I have heard an argument made that it\u2019s not worth spending time teaching fractions in adult ed classes. One reason I\u2019ve heard for this is that students are mostly in class to prepare for the test, and they can use a calculator on the test. Isn\u2019t it more sensible and efficient to just spend one class period teaching them how to do fraction operations on a calculator and then moving on to higher level topics? After all, fractions are difficult and frustrating and it seems like you are always reteaching them anyway. Why not take the easy way out?<\/p>\n\n\n\n
Unfortunately, taking the easy way out often doesn\u2019t pay off in the long term \u2013 and in this case, it doesn\u2019t pay off in the short term either. It doesn\u2019t pay off in the long term because students miss out on real learning and sense-making that can help them make sense of the real-world math they will encounter. It doesn\u2019t pay off in the short term because there\u2019s more to solving test questions about fractions than just doing operations. High school equivalency tests are designed to test students\u2019 mathematical reasoning, not their ability to use calculators.<\/p>\n\n\n\n
Here is this month\u2019s challenge. Imagine you are a student who is expert in doing fraction operations on the calculator but that is all you have learned about fractions. Would you be able to figure this out?<\/p>\n\n\n\n
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<\/a><\/figure><\/div>\n\n\n\n<\/figure>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?<\/p>\n<\/div><\/div>\n\n\n\n Here are some possible approaches:<\/p>\n<\/div><\/div>\n\n\n\n 1.Estimate!<\/span><\/strong> The snail has been traveling for The snail is already more than halfway across the garden, so answer choices (a)<\/strong> and (b)<\/strong> don\u2019t make sense because they are less than half. Answer choices (c)<\/strong> and (d)<\/strong> are both more than one, and it doesn\u2019t look like the snail is going to make it past the end of the garden in only more 15 minutes, so those don\u2019t make sense either. That leaves only one possible answer! (What fraction understandings were used here?)<\/p>\n\n\n\n 2.Use a Singapore strip diagram.<\/span><\/strong> A student might start with a bar representing the A student who understands that Filling in the fact that the snail covers one block every 3.Reason<\/span><\/strong> proportionally.<\/strong> <\/span>This task is about something moving at a constant rate. In other words, the distance the snail covers is proportional to the amount of time it has been traveling. A student might reason that 15 minutes is one-third of 45 minutes so the snail would cross an additional third of the distance it had already covered. A student who understands that Did you notice that none of these approaches involved that old standard, \u201cChoose and apply an operation\u201d? Even after building a deep understanding of what is going on in this task, it may not be obvious which fraction operation, if any, is the \u2018right\u2019 one. It turns out that you can<\/em> get the answer to this task using a fraction operation, so a calculator could be helpful to you if<\/em><\/strong> you can figure out which operation makes sense for the situation.<\/p>\n\n\n\n (Psst… want to know which operation it is? You can find the answer by dividing Sarah<\/em> Lonberg-Lew has been teaching and tutoring math in one form or another since college. She has worked with students ranging in age from 7 to 70, but currently focuses on adult basic education and high school equivalency. Sarah\u2019s work with the SABES Mathematics and Adult Numeracy Curriculum & Instruction PD Center<\/a> at AV°ÍÊ¿<\/a> includes developing and facilitating trainings and assisting programs with curriculum development. She is the treasurer for the Adult Numeracy Network<\/a>.<\/em><\/p>\n<\/div><\/div>\n\n\n\n <\/p>\n<\/a><\/figure>\n\n\n\n<\/a><\/figure>\n\n\n\n<\/a><\/figure>\n\n\n\n<\/a><\/figure>\n\n\n\n
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