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>What key questions can I ask students to guide them to overarching >understandings about fractions and decimals as related to number sense? >What concepts do they need to understand at fifth grade regarding >fractions and decimals, please? Dear Charles and Jan, I went to the website for my state department of education, and the website for the National council of teachers of mathematics. Here is what they say about number sense and rational numbers: Because rational numbers play such a critical role in the development of proportional reasoning and advanced mathematical thinking, it is very important that students master them. The study of whole numbers, fractions and decimals in the elementary grades builds the framework for extensions in rational number study in the middle grades. Proportional reasoning is the key to making connections to many middle school topics. It is important that students be able to … work flexibly with fractions, decimals and percents to solve problems compare and order fractions, decimals and percents efficiently and find their approximate locations on a number line develop meanings for percents greater than 100 and less than 1 understand and use ratios and proportions to represent quantitative relationships The ideas I wish my sixth grade students would know coming in the door are that amounts can be represented by different names without changing the amount. For example, “one half” can be represented as a fraction ½, or equivalent fractions like 2/4, 3/6 etc. But it can also be represented by 50%, and the decimal 0.5 (or equivalent decimals like 0.50 etc.) I would like my students to have a mental image for what happens as fractional amounts increase or decrease… in other words, how much of the whole is shaded or present, and how much ISN'T shaded. I would like them to be able to determine where amounts belong on a number line, and to have a rough idea of whether a fraction or decimal was closer to 0, ½ or 1, or if it was greater than 1, without a great deal of consideration – I would like that to be a fairly automatic activity. And I would like them to have a solid foundation of whole number computation (adding, subtracting, multiplying, dividing, factors, multiples) so that I can use what they know to build fraction and decimal computation skills. Of course, these are lofty dreams, and I usually have students who are still developing these understandings in middle school, and we move from where we are to where we need to go. Hope this gives you some place to start. :-) -Gail, for the T2T service Thanks for visiting our on-line community. Visit Teacher2Teacher again at http://mathforum.org/t2t/ It is now possible to make a financial contribution to help The Math Forum. Please read more about this possibility: http://www.drexel.edu/ia/mathforum/.
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