Fractions, Decimals, and Percents

Submitted by Brooke Istas on Tue, 03/15/2022 - 13:22
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I had a discussion with some colleagues today about talking to adult learners about the meaning of fractions.  They shared how they were discussing 5/8 with a student.  They were asking them if it was more or less than a half and also how much more would be needed to make a whole.  This instructor shared how surprised they were that the student didn't understand the question but knew the procedures for mathematical operations.  

I also shared how I recently had an IET student studying to be a machinist who had passed the GED but didn't understand or know how to read a tape measure.

Another colleague found a resource for online teaching on matching, fractions, decimals, and percents: https://nrich.maths.org/1249

What are others experiencing and how are you helping our learners?

Comments

Hi Brooke.

Thanks for the link to the matching game. 

On the same web page I found this link: https://nrich.maths.org/4519

It's called a FRACTION WALL. It shows the whole 1 on the bottom, and then smaller and smaller divisions of 1 as you move up the wall. 

It all goes back to an understanding of = (the equals sign) as a relationship, not an operation. The idea that 2/4 is the same size as 1/2  is a new one for many adult students. 

If people want a more complete idea of what their students need before being able to understand fractions as a relationship, I suggest the 2008 article in Focus on Basics: Using Part-Whole Thinking in Math. When adult learners see fractions as a relationship - as "the parts you care about (numerator) compared to ALL the parts in the whole (denominator)" - then they understand fractions.

Here's the link to the article.

www.ncsall.net/fileadmin/resources/fob/2008/fob_9a.pdf

Dorothea Steinke

(Questions? send a message to my new email:  numberworks.ds@gmail.com)

I often refer folks to that Focus on Basics article ? 

 

I did a little division review lesson with my Tuesday Teens – I see  them once a week for a couple of hours, tho’ not the past two weeks, and we do Reading Plus… and I’ve been springing math things on them, starting with finding area with cheezits, working w/ area and perimeter… and couching it all in terms of finding parts and wholes.  

 

So, we figured out some sides of rectangles knowing the area – finding the part…

 

And I tossed in that we can express division as a fraction, e.g. 40/8    35/5….

 

The last question was “can you think of another way to say 3/1”?   -- nope.   Next session we’re going to experiment with that.   I’m hoping to play with generalizing what happens when you multiply top and bottom by the same thing, but … I also need to make sure the division has meaning.  

Sigh, there was, when the internet was a wee bairn, a cool online "ruler game."  Now it's full of popups and ads and things to download automatically.... I might sniff out things like it though.   

 

OH!   It seems somebody did buy the rights to it ;) The Ruler Game - Learn To Read A RSuler (globalclassroom.org)   see how this rolls!  (LOL it's quarter 'til five here at the library during spring break and ... they've just turned all the lights out, so I'm going to head out! 

I like the Empower Series, particularly Using Benchmarks Fractions and Operations, and Split It Up, More Fractions, Decimals, and Percents. The last time I taught fractions, we started with lots of pictures  such as a dozen eggs, a clock, and various quantities of things. I asked how many was half of each quantity (the whole). Using the above mentioned book, I asked which numbers were more than a half and less than a half. We eventually moved to fractions with the same denominator but different numerators and asked which were more than a half and less than a half. It was exciting when they could recognize more than or less than a half, information that I take for granted. The series moves on to determine half of a half, then 3/4, etc.

Hi All,

As Dorothea suggests, I describe the equals sign as signifying a relationship.  The students in my Adult Basic Education class sometimes do struggle with the idea, for example, that 50% is the same as 1/2 or 0.5.  I present the fact as 50% = 0.5 and explain that 50% is the same as 0.5.  I also use real-world examples.  For instance, we could say that 50% of the cost of a shirt is the same as thinking of the cost of the shirt as a whole ("1") with 50% of the cost being the same as 0.5.   

Thanks,

Jonathan 

.... I was reflecting today that ... my students doing growth rates and probability... if they've had more experience with thinking of wholes and parts the concepts would make so much more sense!!! 

   I did an exercise with my Tuesday Teens with 1 - 1/n      and then different things.... it was very helpful for getting them thinking about things differently. They had their last session and several of them said that well, they knew most of the stuff we were doing BUT had not realized there were differentways to get there, and they did better onthe TABE :) 
     I was even more pleased with when we talked about dividing things by two and multiplying by 1/2  being the same thing and ... that they could divide 82 by two mentally by figuring out half of 80 and half of 2.... place value started making more sense...

The Math and Numeracy held a discussion about Equity in the Mathematics Classroom and the participants spoke about their experiences with Fractions, Decimals, and Percents.  The group talked about bringing in items from the grocery store to help students work with Percents and Decimals, and a few talked about helping adults see how decimals and percents can be represented as a fraction.  A group stated that they teach immigrant populations and it seemed that they had difficulty with these concepts.  So I am curious.  Do other instructors struggle with teaching fractions, decimals, and percents with ELL and if so, do you have any suggestions for other instructors?

 

Hi Brooke,

Thanks for your question.  I don't have any exotic recommendations at this point, but referring students back to explanations of the processes for converting between fractions, decimals, and percents and giving students abundant practice is helpful.  I encourage students to provide answers in any way they can at first, whether that be writing in the chat in Zoom, showing their work on a whiteboard, or verbally explaining.  I like to have students work in small groups in breakout rooms where they can compare answers and explain to each other math processes such as converting between decimals and percents.

Once students demonstrate understanding, I attempt to have them explain answers in a way that they might not be completely comfortable with.  For example, for someone who prefers to give verbal explanations, I might ask that individual to write the explanation out in complete sentences.  In this way, they deepen their understanding of the math concept and obtain practice with a different skill at the same time.

-Jonathan  

 

I'm late to the table, but I have appreciated reading everyone else's posts so far. I do teach and practice fraction, decimal, percent equivalencies with my GED math students. I'm trying to attach some fun ways I have had them practice in the past. I hope you can access these activities.

Thank you Brooke for sharing:  https://nrich.maths.org/1249 This is really good. I also find these old school visual fractions games useful: https://visualfractions.com/games/

Visualfractions.com also has a youtube channel where they post short videos explaining fractions: https://www.youtube.com/channel/UCGD7DZeBupPTAdHrxRmIzYw . I found this video helpful to explain fraction to decimal conversion: https://www.youtube.com/watch?v=eUKBu1J3EYw . 

"Connecting representations"  is one of my favorite Language Learning Routine (or something like that/???)   and calling it that and doing it regularly really helps build comprehension.