and-a-half-apples-to-1-baskets-double-number-line-232x130.jpeg 232w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2021\/07\/Planting-Flowers-Day-2-04-Ratio-5-Revealing-a-Rate-1-and-a-half-apples-to-1-baskets-double-number-line-344x193.jpeg 344w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2021\/07\/Planting-Flowers-Day-2-04-Ratio-5-Revealing-a-Rate-1-and-a-half-apples-to-1-baskets-double-number-line-533x300.jpeg 533w\" sizes=\"auto, (max-width: 1920px) 100vw, 1920px\" \/><\/a><\/p>\r\n<p><span style=\"font-weight: 400;\">Note that the model you are intentionally emerging from this set of Math Visual Prompts is a double bar model and\/or a double number line.<\/span><\/p>\r\n<p><b>Facilitator Note<\/b><span style=\"font-weight: 400;\">: <\/span><\/p>\r\n<p><span style=\"font-weight: 400;\">From each of these ratios, two rates can be derived. For example 8 apples : 4 baskets, the two rates can be revealed through partitive division:<\/span><\/p>\r\n<p style=\"text-align: center;\"><b><i>8 apples \u00f7 4 baskets = 2 apples\/basket\u00a0<\/i><\/b><\/p>\r\n<p style=\"text-align: center;\"><span style=\"font-weight: 400;\">and<\/span><\/p>\r\n<p style=\"text-align: center;\"><b><i>4 baskets \u00f7 8 apples = \u00bd basket\/apple.\u00a0<\/i><\/b><\/p>\r\n<p><span style=\"font-weight: 400;\">You can learn more about rates, ratios and the roadmap to proportional relationships through the course: <\/span><a href=\"https:\/\/learn.makemathmoments.com\/courses\/the-concept-holding-your-students-back\/\"><span style=\"font-weight: 400;\">The Concept Holding Your Students Back.<\/span><\/a><\/p>\r\n<h2>While Students Are Working&#8230;<\/h2>\r\n<p><span style=\"font-weight: 400;\">Pay close attention to the strategies that students are using.\u00a0<\/span><\/p>\r\n<p><span style=\"font-weight: 400;\">Are students:\u00a0<\/span><\/p>\r\n<ul>\r\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Using concrete materials to fair share?<\/span><\/li>\r\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Using a concrete or visual array?<\/span><\/li>\r\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Partitioning or scaling a bar model?\u00a0<\/span><\/li>\r\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Using a double number line?<\/span><\/li>\r\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Using a ratio table?<\/span><\/li>\r\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Counting on?<\/span><\/li>\r\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Repeated addition?<\/span><\/li>\r\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Multiplicative thinking?\u00a0<\/span><\/li>\r\n<\/ul>\r\n<p><span style=\"font-weight: 400;\">Document this thinking and use this data to help you determine which students you might consider strategically pulling individually or in small groups to offer guided instruction in order to move them along their developmental continuum.<\/span><\/p>\r\n<h2>Want to Explore These Concepts &amp; Skills Further?<\/h2>\r\n<p><span style=\"font-weight: 400;\">The full 5-day unit of <\/span><a href=\"https:\/\/learn.makemathmoments.com\/task\/planting-flowers\"><span style=\"font-weight: 400;\">ratios and rates real world lessons<\/span><\/a><span style=\"font-weight: 400;\"> can be accessed on 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>Build fluency and flexibility with composed unit ratios and rates revealed through partitive division with these Math Is Visual Prompts.<\/p>\n","protected":false},"author":1,"featured_media":1609,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"video","meta":{"footnotes":""},"categories":[23],"tags":[61,51,52,53,32,33,34],"series":[38,54,83],"class_list":["post-1585","post","type-post","status-publish","format-video","has-post-thumbnail","hentry","category-number","tag-grade-3","tag-grade-4","tag-grade-5","tag-grade-6","tag-grade-7","tag-grade-8","tag-grade-9","post_format-post-format-video","series-division","series-number-talk","series-ratios-and-rates"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Revealing Rates Through Partitive Division - Ratio and Rates<\/title>\n<meta name=\"description\" content=\"Build fluency and flexibility with composed unit ratios and rates revealed through partitive division with these Math Is Visual Prompts.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathisvisual.com\/revealing-rates\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Revealing Rates Through Partitive Division - 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