{"id":1219,"date":"2021-05-01T09:00:00","date_gmt":"2021-05-01T09:00:00","guid":{"rendered":"https:\/\/www.terc.edu\/adultnumeracycenter\/?p=1219"},"modified":"2021-04-15T19:38:26","modified_gmt":"2021-04-15T19:38:26","slug":"will-this-be-on-the-test-may-2021","status":"publish","type":"post","link":"https:\/\/www.terc.edu\/adultnumeracycenter\/will-this-be-on-the-test-may-2021\/","title":{"rendered":"Will This Be on the Test? (May 2021)"},"content":{"rendered":"\n

by Sarah Lonberg-Lew<\/p>\n\n\n\n

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Welcome to the latest installment of our monthly series, \u201cWill This Be on the Test?\u201d Each month, we\u2019ll feature a new question similar to something adult learners might see on a high school equivalency test and a discussion of how one might go about tackling the problem conceptually.<\/em><\/p>\n\n\n\n

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In the April 2021 WTBotT blog, I talked about how the data domain encompasses many different kinds of reasoning \u2013 number sense, proportional reasoning, and even geometry! This month let\u2019s look at a question from geometry that might come up in a data context. Here is Dericia\u2019s sales graph again, this time with a geometry question:<\/p>\n\n\n\n

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Before you read further, allow yourself to bring your full mathematical reasoning power to bear on this challenge. How many strategies can you think of? What visuals could you use to help you solve this? Also ask yourself, what skills and understandings do students really<\/em> need to be able to answer this?<\/h5>\n\n\n\n

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Also, here\u2019s something to consider before we get into some problem-solving strategies: why do you think one of the answer choices is 20\u00b0? Why might a student pick that answer? It could be partly because of the way the student has been taught. There are a lot of topics to learn in math class, and they are often in isolation and without context. For students with limited conceptual understanding of how math topics and operations relate to each other, it is easy to mix up the rules and symbols. Even a student who can give an answer as a percent when doing a unit on percents and in degrees when doing a unit on angles may mix up the two when they are presented so close together in a high-pressure situation. A student who has not developed confidence in their own ability to make sense of problems and persevere in solving them will likely pounce on the incorrect answer option (a)<\/strong>, thinking that if the pie chart piece is 20%, the angle must be 20\u00b0.<\/p>\n\n\n\n

Now, here are some possible approaches one could use to reason to the correct answer:<\/p>\n\n\n\n

1. Estimate!<\/strong> Building familiarity with the sizes of angles, especially by connecting them to things students know in the real world, will prepare students well to eliminate unreasonable answers without the need to do any calculation. A student who can eyeball a 90\u00b0 angle can quickly assess that the angle for the mugs section is less than 90\u00b0 but not a lot less. How much less? That\u2019s hard to tell, but since 72\u00b0 and 80\u00b0 are the only choices that can reasonably be described as a little less than 90\u00b0, the choices are cut down to just two options very quickly \u2013 a win in a testing situation!<\/p>\n\n\n\n

2. Measure!<\/strong> Even though students can\u2019t use protractors during the test and this question is likely on a computer screen, that doesn\u2019t mean that they can\u2019t still use measuring tools! A quick angle-measuring tool can be made by ripping off one corner of a piece of scrap paper. Using this tool will quickly show how the angle in the problem compares to the 90\u00b0 of the paper corner. As a bonus, folding the corner in half makes a handy 45\u00b0 reference, too.<\/p>\n\n\n\n

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Tearing off the corner of a piece of paper makes a handy reference for 90\u00b0. Folding it in half makes 45<\/em>\u00b0.<\/figcaption><\/figure><\/div>\n\n\n\n

While I\u2019m not suggesting that you teach this to your students as a \u201ctrick\u201d, it is reminder that teachers can connect angles to the real world by linking them to things students already know. This can build understanding and prepare them for the test at the same time. Connecting angles to real objects may help students avoid the trap of confusing the percentage in the section with the measure of the angle.<\/p>\n\n\n\n

3. Guess-and-check.<\/strong> A nice follow-up to estimating, whether by eye or with a hand-made reference, is to use a guess-and-check strategy to narrow down those two remaining choices to one correct one. A student might reason like this, adding on groups of 20% until they get to 100%:<\/p>\n\n\n\n

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There are other ways to check these guesses. A shorter way would be to multiply each by five because 20% x 5 = 100%. The important thing is that students can bring their knowledge and understandings to bear in a variety of ways.<\/p>\n\n\n\n

4. Reason proportionally!<\/strong> Did you notice that the guess-and-check strategy was another example of proportional reasoning? Proportional reasoning shows up in so many contexts. Teaching it richly and deeply prepares students to use it flexibly in the many contexts in which it arises, both on the test and in their lives. Here are two more proportional reasoning approaches a student could take for this task:<\/p>\n\n\n\n