Q&A #16541

fractions and decimals related to number sense

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From: Gail (for Teacher2Teacher Service)
Date: Jan 21, 2006 at 13:33:56
Subject: Re: fractions and decimals related to number sense

>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 

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

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