Hello, all. I am part of the Adult Numeracy Initiative (ANI) cohort currently running in Vermont. One activity we've done is the "Number of the Day*," which seems to be very easy to integrate into any routine.
One question I have is finding interesting ways to get students to "see" fractions, decimals, and percents as different representations of the same thing. Any hints? I'm going to use a number line to demonstrate how the three can be related, but any other ideas? Any good, realistic and real-life ideas to use?
Thanks from St. Johnsbury, VT!
--Jen Way
*Number of the Day: Put a number on the board and have students create the questions that go with the answer
- You can use the activity as a quick assessment of what your students know and are not so comfortable with (if a student wrote a lot of addition and subtraction, but only wrote a few multiplication and no division, you can see where a student may not be comfortable)
Comments
Hi Jen.
I have titled this post with what I repeat - and repeat and repeat - to my students about what is on both sides of the equal sign. (Lots of misconceptions there.) I also use those words to describe fractions, decimals, and percents.
For everyday topics, I have used: CLOCKS - analog (round with hands) and digital (numbers only). It is not the perfect analogy, but it gets them thinking that there can be more than one way to say the same thing with numbers. Common usage of "quarter hour" and "half hour" comes into play here. Also, in timing for sports events (think Olympic downhill skiing), the seconds are split into thousandths (decimals). How would that look as a fraction of a second?
Also, if some in your class are familiar with METRIC measurement, you can relate the metric decimals - centimeters and millimeters (as parts of the whole) to the fractions of a foot or yard (inches) of STANDARD (or "English") measurement. Sometimes rulers have inches measured in fractions, sometimes in decimals.
Also try using word synonyms. If something is "high" it is also "tall." Does that make it a different size? No.
I think the problems people have with equivalency of fractions and decimals go back to an understanding of the equal sign. (See the Stigler / Givven/ Thompson article - What Community College Developmental Mathematics Students Understand about Mathematics, MathAMATYC Educator ~ Vol. 1, No. 3 ~ May 2010.) On the first day of class, the first thing I taught was the meaning of =. I asked the students to tell me if they wanted me to use a nickname or a different name than the one on the registration list. I wrote the registered names and the nicknames on the board, put an equal sign between them, and asked students, "What did I write and why did I write it?" Someone usually came up with the answer - "It means the same thing." That is what students need to understand about the equal sign before the equivalency of fractions, decimals and percents really makes sense.
Let me know if this helps.
Dorothea Stienke
Lafayette, CO
My first thought about "real life fractions that people would actually use" was time, just because of its familiarity and because a big analog clock is visual. Lots of people recognize that half an hour is 30 minutes -- and the ones who kinda know it get happy and feel like they do know it sometimes when I show them the clock and that sixty is the whole circle...
Common core talks about fractions as units first, and working with what happens to 1/5 + 1/5 and that sort of thing (I think I would do most work with the ones that dont' do repeating decimals, adn then work in those tricky thirds and sixths and sevenths). I think lots of students would understand that better than when we toss in all the assorted combinations at once.
Jen, there used to be a really cool tool that involved mixing paint and showing the results in multiple formats. Unfortunately, that tool was created in shockwave and that code is not operational on most devices and many browsers today. I have replicated the intent of the tool today in Google Sheets and I offer the following link as a possible resource. Please refer to the instructions page as the tool itself is of limited value unless good questions are used along with it. I have started a few questions out, but I ran out of time this morning. I did create an interactive link so that anyone can add in good thoughtful questions into the tool automatically, so if you or anyone else would like to add in nice questions that teachers could offer students with this tool, please do so.
Summary of the tool: Choose how many blue cans of paint and how many white cans from a drop down list. As those values are selected the appropriate measures show up in all formats so learners can see how all of them are related. This creates a bit of a lab where teacher poses a question, students write down their conjectures, discuss those conjectures then come to the tool to test out different suggestions, then students return to their conjectures to modify and record their new findings. Finally a wrap up with more formalized lecture can be used to take this conceptual play and reinforce it with more traditional lectures about procedures and vocabulary and syntax. Please realize I just built this this morning so it may be rough or may have much room for improvement. All suggestions and feedback are welcome and appreciated :)
Link to tool is here: https://docs.google.com/spreadsheets/d/1eMQzFtIth43fo5vY28mqUqvIDJGTtD6DiVMX9kWlXTI/edit?usp=sharing (EDIT: fixed link to get to version so you have drop down options in each field)
Pretty nifty! I realize that one of the huge cultural shifts in using technology for learning is being able to "undo." I clicked on things and ... seems they're locked in so I can't change them.
I think one obvious refinement would be to have the instructions "on top" :)
S.Jones, could you clarify what is locked in? I did try to protect the sheet so that the only values that you should be able to change are the number of blue paint cans and the number of white, the rest is automatically populated. I shared the document as view only so that may restrict people from even choosing an option in the drop down boxes for blue and white paint. If you are not able to type in a number or choose from the drop down lists in the blue or white paint boxes please let me know and I will try fiddling with the settings. Of course, one could go File-Make A Copy and have their own version of this tool that is fully editable (the joys of Google being re-mixable) If you can change the numbers, please don't feel you need to undo as it is designed so that anyone can pop in and change numbers (if I set that up right).
I do agree that at least some brief instructions could go on the top of the tool, but the list of questions and suggestions probably need to be out of the way on that second tab. I will be adding in the feature of including ratios both in the 3:2 format but also in sentence format ( "For every 3 blue cans there are 2 white cans")